|\^/|     Maple 12 (IBM INTEL LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
>  #BEGIN OUTFILE1
>  
>  # Begin Function number 3
>  display_alot := proc(iter)
>  global
>  ALWAYS,
>  INFO,
>  glob_max_terms,
>  DEBUGMASSIVE,
>  DEBUGL,
>  glob_iolevel,
>  #Top Generate Globals Decl
>  glob_log10abserr,
>  glob_orig_start_sec,
>  glob_smallish_float,
>  glob_max_trunc_err,
>  glob_last_good_h,
>  glob_disp_incr,
>  glob_reached_optimal_h,
>  glob_initial_pass,
>  sec_in_min,
>  glob_clock_start_sec,
>  glob_clock_sec,
>  min_in_hour,
>  djd_debug,
>  glob_max_minutes,
>  glob_iter,
>  glob_start,
>  glob_max_iter,
>  glob_max_hours,
>  glob_relerr,
>  glob_abserr,
>  glob_log10_abserr,
>  glob_small_float,
>  glob_optimal_clock_start_sec,
>  glob_not_yet_finished,
>  glob_display_flag,
>  glob_warned,
>  glob_optimal_start,
>  glob_hmin,
>  glob_max_opt_iter,
>  glob_percent_done,
>  glob_normmax,
>  glob_max_sec,
>  glob_look_poles,
>  glob_optimal_done,
>  glob_almost_1,
>  years_in_century,
>  days_in_year,
>  glob_optimal_expect_sec,
>  glob_max_order,
>  glob_hmax,
>  glob_html_log,
>  glob_unchanged_h_cnt,
>  centuries_in_millinium,
>  glob_current_iter,
>  glob_curr_iter_when_opt,
>  glob_max_rel_trunc_err,
>  glob_log10_relerr,
>  glob_not_yet_start_msg,
>  hours_in_day,
>  glob_dump,
>  glob_warned2,
>  glob_dump_analytic,
>  glob_hmin_init,
>  glob_h,
>  glob_log10normmin,
>  glob_log10relerr,
>  MAX_UNCHANGED,
>  glob_no_eqs,
>  glob_large_float,
>  djd_debug2,
>  #Bottom Generate Globals Decl
>  #BEGIN CONST
>  array_const_3D0,
>  array_const_4D0,
>  array_const_0D0,
>  array_const_1,
>  array_const_2,
>  array_const_2D0,
>  #END CONST
>  array_pole,
>  array_norms,
>  array_1st_rel_error,
>  array_x1_init,
>  array_m1,
>  array_x2,
>  array_x1,
>  array_tmp10,
>  array_tmp11,
>  array_tmp12,
>  array_tmp13,
>  array_tmp14,
>  array_tmp15,
>  array_tmp16,
>  array_tmp17,
>  array_type_pole,
>  array_x2_init,
>  array_t,
>  array_last_rel_error,
>  array_tmp0,
>  array_tmp1,
>  array_tmp2,
>  array_tmp3,
>  array_tmp4,
>  array_tmp5,
>  array_tmp6,
>  array_tmp7,
>  array_tmp8,
>  array_tmp9,
>  array_x2_higher_work2,
>  array_x1_higher_work,
>  array_x2_higher_work,
>  array_poles,
>  array_real_pole,
>  array_x2_higher,
>  array_complex_pole,
>  array_x1_higher_work2,
>  array_x1_higher,
>  glob_last;
>  
>  local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
>  #TOP DISPLAY ALOT
>  if (iter >= 0)  then # if number 1
>   ind_var := array_t[1];
>   omniout_float(ALWAYS,"t[1]                             ",33,ind_var,20," ");
>   analytic_val_y := exact_soln_x2(ind_var);
>   omniout_float(ALWAYS,"x2[1] (analytic)                 ",33,analytic_val_y,20," ");
>   term_no   :=  1;
>   numeric_val := array_x2[term_no];
>   abserr := abs(numeric_val - analytic_val_y);
>   omniout_float(ALWAYS,"x2[1] (numeric)                  ",33,numeric_val,20," ");
>   if (abs(analytic_val_y) <> 0.0)  then # if number 2
>     relerr := abserr*100.0/abs(analytic_val_y);
>     else
>     relerr :=  -1.0  ;
>     fi;# end if 2
>   ;
>   if glob_iter  = 1 then # if number 2
>     array_1st_rel_error[1] := relerr;
>     else
>     array_last_rel_error[1] := relerr;
>     fi;# end if 2
>   ;
>   omniout_float(ALWAYS,"absolute error                   ",4,abserr,20," ");
>   omniout_float(ALWAYS,"relative error                   ",4,relerr,20,"%");
>   omniout_float(ALWAYS,"h                                ",4,glob_h,20," ");
>   ;
>   analytic_val_y := exact_soln_x1(ind_var);
>   omniout_float(ALWAYS,"x1[1] (analytic)                 ",33,analytic_val_y,20," ");
>   term_no   :=  1;
>   numeric_val := array_x1[term_no];
>   abserr := abs(numeric_val - analytic_val_y);
>   omniout_float(ALWAYS,"x1[1] (numeric)                  ",33,numeric_val,20," ");
>   if (abs(analytic_val_y) <> 0.0)  then # if number 2
>     relerr := abserr*100.0/abs(analytic_val_y);
>     else
>     relerr :=  -1.0  ;
>     fi;# end if 2
>   ;
>   if glob_iter  = 1 then # if number 2
>     array_1st_rel_error[2] := relerr;
>     else
>     array_last_rel_error[2] := relerr;
>     fi;# end if 2
>   ;
>   omniout_float(ALWAYS,"absolute error                   ",4,abserr,20," ");
>   omniout_float(ALWAYS,"relative error                   ",4,relerr,20,"%");
>   omniout_float(ALWAYS,"h                                ",4,glob_h,20," ");
>   #BOTTOM DISPLAY ALOT
>   fi;# end if 1
>  ;
>  # End Function number 3
>  end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global ALWAYS, INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_log10abserr, glob_orig_start_sec, glob_smallish_float,
glob_max_trunc_err, glob_last_good_h, glob_disp_incr,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug, glob_max_minutes, glob_iter,
glob_start, glob_max_iter, glob_max_hours, glob_relerr, glob_abserr,
glob_log10_abserr, glob_small_float, glob_optimal_clock_start_sec,
glob_not_yet_finished, glob_display_flag, glob_warned, glob_optimal_start,
glob_hmin, glob_max_opt_iter, glob_percent_done, glob_normmax, glob_max_sec,
glob_look_poles, glob_optimal_done, glob_almost_1, years_in_century,
days_in_year, glob_optimal_expect_sec, glob_max_order, glob_hmax,
glob_html_log, glob_unchanged_h_cnt, centuries_in_millinium,
glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err,
glob_log10_relerr, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_warned2, glob_dump_analytic, glob_hmin_init, glob_h, glob_log10normmin,
glob_log10relerr, MAX_UNCHANGED, glob_no_eqs, glob_large_float, djd_debug2,
array_const_3D0, array_const_4D0, array_const_0D0, array_const_1,
array_const_2, array_const_2D0, array_pole, array_norms,
array_1st_rel_error, array_x1_init, array_m1, array_x2, array_x1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x2_init,
array_t, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_x2_higher_work2, array_x1_higher_work,
array_x2_higher_work, array_poles, array_real_pole, array_x2_higher,
array_complex_pole, array_x1_higher_work2, array_x1_higher, glob_last;
    if 0 <= iter then
        ind_var := array_t[1];
        omniout_float(ALWAYS, "t[1]                             ", 33,
            ind_var, 20, " ");
        analytic_val_y := exact_soln_x2(ind_var);
        omniout_float(ALWAYS, "x2[1] (analytic)                 ", 33,
            analytic_val_y, 20, " ");
        term_no := 1;
        numeric_val := array_x2[term_no];
        abserr := abs(numeric_val - analytic_val_y);
        omniout_float(ALWAYS, "x2[1] (numeric)                  ", 33,
            numeric_val, 20, " ");
        if abs(analytic_val_y) <> 0. then
            relerr := abserr*100.0/abs(analytic_val_y)
        else relerr := -1.0
        end if;
        if glob_iter = 1 then array_1st_rel_error[1] := relerr
        else array_last_rel_error[1] := relerr
        end if;
        omniout_float(ALWAYS, "absolute error                   ", 4,
            abserr, 20, " ");
        omniout_float(ALWAYS, "relative error                   ", 4,
            relerr, 20, "%");
        omniout_float(ALWAYS, "h                                ", 4,
            glob_h, 20, " ");
        analytic_val_y := exact_soln_x1(ind_var);
        omniout_float(ALWAYS, "x1[1] (analytic)                 ", 33,
            analytic_val_y, 20, " ");
        term_no := 1;
        numeric_val := array_x1[term_no];
        abserr := abs(numeric_val - analytic_val_y);
        omniout_float(ALWAYS, "x1[1] (numeric)                  ", 33,
            numeric_val, 20, " ");
        if abs(analytic_val_y) <> 0. then
            relerr := abserr*100.0/abs(analytic_val_y)
        else relerr := -1.0
        end if;
        if glob_iter = 1 then array_1st_rel_error[2] := relerr
        else array_last_rel_error[2] := relerr
        end if;
        omniout_float(ALWAYS, "absolute error                   ", 4,
            abserr, 20, " ");
        omniout_float(ALWAYS, "relative error                   ", 4,
            relerr, 20, "%");
        omniout_float(ALWAYS, "h                                ", 4,
            glob_h, 20, " ")
    end if
end proc

>   # Begin Function number 4
>  adjust_for_pole := proc(h_param)
>  global
>  ALWAYS,
>  INFO,
>  glob_max_terms,
>  DEBUGMASSIVE,
>  DEBUGL,
>  glob_iolevel,
>  #Top Generate Globals Decl
>  glob_log10abserr,
>  glob_orig_start_sec,
>  glob_smallish_float,
>  glob_max_trunc_err,
>  glob_last_good_h,
>  glob_disp_incr,
>  glob_reached_optimal_h,
>  glob_initial_pass,
>  sec_in_min,
>  glob_clock_start_sec,
>  glob_clock_sec,
>  min_in_hour,
>  djd_debug,
>  glob_max_minutes,
>  glob_iter,
>  glob_start,
>  glob_max_iter,
>  glob_max_hours,
>  glob_relerr,
>  glob_abserr,
>  glob_log10_abserr,
>  glob_small_float,
>  glob_optimal_clock_start_sec,
>  glob_not_yet_finished,
>  glob_display_flag,
>  glob_warned,
>  glob_optimal_start,
>  glob_hmin,
>  glob_max_opt_iter,
>  glob_percent_done,
>  glob_normmax,
>  glob_max_sec,
>  glob_look_poles,
>  glob_optimal_done,
>  glob_almost_1,
>  years_in_century,
>  days_in_year,
>  glob_optimal_expect_sec,
>  glob_max_order,
>  glob_hmax,
>  glob_html_log,
>  glob_unchanged_h_cnt,
>  centuries_in_millinium,
>  glob_current_iter,
>  glob_curr_iter_when_opt,
>  glob_max_rel_trunc_err,
>  glob_log10_relerr,
>  glob_not_yet_start_msg,
>  hours_in_day,
>  glob_dump,
>  glob_warned2,
>  glob_dump_analytic,
>  glob_hmin_init,
>  glob_h,
>  glob_log10normmin,
>  glob_log10relerr,
>  MAX_UNCHANGED,
>  glob_no_eqs,
>  glob_large_float,
>  djd_debug2,
>  #Bottom Generate Globals Decl
>  #BEGIN CONST
>  array_const_3D0,
>  array_const_4D0,
>  array_const_0D0,
>  array_const_1,
>  array_const_2,
>  array_const_2D0,
>  #END CONST
>  array_pole,
>  array_norms,
>  array_1st_rel_error,
>  array_x1_init,
>  array_m1,
>  array_x2,
>  array_x1,
>  array_tmp10,
>  array_tmp11,
>  array_tmp12,
>  array_tmp13,
>  array_tmp14,
>  array_tmp15,
>  array_tmp16,
>  array_tmp17,
>  array_type_pole,
>  array_x2_init,
>  array_t,
>  array_last_rel_error,
>  array_tmp0,
>  array_tmp1,
>  array_tmp2,
>  array_tmp3,
>  array_tmp4,
>  array_tmp5,
>  array_tmp6,
>  array_tmp7,
>  array_tmp8,
>  array_tmp9,
>  array_x2_higher_work2,
>  array_x1_higher_work,
>  array_x2_higher_work,
>  array_poles,
>  array_real_pole,
>  array_x2_higher,
>  array_complex_pole,
>  array_x1_higher_work2,
>  array_x1_higher,
>  glob_last;
>  
>  local hnew, sz2, tmp;
>  #TOP ADJUST FOR POLE
>  
>  hnew   :=  h_param;
>  glob_normmax   :=  glob_small_float;
>  if (abs(array_x2_higher[1,1]) > glob_small_float)  then # if number 1
>   tmp   :=  abs(array_x2_higher[1,1]);
>   if (tmp < glob_normmax)  then # if number 2
>     glob_normmax   :=  tmp;
>     fi;# end if 2
>   fi;# end if 1
>  ;
>  if (abs(array_x1_higher[1,1]) > glob_small_float)  then # if number 1
>   tmp   :=  abs(array_x1_higher[1,1]);
>   if (tmp < glob_normmax)  then # if number 2
>     glob_normmax   :=  tmp;
>     fi;# end if 2
>   fi;# end if 1
>  ;
>  if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float))  then # if number 1
>   sz2   :=  array_pole[1]/10.0;
>   if (sz2 < hnew)  then # if number 2
>     omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
>     omniout_str(INFO,"Reached Optimal");
>     newline();
>     return(hnew);
>     fi;# end if 2
>   fi;# end if 1
>  ;
>  if (not glob_reached_optimal_h)  then # if number 1
>   glob_reached_optimal_h   :=  true;
>   glob_curr_iter_when_opt   :=  glob_current_iter;
>   glob_optimal_clock_start_sec   := elapsed_time_seconds();
>   glob_optimal_start    := array_t[1];
>   fi;# end if 1
>  ;
>  hnew   :=  sz2;
>  #END block
>  #BOTTOM ADJUST FOR POLE
>  # End Function number 4
>  end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global ALWAYS, INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_log10abserr, glob_orig_start_sec, glob_smallish_float,
glob_max_trunc_err, glob_last_good_h, glob_disp_incr,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug, glob_max_minutes, glob_iter,
glob_start, glob_max_iter, glob_max_hours, glob_relerr, glob_abserr,
glob_log10_abserr, glob_small_float, glob_optimal_clock_start_sec,
glob_not_yet_finished, glob_display_flag, glob_warned, glob_optimal_start,
glob_hmin, glob_max_opt_iter, glob_percent_done, glob_normmax, glob_max_sec,
glob_look_poles, glob_optimal_done, glob_almost_1, years_in_century,
days_in_year, glob_optimal_expect_sec, glob_max_order, glob_hmax,
glob_html_log, glob_unchanged_h_cnt, centuries_in_millinium,
glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err,
glob_log10_relerr, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_warned2, glob_dump_analytic, glob_hmin_init, glob_h, glob_log10normmin,
glob_log10relerr, MAX_UNCHANGED, glob_no_eqs, glob_large_float, djd_debug2,
array_const_3D0, array_const_4D0, array_const_0D0, array_const_1,
array_const_2, array_const_2D0, array_pole, array_norms,
array_1st_rel_error, array_x1_init, array_m1, array_x2, array_x1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x2_init,
array_t, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_x2_higher_work2, array_x1_higher_work,
array_x2_higher_work, array_poles, array_real_pole, array_x2_higher,
array_complex_pole, array_x1_higher_work2, array_x1_higher, glob_last;
    hnew := h_param;
    glob_normmax := glob_small_float;
    if glob_small_float < abs(array_x2_higher[1, 1]) then
        tmp := abs(array_x2_higher[1, 1]);
        if tmp < glob_normmax then glob_normmax := tmp end if
    end if;
    if glob_small_float < abs(array_x1_higher[1, 1]) then
        tmp := abs(array_x1_higher[1, 1]);
        if tmp < glob_normmax then glob_normmax := tmp end if
    end if;
    if glob_look_poles and glob_small_float < abs(array_pole[1]) and
    array_pole[1] <> glob_large_float then
        sz2 := array_pole[1]/10.0;
        if sz2 < hnew then
            omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
                "due to singularity.");
            omniout_str(INFO, "Reached Optimal");
            newline();
            return hnew
        end if
    end if;
    if not glob_reached_optimal_h then
        glob_reached_optimal_h := true;
        glob_curr_iter_when_opt := glob_current_iter;
        glob_optimal_clock_start_sec := elapsed_time_seconds();
        glob_optimal_start := array_t[1]
    end if;
    hnew := sz2
end proc

>   # Begin Function number 5
>  prog_report := proc(t_start,t_end)
>  global
>  ALWAYS,
>  INFO,
>  glob_max_terms,
>  DEBUGMASSIVE,
>  DEBUGL,
>  glob_iolevel,
>  #Top Generate Globals Decl
>  glob_log10abserr,
>  glob_orig_start_sec,
>  glob_smallish_float,
>  glob_max_trunc_err,
>  glob_last_good_h,
>  glob_disp_incr,
>  glob_reached_optimal_h,
>  glob_initial_pass,
>  sec_in_min,
>  glob_clock_start_sec,
>  glob_clock_sec,
>  min_in_hour,
>  djd_debug,
>  glob_max_minutes,
>  glob_iter,
>  glob_start,
>  glob_max_iter,
>  glob_max_hours,
>  glob_relerr,
>  glob_abserr,
>  glob_log10_abserr,
>  glob_small_float,
>  glob_optimal_clock_start_sec,
>  glob_not_yet_finished,
>  glob_display_flag,
>  glob_warned,
>  glob_optimal_start,
>  glob_hmin,
>  glob_max_opt_iter,
>  glob_percent_done,
>  glob_normmax,
>  glob_max_sec,
>  glob_look_poles,
>  glob_optimal_done,
>  glob_almost_1,
>  years_in_century,
>  days_in_year,
>  glob_optimal_expect_sec,
>  glob_max_order,
>  glob_hmax,
>  glob_html_log,
>  glob_unchanged_h_cnt,
>  centuries_in_millinium,
>  glob_current_iter,
>  glob_curr_iter_when_opt,
>  glob_max_rel_trunc_err,
>  glob_log10_relerr,
>  glob_not_yet_start_msg,
>  hours_in_day,
>  glob_dump,
>  glob_warned2,
>  glob_dump_analytic,
>  glob_hmin_init,
>  glob_h,
>  glob_log10normmin,
>  glob_log10relerr,
>  MAX_UNCHANGED,
>  glob_no_eqs,
>  glob_large_float,
>  djd_debug2,
>  #Bottom Generate Globals Decl
>  #BEGIN CONST
>  array_const_3D0,
>  array_const_4D0,
>  array_const_0D0,
>  array_const_1,
>  array_const_2,
>  array_const_2D0,
>  #END CONST
>  array_pole,
>  array_norms,
>  array_1st_rel_error,
>  array_x1_init,
>  array_m1,
>  array_x2,
>  array_x1,
>  array_tmp10,
>  array_tmp11,
>  array_tmp12,
>  array_tmp13,
>  array_tmp14,
>  array_tmp15,
>  array_tmp16,
>  array_tmp17,
>  array_type_pole,
>  array_x2_init,
>  array_t,
>  array_last_rel_error,
>  array_tmp0,
>  array_tmp1,
>  array_tmp2,
>  array_tmp3,
>  array_tmp4,
>  array_tmp5,
>  array_tmp6,
>  array_tmp7,
>  array_tmp8,
>  array_tmp9,
>  array_x2_higher_work2,
>  array_x1_higher_work,
>  array_x2_higher_work,
>  array_poles,
>  array_real_pole,
>  array_x2_higher,
>  array_complex_pole,
>  array_x1_higher_work2,
>  array_x1_higher,
>  glob_last;
>  
>  local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
>  #TOP PROGRESS REPORT
>  clock_sec1   := elapsed_time_seconds();
>  total_clock_sec   :=  convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
>  glob_clock_sec   :=  convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
>  left_sec   :=  convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
>  expect_sec   :=  comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h)  ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
>  opt_clock_sec   := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
>  glob_optimal_expect_sec   :=  comp_expect_sec(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
>  percent_done   :=  comp_percent(convfloat(t_end),convfloat(t_start),convfloat(array_t[1]) + convfloat(glob_h));
>  glob_percent_done := percent_done;
>  omniout_str_noeol(INFO,"Total Elapsed Time              ");
>  omniout_timestr(convfloat(total_clock_sec));
>  omniout_str_noeol(INFO,"Elapsed Time(since restart)     ");
>  omniout_timestr(convfloat(glob_clock_sec));
>  if convfloat(percent_done) < convfloat(100.0)  then # if number 1
>   omniout_str_noeol(INFO,"Expected Time Remaining         ");
>   omniout_timestr(convfloat(expect_sec));
>   omniout_str_noeol(INFO,"Optimized Time Remaining        ");
>   omniout_timestr(convfloat(glob_optimal_expect_sec));
>   fi;# end if 1
>  ;
>  omniout_str_noeol(INFO,"Time to Timeout                 ");
>  omniout_timestr(convfloat(left_sec));
>  omniout_float(INFO,    "Percent Done                    ",33,percent_done,4,"%");
>  #BOTTOM PROGRESS REPORT
>  # End Function number 5
>  end;
prog_report := proc(t_start, t_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_log10abserr, glob_orig_start_sec, glob_smallish_float,
glob_max_trunc_err, glob_last_good_h, glob_disp_incr,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug, glob_max_minutes, glob_iter,
glob_start, glob_max_iter, glob_max_hours, glob_relerr, glob_abserr,
glob_log10_abserr, glob_small_float, glob_optimal_clock_start_sec,
glob_not_yet_finished, glob_display_flag, glob_warned, glob_optimal_start,
glob_hmin, glob_max_opt_iter, glob_percent_done, glob_normmax, glob_max_sec,
glob_look_poles, glob_optimal_done, glob_almost_1, years_in_century,
days_in_year, glob_optimal_expect_sec, glob_max_order, glob_hmax,
glob_html_log, glob_unchanged_h_cnt, centuries_in_millinium,
glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err,
glob_log10_relerr, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_warned2, glob_dump_analytic, glob_hmin_init, glob_h, glob_log10normmin,
glob_log10relerr, MAX_UNCHANGED, glob_no_eqs, glob_large_float, djd_debug2,
array_const_3D0, array_const_4D0, array_const_0D0, array_const_1,
array_const_2, array_const_2D0, array_pole, array_norms,
array_1st_rel_error, array_x1_init, array_m1, array_x2, array_x1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x2_init,
array_t, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_x2_higher_work2, array_x1_higher_work,
array_x2_higher_work, array_poles, array_real_pole, array_x2_higher,
array_complex_pole, array_x1_higher_work2, array_x1_higher, glob_last;
    clock_sec1 := elapsed_time_seconds();
    total_clock_sec :=
        convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
    glob_clock_sec :=
        convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
    left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
         - convfloat(clock_sec1);
    expect_sec := comp_expect_sec(convfloat(t_end), convfloat(t_start),
        convfloat(array_t[1]) + convfloat(glob_h),
        convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
    opt_clock_sec :=
        convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
    glob_optimal_expect_sec := comp_expect_sec(convfloat(t_end),
        convfloat(t_start), convfloat(array_t[1]) + convfloat(glob_h),
        convfloat(opt_clock_sec));
    percent_done := comp_percent(convfloat(t_end), convfloat(t_start),
        convfloat(array_t[1]) + convfloat(glob_h));
    glob_percent_done := percent_done;
    omniout_str_noeol(INFO, "Total Elapsed Time              ");
    omniout_timestr(convfloat(total_clock_sec));
    omniout_str_noeol(INFO, "Elapsed Time(since restart)     ");
    omniout_timestr(convfloat(glob_clock_sec));
    if convfloat(percent_done) < convfloat(100.0) then
        omniout_str_noeol(INFO, "Expected Time Remaining         ");
        omniout_timestr(convfloat(expect_sec));
        omniout_str_noeol(INFO, "Optimized Time Remaining        ");
        omniout_timestr(convfloat(glob_optimal_expect_sec))
    end if;
    omniout_str_noeol(INFO, "Time to Timeout                 ");
    omniout_timestr(convfloat(left_sec));
    omniout_float(INFO, "Percent Done                    ", 33,
        percent_done, 4, "%")
end proc

>   # Begin Function number 6
>  check_for_pole := proc()
>  global
>  ALWAYS,
>  INFO,
>  glob_max_terms,
>  DEBUGMASSIVE,
>  DEBUGL,
>  glob_iolevel,
>  #Top Generate Globals Decl
>  glob_log10abserr,
>  glob_orig_start_sec,
>  glob_smallish_float,
>  glob_max_trunc_err,
>  glob_last_good_h,
>  glob_disp_incr,
>  glob_reached_optimal_h,
>  glob_initial_pass,
>  sec_in_min,
>  glob_clock_start_sec,
>  glob_clock_sec,
>  min_in_hour,
>  djd_debug,
>  glob_max_minutes,
>  glob_iter,
>  glob_start,
>  glob_max_iter,
>  glob_max_hours,
>  glob_relerr,
>  glob_abserr,
>  glob_log10_abserr,
>  glob_small_float,
>  glob_optimal_clock_start_sec,
>  glob_not_yet_finished,
>  glob_display_flag,
>  glob_warned,
>  glob_optimal_start,
>  glob_hmin,
>  glob_max_opt_iter,
>  glob_percent_done,
>  glob_normmax,
>  glob_max_sec,
>  glob_look_poles,
>  glob_optimal_done,
>  glob_almost_1,
>  years_in_century,
>  days_in_year,
>  glob_optimal_expect_sec,
>  glob_max_order,
>  glob_hmax,
>  glob_html_log,
>  glob_unchanged_h_cnt,
>  centuries_in_millinium,
>  glob_current_iter,
>  glob_curr_iter_when_opt,
>  glob_max_rel_trunc_err,
>  glob_log10_relerr,
>  glob_not_yet_start_msg,
>  hours_in_day,
>  glob_dump,
>  glob_warned2,
>  glob_dump_analytic,
>  glob_hmin_init,
>  glob_h,
>  glob_log10normmin,
>  glob_log10relerr,
>  MAX_UNCHANGED,
>  glob_no_eqs,
>  glob_large_float,
>  djd_debug2,
>  #Bottom Generate Globals Decl
>  #BEGIN CONST
>  array_const_3D0,
>  array_const_4D0,
>  array_const_0D0,
>  array_const_1,
>  array_const_2,
>  array_const_2D0,
>  #END CONST
>  array_pole,
>  array_norms,
>  array_1st_rel_error,
>  array_x1_init,
>  array_m1,
>  array_x2,
>  array_x1,
>  array_tmp10,
>  array_tmp11,
>  array_tmp12,
>  array_tmp13,
>  array_tmp14,
>  array_tmp15,
>  array_tmp16,
>  array_tmp17,
>  array_type_pole,
>  array_x2_init,
>  array_t,
>  array_last_rel_error,
>  array_tmp0,
>  array_tmp1,
>  array_tmp2,
>  array_tmp3,
>  array_tmp4,
>  array_tmp5,
>  array_tmp6,
>  array_tmp7,
>  array_tmp8,
>  array_tmp9,
>  array_x2_higher_work2,
>  array_x1_higher_work,
>  array_x2_higher_work,
>  array_poles,
>  array_real_pole,
>  array_x2_higher,
>  array_complex_pole,
>  array_x1_higher_work2,
>  array_x1_higher,
>  glob_last;
>  
>  local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found;
>  #TOP CHECK FOR POLE
>  #IN RADII REAL EQ = 1
>  #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
>  #Applies to pole of arbitrary r_order on the real axis,
>  #Due to Prof. George Corliss.
>  n  :=  glob_max_terms;
>  m  :=  n - 2 - 1;
>  while ((m >= 10) and ((abs(array_x2_higher[1,m]) < glob_small_float) or (abs(array_x2_higher[1,m-1]) < glob_small_float) or (abs(array_x2_higher[1,m-2]) < glob_small_float )))  do # do number 2
>   m  :=  m - 1;
>   od;# end do number 2
>  ;
>  if (m > 10)  then # if number 1
>   rm0  := array_x2_higher[1,m]/array_x2_higher[1,m-1];
>   rm1  := array_x2_higher[1,m-1]/array_x2_higher[1,m-2];
>   hdrc  := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
>   if (abs(hdrc) > glob_small_float)   then # if number 2
>     rcs  :=  glob_h/hdrc;
>     ord_no  :=  convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
>     array_real_pole[1,1] :=  rcs;
>     array_real_pole[1,2] :=   ord_no;
>     else
>     array_real_pole[1,1] :=  glob_large_float;
>     array_real_pole[1,2] :=  glob_large_float;
>     fi;# end if 2
>   else
>   array_real_pole[1,1] :=  glob_large_float;
>   array_real_pole[1,2] :=  glob_large_float;
>   fi;# end if 1
>  ;
>  #BOTTOM RADII REAL EQ = 1
>  #IN RADII REAL EQ = 2
>  #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
>  #Applies to pole of arbitrary r_order on the real axis,
>  #Due to Prof. George Corliss.
>  n  :=  glob_max_terms;
>  m  :=  n - 1 - 1;
>  while ((m >= 10) and ((abs(array_x1_higher[1,m]) < glob_small_float) or (abs(array_x1_higher[1,m-1]) < glob_small_float) or (abs(array_x1_higher[1,m-2]) < glob_small_float )))  do # do number 2
>   m  :=  m - 1;
>   od;# end do number 2
>  ;
>  if (m > 10)  then # if number 1
>   rm0  := array_x1_higher[1,m]/array_x1_higher[1,m-1];
>   rm1  := array_x1_higher[1,m-1]/array_x1_higher[1,m-2];
>   hdrc  := convfloat(m-1)*rm0-convfloat(m-2)*rm1;
>   if (abs(hdrc) > glob_small_float)   then # if number 2
>     rcs  :=  glob_h/hdrc;
>     ord_no  :=  convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0;
>     array_real_pole[2,1] :=  rcs;
>     array_real_pole[2,2] :=   ord_no;
>     else
>     array_real_pole[2,1] :=  glob_large_float;
>     array_real_pole[2,2] :=  glob_large_float;
>     fi;# end if 2
>   else
>   array_real_pole[2,1] :=  glob_large_float;
>   array_real_pole[2,2] :=  glob_large_float;
>   fi;# end if 1
>  ;
>  #BOTTOM RADII REAL EQ = 2
>  #TOP RADII COMPLEX EQ = 1
>  #Computes radius of convergence for complex conjugate pair of poles.
>  #from 6 adjacent Taylor series terms
>  #Also computes r_order of poles.
>  #Due to Manuel Prieto.
>  #With a correction by Dennis J. Darland
>  n  :=  glob_max_terms - 2 - 1;
>  cnt  :=  0;
>  while ((cnt < 5)  and (n >= 10))  do # do number 2
>   if (abs(array_x2_higher[1,n]) > glob_small_float)  then # if number 1
>     cnt  :=  cnt + 1;
>     else
>     cnt  :=  0;
>     fi;# end if 1
>   ;
>   n  :=  n - 1;
>   od;# end do number 2
>  ;
>  m  :=  n + cnt;
>  if (m <= 10)  then # if number 1
>   array_complex_pole[1,1] :=  glob_large_float;
>   array_complex_pole[1,2] :=  glob_large_float;
>   elif (abs(array_x2_higher[1,m]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x2_higher[1,m-5]) >= (glob_large_float))  then # if number 2
>     array_complex_pole[1,1] :=  glob_large_float;
>     array_complex_pole[1,2] :=  glob_large_float;
>     else
>     rm0  :=  (array_x2_higher[1,m])/(array_x2_higher[1,m-1]);
>     rm1  :=  (array_x2_higher[1,m-1])/(array_x2_higher[1,m-2]);
>     rm2  :=  (array_x2_higher[1,m-2])/(array_x2_higher[1,m-3]);
>     rm3  :=  (array_x2_higher[1,m-3])/(array_x2_higher[1,m-4]);
>     rm4  :=  (array_x2_higher[1,m-4])/(array_x2_higher[1,m-5]);
>     nr1  :=  convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
>     nr2  :=  convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
>     dr1  :=  (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
>     dr2  :=  (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
>     ds1  :=  3.0/rm1 - 8.0/rm2 + 5.0/rm3;
>     ds2  :=  3.0/rm2 - 8.0/rm3 + 5.0/rm4;
>     if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float))  then # if number 3
>       array_complex_pole[1,1] :=  glob_large_float;
>       array_complex_pole[1,2] :=  glob_large_float;
>       else
>       if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float)  then # if number 4
>         rcs  :=  ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
>         #(Manuels)  rcs  :=  (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
>         ord_no  :=  (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
>         if (abs(rcs) > glob_small_float)  then # if number 5
>           if (rcs > 0.0)  then # if number 6
>             rad_c  :=  sqrt(rcs) * glob_h;
>             else
>             rad_c  :=  glob_large_float;
>             fi;# end if 6
>           else
>           rad_c  :=  glob_large_float;
>           ord_no  :=  glob_large_float;
>           fi;# end if 5
>         else
>         rad_c  :=  glob_large_float;
>         ord_no  :=  glob_large_float;
>         fi;# end if 4
>       fi;# end if 3
>     ;
>     array_complex_pole[1,1] :=  rad_c;
>     array_complex_pole[1,2] :=  ord_no;
>     fi;# end if 2
>   ;
>   #BOTTOM RADII COMPLEX EQ = 1
>   #TOP RADII COMPLEX EQ = 2
>   #Computes radius of convergence for complex conjugate pair of poles.
>   #from 6 adjacent Taylor series terms
>   #Also computes r_order of poles.
>   #Due to Manuel Prieto.
>   #With a correction by Dennis J. Darland
>   n  :=  glob_max_terms - 1 - 1;
>   cnt  :=  0;
>   while ((cnt < 5)  and (n >= 10))  do # do number 2
>     if (abs(array_x1_higher[1,n]) > glob_small_float)  then # if number 2
>       cnt  :=  cnt + 1;
>       else
>       cnt  :=  0;
>       fi;# end if 2
>     ;
>     n  :=  n - 1;
>     od;# end do number 2
>   ;
>   m  :=  n + cnt;
>   if (m <= 10)  then # if number 2
>     array_complex_pole[2,1] :=  glob_large_float;
>     array_complex_pole[2,2] :=  glob_large_float;
>     elif (abs(array_x1_higher[1,m]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_x1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_x1_higher[1,m-5]) >= (glob_large_float))  then # if number 3
>       array_complex_pole[2,1] :=  glob_large_float;
>       array_complex_pole[2,2] :=  glob_large_float;
>       else
>       rm0  :=  (array_x1_higher[1,m])/(array_x1_higher[1,m-1]);
>       rm1  :=  (array_x1_higher[1,m-1])/(array_x1_higher[1,m-2]);
>       rm2  :=  (array_x1_higher[1,m-2])/(array_x1_higher[1,m-3]);
>       rm3  :=  (array_x1_higher[1,m-3])/(array_x1_higher[1,m-4]);
>       rm4  :=  (array_x1_higher[1,m-4])/(array_x1_higher[1,m-5]);
>       nr1  :=  convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
>       nr2  :=  convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
>       dr1  :=  (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
>       dr2  :=  (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
>       ds1  :=  3.0/rm1 - 8.0/rm2 + 5.0/rm3;
>       ds2  :=  3.0/rm2 - 8.0/rm3 + 5.0/rm4;
>       if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float))  then # if number 4
>         array_complex_pole[2,1] :=  glob_large_float;
>         array_complex_pole[2,2] :=  glob_large_float;
>         else
>         if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float)  then # if number 5
>           rcs  :=  ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
>           #(Manuels)  rcs  :=  (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
>           ord_no  :=  (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
>           if (abs(rcs) > glob_small_float)  then # if number 6
>             if (rcs > 0.0)  then # if number 7
>               rad_c  :=  sqrt(rcs) * glob_h;
>               else
>               rad_c  :=  glob_large_float;
>               fi;# end if 7
>             else
>             rad_c  :=  glob_large_float;
>             ord_no  :=  glob_large_float;
>             fi;# end if 6
>           else
>           rad_c  :=  glob_large_float;
>           ord_no  :=  glob_large_float;
>           fi;# end if 5
>         fi;# end if 4
>       ;
>       array_complex_pole[2,1] :=  rad_c;
>       array_complex_pole[2,2] :=  ord_no;
>       fi;# end if 3
>     ;
>     #BOTTOM RADII COMPLEX EQ = 2
>     found := false;
>     #TOP WHICH RADII EQ = 1
>     if not found and ((array_real_pole[1,1] =  glob_large_float) or (array_real_pole[1,2] =  glob_large_float)) and ((array_complex_pole[1,1] <>  glob_large_float) and (array_complex_pole[1,2] <>  glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))   then # if number 3
>       array_poles[1,1] :=  array_complex_pole[1,1];
>       array_poles[1,2] :=  array_complex_pole[1,2];
>       found := true;
>       array_type_pole[1] := 2;
>       if (glob_display_flag)   then # if number 4
>         omniout_str(ALWAYS,"Complex estimate of poles used");
>         fi;# end if 4
>       ;
>       fi;# end if 3
>     ;
>     if  not found and ((array_real_pole[1,1] <>  glob_large_float) and (array_real_pole[1,2] <>  glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] =  glob_large_float) or (array_complex_pole[1,2] =  glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))  then # if number 3
>       array_poles[1,1] :=  array_real_pole[1,1];
>       array_poles[1,2] :=  array_real_pole[1,2];
>       found := true;
>       array_type_pole[1] := 1;
>       if (glob_display_flag)  then # if number 4
>         omniout_str(ALWAYS,"Real estimate of pole used");
>         fi;# end if 4
>       ;
>       fi;# end if 3
>     ;
>     if not found and (((array_real_pole[1,1] =  glob_large_float) or (array_real_pole[1,2] =  glob_large_float)) and ((array_complex_pole[1,1] =  glob_large_float) or (array_complex_pole[1,2] =  glob_large_float)))  then # if number 3
>       array_poles[1,1] :=  glob_large_float;
>       array_poles[1,2] :=  glob_large_float;
>       found := true;
>       array_type_pole[1] := 3;
>       if (glob_display_flag)  then # if number 4
>         omniout_str(ALWAYS,"NO POLE");
>         fi;# end if 4
>       ;
>       fi;# end if 3
>     ;
>     if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0))  then # if number 3
>       array_poles[1,1] :=  array_real_pole[1,1];
>       array_poles[1,2] :=  array_real_pole[1,2];
>       found := true;
>       array_type_pole[1] := 1;
>       if (glob_display_flag)   then # if number 4
>         omniout_str(ALWAYS,"Real estimate of pole used");
>         fi;# end if 4
>       ;
>       fi;# end if 3
>     ;
>     if not found and ((array_complex_pole[1,1] <>  glob_large_float) and (array_complex_pole[1,2] <>  glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))  then # if number 3
>       array_poles[1,1] :=  array_complex_pole[1,1];
>       array_poles[1,2] :=  array_complex_pole[1,2];
>       array_type_pole[1] := 2;
>       found := true;
>       if (glob_display_flag)  then # if number 4
>         omniout_str(ALWAYS,"Complex estimate of poles used");
>         fi;# end if 4
>       ;
>       fi;# end if 3
>     ;
>     if not found  then # if number 3
>       array_poles[1,1] :=  glob_large_float;
>       array_poles[1,2] :=  glob_large_float;
>       array_type_pole[1] := 3;
>       if (glob_display_flag)  then # if number 4
>         omniout_str(ALWAYS,"NO POLE");
>         fi;# end if 4
>       ;
>       fi;# end if 3
>     ;
>     #BOTTOM WHICH RADII EQ = 1
>     found := false;
>     #TOP WHICH RADII EQ = 2
>     if not found and ((array_real_pole[2,1] =  glob_large_float) or (array_real_pole[2,2] =  glob_large_float)) and ((array_complex_pole[2,1] <>  glob_large_float) and (array_complex_pole[2,2] <>  glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))   then # if number 3
>       array_poles[2,1] :=  array_complex_pole[2,1];
>       array_poles[2,2] :=  array_complex_pole[2,2];
>       found := true;
>       array_type_pole[2] := 2;
>       if (glob_display_flag)   then # if number 4
>         omniout_str(ALWAYS,"Complex estimate of poles used");
>         fi;# end if 4
>       ;
>       fi;# end if 3
>     ;
>     if  not found and ((array_real_pole[2,1] <>  glob_large_float) and (array_real_pole[2,2] <>  glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] =  glob_large_float) or (array_complex_pole[2,2] =  glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0)))  then # if number 3
>       array_poles[2,1] :=  array_real_pole[2,1];
>       array_poles[2,2] :=  array_real_pole[2,2];
>       found := true;
>       array_type_pole[2] := 1;
>       if (glob_display_flag)  then # if number 4
>         omniout_str(ALWAYS,"Real estimate of pole used");
>         fi;# end if 4
>       ;
>       fi;# end if 3
>     ;
>     if not found and (((array_real_pole[2,1] =  glob_large_float) or (array_real_pole[2,2] =  glob_large_float)) and ((array_complex_pole[2,1] =  glob_large_float) or (array_complex_pole[2,2] =  glob_large_float)))  then # if number 3
>       array_poles[2,1] :=  glob_large_float;
>       array_poles[2,2] :=  glob_large_float;
>       found := true;
>       array_type_pole[2] := 3;
>       if (glob_display_flag)  then # if number 4
>         omniout_str(ALWAYS,"NO POLE");
>         fi;# end if 4
>       ;
>       fi;# end if 3
>     ;
>     if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0))  then # if number 3
>       array_poles[2,1] :=  array_real_pole[2,1];
>       array_poles[2,2] :=  array_real_pole[2,2];
>       found := true;
>       array_type_pole[2] := 1;
>       if (glob_display_flag)   then # if number 4
>         omniout_str(ALWAYS,"Real estimate of pole used");
>         fi;# end if 4
>       ;
>       fi;# end if 3
>     ;
>     if not found and ((array_complex_pole[2,1] <>  glob_large_float) and (array_complex_pole[2,2] <>  glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))  then # if number 3
>       array_poles[2,1] :=  array_complex_pole[2,1];
>       array_poles[2,2] :=  array_complex_pole[2,2];
>       array_type_pole[2] := 2;
>       found := true;
>       if (glob_display_flag)  then # if number 4
>         omniout_str(ALWAYS,"Complex estimate of poles used");
>         fi;# end if 4
>       ;
>       fi;# end if 3
>     ;
>     if not found  then # if number 3
>       array_poles[2,1] :=  glob_large_float;
>       array_poles[2,2] :=  glob_large_float;
>       array_type_pole[2] := 3;
>       if (glob_display_flag)  then # if number 4
>         omniout_str(ALWAYS,"NO POLE");
>         fi;# end if 4
>       ;
>       fi;# end if 3
>     ;
>     #BOTTOM WHICH RADII EQ = 2
>     array_pole[1] :=  glob_large_float;
>     array_pole[2] :=  glob_large_float;
>     #TOP WHICH RADIUS EQ = 1
>     if array_pole[1] > array_poles[1,1] then # if number 3
>       array_pole[1] := array_poles[1,1];
>       array_pole[2] := array_poles[1,2];
>       fi;# end if 3
>     ;
>     #BOTTOM WHICH RADIUS EQ = 1
>     #TOP WHICH RADIUS EQ = 2
>     if array_pole[1] > array_poles[2,1] then # if number 3
>       array_pole[1] := array_poles[2,1];
>       array_pole[2] := array_poles[2,2];
>       fi;# end if 3
>     ;
>     #BOTTOM WHICH RADIUS EQ = 2
>     #BOTTOM CHECK FOR POLE
>     display_pole();
>     # End Function number 6
>     end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found;
global ALWAYS, INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_log10abserr, glob_orig_start_sec, glob_smallish_float,
glob_max_trunc_err, glob_last_good_h, glob_disp_incr,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug, glob_max_minutes, glob_iter,
glob_start, glob_max_iter, glob_max_hours, glob_relerr, glob_abserr,
glob_log10_abserr, glob_small_float, glob_optimal_clock_start_sec,
glob_not_yet_finished, glob_display_flag, glob_warned, glob_optimal_start,
glob_hmin, glob_max_opt_iter, glob_percent_done, glob_normmax, glob_max_sec,
glob_look_poles, glob_optimal_done, glob_almost_1, years_in_century,
days_in_year, glob_optimal_expect_sec, glob_max_order, glob_hmax,
glob_html_log, glob_unchanged_h_cnt, centuries_in_millinium,
glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err,
glob_log10_relerr, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_warned2, glob_dump_analytic, glob_hmin_init, glob_h, glob_log10normmin,
glob_log10relerr, MAX_UNCHANGED, glob_no_eqs, glob_large_float, djd_debug2,
array_const_3D0, array_const_4D0, array_const_0D0, array_const_1,
array_const_2, array_const_2D0, array_pole, array_norms,
array_1st_rel_error, array_x1_init, array_m1, array_x2, array_x1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x2_init,
array_t, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_x2_higher_work2, array_x1_higher_work,
array_x2_higher_work, array_poles, array_real_pole, array_x2_higher,
array_complex_pole, array_x1_higher_work2, array_x1_higher, glob_last;
    n := glob_max_terms;
    m := n - 3;
    while 10 <= m and (abs(array_x2_higher[1, m]) < glob_small_float or
    abs(array_x2_higher[1, m - 1]) < glob_small_float or
    abs(array_x2_higher[1, m - 2]) < glob_small_float) do m := m - 1
    end do;
    if 10 < m then
        rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
        rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
        hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
        if glob_small_float < abs(hdrc) then
            rcs := glob_h/hdrc;
            ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
            array_real_pole[1, 1] := rcs;
            array_real_pole[1, 2] := ord_no
        else
            array_real_pole[1, 1] := glob_large_float;
            array_real_pole[1, 2] := glob_large_float
        end if
    else
        array_real_pole[1, 1] := glob_large_float;
        array_real_pole[1, 2] := glob_large_float
    end if;
    n := glob_max_terms;
    m := n - 2;
    while 10 <= m and (abs(array_x1_higher[1, m]) < glob_small_float or
    abs(array_x1_higher[1, m - 1]) < glob_small_float or
    abs(array_x1_higher[1, m - 2]) < glob_small_float) do m := m - 1
    end do;
    if 10 < m then
        rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
        rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
        hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1;
        if glob_small_float < abs(hdrc) then
            rcs := glob_h/hdrc;
            ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0;
            array_real_pole[2, 1] := rcs;
            array_real_pole[2, 2] := ord_no
        else
            array_real_pole[2, 1] := glob_large_float;
            array_real_pole[2, 2] := glob_large_float
        end if
    else
        array_real_pole[2, 1] := glob_large_float;
        array_real_pole[2, 2] := glob_large_float
    end if;
    n := glob_max_terms - 3;
    cnt := 0;
    while cnt < 5 and 10 <= n do
        if glob_small_float < abs(array_x2_higher[1, n]) then
            cnt := cnt + 1
        else cnt := 0
        end if;
        n := n - 1
    end do;
    m := n + cnt;
    if m <= 10 then
        array_complex_pole[1, 1] := glob_large_float;
        array_complex_pole[1, 2] := glob_large_float
    elif glob_large_float <= abs(array_x2_higher[1, m]) or
    glob_large_float <= abs(array_x2_higher[1, m - 1]) or
    glob_large_float <= abs(array_x2_higher[1, m - 2]) or
    glob_large_float <= abs(array_x2_higher[1, m - 3]) or
    glob_large_float <= abs(array_x2_higher[1, m - 4]) or
    glob_large_float <= abs(array_x2_higher[1, m - 5]) then
        array_complex_pole[1, 1] := glob_large_float;
        array_complex_pole[1, 2] := glob_large_float
    else
        rm0 := array_x2_higher[1, m]/array_x2_higher[1, m - 1];
        rm1 := array_x2_higher[1, m - 1]/array_x2_higher[1, m - 2];
        rm2 := array_x2_higher[1, m - 2]/array_x2_higher[1, m - 3];
        rm3 := array_x2_higher[1, m - 3]/array_x2_higher[1, m - 4];
        rm4 := array_x2_higher[1, m - 4]/array_x2_higher[1, m - 5];
        nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
             + convfloat(m - 3)*rm2;
        nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
             + convfloat(m - 4)*rm3;
        dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
        dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
        ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
        ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
        if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
        abs(dr1) <= glob_small_float then
            array_complex_pole[1, 1] := glob_large_float;
            array_complex_pole[1, 2] := glob_large_float
        else
            if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
                rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
                ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
                if glob_small_float < abs(rcs) then
                    if 0. < rcs then rad_c := sqrt(rcs)*glob_h
                    else rad_c := glob_large_float
                    end if
                else rad_c := glob_large_float; ord_no := glob_large_float
                end if
            else rad_c := glob_large_float; ord_no := glob_large_float
            end if
        end if;
        array_complex_pole[1, 1] := rad_c;
        array_complex_pole[1, 2] := ord_no
    end if;
    n := glob_max_terms - 2;
    cnt := 0;
    while cnt < 5 and 10 <= n do
        if glob_small_float < abs(array_x1_higher[1, n]) then
            cnt := cnt + 1
        else cnt := 0
        end if;
        n := n - 1
    end do;
    m := n + cnt;
    if m <= 10 then
        array_complex_pole[2, 1] := glob_large_float;
        array_complex_pole[2, 2] := glob_large_float
    elif glob_large_float <= abs(array_x1_higher[1, m]) or
    glob_large_float <= abs(array_x1_higher[1, m - 1]) or
    glob_large_float <= abs(array_x1_higher[1, m - 2]) or
    glob_large_float <= abs(array_x1_higher[1, m - 3]) or
    glob_large_float <= abs(array_x1_higher[1, m - 4]) or
    glob_large_float <= abs(array_x1_higher[1, m - 5]) then
        array_complex_pole[2, 1] := glob_large_float;
        array_complex_pole[2, 2] := glob_large_float
    else
        rm0 := array_x1_higher[1, m]/array_x1_higher[1, m - 1];
        rm1 := array_x1_higher[1, m - 1]/array_x1_higher[1, m - 2];
        rm2 := array_x1_higher[1, m - 2]/array_x1_higher[1, m - 3];
        rm3 := array_x1_higher[1, m - 3]/array_x1_higher[1, m - 4];
        rm4 := array_x1_higher[1, m - 4]/array_x1_higher[1, m - 5];
        nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
             + convfloat(m - 3)*rm2;
        nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
             + convfloat(m - 4)*rm3;
        dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
        dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
        ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
        ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
        if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or
        abs(dr1) <= glob_small_float then
            array_complex_pole[2, 1] := glob_large_float;
            array_complex_pole[2, 2] := glob_large_float
        else
            if glob_small_float < abs(nr1*dr2 - nr2*dr1) then
                rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
                ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
                if glob_small_float < abs(rcs) then
                    if 0. < rcs then rad_c := sqrt(rcs)*glob_h
                    else rad_c := glob_large_float
                    end if
                else rad_c := glob_large_float; ord_no := glob_large_float
                end if
            else rad_c := glob_large_float; ord_no := glob_large_float
            end if
        end if;
        array_complex_pole[2, 1] := rad_c;
        array_complex_pole[2, 2] := ord_no
    end if;
    found := false;
    if not found and (array_real_pole[1, 1] = glob_large_float or
    array_real_pole[1, 2] = glob_large_float) and
    array_complex_pole[1, 1] <> glob_large_float and
    array_complex_pole[1, 2] <> glob_large_float and
    0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
        array_poles[1, 1] := array_complex_pole[1, 1];
        array_poles[1, 2] := array_complex_pole[1, 2];
        found := true;
        array_type_pole[1] := 2;
        if glob_display_flag then
            omniout_str(ALWAYS, "Complex estimate of poles used")
        end if
    end if;
    if not found and array_real_pole[1, 1] <> glob_large_float and
    array_real_pole[1, 2] <> glob_large_float and
    0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and (
    array_complex_pole[1, 1] = glob_large_float or
    array_complex_pole[1, 2] = glob_large_float or
    array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
        array_poles[1, 1] := array_real_pole[1, 1];
        array_poles[1, 2] := array_real_pole[1, 2];
        found := true;
        array_type_pole[1] := 1;
        if glob_display_flag then
            omniout_str(ALWAYS, "Real estimate of pole used")
        end if
    end if;
    if not found and (array_real_pole[1, 1] = glob_large_float or
    array_real_pole[1, 2] = glob_large_float) and (
    array_complex_pole[1, 1] = glob_large_float or
    array_complex_pole[1, 2] = glob_large_float) then
        array_poles[1, 1] := glob_large_float;
        array_poles[1, 2] := glob_large_float;
        found := true;
        array_type_pole[1] := 3;
        if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
    end if;
    if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and
    0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then
        array_poles[1, 1] := array_real_pole[1, 1];
        array_poles[1, 2] := array_real_pole[1, 2];
        found := true;
        array_type_pole[1] := 1;
        if glob_display_flag then
            omniout_str(ALWAYS, "Real estimate of pole used")
        end if
    end if;
    if not found and array_complex_pole[1, 1] <> glob_large_float and
    array_complex_pole[1, 2] <> glob_large_float and
    0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
        array_poles[1, 1] := array_complex_pole[1, 1];
        array_poles[1, 2] := array_complex_pole[1, 2];
        array_type_pole[1] := 2;
        found := true;
        if glob_display_flag then
            omniout_str(ALWAYS, "Complex estimate of poles used")
        end if
    end if;
    if not found then
        array_poles[1, 1] := glob_large_float;
        array_poles[1, 2] := glob_large_float;
        array_type_pole[1] := 3;
        if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
    end if;
    found := false;
    if not found and (array_real_pole[2, 1] = glob_large_float or
    array_real_pole[2, 2] = glob_large_float) and
    array_complex_pole[2, 1] <> glob_large_float and
    array_complex_pole[2, 2] <> glob_large_float and
    0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
        array_poles[2, 1] := array_complex_pole[2, 1];
        array_poles[2, 2] := array_complex_pole[2, 2];
        found := true;
        array_type_pole[2] := 2;
        if glob_display_flag then
            omniout_str(ALWAYS, "Complex estimate of poles used")
        end if
    end if;
    if not found and array_real_pole[2, 1] <> glob_large_float and
    array_real_pole[2, 2] <> glob_large_float and
    0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and (
    array_complex_pole[2, 1] = glob_large_float or
    array_complex_pole[2, 2] = glob_large_float or
    array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
        array_poles[2, 1] := array_real_pole[2, 1];
        array_poles[2, 2] := array_real_pole[2, 2];
        found := true;
        array_type_pole[2] := 1;
        if glob_display_flag then
            omniout_str(ALWAYS, "Real estimate of pole used")
        end if
    end if;
    if not found and (array_real_pole[2, 1] = glob_large_float or
    array_real_pole[2, 2] = glob_large_float) and (
    array_complex_pole[2, 1] = glob_large_float or
    array_complex_pole[2, 2] = glob_large_float) then
        array_poles[2, 1] := glob_large_float;
        array_poles[2, 2] := glob_large_float;
        found := true;
        array_type_pole[2] := 3;
        if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
    end if;
    if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and
    0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then
        array_poles[2, 1] := array_real_pole[2, 1];
        array_poles[2, 2] := array_real_pole[2, 2];
        found := true;
        array_type_pole[2] := 1;
        if glob_display_flag then
            omniout_str(ALWAYS, "Real estimate of pole used")
        end if
    end if;
    if not found and array_complex_pole[2, 1] <> glob_large_float and
    array_complex_pole[2, 2] <> glob_large_float and
    0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
        array_poles[2, 1] := array_complex_pole[2, 1];
        array_poles[2, 2] := array_complex_pole[2, 2];
        array_type_pole[2] := 2;
        found := true;
        if glob_display_flag then
            omniout_str(ALWAYS, "Complex estimate of poles used")
        end if
    end if;
    if not found then
        array_poles[2, 1] := glob_large_float;
        array_poles[2, 2] := glob_large_float;
        array_type_pole[2] := 3;
        if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if
    end if;
    array_pole[1] := glob_large_float;
    array_pole[2] := glob_large_float;
    if array_poles[1, 1] < array_pole[1] then
        array_pole[1] := array_poles[1, 1];
        array_pole[2] := array_poles[1, 2]
    end if;
    if array_poles[2, 1] < array_pole[1] then
        array_pole[1] := array_poles[2, 1];
        array_pole[2] := array_poles[2, 2]
    end if;
    display_pole()
end proc

>   # Begin Function number 7
>     get_norms := proc()
>     global
>     ALWAYS,
>     INFO,
>     glob_max_terms,
>     DEBUGMASSIVE,
>     DEBUGL,
>     glob_iolevel,
>     #Top Generate Globals Decl
>     glob_log10abserr,
>     glob_orig_start_sec,
>     glob_smallish_float,
>     glob_max_trunc_err,
>     glob_last_good_h,
>     glob_disp_incr,
>     glob_reached_optimal_h,
>     glob_initial_pass,
>     sec_in_min,
>     glob_clock_start_sec,
>     glob_clock_sec,
>     min_in_hour,
>     djd_debug,
>     glob_max_minutes,
>     glob_iter,
>     glob_start,
>     glob_max_iter,
>     glob_max_hours,
>     glob_relerr,
>     glob_abserr,
>     glob_log10_abserr,
>     glob_small_float,
>     glob_optimal_clock_start_sec,
>     glob_not_yet_finished,
>     glob_display_flag,
>     glob_warned,
>     glob_optimal_start,
>     glob_hmin,
>     glob_max_opt_iter,
>     glob_percent_done,
>     glob_normmax,
>     glob_max_sec,
>     glob_look_poles,
>     glob_optimal_done,
>     glob_almost_1,
>     years_in_century,
>     days_in_year,
>     glob_optimal_expect_sec,
>     glob_max_order,
>     glob_hmax,
>     glob_html_log,
>     glob_unchanged_h_cnt,
>     centuries_in_millinium,
>     glob_current_iter,
>     glob_curr_iter_when_opt,
>     glob_max_rel_trunc_err,
>     glob_log10_relerr,
>     glob_not_yet_start_msg,
>     hours_in_day,
>     glob_dump,
>     glob_warned2,
>     glob_dump_analytic,
>     glob_hmin_init,
>     glob_h,
>     glob_log10normmin,
>     glob_log10relerr,
>     MAX_UNCHANGED,
>     glob_no_eqs,
>     glob_large_float,
>     djd_debug2,
>     #Bottom Generate Globals Decl
>     #BEGIN CONST
>     array_const_3D0,
>     array_const_4D0,
>     array_const_0D0,
>     array_const_1,
>     array_const_2,
>     array_const_2D0,
>     #END CONST
>     array_pole,
>     array_norms,
>     array_1st_rel_error,
>     array_x1_init,
>     array_m1,
>     array_x2,
>     array_x1,
>     array_tmp10,
>     array_tmp11,
>     array_tmp12,
>     array_tmp13,
>     array_tmp14,
>     array_tmp15,
>     array_tmp16,
>     array_tmp17,
>     array_type_pole,
>     array_x2_init,
>     array_t,
>     array_last_rel_error,
>     array_tmp0,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_tmp4,
>     array_tmp5,
>     array_tmp6,
>     array_tmp7,
>     array_tmp8,
>     array_tmp9,
>     array_x2_higher_work2,
>     array_x1_higher_work,
>     array_x2_higher_work,
>     array_poles,
>     array_real_pole,
>     array_x2_higher,
>     array_complex_pole,
>     array_x1_higher_work2,
>     array_x1_higher,
>     glob_last;
>     
>     local iii;
>     if (not glob_initial_pass)  then # if number 3
>       set_z(array_norms,glob_max_terms+1);
>       #TOP GET NORMS
>       iii   :=  1;
>       while (iii <= glob_max_terms)  do # do number 2
>         if (abs(array_x2[iii]) > array_norms[iii]) then # if number 4
>           array_norms[iii] := abs(array_x2[iii]);
>           fi;# end if 4
>         ;
>         iii   :=  iii + 1;
>         od;# end do number 2
>       ;
>       iii   :=  1;
>       while (iii <= glob_max_terms)  do # do number 2
>         if (abs(array_x1[iii]) > array_norms[iii]) then # if number 4
>           array_norms[iii] := abs(array_x1[iii]);
>           fi;# end if 4
>         ;
>         iii   :=  iii + 1;
>         od;# end do number 2
>       #GET NORMS
>       ;
>       fi;# end if 3
>     ;
>     # End Function number 7
>     end;
get_norms := proc()
local iii;
global ALWAYS, INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_log10abserr, glob_orig_start_sec, glob_smallish_float,
glob_max_trunc_err, glob_last_good_h, glob_disp_incr,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug, glob_max_minutes, glob_iter,
glob_start, glob_max_iter, glob_max_hours, glob_relerr, glob_abserr,
glob_log10_abserr, glob_small_float, glob_optimal_clock_start_sec,
glob_not_yet_finished, glob_display_flag, glob_warned, glob_optimal_start,
glob_hmin, glob_max_opt_iter, glob_percent_done, glob_normmax, glob_max_sec,
glob_look_poles, glob_optimal_done, glob_almost_1, years_in_century,
days_in_year, glob_optimal_expect_sec, glob_max_order, glob_hmax,
glob_html_log, glob_unchanged_h_cnt, centuries_in_millinium,
glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err,
glob_log10_relerr, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_warned2, glob_dump_analytic, glob_hmin_init, glob_h, glob_log10normmin,
glob_log10relerr, MAX_UNCHANGED, glob_no_eqs, glob_large_float, djd_debug2,
array_const_3D0, array_const_4D0, array_const_0D0, array_const_1,
array_const_2, array_const_2D0, array_pole, array_norms,
array_1st_rel_error, array_x1_init, array_m1, array_x2, array_x1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x2_init,
array_t, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_x2_higher_work2, array_x1_higher_work,
array_x2_higher_work, array_poles, array_real_pole, array_x2_higher,
array_complex_pole, array_x1_higher_work2, array_x1_higher, glob_last;
    if not glob_initial_pass then
        set_z(array_norms, glob_max_terms + 1);
        iii := 1;
        while iii <= glob_max_terms do
            if array_norms[iii] < abs(array_x2[iii]) then
                array_norms[iii] := abs(array_x2[iii])
            end if;
            iii := iii + 1
        end do;
        iii := 1;
        while iii <= glob_max_terms do
            if array_norms[iii] < abs(array_x1[iii]) then
                array_norms[iii] := abs(array_x1[iii])
            end if;
            iii := iii + 1
        end do
    end if
end proc

>   # Begin Function number 8
>     atomall := proc()
>     global
>     ALWAYS,
>     INFO,
>     glob_max_terms,
>     DEBUGMASSIVE,
>     DEBUGL,
>     glob_iolevel,
>     #Top Generate Globals Decl
>     glob_log10abserr,
>     glob_orig_start_sec,
>     glob_smallish_float,
>     glob_max_trunc_err,
>     glob_last_good_h,
>     glob_disp_incr,
>     glob_reached_optimal_h,
>     glob_initial_pass,
>     sec_in_min,
>     glob_clock_start_sec,
>     glob_clock_sec,
>     min_in_hour,
>     djd_debug,
>     glob_max_minutes,
>     glob_iter,
>     glob_start,
>     glob_max_iter,
>     glob_max_hours,
>     glob_relerr,
>     glob_abserr,
>     glob_log10_abserr,
>     glob_small_float,
>     glob_optimal_clock_start_sec,
>     glob_not_yet_finished,
>     glob_display_flag,
>     glob_warned,
>     glob_optimal_start,
>     glob_hmin,
>     glob_max_opt_iter,
>     glob_percent_done,
>     glob_normmax,
>     glob_max_sec,
>     glob_look_poles,
>     glob_optimal_done,
>     glob_almost_1,
>     years_in_century,
>     days_in_year,
>     glob_optimal_expect_sec,
>     glob_max_order,
>     glob_hmax,
>     glob_html_log,
>     glob_unchanged_h_cnt,
>     centuries_in_millinium,
>     glob_current_iter,
>     glob_curr_iter_when_opt,
>     glob_max_rel_trunc_err,
>     glob_log10_relerr,
>     glob_not_yet_start_msg,
>     hours_in_day,
>     glob_dump,
>     glob_warned2,
>     glob_dump_analytic,
>     glob_hmin_init,
>     glob_h,
>     glob_log10normmin,
>     glob_log10relerr,
>     MAX_UNCHANGED,
>     glob_no_eqs,
>     glob_large_float,
>     djd_debug2,
>     #Bottom Generate Globals Decl
>     #BEGIN CONST
>     array_const_3D0,
>     array_const_4D0,
>     array_const_0D0,
>     array_const_1,
>     array_const_2,
>     array_const_2D0,
>     #END CONST
>     array_pole,
>     array_norms,
>     array_1st_rel_error,
>     array_x1_init,
>     array_m1,
>     array_x2,
>     array_x1,
>     array_tmp10,
>     array_tmp11,
>     array_tmp12,
>     array_tmp13,
>     array_tmp14,
>     array_tmp15,
>     array_tmp16,
>     array_tmp17,
>     array_type_pole,
>     array_x2_init,
>     array_t,
>     array_last_rel_error,
>     array_tmp0,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_tmp4,
>     array_tmp5,
>     array_tmp6,
>     array_tmp7,
>     array_tmp8,
>     array_tmp9,
>     array_x2_higher_work2,
>     array_x1_higher_work,
>     array_x2_higher_work,
>     array_poles,
>     array_real_pole,
>     array_x2_higher,
>     array_complex_pole,
>     array_x1_higher_work2,
>     array_x1_higher,
>     glob_last;
>     
>     local kkk, order_d, adj2, temporary, term;
>     #TOP ATOMALL
>     #END OUTFILE1
>     #BEGIN ATOMHDR1
>     #emit pre diff $eq_no = 1 i = 1
>     array_tmp1[1] := array_x2_higher[2,1];
>     # emit pre mult $eq_no = 1 i = 1
>     array_tmp2[1] :=  (array_const_3D0[1] * (array_tmp1[1]));
>     #emit pre add $eq_no = 1 i = 1
>     array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
>     # emit pre mult $eq_no = 1 i = 1
>     array_tmp4[1] :=  (array_const_2D0[1] * (array_x2[1]));
>     #emit pre sub $eq_no = 1 i = 1
>     array_tmp5[1] :=   (array_tmp3[1] - (array_tmp4[1]));
>     #emit pre diff $eq_no = 1 i = 1
>     array_tmp6[1] := array_x1_higher[3,1];
>     #emit pre sub $eq_no = 1 i = 1
>     array_tmp7[1] :=   (array_tmp5[1] - (array_tmp6[1]));
>     #emit pre diff $eq_no = 1 i = 1
>     array_tmp8[1] := array_x1_higher[2,1];
>     #emit pre sub $eq_no = 1 i = 1
>     array_tmp9[1] :=   (array_tmp7[1] - (array_tmp8[1]));
>     #emit pre add $eq_no = 1 i = 1
>     array_tmp10[1] := array_tmp9[1] + array_x1[1];
>     #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
>     if (1 <= glob_max_terms) then # if number 1
>   temporary := array_tmp10[1] * (glob_h ^ (2)) * factorial_3(0,2);
>   array_x2[3] := temporary;
>   array_x2_higher[1,3] := temporary;
>   temporary := temporary / glob_h * (2.0);
>   array_x2_higher[2,2] := temporary
>   ;
>   temporary := temporary / glob_h * (3.0);
>   array_x2_higher[3,1] := temporary
>   ;
>   fi;# end if 1
>     ;
>     kkk := 2;
>     # emit pre mult $eq_no = 2 i = 1
>     array_tmp12[1] :=  (array_const_4D0[1] * (array_x2[1]));
>     #emit pre diff $eq_no = 2 i = 1
>     array_tmp13[1] := array_x2_higher[2,1];
>     # emit pre mult $eq_no = 2 i = 1
>     array_tmp14[1] :=  (array_const_2D0[1] * (array_tmp13[1]));
>     #emit pre sub $eq_no = 2 i = 1
>     array_tmp15[1] :=   (array_tmp12[1] - (array_tmp14[1]));
>     # emit pre mult $eq_no = 2 i = 1
>     array_tmp16[1] :=  (array_const_2D0[1] * (array_x1[1]));
>     #emit pre sub $eq_no = 2 i = 1
>     array_tmp17[1] :=   (array_tmp15[1] - (array_tmp16[1]));
>     #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
>     if (1 <= glob_max_terms) then # if number 1
>   temporary := array_tmp17[1] * (glob_h ^ (1)) * factorial_3(0,1);
>   array_x1[2] := temporary;
>   array_x1_higher[1,2] := temporary;
>   temporary := temporary / glob_h * (2.0);
>   array_x1_higher[2,1] := temporary
>   ;
>   fi;# end if 1
>     ;
>     kkk := 2;
>     #END ATOMHDR1
>     #BEGIN ATOMHDR2
>     #emit pre diff $eq_no = 1 i = 2
>     array_tmp1[2] := array_x2_higher[2,2];
>     # emit pre mult $eq_no = 1 i = 2
>     array_tmp2[2] :=  ats(2,array_const_3D0,array_tmp1,1);
>     #emit pre add $eq_no = 1 i = 2
>     array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
>     # emit pre mult $eq_no = 1 i = 2
>     array_tmp4[2] :=  ats(2,array_const_2D0,array_x2,1);
>     #emit pre sub $eq_no = 1 i = 2
>     array_tmp5[2] :=   (array_tmp3[2] - (array_tmp4[2]));
>     #emit pre diff $eq_no = 1 i = 2
>     array_tmp6[2] := array_x1_higher[3,2];
>     #emit pre sub $eq_no = 1 i = 2
>     array_tmp7[2] :=   (array_tmp5[2] - (array_tmp6[2]));
>     #emit pre diff $eq_no = 1 i = 2
>     array_tmp8[2] := array_x1_higher[2,2];
>     #emit pre sub $eq_no = 1 i = 2
>     array_tmp9[2] :=   (array_tmp7[2] - (array_tmp8[2]));
>     #emit pre add $eq_no = 1 i = 2
>     array_tmp10[2] := array_tmp9[2] + array_x1[2];
>     #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
>     if (2 <= glob_max_terms) then # if number 1
>   temporary := array_tmp10[2] * (glob_h ^ (2)) * factorial_3(1,3);
>   array_x2[4] := temporary;
>   array_x2_higher[1,4] := temporary;
>   temporary := temporary / glob_h * (2.0);
>   array_x2_higher[2,3] := temporary
>   ;
>   temporary := temporary / glob_h * (3.0);
>   array_x2_higher[3,2] := temporary
>   ;
>   fi;# end if 1
>     ;
>     kkk := 3;
>     # emit pre mult $eq_no = 2 i = 2
>     array_tmp12[2] :=  ats(2,array_const_4D0,array_x2,1);
>     #emit pre diff $eq_no = 2 i = 2
>     array_tmp13[2] := array_x2_higher[2,2];
>     # emit pre mult $eq_no = 2 i = 2
>     array_tmp14[2] :=  ats(2,array_const_2D0,array_tmp13,1);
>     #emit pre sub $eq_no = 2 i = 2
>     array_tmp15[2] :=   (array_tmp12[2] - (array_tmp14[2]));
>     # emit pre mult $eq_no = 2 i = 2
>     array_tmp16[2] :=  ats(2,array_const_2D0,array_x1,1);
>     #emit pre sub $eq_no = 2 i = 2
>     array_tmp17[2] :=   (array_tmp15[2] - (array_tmp16[2]));
>     #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
>     if (2 <= glob_max_terms) then # if number 1
>   temporary := array_tmp17[2] * (glob_h ^ (1)) * factorial_3(1,2);
>   array_x1[3] := temporary;
>   array_x1_higher[1,3] := temporary;
>   temporary := temporary / glob_h * (2.0);
>   array_x1_higher[2,2] := temporary
>   ;
>   fi;# end if 1
>     ;
>     kkk := 3;
>     #END ATOMHDR2
>     #BEGIN ATOMHDR3
>     #emit pre diff $eq_no = 1 i = 3
>     array_tmp1[3] := array_x2_higher[2,3];
>     # emit pre mult $eq_no = 1 i = 3
>     array_tmp2[3] :=  ats(3,array_const_3D0,array_tmp1,1);
>     #emit pre add $eq_no = 1 i = 3
>     array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
>     # emit pre mult $eq_no = 1 i = 3
>     array_tmp4[3] :=  ats(3,array_const_2D0,array_x2,1);
>     #emit pre sub $eq_no = 1 i = 3
>     array_tmp5[3] :=   (array_tmp3[3] - (array_tmp4[3]));
>     #emit pre diff $eq_no = 1 i = 3
>     array_tmp6[3] := array_x1_higher[3,3];
>     #emit pre sub $eq_no = 1 i = 3
>     array_tmp7[3] :=   (array_tmp5[3] - (array_tmp6[3]));
>     #emit pre diff $eq_no = 1 i = 3
>     array_tmp8[3] := array_x1_higher[2,3];
>     #emit pre sub $eq_no = 1 i = 3
>     array_tmp9[3] :=   (array_tmp7[3] - (array_tmp8[3]));
>     #emit pre add $eq_no = 1 i = 3
>     array_tmp10[3] := array_tmp9[3] + array_x1[3];
>     #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
>     if (3 <= glob_max_terms) then # if number 1
>   temporary := array_tmp10[3] * (glob_h ^ (2)) * factorial_3(2,4);
>   array_x2[5] := temporary;
>   array_x2_higher[1,5] := temporary;
>   temporary := temporary / glob_h * (2.0);
>   array_x2_higher[2,4] := temporary
>   ;
>   temporary := temporary / glob_h * (3.0);
>   array_x2_higher[3,3] := temporary
>   ;
>   fi;# end if 1
>     ;
>     kkk := 4;
>     # emit pre mult $eq_no = 2 i = 3
>     array_tmp12[3] :=  ats(3,array_const_4D0,array_x2,1);
>     #emit pre diff $eq_no = 2 i = 3
>     array_tmp13[3] := array_x2_higher[2,3];
>     # emit pre mult $eq_no = 2 i = 3
>     array_tmp14[3] :=  ats(3,array_const_2D0,array_tmp13,1);
>     #emit pre sub $eq_no = 2 i = 3
>     array_tmp15[3] :=   (array_tmp12[3] - (array_tmp14[3]));
>     # emit pre mult $eq_no = 2 i = 3
>     array_tmp16[3] :=  ats(3,array_const_2D0,array_x1,1);
>     #emit pre sub $eq_no = 2 i = 3
>     array_tmp17[3] :=   (array_tmp15[3] - (array_tmp16[3]));
>     #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
>     if (3 <= glob_max_terms) then # if number 1
>   temporary := array_tmp17[3] * (glob_h ^ (1)) * factorial_3(2,3);
>   array_x1[4] := temporary;
>   array_x1_higher[1,4] := temporary;
>   temporary := temporary / glob_h * (2.0);
>   array_x1_higher[2,3] := temporary
>   ;
>   fi;# end if 1
>     ;
>     kkk := 4;
>     #END ATOMHDR3
>     #BEGIN ATOMHDR4
>     #emit pre diff $eq_no = 1 i = 4
>     array_tmp1[4] := array_x2_higher[2,4];
>     # emit pre mult $eq_no = 1 i = 4
>     array_tmp2[4] :=  ats(4,array_const_3D0,array_tmp1,1);
>     #emit pre add $eq_no = 1 i = 4
>     array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
>     # emit pre mult $eq_no = 1 i = 4
>     array_tmp4[4] :=  ats(4,array_const_2D0,array_x2,1);
>     #emit pre sub $eq_no = 1 i = 4
>     array_tmp5[4] :=   (array_tmp3[4] - (array_tmp4[4]));
>     #emit pre diff $eq_no = 1 i = 4
>     array_tmp6[4] := array_x1_higher[3,4];
>     #emit pre sub $eq_no = 1 i = 4
>     array_tmp7[4] :=   (array_tmp5[4] - (array_tmp6[4]));
>     #emit pre diff $eq_no = 1 i = 4
>     array_tmp8[4] := array_x1_higher[2,4];
>     #emit pre sub $eq_no = 1 i = 4
>     array_tmp9[4] :=   (array_tmp7[4] - (array_tmp8[4]));
>     #emit pre add $eq_no = 1 i = 4
>     array_tmp10[4] := array_tmp9[4] + array_x1[4];
>     #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
>     if (4 <= glob_max_terms) then # if number 1
>   temporary := array_tmp10[4] * (glob_h ^ (2)) * factorial_3(3,5);
>   array_x2[6] := temporary;
>   array_x2_higher[1,6] := temporary;
>   temporary := temporary / glob_h * (2.0);
>   array_x2_higher[2,5] := temporary
>   ;
>   temporary := temporary / glob_h * (3.0);
>   array_x2_higher[3,4] := temporary
>   ;
>   fi;# end if 1
>     ;
>     kkk := 5;
>     # emit pre mult $eq_no = 2 i = 4
>     array_tmp12[4] :=  ats(4,array_const_4D0,array_x2,1);
>     #emit pre diff $eq_no = 2 i = 4
>     array_tmp13[4] := array_x2_higher[2,4];
>     # emit pre mult $eq_no = 2 i = 4
>     array_tmp14[4] :=  ats(4,array_const_2D0,array_tmp13,1);
>     #emit pre sub $eq_no = 2 i = 4
>     array_tmp15[4] :=   (array_tmp12[4] - (array_tmp14[4]));
>     # emit pre mult $eq_no = 2 i = 4
>     array_tmp16[4] :=  ats(4,array_const_2D0,array_x1,1);
>     #emit pre sub $eq_no = 2 i = 4
>     array_tmp17[4] :=   (array_tmp15[4] - (array_tmp16[4]));
>     #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
>     if (4 <= glob_max_terms) then # if number 1
>   temporary := array_tmp17[4] * (glob_h ^ (1)) * factorial_3(3,4);
>   array_x1[5] := temporary;
>   array_x1_higher[1,5] := temporary;
>   temporary := temporary / glob_h * (2.0);
>   array_x1_higher[2,4] := temporary
>   ;
>   fi;# end if 1
>     ;
>     kkk := 5;
>     #END ATOMHDR4
>     #BEGIN ATOMHDR5
>     #emit pre diff $eq_no = 1 i = 5
>     array_tmp1[5] := array_x2_higher[2,5];
>     # emit pre mult $eq_no = 1 i = 5
>     array_tmp2[5] :=  ats(5,array_const_3D0,array_tmp1,1);
>     #emit pre add $eq_no = 1 i = 5
>     array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
>     # emit pre mult $eq_no = 1 i = 5
>     array_tmp4[5] :=  ats(5,array_const_2D0,array_x2,1);
>     #emit pre sub $eq_no = 1 i = 5
>     array_tmp5[5] :=   (array_tmp3[5] - (array_tmp4[5]));
>     #emit pre diff $eq_no = 1 i = 5
>     array_tmp6[5] := array_x1_higher[3,5];
>     #emit pre sub $eq_no = 1 i = 5
>     array_tmp7[5] :=   (array_tmp5[5] - (array_tmp6[5]));
>     #emit pre diff $eq_no = 1 i = 5
>     array_tmp8[5] := array_x1_higher[2,5];
>     #emit pre sub $eq_no = 1 i = 5
>     array_tmp9[5] :=   (array_tmp7[5] - (array_tmp8[5]));
>     #emit pre add $eq_no = 1 i = 5
>     array_tmp10[5] := array_tmp9[5] + array_x1[5];
>     #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
>     if (5 <= glob_max_terms) then # if number 1
>   temporary := array_tmp10[5] * (glob_h ^ (2)) * factorial_3(4,6);
>   array_x2[7] := temporary;
>   array_x2_higher[1,7] := temporary;
>   temporary := temporary / glob_h * (2.0);
>   array_x2_higher[2,6] := temporary
>   ;
>   temporary := temporary / glob_h * (3.0);
>   array_x2_higher[3,5] := temporary
>   ;
>   fi;# end if 1
>     ;
>     kkk := 6;
>     # emit pre mult $eq_no = 2 i = 5
>     array_tmp12[5] :=  ats(5,array_const_4D0,array_x2,1);
>     #emit pre diff $eq_no = 2 i = 5
>     array_tmp13[5] := array_x2_higher[2,5];
>     # emit pre mult $eq_no = 2 i = 5
>     array_tmp14[5] :=  ats(5,array_const_2D0,array_tmp13,1);
>     #emit pre sub $eq_no = 2 i = 5
>     array_tmp15[5] :=   (array_tmp12[5] - (array_tmp14[5]));
>     # emit pre mult $eq_no = 2 i = 5
>     array_tmp16[5] :=  ats(5,array_const_2D0,array_x1,1);
>     #emit pre sub $eq_no = 2 i = 5
>     array_tmp17[5] :=   (array_tmp15[5] - (array_tmp16[5]));
>     #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
>     if (5 <= glob_max_terms) then # if number 1
>   temporary := array_tmp17[5] * (glob_h ^ (1)) * factorial_3(4,5);
>   array_x1[6] := temporary;
>   array_x1_higher[1,6] := temporary;
>   temporary := temporary / glob_h * (2.0);
>   array_x1_higher[2,5] := temporary
>   ;
>   fi;# end if 1
>     ;
>     kkk := 6;
>     #END ATOMHDR5
>     #BEGIN OUTFILE3
>     #Top Atomall While Loop-- outfile3
>     while (kkk <= glob_max_terms) do # do number 1
>     #END OUTFILE3
>     #BEGIN OUTFILE4
>     #emit diff $eq_no = 1
>     array_tmp1[kkk] :=  array_x2_higher[2,kkk];
>     #emit mult $eq_no = 1
>     array_tmp2[kkk] :=  ats(kkk,array_const_3D0,array_tmp1,1);
>     #emit add $eq_no = 1
>     array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
>     #emit mult $eq_no = 1
>     array_tmp4[kkk] :=  ats(kkk,array_const_2D0,array_x2,1);
>     #emit sub $eq_no = 1
>     array_tmp5[kkk] :=   (array_tmp3[kkk] - (array_tmp4[kkk]));
>     #emit diff $eq_no = 1
>     array_tmp6[kkk] :=  array_x1_higher[3,kkk];
>     #emit sub $eq_no = 1
>     array_tmp7[kkk] :=   (array_tmp5[kkk] - (array_tmp6[kkk]));
>     #emit diff $eq_no = 1
>     array_tmp8[kkk] :=  array_x1_higher[2,kkk];
>     #emit sub $eq_no = 1
>     array_tmp9[kkk] :=   (array_tmp7[kkk] - (array_tmp8[kkk]));
>     #emit add $eq_no = 1
>     array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
>     #emit assign $eq_no = 1
>     order_d  := 2;
>     if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
>   temporary :=  array_tmp10[kkk] * (glob_h ^ (order_d))  / factorial_3((kkk - 1),(kkk + order_d - 1));
>   array_x2[kkk + order_d] := temporary;
>   array_x2_higher[1,kkk + order_d] := temporary;
>   term := kkk + order_d - 1;
>   adj2 := 2;
>   while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
>  temporary := temporary / glob_h * convfp(adj2);
>  array_x2_higher[adj2,term] := temporary;
>  adj2 := adj2 + 1;
>  term  := term - 1;
>  od;# end do number 2
>   fi;# end if 1
>     ;
>     #emit mult $eq_no = 2
>     array_tmp12[kkk] :=  ats(kkk,array_const_4D0,array_x2,1);
>     #emit diff $eq_no = 2
>     array_tmp13[kkk] :=  array_x2_higher[2,kkk];
>     #emit mult $eq_no = 2
>     array_tmp14[kkk] :=  ats(kkk,array_const_2D0,array_tmp13,1);
>     #emit sub $eq_no = 2
>     array_tmp15[kkk] :=   (array_tmp12[kkk] - (array_tmp14[kkk]));
>     #emit mult $eq_no = 2
>     array_tmp16[kkk] :=  ats(kkk,array_const_2D0,array_x1,1);
>     #emit sub $eq_no = 2
>     array_tmp17[kkk] :=   (array_tmp15[kkk] - (array_tmp16[kkk]));
>     #emit assign $eq_no = 2
>     order_d  := 1;
>     if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
>   temporary :=  array_tmp17[kkk] * (glob_h ^ (order_d))  / factorial_3((kkk - 1),(kkk + order_d - 1));
>   array_x1[kkk + order_d] := temporary;
>   array_x1_higher[1,kkk + order_d] := temporary;
>   term := kkk + order_d - 1;
>   adj2 := 2;
>   while (adj2 <= order_d + 1) and (term >= 1) do # do number 2
>  temporary := temporary / glob_h * convfp(adj2);
>  array_x1_higher[adj2,term] := temporary;
>  adj2 := adj2 + 1;
>  term  := term - 1;
>  od;# end do number 2
>   fi;# end if 1
>     ;
>     kkk   :=  kkk + 1;
>     od;# end do number 1
>  ;
>  #BOTTOM ATOMALL
>  #END OUTFILE4
>  #BEGIN OUTFILE5
>  # End Function number 8
>  end;
atomall := proc()
local kkk, order_d, adj2, temporary, term;
global ALWAYS, INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_log10abserr, glob_orig_start_sec, glob_smallish_float,
glob_max_trunc_err, glob_last_good_h, glob_disp_incr,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug, glob_max_minutes, glob_iter,
glob_start, glob_max_iter, glob_max_hours, glob_relerr, glob_abserr,
glob_log10_abserr, glob_small_float, glob_optimal_clock_start_sec,
glob_not_yet_finished, glob_display_flag, glob_warned, glob_optimal_start,
glob_hmin, glob_max_opt_iter, glob_percent_done, glob_normmax, glob_max_sec,
glob_look_poles, glob_optimal_done, glob_almost_1, years_in_century,
days_in_year, glob_optimal_expect_sec, glob_max_order, glob_hmax,
glob_html_log, glob_unchanged_h_cnt, centuries_in_millinium,
glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err,
glob_log10_relerr, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_warned2, glob_dump_analytic, glob_hmin_init, glob_h, glob_log10normmin,
glob_log10relerr, MAX_UNCHANGED, glob_no_eqs, glob_large_float, djd_debug2,
array_const_3D0, array_const_4D0, array_const_0D0, array_const_1,
array_const_2, array_const_2D0, array_pole, array_norms,
array_1st_rel_error, array_x1_init, array_m1, array_x2, array_x1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x2_init,
array_t, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_x2_higher_work2, array_x1_higher_work,
array_x2_higher_work, array_poles, array_real_pole, array_x2_higher,
array_complex_pole, array_x1_higher_work2, array_x1_higher, glob_last;
    array_tmp1[1] := array_x2_higher[2, 1];
    array_tmp2[1] := array_const_3D0[1]*array_tmp1[1];
    array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
    array_tmp4[1] := array_const_2D0[1]*array_x2[1];
    array_tmp5[1] := array_tmp3[1] - array_tmp4[1];
    array_tmp6[1] := array_x1_higher[3, 1];
    array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
    array_tmp8[1] := array_x1_higher[2, 1];
    array_tmp9[1] := array_tmp7[1] - array_tmp8[1];
    array_tmp10[1] := array_tmp9[1] + array_x1[1];
    if 1 <= glob_max_terms then
        temporary := array_tmp10[1]*glob_h^2*factorial_3(0, 2);
        array_x2[3] := temporary;
        array_x2_higher[1, 3] := temporary;
        temporary := temporary*2.0/glob_h;
        array_x2_higher[2, 2] := temporary;
        temporary := temporary*3.0/glob_h;
        array_x2_higher[3, 1] := temporary
    end if;
    kkk := 2;
    array_tmp12[1] := array_const_4D0[1]*array_x2[1];
    array_tmp13[1] := array_x2_higher[2, 1];
    array_tmp14[1] := array_const_2D0[1]*array_tmp13[1];
    array_tmp15[1] := array_tmp12[1] - array_tmp14[1];
    array_tmp16[1] := array_const_2D0[1]*array_x1[1];
    array_tmp17[1] := array_tmp15[1] - array_tmp16[1];
    if 1 <= glob_max_terms then
        temporary := array_tmp17[1]*glob_h*factorial_3(0, 1);
        array_x1[2] := temporary;
        array_x1_higher[1, 2] := temporary;
        temporary := temporary*2.0/glob_h;
        array_x1_higher[2, 1] := temporary
    end if;
    kkk := 2;
    array_tmp1[2] := array_x2_higher[2, 2];
    array_tmp2[2] := ats(2, array_const_3D0, array_tmp1, 1);
    array_tmp3[2] := array_const_0D0[2] + array_tmp2[2];
    array_tmp4[2] := ats(2, array_const_2D0, array_x2, 1);
    array_tmp5[2] := array_tmp3[2] - array_tmp4[2];
    array_tmp6[2] := array_x1_higher[3, 2];
    array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
    array_tmp8[2] := array_x1_higher[2, 2];
    array_tmp9[2] := array_tmp7[2] - array_tmp8[2];
    array_tmp10[2] := array_tmp9[2] + array_x1[2];
    if 2 <= glob_max_terms then
        temporary := array_tmp10[2]*glob_h^2*factorial_3(1, 3);
        array_x2[4] := temporary;
        array_x2_higher[1, 4] := temporary;
        temporary := temporary*2.0/glob_h;
        array_x2_higher[2, 3] := temporary;
        temporary := temporary*3.0/glob_h;
        array_x2_higher[3, 2] := temporary
    end if;
    kkk := 3;
    array_tmp12[2] := ats(2, array_const_4D0, array_x2, 1);
    array_tmp13[2] := array_x2_higher[2, 2];
    array_tmp14[2] := ats(2, array_const_2D0, array_tmp13, 1);
    array_tmp15[2] := array_tmp12[2] - array_tmp14[2];
    array_tmp16[2] := ats(2, array_const_2D0, array_x1, 1);
    array_tmp17[2] := array_tmp15[2] - array_tmp16[2];
    if 2 <= glob_max_terms then
        temporary := array_tmp17[2]*glob_h*factorial_3(1, 2);
        array_x1[3] := temporary;
        array_x1_higher[1, 3] := temporary;
        temporary := temporary*2.0/glob_h;
        array_x1_higher[2, 2] := temporary
    end if;
    kkk := 3;
    array_tmp1[3] := array_x2_higher[2, 3];
    array_tmp2[3] := ats(3, array_const_3D0, array_tmp1, 1);
    array_tmp3[3] := array_const_0D0[3] + array_tmp2[3];
    array_tmp4[3] := ats(3, array_const_2D0, array_x2, 1);
    array_tmp5[3] := array_tmp3[3] - array_tmp4[3];
    array_tmp6[3] := array_x1_higher[3, 3];
    array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
    array_tmp8[3] := array_x1_higher[2, 3];
    array_tmp9[3] := array_tmp7[3] - array_tmp8[3];
    array_tmp10[3] := array_tmp9[3] + array_x1[3];
    if 3 <= glob_max_terms then
        temporary := array_tmp10[3]*glob_h^2*factorial_3(2, 4);
        array_x2[5] := temporary;
        array_x2_higher[1, 5] := temporary;
        temporary := temporary*2.0/glob_h;
        array_x2_higher[2, 4] := temporary;
        temporary := temporary*3.0/glob_h;
        array_x2_higher[3, 3] := temporary
    end if;
    kkk := 4;
    array_tmp12[3] := ats(3, array_const_4D0, array_x2, 1);
    array_tmp13[3] := array_x2_higher[2, 3];
    array_tmp14[3] := ats(3, array_const_2D0, array_tmp13, 1);
    array_tmp15[3] := array_tmp12[3] - array_tmp14[3];
    array_tmp16[3] := ats(3, array_const_2D0, array_x1, 1);
    array_tmp17[3] := array_tmp15[3] - array_tmp16[3];
    if 3 <= glob_max_terms then
        temporary := array_tmp17[3]*glob_h*factorial_3(2, 3);
        array_x1[4] := temporary;
        array_x1_higher[1, 4] := temporary;
        temporary := temporary*2.0/glob_h;
        array_x1_higher[2, 3] := temporary
    end if;
    kkk := 4;
    array_tmp1[4] := array_x2_higher[2, 4];
    array_tmp2[4] := ats(4, array_const_3D0, array_tmp1, 1);
    array_tmp3[4] := array_const_0D0[4] + array_tmp2[4];
    array_tmp4[4] := ats(4, array_const_2D0, array_x2, 1);
    array_tmp5[4] := array_tmp3[4] - array_tmp4[4];
    array_tmp6[4] := array_x1_higher[3, 4];
    array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
    array_tmp8[4] := array_x1_higher[2, 4];
    array_tmp9[4] := array_tmp7[4] - array_tmp8[4];
    array_tmp10[4] := array_tmp9[4] + array_x1[4];
    if 4 <= glob_max_terms then
        temporary := array_tmp10[4]*glob_h^2*factorial_3(3, 5);
        array_x2[6] := temporary;
        array_x2_higher[1, 6] := temporary;
        temporary := temporary*2.0/glob_h;
        array_x2_higher[2, 5] := temporary;
        temporary := temporary*3.0/glob_h;
        array_x2_higher[3, 4] := temporary
    end if;
    kkk := 5;
    array_tmp12[4] := ats(4, array_const_4D0, array_x2, 1);
    array_tmp13[4] := array_x2_higher[2, 4];
    array_tmp14[4] := ats(4, array_const_2D0, array_tmp13, 1);
    array_tmp15[4] := array_tmp12[4] - array_tmp14[4];
    array_tmp16[4] := ats(4, array_const_2D0, array_x1, 1);
    array_tmp17[4] := array_tmp15[4] - array_tmp16[4];
    if 4 <= glob_max_terms then
        temporary := array_tmp17[4]*glob_h*factorial_3(3, 4);
        array_x1[5] := temporary;
        array_x1_higher[1, 5] := temporary;
        temporary := temporary*2.0/glob_h;
        array_x1_higher[2, 4] := temporary
    end if;
    kkk := 5;
    array_tmp1[5] := array_x2_higher[2, 5];
    array_tmp2[5] := ats(5, array_const_3D0, array_tmp1, 1);
    array_tmp3[5] := array_const_0D0[5] + array_tmp2[5];
    array_tmp4[5] := ats(5, array_const_2D0, array_x2, 1);
    array_tmp5[5] := array_tmp3[5] - array_tmp4[5];
    array_tmp6[5] := array_x1_higher[3, 5];
    array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
    array_tmp8[5] := array_x1_higher[2, 5];
    array_tmp9[5] := array_tmp7[5] - array_tmp8[5];
    array_tmp10[5] := array_tmp9[5] + array_x1[5];
    if 5 <= glob_max_terms then
        temporary := array_tmp10[5]*glob_h^2*factorial_3(4, 6);
        array_x2[7] := temporary;
        array_x2_higher[1, 7] := temporary;
        temporary := temporary*2.0/glob_h;
        array_x2_higher[2, 6] := temporary;
        temporary := temporary*3.0/glob_h;
        array_x2_higher[3, 5] := temporary
    end if;
    kkk := 6;
    array_tmp12[5] := ats(5, array_const_4D0, array_x2, 1);
    array_tmp13[5] := array_x2_higher[2, 5];
    array_tmp14[5] := ats(5, array_const_2D0, array_tmp13, 1);
    array_tmp15[5] := array_tmp12[5] - array_tmp14[5];
    array_tmp16[5] := ats(5, array_const_2D0, array_x1, 1);
    array_tmp17[5] := array_tmp15[5] - array_tmp16[5];
    if 5 <= glob_max_terms then
        temporary := array_tmp17[5]*glob_h*factorial_3(4, 5);
        array_x1[6] := temporary;
        array_x1_higher[1, 6] := temporary;
        temporary := temporary*2.0/glob_h;
        array_x1_higher[2, 5] := temporary
    end if;
    kkk := 6;
    while kkk <= glob_max_terms do
        array_tmp1[kkk] := array_x2_higher[2, kkk];
        array_tmp2[kkk] := ats(kkk, array_const_3D0, array_tmp1, 1);
        array_tmp3[kkk] := array_const_0D0[kkk] + array_tmp2[kkk];
        array_tmp4[kkk] := ats(kkk, array_const_2D0, array_x2, 1);
        array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk];
        array_tmp6[kkk] := array_x1_higher[3, kkk];
        array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
        array_tmp8[kkk] := array_x1_higher[2, kkk];
        array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk];
        array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
        order_d := 2;
        if kkk + order_d + 1 <= glob_max_terms then
            temporary := array_tmp10[kkk]*glob_h^order_d/
                factorial_3(kkk - 1, kkk + order_d - 1);
            array_x2[kkk + order_d] := temporary;
            array_x2_higher[1, kkk + order_d] := temporary;
            term := kkk + order_d - 1;
            adj2 := 2;
            while adj2 <= order_d + 1 and 1 <= term do
                temporary := temporary*convfp(adj2)/glob_h;
                array_x2_higher[adj2, term] := temporary;
                adj2 := adj2 + 1;
                term := term - 1
            end do
        end if;
        array_tmp12[kkk] := ats(kkk, array_const_4D0, array_x2, 1);
        array_tmp13[kkk] := array_x2_higher[2, kkk];
        array_tmp14[kkk] := ats(kkk, array_const_2D0, array_tmp13, 1);
        array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk];
        array_tmp16[kkk] := ats(kkk, array_const_2D0, array_x1, 1);
        array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk];
        order_d := 1;
        if kkk + order_d + 1 <= glob_max_terms then
            temporary := array_tmp17[kkk]*glob_h^order_d/
                factorial_3(kkk - 1, kkk + order_d - 1);
            array_x1[kkk + order_d] := temporary;
            array_x1_higher[1, kkk + order_d] := temporary;
            term := kkk + order_d - 1;
            adj2 := 2;
            while adj2 <= order_d + 1 and 1 <= term do
                temporary := temporary*convfp(adj2)/glob_h;
                array_x1_higher[adj2, term] := temporary;
                adj2 := adj2 + 1;
                term := term - 1
            end do
        end if;
        kkk := kkk + 1
    end do
end proc

>   #BEGIN ATS LIBRARY BLOCK
>   omniout_str := proc(iolevel,str)
>   global glob_iolevel;
>   if (glob_iolevel >= iolevel) then
>   printf("%s\n",str);
>   fi;
>   # End Function number 1
>   end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
    if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc

>         omniout_str_noeol := proc(iolevel,str)
>         global glob_iolevel;
>         if (glob_iolevel >= iolevel) then
>         printf("%s",str);
>         fi;
>         # End Function number 1
>         end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
    if iolevel <= glob_iolevel then printf("%s", str) end if
end proc

>           omniout_labstr := proc(iolevel,label,str)
>           global glob_iolevel;
>           if (glob_iolevel >= iolevel) then
>           print(label,str);
>           fi;
>           # End Function number 1
>           end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
    if iolevel <= glob_iolevel then print(label, str) end if
end proc

>             omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
>             global glob_iolevel;
>             if (glob_iolevel >= iolevel) then
>             if vallen = 4 then
>             printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
>             else
>             printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
>             fi;
>             fi;
>             # End Function number 1
>             end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
    if iolevel <= glob_iolevel then
        if vallen = 4 then
            printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
        else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
        end if
    end if
end proc

>               omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
>               global glob_iolevel;
>               if (glob_iolevel >= iolevel) then
>               if vallen = 5 then
>               printf("%-30s = %-32d  %s\n",prelabel,value, postlabel);
>               else
>               printf("%-30s = %-32d  %s \n",prelabel,value, postlabel);
>               fi;
>               fi;
>               # End Function number 1
>               end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
    if iolevel <= glob_iolevel then
        if vallen = 5 then
            printf("%-30s = %-32d  %s\n", prelabel, value, postlabel)
        else printf("%-30s = %-32d  %s \n", prelabel, value, postlabel)
        end if
    end if
end proc

>                 omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
>                 global glob_iolevel;
>                 if (glob_iolevel >= iolevel) then
>                 print(prelabel,"[",elemnt,"]",value, postlabel);
>                 fi;
>                 # End Function number 1
>                 end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
    if iolevel <= glob_iolevel then
        print(prelabel, "[", elemnt, "]", value, postlabel)
    end if
end proc

>                   dump_series := proc(iolevel,dump_label,series_name,
>                   array_series,numb)
>                   global glob_iolevel;
>                   local i;
>                   if (glob_iolevel >= iolevel) then
>                   i := 1;
>                   while (i <= numb) do
>                   print(dump_label,series_name
>                   ,i,array_series[i]);
>                   i := i + 1;
>                   od;
>                   fi;
>                   # End Function number 1
>                   end;
dump_series := proc(iolevel, dump_label, series_name, array_series, numb)
local i;
global glob_iolevel;
    if iolevel <= glob_iolevel then
        i := 1;
        while i <= numb do
            print(dump_label, series_name, i, array_series[i]); i := i + 1
        end do
    end if
end proc

>                     dump_series_2 := proc(iolevel,dump_label,series_name2,
>                     array_series2,numb,subnum,array_x)
>                     global glob_iolevel;
>                     local i,sub,ts_term;
>                     if (glob_iolevel >= iolevel) then
>                     sub := 1;
>                     while (sub <= subnum) do
>                     i :=  1;
>                     while (i <= numb) do
>                     print(dump_label,series_name2,sub,i,array_series2[sub,i]);
>                     od;
>                     sub :=  sub + 1;
>                     od;
>                     fi;
>                     # End Function number 1
>                     end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x)
local i, sub, ts_term;
global glob_iolevel;
    if iolevel <= glob_iolevel then
        sub := 1;
        while sub <= subnum do
            i := 1;
            while i <= numb do print(dump_label, series_name2, sub, i,
                array_series2[sub, i])
            end do;
            sub := sub + 1
        end do
    end if
end proc

>                       cs_info := proc(iolevel,str)
>                       global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
>                       if (glob_iolevel >= iolevel) then
>                       print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
>                       fi;
>                       # End Function number 1
>                       end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
    if iolevel <= glob_iolevel then print("cs_info ", str,
        " glob_correct_start_flag = ", glob_correct_start_flag,
        "glob_h := ", glob_h, "glob_reached_optimal_h := ",
        glob_reached_optimal_h)
    end if
end proc

>                         # Begin Function number 2
>                       logitem_time := proc(fd,secs_in)
>                       global  centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
>                       local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
>                       secs  :=  (secs_in);
>                       if (secs > 0.0)  then # if number 1
>                     sec_in_millinium  :=   convfloat(sec_in_min *  min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
>                     milliniums  :=  convfloat(secs / sec_in_millinium);
>                     millinium_int  :=  floor(milliniums);
>                     centuries  :=  (milliniums - millinium_int)*centuries_in_millinium;
>                     cent_int  :=  floor(centuries);
>                     years  :=  (centuries - cent_int) * years_in_century;
>                     years_int  :=  floor(years);
>                     days  :=  (years - years_int) * days_in_year;
>                     days_int  :=  floor(days);
>                     hours  :=  (days - days_int) * hours_in_day;
>                     hours_int  :=  floor(hours);
>                     minutes  :=  (hours - hours_int) * min_in_hour;
>                     minutes_int  :=  floor(minutes);
>                     seconds  :=  (minutes - minutes_int) * sec_in_min;
>                     sec_int  :=  floor(seconds);
>                     fprintf(fd,"<td>");
>                     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,"</td>");
>             # 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, "<td>");
        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, "</td>")
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,"<td>");
>     fprintf(file,"ditto");
>     fprintf(file,"</td>");
>     # End Function number 6
>     end;
logditto := proc(file)
    fprintf(file, "<td>"); fprintf(file, "ditto"); fprintf(file, "</td>")
end proc

>       # Begin Function number 7
>     logitem_integer := proc(file,n)
>     fprintf(file,"<td>");
>     fprintf(file,"%d",n);
>     fprintf(file,"</td>");
>     # End Function number 7
>     end;
logitem_integer := proc(file, n)
    fprintf(file, "<td>"); fprintf(file, "%d", n); fprintf(file, "</td>")
end proc

>       # Begin Function number 8
>     logitem_str := proc(file,str)
>     fprintf(file,"<td>");
>     fprintf(file,str);
>     fprintf(file,"</td>");
>     # End Function number 8
>     end;
logitem_str := proc(file, str)
    fprintf(file, "<td>"); fprintf(file, str); fprintf(file, "</td>")
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,"<td>");
>     fprintf(file,"%g",x);
>     fprintf(file,"</td>");
>     # End Function number 10
>     end;
logitem_float := proc(file, x)
    fprintf(file, "<td>"); fprintf(file, "%g", x); fprintf(file, "</td>")
end proc

>       # Begin Function number 11
>     logitem_pole := proc(file,pole)
>     fprintf(file,"<td>");
>     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,"</td>");
>  # End Function number 11
>  end;
logitem_pole := proc(file, pole)
    fprintf(file, "<td>");
    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, "</td>")
end proc

>   # Begin Function number 12
>  logstart := proc(file)
>  fprintf(file,"<tr>");
>  # End Function number 12
>  end;
             logstart := proc(file) fprintf(file, "<tr>") end proc

>   # Begin Function number 13
>  logend := proc(file)
>  fprintf(file,"</tr>\n");
>  # End Function number 13
>  end;
             logend := proc(file) fprintf(file, "</tr>\n") end proc

>   # Begin Function number 14
>  chk_data := proc()
>  global glob_max_iter,ALWAYS, glob_max_terms;
>  local  errflag;
>  errflag  :=  false;
>  
>  if ((glob_max_terms < 15) or (glob_max_terms > 512))  then # if number 13
>   omniout_str(ALWAYS,"Illegal max_terms =  -- Using 30");
>   glob_max_terms  :=  30;
>   fi;# end if 13
>  ;
>  if (glob_max_iter < 2)  then # if number 13
>   omniout_str(ALWAYS,"Illegal max_iter");
>   errflag  :=  true;
>   fi;# end if 13
>  ;
>  if (errflag)   then # if number 13
>   
>   quit;
>   fi;# end if 13
>  # End Function number 14
>  end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
    errflag := false;
    if glob_max_terms < 15 or 512 < glob_max_terms then
        omniout_str(ALWAYS, "Illegal max_terms =  -- Using 30");
        glob_max_terms := 30
    end if;
    if glob_max_iter < 2 then
        omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
    end if;
    if errflag then quit end if
end proc

>   
>   # Begin Function number 15
>  comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec)
>  global glob_small_float;
>  local ms2, rrr, sec_left, sub1, sub2;
>  ;
>  ms2  :=   clock_sec;
>  sub1  :=   (t_end2-t_start2);
>  sub2  :=   (t2-t_start2);
>  if (sub1  =  0.0)  then # if number 13
>   sec_left  :=  0.0;
>   else
>   if (abs(sub2) > 0.0)  then # if number 14
>     rrr  :=  (sub1/sub2);
>     sec_left  :=  rrr * ms2 - ms2;
>     else
>     sec_left  :=  0.0;
>     fi;# end if 14
>   fi;# end if 13
>  ;
>  sec_left;
>  # End Function number 15
>  end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
    ms2 := clock_sec;
    sub1 := t_end2 - t_start2;
    sub2 := t2 - t_start2;
    if sub1 = 0. then sec_left := 0.
    else
        if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
        else sec_left := 0.
        end if
    end if;
    sec_left
end proc

>   
>   # Begin Function number 16
>  comp_percent := proc(t_end2,t_start2,t2)
>  global glob_small_float;
>  local rrr, sub1, sub2;
>  sub1  :=  (t_end2-t_start2);
>  sub2  :=  (t2-t_start2);
>  if (abs(sub2) > glob_small_float)  then # if number 13
>   rrr  :=  (100.0*sub2)/sub1;
>   else
>   rrr  :=  0.0;
>   fi;# end if 13
>  ;
>  rrr
>  # End Function number 16
>  end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
    sub1 := t_end2 - t_start2;
    sub2 := t2 - t_start2;
    if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1
    else rrr := 0.
    end if;
    rrr
end proc

>   
>   # Begin Function number 17
>  factorial_1 := proc(nnn)
>  nnn!;
>  
>  # End Function number 17
>  end;
                     factorial_1 := proc(nnn) nnn! end proc

>   
>   # Begin Function number 18
>  factorial_3 := proc(mmm2,nnn2)
>  (mmm2!)/(nnn2!);
>  
>  # End Function number 18
>  end;
              factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc

>   # Begin Function number 19
>  convfp := proc(mmm)
>  (mmm);
>  
>  # End Function number 19
>  end;
                        convfp := proc(mmm) mmm end proc

>   # Begin Function number 20
>  convfloat := proc(mmm)
>  (mmm);
>  
>  # End Function number 20
>  end;
                      convfloat := proc(mmm) mmm end proc

>   elapsed_time_seconds := proc()
>   time();
>   end;
                 elapsed_time_seconds := proc() time() end proc

>   
>   
>   
>   #END ATS LIBRARY BLOCK
>   #BEGIN USER DEF BLOCK
>   #BEGIN USER DEF BLOCK
>   exact_soln_x1 := proc(t)
>   local c1,c2,c3;
>   c1 := 0.0001;
>   c2 := 0.0002;
>   c3 := 0.0003;
>   2.0 * c1 + 6.0 * c3 * exp(-t);
>   end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
    c1 := 0.0001; c2 := 0.0002; c3 := 0.0003; 2.0*c1 + 6.0*c3*exp(-t)
end proc

>   exact_soln_x2 := proc(t)
>   local c1,c2,c3;
>   c1 := 0.0001;
>   c2 := 0.0002;
>   c3 := 0.0003;
>   c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
>   end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
    c1 := 0.0001;
    c2 := 0.0002;
    c3 := 0.0003;
    c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc

>   exact_soln_x2p := proc(t)
>   local c1,c2,c3;
>   c1 := 0.0001;
>   c2 := 0.0002;
>   c3 := 0.0003;
>   2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
>   end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
    c1 := 0.0001;
    c2 := 0.0002;
    c3 := 0.0003;
    2.0*c2*exp(2.0*t) - c3*exp(-t)
end proc

>   #END USER DEF BLOCK
>   #END USER DEF BLOCK
>   #END OUTFILE5
>   # Begin Function number 2
>   mainprog := proc()
>   #BEGIN OUTFIEMAIN
>   local d1,d2,d3,d4,est_err_2,niii,done_once,
>   term,ord,order_diff,term_no,html_log_file,
>   rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
>   t_start,t_end
>   ,it, log10norm, max_terms, opt_iter, tmp;
>   #Top Generate Globals Definition
>   #Bottom Generate Globals Deninition
>   global
>   ALWAYS,
>   INFO,
>   glob_max_terms,
>   DEBUGMASSIVE,
>   DEBUGL,
>   glob_iolevel,
>   #Top Generate Globals Decl
>   glob_log10abserr,
>   glob_orig_start_sec,
>   glob_smallish_float,
>   glob_max_trunc_err,
>   glob_last_good_h,
>   glob_disp_incr,
>   glob_reached_optimal_h,
>   glob_initial_pass,
>   sec_in_min,
>   glob_clock_start_sec,
>   glob_clock_sec,
>   min_in_hour,
>   djd_debug,
>   glob_max_minutes,
>   glob_iter,
>   glob_start,
>   glob_max_iter,
>   glob_max_hours,
>   glob_relerr,
>   glob_abserr,
>   glob_log10_abserr,
>   glob_small_float,
>   glob_optimal_clock_start_sec,
>   glob_not_yet_finished,
>   glob_display_flag,
>   glob_warned,
>   glob_optimal_start,
>   glob_hmin,
>   glob_max_opt_iter,
>   glob_percent_done,
>   glob_normmax,
>   glob_max_sec,
>   glob_look_poles,
>   glob_optimal_done,
>   glob_almost_1,
>   years_in_century,
>   days_in_year,
>   glob_optimal_expect_sec,
>   glob_max_order,
>   glob_hmax,
>   glob_html_log,
>   glob_unchanged_h_cnt,
>   centuries_in_millinium,
>   glob_current_iter,
>   glob_curr_iter_when_opt,
>   glob_max_rel_trunc_err,
>   glob_log10_relerr,
>   glob_not_yet_start_msg,
>   hours_in_day,
>   glob_dump,
>   glob_warned2,
>   glob_dump_analytic,
>   glob_hmin_init,
>   glob_h,
>   glob_log10normmin,
>   glob_log10relerr,
>   MAX_UNCHANGED,
>   glob_no_eqs,
>   glob_large_float,
>   djd_debug2,
>   #Bottom Generate Globals Decl
>   #BEGIN CONST
>   array_const_3D0,
>   array_const_4D0,
>   array_const_0D0,
>   array_const_1,
>   array_const_2,
>   array_const_2D0,
>   #END CONST
>   array_pole,
>   array_norms,
>   array_1st_rel_error,
>   array_x1_init,
>   array_m1,
>   array_x2,
>   array_x1,
>   array_tmp10,
>   array_tmp11,
>   array_tmp12,
>   array_tmp13,
>   array_tmp14,
>   array_tmp15,
>   array_tmp16,
>   array_tmp17,
>   array_type_pole,
>   array_x2_init,
>   array_t,
>   array_last_rel_error,
>   array_tmp0,
>   array_tmp1,
>   array_tmp2,
>   array_tmp3,
>   array_tmp4,
>   array_tmp5,
>   array_tmp6,
>   array_tmp7,
>   array_tmp8,
>   array_tmp9,
>   array_x2_higher_work2,
>   array_x1_higher_work,
>   array_x2_higher_work,
>   array_poles,
>   array_real_pole,
>   array_x2_higher,
>   array_complex_pole,
>   array_x1_higher_work2,
>   array_x1_higher,
>   glob_last;
>   glob_last;
>   ALWAYS := 1;
>   INFO := 2;
>   DEBUGL := 3;
>   DEBUGMASSIVE := 4;
>   glob_iolevel := INFO;
>   ALWAYS := 1;
>   INFO := 2;
>   glob_max_terms := 30;
>   DEBUGMASSIVE := 4;
>   DEBUGL := 3;
>   glob_iolevel := 5;
>   glob_log10abserr := 0.0;
>   glob_orig_start_sec := 0.0;
>   glob_smallish_float := 0.1e-100;
>   glob_max_trunc_err := 0.1e-10;
>   glob_last_good_h := 0.1;
>   glob_disp_incr := 0.1;
>   glob_reached_optimal_h := false;
>   glob_initial_pass := true;
>   sec_in_min := 60.0;
>   glob_clock_start_sec := 0.0;
>   glob_clock_sec := 0.0;
>   min_in_hour := 60.0;
>   djd_debug := true;
>   glob_max_minutes := 0.0;
>   glob_iter := 0;
>   glob_start := 0;
>   glob_max_iter := 1000;
>   glob_max_hours := 0.0;
>   glob_relerr := 0.1e-10;
>   glob_abserr := 0.1e-10;
>   glob_log10_abserr := 0.1e-10;
>   glob_small_float := 0.1e-50;
>   glob_optimal_clock_start_sec := 0.0;
>   glob_not_yet_finished := true;
>   glob_display_flag := true;
>   glob_warned := false;
>   glob_optimal_start := 0.0;
>   glob_hmin := 0.00000000001;
>   glob_max_opt_iter := 10;
>   glob_percent_done := 0.0;
>   glob_normmax := 0.0;
>   glob_max_sec := 10000.0;
>   glob_look_poles := false;
>   glob_optimal_done := false;
>   glob_almost_1 := 0.9990;
>   years_in_century := 100.0;
>   days_in_year := 365.0;
>   glob_optimal_expect_sec := 0.1;
>   glob_max_order := 30;
>   glob_hmax := 1.0;
>   glob_html_log := true;
>   glob_unchanged_h_cnt := 0;
>   centuries_in_millinium := 10.0;
>   glob_current_iter := 0;
>   glob_curr_iter_when_opt := 0;
>   glob_max_rel_trunc_err := 0.1e-10;
>   glob_log10_relerr := 0.1e-10;
>   glob_not_yet_start_msg := true;
>   hours_in_day := 24.0;
>   glob_dump := false;
>   glob_warned2 := false;
>   glob_dump_analytic := false;
>   glob_hmin_init := 0.001;
>   glob_h := 0.1;
>   glob_log10normmin := 0.1;
>   glob_log10relerr := 0.0;
>   MAX_UNCHANGED := 10;
>   glob_no_eqs := 0;
>   glob_large_float := 9.0e100;
>   djd_debug2 := 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/complicatedrevpostode.ode#################");
>   omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
>   omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;");
>   omniout_str(ALWAYS,"!");
>   omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>   omniout_str(ALWAYS,"Digits := 32;");
>   omniout_str(ALWAYS,"max_terms := 30;");
>   omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>   omniout_str(ALWAYS,"!");
>   omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>   omniout_str(ALWAYS,"t_start := 0.5;");
>   omniout_str(ALWAYS,"t_end := 5.0;");
>   omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);");
>   omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);");
>   omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);");
>   omniout_str(ALWAYS,"glob_h := 0.00001 ;");
>   omniout_str(ALWAYS,"glob_look_poles := true;");
>   omniout_str(ALWAYS,"glob_max_iter := 10;");
>   omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
>   omniout_str(ALWAYS,"#BEGIN OVERRIDE  BLOCK");
>   omniout_str(ALWAYS,"glob_h := 0.0005 ;");
>   omniout_str(ALWAYS,"glob_look_poles := true;");
>   omniout_str(ALWAYS,"glob_max_iter := 100;");
>   omniout_str(ALWAYS,"glob_max_minutes := 15;");
>   omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>   omniout_str(ALWAYS,"!");
>   omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>   omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
>   omniout_str(ALWAYS,"local c1,c2,c3;");
>   omniout_str(ALWAYS,"c1 := 0.0001;");
>   omniout_str(ALWAYS,"c2 := 0.0002;");
>   omniout_str(ALWAYS,"c3 := 0.0003;");
>   omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);");
>   omniout_str(ALWAYS,"end;");
>   omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
>   omniout_str(ALWAYS,"local c1,c2,c3;");
>   omniout_str(ALWAYS,"c1 := 0.0001;");
>   omniout_str(ALWAYS,"c2 := 0.0002;");
>   omniout_str(ALWAYS,"c3 := 0.0003;");
>   omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
>   omniout_str(ALWAYS,"end;");
>   omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
>   omniout_str(ALWAYS,"local c1,c2,c3;");
>   omniout_str(ALWAYS,"c1 := 0.0001;");
>   omniout_str(ALWAYS,"c2 := 0.0002;");
>   omniout_str(ALWAYS,"c3 := 0.0003;");
>   omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
>   omniout_str(ALWAYS,"end;");
>   omniout_str(ALWAYS,"#END USER DEF BLOCK");
>   omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>   glob_unchanged_h_cnt   :=  0;
>   glob_warned   :=  false;
>   glob_warned2   :=  false;
>   glob_small_float   :=  1.0e-200;
>   glob_smallish_float   :=  1.0e-64;
>   glob_large_float   :=  1.0e100;
>   glob_almost_1   :=  0.99;
>   glob_log10_abserr   :=  -8.0;
>   glob_log10_relerr   :=  -8.0;
>   glob_hmax   :=  0.01;
>   #BEGIN FIRST INPUT BLOCK
>   #BEGIN FIRST INPUT BLOCK
>   Digits := 32;
>   max_terms := 30;
>   #END FIRST INPUT BLOCK
>   #END FIRST INPUT BLOCK
>   #START OF INITS AFTER INPUT BLOCK
>   glob_max_terms := max_terms;
>   glob_html_log := true;
>   #END OF INITS AFTER INPUT BLOCK
>   array_pole:= Array(1..(max_terms + 1),[]);
>   array_norms:= Array(1..(max_terms + 1),[]);
>   array_1st_rel_error:= Array(1..(max_terms + 1),[]);
>   array_x1_init:= Array(1..(max_terms + 1),[]);
>   array_m1:= Array(1..(max_terms + 1),[]);
>   array_x2:= Array(1..(max_terms + 1),[]);
>   array_x1:= Array(1..(max_terms + 1),[]);
>   array_tmp10:= Array(1..(max_terms + 1),[]);
>   array_tmp11:= Array(1..(max_terms + 1),[]);
>   array_tmp12:= Array(1..(max_terms + 1),[]);
>   array_tmp13:= Array(1..(max_terms + 1),[]);
>   array_tmp14:= Array(1..(max_terms + 1),[]);
>   array_tmp15:= Array(1..(max_terms + 1),[]);
>   array_tmp16:= Array(1..(max_terms + 1),[]);
>   array_tmp17:= Array(1..(max_terms + 1),[]);
>   array_type_pole:= Array(1..(max_terms + 1),[]);
>   array_x2_init:= Array(1..(max_terms + 1),[]);
>   array_t:= Array(1..(max_terms + 1),[]);
>   array_last_rel_error:= Array(1..(max_terms + 1),[]);
>   array_tmp0:= Array(1..(max_terms + 1),[]);
>   array_tmp1:= Array(1..(max_terms + 1),[]);
>   array_tmp2:= Array(1..(max_terms + 1),[]);
>   array_tmp3:= Array(1..(max_terms + 1),[]);
>   array_tmp4:= Array(1..(max_terms + 1),[]);
>   array_tmp5:= Array(1..(max_terms + 1),[]);
>   array_tmp6:= Array(1..(max_terms + 1),[]);
>   array_tmp7:= Array(1..(max_terms + 1),[]);
>   array_tmp8:= Array(1..(max_terms + 1),[]);
>   array_tmp9:= Array(1..(max_terms + 1),[]);
>   array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
>   array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
>   array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
>   array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
>   array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
>   array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
>   array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
>   array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
>   array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_pole[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_norms[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_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_x1_init[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_m1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_x2[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_x1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp10[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp11[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp12[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp13[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp14[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp15[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp16[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp17[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_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_t[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_last_rel_error[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_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
>   ;
>   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 <=3 do # do number 2
>  term := 1;
>  while term <= max_terms do # do number 3
>   array_x2_higher_work[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=2 do # do number 2
>  term := 1;
>  while term <= 3 do # do number 3
>   array_poles[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=2 do # do number 2
>  term := 1;
>  while term <= 3 do # do number 3
>   array_real_pole[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=3 do # do number 2
>  term := 1;
>  while term <= max_terms do # do number 3
>   array_x2_higher[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=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
>   ;
>   #BEGIN ARRAYS DEFINED AND INITIALIZATED
>   array_x1 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_x1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_x2 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_x2[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp17 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp17[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp16 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp16[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp15 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp15[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp14 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp14[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp13 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp13[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp12 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp12[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp11 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp11[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp10 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp10[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_t := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_t[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp9 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp9[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp8 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp8[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp7 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp7[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp6 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp6[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp5 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp5[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp4 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp4[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp3 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp3[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp2 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp2[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp1 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp0 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp0[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_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_4D0 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_const_4D0[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_const_4D0[1]   := 4.0;
>   array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_const_0D0[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_const_0D0[1]   := 0.0;
>   array_const_1 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_const_1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_const_1[1]   := 1;
>   array_const_2 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_const_2[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_const_2[1]   := 2;
>   array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_const_2D0[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_const_2D0[1]   := 2.0;
>   array_m1 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_m1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_m1[1]   :=  -1.0;
>   #END ARRAYS DEFINED AND INITIALIZATED
>   #TOP SECOND INPUT BLOCK
>   #BEGIN SECOND INPUT BLOCK
>   #BEGIN SECOND INPUT BLOCK
>   t_start := 0.5;
>   t_end := 5.0;
>   array_x1_init[1] := exact_soln_x1(t_start);
>   array_x2_init[1] := exact_soln_x2(t_start);
>   array_x2_init[2] := exact_soln_x2p(t_start);
>   glob_h := 0.00001 ;
>   glob_look_poles := true;
>   glob_max_iter := 10;
>   #END SECOND INPUT BLOCK
>   #BEGIN OVERRIDE  BLOCK
>   glob_h := 0.0005 ;
>   glob_look_poles := true;
>   glob_max_iter := 100;
>   glob_max_minutes := 15;
>   #END OVERRIDE BLOCK
>   #END SECOND INPUT BLOCK
>   #BEGIN INITS AFTER SECOND INPUT BLOCK
>   glob_last_good_h := glob_h;
>   glob_max_terms   := max_terms;
>   glob_max_sec   := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
>   glob_abserr   :=  10.0 ^ (glob_log10_abserr);
>   glob_relerr   :=  10.0 ^ (glob_log10_relerr);
>   chk_data();
>   #AFTER INITS AFTER SECOND INPUT BLOCK
>   if glob_html_log  then # if number 3
>       html_log_file := fopen("html/entry.html",WRITE,TEXT);
>       fi;# end if 3
>     ;
>     #BEGIN SOLUTION CODE
>     omniout_str(ALWAYS,"START of Soultion");
>     #Start Series -- INITIALIZE FOR SOLUTION
>     array_t[1]   := t_start;
>     array_t[2]   :=  glob_h;
>     order_diff := 2;
>     #Start Series array_x2
>     term_no   :=  1;
>     while (term_no <= order_diff) do # do number 2
>       array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
>       term_no   :=  term_no + 1;
>       od;# end do number 2
>     ;
>     rows   :=  order_diff;
>     r_order   :=  1;
>     while (r_order <= rows) do # do number 2
>       term_no   :=  1;
>       while (term_no <= (rows - r_order + 1)) do # do number 3
>         it  := term_no + r_order - 1;
>         array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
>         term_no   :=  term_no + 1;
>         od;# end do number 3
>       ;
>       r_order   :=  r_order + 1;
>       od;# end do number 2
>     ;
>     order_diff := 1;
>     #Start Series array_x1
>     term_no   :=  1;
>     while (term_no <= order_diff) do # do number 2
>       array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
>       term_no   :=  term_no + 1;
>       od;# end do number 2
>     ;
>     rows   :=  order_diff;
>     r_order   :=  1;
>     while (r_order <= rows) do # do number 2
>       term_no   :=  1;
>       while (term_no <= (rows - r_order + 1)) do # do number 3
>         it  := term_no + r_order - 1;
>         array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
>         term_no   :=  term_no + 1;
>         od;# end do number 3
>       ;
>       r_order   :=  r_order + 1;
>       od;# end do number 2
>     ;
>     current_iter   :=  1;
>     glob_clock_start_sec   := elapsed_time_seconds();
>     start_array_x2();
>     if (abs(array_x2_higher[1,1]) > glob_small_float)  then # if number 3
>       tmp   :=  abs(array_x2_higher[1,1]);
>       log10norm   :=  (log10(tmp));
>       if (log10norm < glob_log10normmin)  then # if number 4
>         glob_log10normmin   :=  log10norm;
>         fi;# end if 4
>       fi;# end if 3
>     ;
>     display_alot(current_iter)
>     ;
>     start_array_x1();
>     if (abs(array_x1_higher[1,1]) > glob_small_float)  then # if number 3
>       tmp   :=  abs(array_x1_higher[1,1]);
>       log10norm   :=  (log10(tmp));
>       if (log10norm < glob_log10normmin)  then # if number 4
>         glob_log10normmin   :=  log10norm;
>         fi;# end if 4
>       fi;# end if 3
>     ;
>     display_alot(current_iter)
>     ;
>     glob_clock_sec   :=  elapsed_time_seconds();
>     glob_current_iter   :=  0;
>     glob_iter   :=  0;
>     omniout_str(DEBUGL," ");
>     glob_reached_optimal_h   :=  true;
>     glob_optimal_clock_start_sec := elapsed_time_seconds();
>     while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
>       #left paren 0001C
>       omniout_str(INFO," ");
>       omniout_str(INFO,"TOP MAIN SOLVE Loop");
>       glob_iter   :=  glob_iter + 1;
>       glob_clock_sec   := elapsed_time_seconds();
>       glob_current_iter   :=  glob_current_iter + 1;
>       atomall();
>       if (glob_look_poles)  then # if number 3
>         #left paren 0004C
>         check_for_pole();
>         fi;# end if 3
>       ;#was right paren 0004C
>       array_t[1]   := array_t[1] + glob_h;
>       array_t[2]   :=  glob_h;
>       order_diff := 2;
>       #Jump Series array_x2
>       #START PART 1  SUM AND ADJUST
>       #START SUM AND ADJUST EQ =1
>       #sum_and_adjust array_x2
>       order_diff := 2;
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 2;
>       ord := 3;
>       calc_term := 1;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 3;
>       calc_term := 1;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 2;
>       ord := 2;
>       calc_term := 2;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 2;
>       calc_term := 2;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 2;
>       ord := 2;
>       calc_term := 1;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 2;
>       calc_term := 1;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 2;
>       ord := 1;
>       calc_term := 3;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 3;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 2;
>       ord := 1;
>       calc_term := 2;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 2;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 2;
>       ord := 1;
>       calc_term := 1;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 1;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #END SUM AND ADJUST EQ =1
>       #END PART 1
>       #START PART 2  MOVE TERMS to REGULAR Array
>       term_no := glob_max_terms;
>       while (term_no >= 1) do # do number 3
>         array_x2[term_no] := array_x2_higher_work2[1,term_no];
>         ord := 1;
>         while ord <= order_diff  do # do number 4
>           array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no];
>           ord := ord + 1;
>           od;# end do number 4
>         ;
>         term_no   :=  term_no - 1;
>         od;# end do number 3
>       ;
>       #END PART 2 HEVE MOVED TERMS to REGULAR Array
>       order_diff := 1;
>       #Jump Series array_x1
>       #START PART 1  SUM AND ADJUST
>       #START SUM AND ADJUST EQ =2
>       #sum_and_adjust array_x1
>       order_diff := 1;
>       #BEFORE ADJUST SUBSERIES EQ =2
>       order_diff := 1;
>       ord := 2;
>       calc_term := 1;
>       #adjust_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =2
>       #BEFORE SUM SUBSERIES EQ =2
>       order_diff := 1;
>       temp_sum := 0.0;
>       ord := 2;
>       calc_term := 1;
>       #sum_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x1_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =2
>       #BEFORE ADJUST SUBSERIES EQ =2
>       order_diff := 1;
>       ord := 1;
>       calc_term := 2;
>       #adjust_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =2
>       #BEFORE SUM SUBSERIES EQ =2
>       order_diff := 1;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 2;
>       #sum_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x1_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =2
>       #BEFORE ADJUST SUBSERIES EQ =2
>       order_diff := 1;
>       ord := 1;
>       calc_term := 1;
>       #adjust_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =2
>       #BEFORE SUM SUBSERIES EQ =2
>       order_diff := 1;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 1;
>       #sum_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x1_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =2
>       #END SUM AND ADJUST EQ =2
>       #END PART 1
>       #START PART 2  MOVE TERMS to REGULAR Array
>       term_no := glob_max_terms;
>       while (term_no >= 1) do # do number 3
>         array_x1[term_no] := array_x1_higher_work2[1,term_no];
>         ord := 1;
>         while ord <= order_diff  do # do number 4
>           array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no];
>           ord := ord + 1;
>           od;# end do number 4
>         ;
>         term_no   :=  term_no - 1;
>         od;# end do number 3
>       ;
>       #END PART 2 HEVE MOVED TERMS to REGULAR Array
>       display_alot(current_iter)
>       ;
>       od;# end do number 2
>     ;#right paren 0001C
>     omniout_str(ALWAYS,"Finished!");
>     if (glob_iter >= glob_max_iter)  then # if number 3
>       omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
>       fi;# end if 3
>     ;
>     if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec  )) then # if number 3
>       omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
>       fi;# end if 3
>     ;
>     glob_clock_sec   := elapsed_time_seconds();
>     omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
>     omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;");
>     omniout_int(INFO,"Iterations                       ",32,glob_iter,4," ")
>     ;
>     prog_report(t_start,t_end);
>     if glob_html_log  then # if number 3
>       logstart(html_log_file);
>       logitem_str(html_log_file,"2012-06-02T01:56:50-05:00")
>       ;
>       logitem_str(html_log_file,"Maple")
>       ;
>       logitem_str(html_log_file,"<a href=\"complicatedrev.ode.txt\">complicatedrev</a>")
>       ;
>       logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;")
>       ;
>       logitem_float(html_log_file,t_start)
>       ;
>       logitem_float(html_log_file,t_end)
>       ;
>       logitem_float(html_log_file,array_t[1])
>       ;
>       logitem_float(html_log_file,glob_h)
>       ;
>       logitem_integer(html_log_file,Digits)
>       ;
>       ;
>       logitem_integer(html_log_file,glob_max_terms)
>       ;
>       logitem_float(html_log_file,array_1st_rel_error[1])
>       ;
>       logitem_float(html_log_file,array_last_rel_error[1])
>       ;
>       logitem_integer(html_log_file,glob_iter)
>       ;
>       logitem_pole(html_log_file,array_type_pole[1])
>       ;
>       if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 4
>         logitem_float(html_log_file,array_pole[1])
>         ;
>         logitem_float(html_log_file,array_pole[2])
>         ;
>         0;
>         else
>         logitem_str(html_log_file,"NA")
>         ;
>         logitem_str(html_log_file,"NA")
>         ;
>         0;
>         fi;# end if 4
>       ;
>       logitem_time(html_log_file,convfloat(glob_clock_sec))
>       ;
>       if glob_percent_done < 100.0  then # if number 4
>         logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
>         ;
>         0
>         else
>         logitem_str(html_log_file,"Done")
>         ;
>         0
>         fi;# end if 4
>       ;
>       log_revs(html_log_file,"<td> 076 </td>")
>       ;
>       logitem_str(html_log_file,"<a href=\"diffeq.complicatedrev.mxt.txt\">complicatedrev diffeq.mxt</a>")
>       ;
>       logitem_str(html_log_file,"<a href=\"results.complicatedrev.mxt.txt\">complicatedrev maple results</a>")
>       ;
>       logitem_str(html_log_file,"sub iter once eqs reversed")
>       ;
>       logend(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;")
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       ;
>       logditto(html_log_file)
>       ;
>       logitem_float(html_log_file,array_1st_rel_error[2])
>       ;
>       logitem_float(html_log_file,array_last_rel_error[2])
>       ;
>       logditto(html_log_file)
>       ;
>       logitem_pole(html_log_file,array_type_pole[2])
>       ;
>       if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 4
>         logitem_float(html_log_file,array_pole[1])
>         ;
>         logitem_float(html_log_file,array_pole[2])
>         ;
>         0;
>         else
>         logitem_str(html_log_file,"NA")
>         ;
>         logitem_str(html_log_file,"NA")
>         ;
>         0;
>         fi;# end if 4
>       ;
>       logditto(html_log_file)
>       ;
>       if glob_percent_done < 100.0  then # if number 4
>         logditto(html_log_file)
>         ;
>         0
>         else
>         logditto(html_log_file)
>         ;
>         0
>         fi;# end if 4
>       ;
>       logditto(html_log_file);
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logend(html_log_file)
>       ;
>       ;
>       fi;# end if 3
>     ;
>     if glob_html_log  then # if number 3
>       fclose(html_log_file);
>       fi;# end if 3
>     ;
>     ;;
>     #END OUTFILEMAIN
>     # End Function number 8
>     end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp;
global ALWAYS, INFO, glob_max_terms, DEBUGMASSIVE, DEBUGL, glob_iolevel,
glob_log10abserr, glob_orig_start_sec, glob_smallish_float,
glob_max_trunc_err, glob_last_good_h, glob_disp_incr,
glob_reached_optimal_h, glob_initial_pass, sec_in_min, glob_clock_start_sec,
glob_clock_sec, min_in_hour, djd_debug, glob_max_minutes, glob_iter,
glob_start, glob_max_iter, glob_max_hours, glob_relerr, glob_abserr,
glob_log10_abserr, glob_small_float, glob_optimal_clock_start_sec,
glob_not_yet_finished, glob_display_flag, glob_warned, glob_optimal_start,
glob_hmin, glob_max_opt_iter, glob_percent_done, glob_normmax, glob_max_sec,
glob_look_poles, glob_optimal_done, glob_almost_1, years_in_century,
days_in_year, glob_optimal_expect_sec, glob_max_order, glob_hmax,
glob_html_log, glob_unchanged_h_cnt, centuries_in_millinium,
glob_current_iter, glob_curr_iter_when_opt, glob_max_rel_trunc_err,
glob_log10_relerr, glob_not_yet_start_msg, hours_in_day, glob_dump,
glob_warned2, glob_dump_analytic, glob_hmin_init, glob_h, glob_log10normmin,
glob_log10relerr, MAX_UNCHANGED, glob_no_eqs, glob_large_float, djd_debug2,
array_const_3D0, array_const_4D0, array_const_0D0, array_const_1,
array_const_2, array_const_2D0, array_pole, array_norms,
array_1st_rel_error, array_x1_init, array_m1, array_x2, array_x1,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x2_init,
array_t, array_last_rel_error, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_x2_higher_work2, array_x1_higher_work,
array_x2_higher_work, array_poles, array_real_pole, array_x2_higher,
array_complex_pole, array_x1_higher_work2, array_x1_higher, glob_last;
    glob_last;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    glob_iolevel := INFO;
    ALWAYS := 1;
    INFO := 2;
    glob_max_terms := 30;
    DEBUGMASSIVE := 4;
    DEBUGL := 3;
    glob_iolevel := 5;
    glob_log10abserr := 0.;
    glob_orig_start_sec := 0.;
    glob_smallish_float := 0.1*10^(-100);
    glob_max_trunc_err := 0.1*10^(-10);
    glob_last_good_h := 0.1;
    glob_disp_incr := 0.1;
    glob_reached_optimal_h := false;
    glob_initial_pass := true;
    sec_in_min := 60.0;
    glob_clock_start_sec := 0.;
    glob_clock_sec := 0.;
    min_in_hour := 60.0;
    djd_debug := true;
    glob_max_minutes := 0.;
    glob_iter := 0;
    glob_start := 0;
    glob_max_iter := 1000;
    glob_max_hours := 0.;
    glob_relerr := 0.1*10^(-10);
    glob_abserr := 0.1*10^(-10);
    glob_log10_abserr := 0.1*10^(-10);
    glob_small_float := 0.1*10^(-50);
    glob_optimal_clock_start_sec := 0.;
    glob_not_yet_finished := true;
    glob_display_flag := true;
    glob_warned := false;
    glob_optimal_start := 0.;
    glob_hmin := 0.1*10^(-10);
    glob_max_opt_iter := 10;
    glob_percent_done := 0.;
    glob_normmax := 0.;
    glob_max_sec := 10000.0;
    glob_look_poles := false;
    glob_optimal_done := false;
    glob_almost_1 := 0.9990;
    years_in_century := 100.0;
    days_in_year := 365.0;
    glob_optimal_expect_sec := 0.1;
    glob_max_order := 30;
    glob_hmax := 1.0;
    glob_html_log := true;
    glob_unchanged_h_cnt := 0;
    centuries_in_millinium := 10.0;
    glob_current_iter := 0;
    glob_curr_iter_when_opt := 0;
    glob_max_rel_trunc_err := 0.1*10^(-10);
    glob_log10_relerr := 0.1*10^(-10);
    glob_not_yet_start_msg := true;
    hours_in_day := 24.0;
    glob_dump := false;
    glob_warned2 := false;
    glob_dump_analytic := false;
    glob_hmin_init := 0.001;
    glob_h := 0.1;
    glob_log10normmin := 0.1;
    glob_log10relerr := 0.;
    MAX_UNCHANGED := 10;
    glob_no_eqs := 0;
    glob_large_float := 0.90*10^101;
    djd_debug2 := 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/complicatedrevpostode.ode#################");
    omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \
        diff(x1,t,2) - diff (x1,t,1) + x1;");
    omniout_str(ALWAYS,
        "diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits := 32;");
    omniout_str(ALWAYS, "max_terms := 30;");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "t_start := 0.5;");
    omniout_str(ALWAYS, "t_end := 5.0;");
    omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);");
    omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);");
    omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);");
    omniout_str(ALWAYS, "glob_h := 0.00001 ;");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "glob_max_iter := 10;");
    omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN OVERRIDE  BLOCK");
    omniout_str(ALWAYS, "glob_h := 0.0005 ;");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "glob_max_iter := 100;");
    omniout_str(ALWAYS, "glob_max_minutes := 15;");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := 0.0001;");
    omniout_str(ALWAYS, "c2 := 0.0002;");
    omniout_str(ALWAYS, "c3 := 0.0003;");
    omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := 0.0001;");
    omniout_str(ALWAYS, "c2 := 0.0002;");
    omniout_str(ALWAYS, "c3 := 0.0003;");
    omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := 0.0001;");
    omniout_str(ALWAYS, "c2 := 0.0002;");
    omniout_str(ALWAYS, "c3 := 0.0003;");
    omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := 0.10*10^(-199);
    glob_smallish_float := 0.10*10^(-63);
    glob_large_float := 0.10*10^101;
    glob_almost_1 := 0.99;
    glob_log10_abserr := -8.0;
    glob_log10_relerr := -8.0;
    glob_hmax := 0.01;
    Digits := 32;
    max_terms := 30;
    glob_max_terms := max_terms;
    glob_html_log := true;
    array_pole := Array(1 .. max_terms + 1, []);
    array_norms := Array(1 .. max_terms + 1, []);
    array_1st_rel_error := Array(1 .. max_terms + 1, []);
    array_x1_init := Array(1 .. max_terms + 1, []);
    array_m1 := Array(1 .. max_terms + 1, []);
    array_x2 := Array(1 .. max_terms + 1, []);
    array_x1 := Array(1 .. max_terms + 1, []);
    array_tmp10 := Array(1 .. max_terms + 1, []);
    array_tmp11 := Array(1 .. max_terms + 1, []);
    array_tmp12 := Array(1 .. max_terms + 1, []);
    array_tmp13 := Array(1 .. max_terms + 1, []);
    array_tmp14 := Array(1 .. max_terms + 1, []);
    array_tmp15 := Array(1 .. max_terms + 1, []);
    array_tmp16 := Array(1 .. max_terms + 1, []);
    array_tmp17 := Array(1 .. max_terms + 1, []);
    array_type_pole := Array(1 .. max_terms + 1, []);
    array_x2_init := Array(1 .. max_terms + 1, []);
    array_t := Array(1 .. max_terms + 1, []);
    array_last_rel_error := Array(1 .. max_terms + 1, []);
    array_tmp0 := Array(1 .. max_terms + 1, []);
    array_tmp1 := Array(1 .. max_terms + 1, []);
    array_tmp2 := Array(1 .. max_terms + 1, []);
    array_tmp3 := Array(1 .. max_terms + 1, []);
    array_tmp4 := Array(1 .. max_terms + 1, []);
    array_tmp5 := Array(1 .. max_terms + 1, []);
    array_tmp6 := Array(1 .. max_terms + 1, []);
    array_tmp7 := Array(1 .. max_terms + 1, []);
    array_tmp8 := Array(1 .. max_terms + 1, []);
    array_tmp9 := Array(1 .. max_terms + 1, []);
    array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
    array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
    array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
    array_poles := Array(1 .. 3, 1 .. 4, []);
    array_real_pole := Array(1 .. 3, 1 .. 4, []);
    array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
    array_complex_pole := Array(1 .. 3, 1 .. 4, []);
    array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
    array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
    term := 1;
    while term <= max_terms do array_pole[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_norms[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do
        array_1st_rel_error[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_x1_init[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_m1[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_x2[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_x1[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp10[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp11[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp12[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp13[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp14[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp15[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp16[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp17[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do
        array_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_t[term] := 0.; term := term + 1 end do
    ;
    term := 1;
    while term <= max_terms do
        array_last_rel_error[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_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;
    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 <= 3 do
        term := 1;
        while term <= max_terms do
            array_x2_higher_work[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do
            array_real_pole[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= max_terms do
            array_x2_higher[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 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;
    array_x1 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1
    end do;
    array_x2 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1
    end do;
    array_tmp17 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp17[term] := 0.; term := term + 1
    end do;
    array_tmp16 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp16[term] := 0.; term := term + 1
    end do;
    array_tmp15 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp15[term] := 0.; term := term + 1
    end do;
    array_tmp14 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp14[term] := 0.; term := term + 1
    end do;
    array_tmp13 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp13[term] := 0.; term := term + 1
    end do;
    array_tmp12 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp12[term] := 0.; term := term + 1
    end do;
    array_tmp11 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp11[term] := 0.; term := term + 1
    end do;
    array_tmp10 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp10[term] := 0.; term := term + 1
    end do;
    array_t := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1
    end do;
    array_tmp9 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1
    end do;
    array_tmp8 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
    end do;
    array_tmp7 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1
    end do;
    array_tmp6 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
    end do;
    array_tmp5 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
    end do;
    array_tmp4 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
    end do;
    array_tmp3 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
    end do;
    array_tmp2 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
    end do;
    array_tmp1 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
    end do;
    array_tmp0 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
    end do;
    array_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_4D0 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_const_4D0[term] := 0.; term := term + 1
    end do;
    array_const_4D0[1] := 4.0;
    array_const_0D0 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_const_0D0[term] := 0.; term := term + 1
    end do;
    array_const_0D0[1] := 0.;
    array_const_1 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_const_1[term] := 0.; term := term + 1
    end do;
    array_const_1[1] := 1;
    array_const_2 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_const_2[term] := 0.; term := term + 1
    end do;
    array_const_2[1] := 2;
    array_const_2D0 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_const_2D0[term] := 0.; term := term + 1
    end do;
    array_const_2D0[1] := 2.0;
    array_m1 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms do array_m1[term] := 0.; term := term + 1
    end do;
    array_m1[1] := -1.0;
    t_start := 0.5;
    t_end := 5.0;
    array_x1_init[1] := exact_soln_x1(t_start);
    array_x2_init[1] := exact_soln_x2(t_start);
    array_x2_init[2] := exact_soln_x2p(t_start);
    glob_h := 0.00001;
    glob_look_poles := true;
    glob_max_iter := 10;
    glob_h := 0.0005;
    glob_look_poles := true;
    glob_max_iter := 100;
    glob_max_minutes := 15;
    glob_last_good_h := glob_h;
    glob_max_terms := max_terms;
    glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
         + convfloat(3600.0)*convfloat(glob_max_hours);
    glob_abserr := 10.0^glob_log10_abserr;
    glob_relerr := 10.0^glob_log10_relerr;
    chk_data();
    if glob_html_log then
        html_log_file := fopen("html/entry.html", WRITE, TEXT)
    end if;
    omniout_str(ALWAYS, "START of Soultion");
    array_t[1] := t_start;
    array_t[2] := glob_h;
    order_diff := 2;
    term_no := 1;
    while term_no <= order_diff do
        array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/
            factorial_1(term_no - 1);
        term_no := term_no + 1
    end do;
    rows := order_diff;
    r_order := 1;
    while r_order <= rows do
        term_no := 1;
        while term_no <= rows - r_order + 1 do
            it := term_no + r_order - 1;
            array_x2_higher[r_order, term_no] := array_x2_init[it]*
                glob_h^(term_no - 1)/factorial_1(term_no - 1);
            term_no := term_no + 1
        end do;
        r_order := r_order + 1
    end do;
    order_diff := 1;
    term_no := 1;
    while term_no <= order_diff do
        array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/
            factorial_1(term_no - 1);
        term_no := term_no + 1
    end do;
    rows := order_diff;
    r_order := 1;
    while r_order <= rows do
        term_no := 1;
        while term_no <= rows - r_order + 1 do
            it := term_no + r_order - 1;
            array_x1_higher[r_order, term_no] := array_x1_init[it]*
                glob_h^(term_no - 1)/factorial_1(term_no - 1);
            term_no := term_no + 1
        end do;
        r_order := r_order + 1
    end do;
    current_iter := 1;
    glob_clock_start_sec := elapsed_time_seconds();
    start_array_x2();
    if glob_small_float < abs(array_x2_higher[1, 1]) then
        tmp := abs(array_x2_higher[1, 1]);
        log10norm := log10(tmp);
        if log10norm < glob_log10normmin then
            glob_log10normmin := log10norm
        end if
    end if;
    display_alot(current_iter);
    start_array_x1();
    if glob_small_float < abs(array_x1_higher[1, 1]) then
        tmp := abs(array_x1_higher[1, 1]);
        log10norm := log10(tmp);
        if log10norm < glob_log10normmin then
            glob_log10normmin := log10norm
        end if
    end if;
    display_alot(current_iter);
    glob_clock_sec := elapsed_time_seconds();
    glob_current_iter := 0;
    glob_iter := 0;
    omniout_str(DEBUGL, " ");
    glob_reached_optimal_h := true;
    glob_optimal_clock_start_sec := elapsed_time_seconds();
    while glob_current_iter < glob_max_iter and array_t[1] <= t_end and
    convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
    convfloat(glob_max_sec) do
        omniout_str(INFO, " ");
        omniout_str(INFO, "TOP MAIN SOLVE Loop");
        glob_iter := glob_iter + 1;
        glob_clock_sec := elapsed_time_seconds();
        glob_current_iter := glob_current_iter + 1;
        atomall();
        if glob_look_poles then check_for_pole() end if;
        array_t[1] := array_t[1] + glob_h;
        array_t[2] := glob_h;
        order_diff := 2;
        order_diff := 2;
        order_diff := 2;
        ord := 3;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 3;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 2;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 2;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 2;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 2;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 1;
        calc_term := 3;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 1;
        calc_term := 3;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 1;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 1;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 1;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 1;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        term_no := glob_max_terms;
        while 1 <= term_no do
            array_x2[term_no] := array_x2_higher_work2[1, term_no];
            ord := 1;
            while ord <= order_diff do
                array_x2_higher[ord, term_no] :=
                    array_x2_higher_work2[ord, term_no];
                ord := ord + 1
            end do;
            term_no := term_no - 1
        end do;
        order_diff := 1;
        order_diff := 1;
        order_diff := 1;
        ord := 2;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 1;
        temp_sum := 0.;
        ord := 2;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x1_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x1_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 1;
        ord := 1;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 1;
        temp_sum := 0.;
        ord := 1;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x1_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x1_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 1;
        ord := 1;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 1;
        temp_sum := 0.;
        ord := 1;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x1_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x1_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        term_no := glob_max_terms;
        while 1 <= term_no do
            array_x1[term_no] := array_x1_higher_work2[1, term_no];
            ord := 1;
            while ord <= order_diff do
                array_x1_higher[ord, term_no] :=
                    array_x1_higher_work2[ord, term_no];
                ord := ord + 1
            end do;
            term_no := term_no - 1
        end do;
        display_alot(current_iter)
    end do;
    omniout_str(ALWAYS, "Finished!");
    if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
        "Maximum Iterations Reached before Solution Completed!")
    end if;
    if convfloat(glob_max_sec) <=
    elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
        omniout_str(ALWAYS,
        "Maximum Time Reached before Solution Completed!")
    end if;
    glob_clock_sec := elapsed_time_seconds();
    omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
        ff(x1,t,2) - diff (x1,t,1) + x1;");
    omniout_str(INFO,
        "diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;");
    omniout_int(INFO, "Iterations                       ", 32, glob_iter, 4,
        " ");
    prog_report(t_start, t_end);
    if glob_html_log then
        logstart(html_log_file);
        logitem_str(html_log_file, "2012-06-02T01:56:50-05:00");
        logitem_str(html_log_file, "Maple");
        logitem_str(html_log_file,
            "<a href=\"complicatedrev.ode.txt\">complicatedrev</a>");
        logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \
            2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
        logitem_float(html_log_file, t_start);
        logitem_float(html_log_file, t_end);
        logitem_float(html_log_file, array_t[1]);
        logitem_float(html_log_file, glob_h);
        logitem_integer(html_log_file, Digits);
        logitem_integer(html_log_file, glob_max_terms);
        logitem_float(html_log_file, array_1st_rel_error[1]);
        logitem_float(html_log_file, array_last_rel_error[1]);
        logitem_integer(html_log_file, glob_iter);
        logitem_pole(html_log_file, array_type_pole[1]);
        if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
            logitem_float(html_log_file, array_pole[1]);
            logitem_float(html_log_file, array_pole[2]);
            0
        else
            logitem_str(html_log_file, "NA");
            logitem_str(html_log_file, "NA");
            0
        end if;
        logitem_time(html_log_file, convfloat(glob_clock_sec));
        if glob_percent_done < 100.0 then
            logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
                ;
            0
        else logitem_str(html_log_file, "Done"); 0
        end if;
        log_revs(html_log_file, "<td> 076 </td>");
        logitem_str(html_log_file, "<a href=\"diffeq.complicatedrev.mxt.t\
            xt\">complicatedrev diffeq.mxt</a>");
        logitem_str(html_log_file, "<a href=\"results.complicatedrev.mxt.\
            txt\">complicatedrev maple results</a>");
        logitem_str(html_log_file, "sub iter once eqs reversed");
        logend(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logitem_str(html_log_file,
            "diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;")
            ;
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logitem_float(html_log_file, array_1st_rel_error[2]);
        logitem_float(html_log_file, array_last_rel_error[2]);
        logditto(html_log_file);
        logitem_pole(html_log_file, array_type_pole[2]);
        if array_type_pole[2] = 1 or array_type_pole[2] = 2 then
            logitem_float(html_log_file, array_pole[1]);
            logitem_float(html_log_file, array_pole[2]);
            0
        else
            logitem_str(html_log_file, "NA");
            logitem_str(html_log_file, "NA");
            0
        end if;
        logditto(html_log_file);
        if glob_percent_done < 100.0 then logditto(html_log_file); 0
        else logditto(html_log_file); 0
        end if;
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logend(html_log_file)
    end if;
    if glob_html_log then fclose(html_log_file) end if
end proc

>   mainprog();
##############ECHO OF PROBLEM#################
##############temp/complicatedrevpostode.ode#################
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
#END FIRST INPUT BLOCK
!
#BEGIN SECOND INPUT BLOCK
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
glob_h := 0.0005 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1]                              = 0.5                                          
x2[1] (analytic)                  = 0.00082561556360559907415319735476789        
x2[1] (numeric)                   = 0.00082561556360559907415319735476789        
absolute error                    = 0                                            
relative error                    = 0                                          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012917551874827401624868391629841         
x1[1] (numeric)                   = 0.0012917551874827401624868391629841         
absolute error                    = 0                                            
relative error                    = 0                                          % 
h                                 = 0.0005                                       
t[1]                              = 0.5                                          
x2[1] (analytic)                  = 0.00082561556360559907415319735476789        
x2[1] (numeric)                   = 0.00082561556360559907415319735476789        
absolute error                    = 0                                            
relative error                    = 0                                          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012917551874827401624868391629841         
x1[1] (numeric)                   = 0.0012917551874827401624868391629841         
absolute error                    = 0                                            
relative error                    = 0                                          % 
h                                 = 0.0005                                       
 
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5005                                       
x2[1] (analytic)                  = 0.00082606853503225828165826201261726        
x2[1] (numeric)                   = 0.00082606853503224742496199848942521        
absolute error                    = 1.085669626352319205e-17                     
relative error                    = 1.3142609605750489028871098278662e-12      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012912094463356551708370721480129         
x1[1] (numeric)                   = 0.0012912094463935537320044961503858         
absolute error                    = 5.78985611674240023729e-14                   
relative error                    = 4.4840565046774785484100279208153e-09      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.501                                        
x2[1] (analytic)                  = 0.00082652209612631802672115172787186        
x2[1] (numeric)                   = 0.00082652236917871181444490180802587        
absolute error                    = 2.7305239378772375008015401e-10              
relative error                    = 3.3036309019135156481730720087571e-05      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012906639779909374464836782020351         
x1[1] (numeric)                   = 0.0012906634326152478944466622182676         
absolute error                    = 5.453756895520370159837675e-10               
relative error                    = 4.2255435872702913342893826412353e-05      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5015                                       
x2[1] (analytic)                  = 0.00082697624740952299139053885956424        
x2[1] (numeric)                   = 0.00082697734009682215098165840053891        
absolute error                    = 1.09268729915959111954097467e-09             
relative error                    = 0.00013213043332047318361124483248855      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012901187823122199004062452509559         
x1[1] (numeric)                   = 0.0012901166009833348385789830242253         
absolute error                    = 2.1813288850618272622267306e-09              
relative error                    = 0.00016907969366606173562826001003325      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.502                                        
x2[1] (analytic)                  = 0.0008274309894041739636559251804687         
x2[1] (numeric)                   = 0.00082743344958282581125025435437209        
absolute error                    = 2.46017865184759432917390339e-09             
relative error                    = 0.00029732735217219119465035490510573      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012895738591632036100858259251            
x1[1] (numeric)                   = 0.0012895689511201653583496595701363         
absolute error                    = 4.9080430382517361663549637e-09              
relative error                    = 0.00038059417871858340196935826475707      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5025                                       
x2[1] (analytic)                  = 0.00082788632263312837678584048126422        
x2[1] (numeric)                   = 0.00082789069979867778436229143634121        
absolute error                    = 4.37716554940757645095507699e-09             
relative error                    = 0.00052871577047991461749320260068501      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012890292084076577854302062195851         
x1[1] (numeric)                   = 0.0012890204818007836603861417926064         
absolute error                    = 8.7266068741250440644269787e-09              
relative error                    = 0.00067699062342466634638148842944759      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3.8MB, alloc=2.9MB, time=0.17
t[1]                              = 0.503                                        
x2[1] (analytic)                  = 0.0008283422476198008492141699458837         
x2[1] (numeric)                   = 0.00082834909290945412296271212375481        
absolute error                    = 6.84528965327374854217787111e-09             
relative error                    = 0.00082638422378471444851807544967438      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012884848299094197347162072617323         
x1[1] (numeric)                   = 0.0012884711917996072253248320174261         
absolute error                    = 1.36381098125093913752443062e-08             
relative error                    = 0.0010584610308115267592928474238963       % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5035                                       
x2[1] (analytic)                  = 0.00082879876488816372497515444163463        
x2[1] (numeric)                   = 0.00082880863108406243138106858035202        
absolute error                    = 9.86619589870640591413871739e-09             
relative error                    = 0.0011904211633372461167123633345959       % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012879407235323948305490116710912         
x1[1] (numeric)                   = 0.0012879210798788657026601865303412         
absolute error                    = 1.96436535291278888251407500e-08             
relative error                    = 0.0015251985724352168395476949506296       % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.504                                        
x2[1] (analytic)                  = 0.00082925587496274761468760841422102        
x2[1] (numeric)                   = 0.00082926931650288987642419140960385        
absolute error                    = 1.344154014226173658299538283e-08            
relative error                    = 0.001620915877486616107635828350292        % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012873968891405564758385060019091         
x1[1] (numeric)                   = 0.0012873701442357470932520860842079         
absolute error                    = 2.67449048093825864199177012e-08             
relative error                    = 0.0020774405340715880211814027101181       % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5045                                       
x2[1] (analytic)                  = 0.00082971357836864193708890062488759        
x2[1] (numeric)                   = 0.00082973115172195334224393791823925        
absolute error                    = 1.757335331140515503729335166e-08            
relative error                    = 0.0021180023769114828258792099997486       % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012868533265979460697926307621308         
x1[1] (numeric)                   = 0.0012868183580214711297558639388787         
absolute error                    = 3.49685764749400367668232521e-08             
relative error                    = 0.0027173707952705423473265584406399       % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.505                                        
x2[1] (analytic)                  = 0.00083017187563149546111924351454314        
x2[1] (numeric)                   = 0.00083019415409082010534473021335569        
absolute error                    = 2.227845932464422548669881255e-08            
relative error                    = 0.0026835960092839134659065324529361       % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012863100357686729739277295072664         
x1[1] (numeric)                   = 0.0012862647734715930959051797356496         
absolute error                    = 4.52622970798780225497716168e-08             
relative error                    = 0.0035187704224689645134961646917096       % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5055                                       
x2[1] (analytic)                  = 0.0008306307672775168485568375279051         
x2[1] (numeric)                   = 0.00083065883404279133487294603728788        
absolute error                    = 2.806676527448631610850938278e-08            
relative error                    = 0.0033789701008160590770708665278057       % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012857670165169144780958885117126         
x1[1] (numeric)                   = 0.0012856802253246789123874176564892         
absolute error                    = 8.67911922355657084708552234e-08             
relative error                    = 0.0067501492199324865757753674433221       % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.506                                        
x2[1] (analytic)                  = 0.00083109025383347519720441727943742        
x2[1] (numeric)                   = 0.00083113955772287099796816254638673        
absolute error                    = 4.930388939580076374526694931e-08            
relative error                    = 0.0059324350355911813507153967462484       % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012852242687069157665292585243653         
x1[1] (numeric)                   = 0.0012843118564716136515708230847805         
absolute error                    = 9.124122353021149584354395848e-07            
relative error                    = 0.070992453030793386397126660243853        % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Complex estimate of poles used
NO POLE
Radius of convergence             = 9.530e-05                                    
Order of pole                     = 1.449                                        
t[1]                              = 0.5065                                       
x2[1] (analytic)                  = 0.00083155033582670058462774699213345        
x2[1] (numeric)                   = 0.00083197980390481376775896271051958        
absolute error                    = 4.2946807811318313121571838613e-07           
relative error                    = 0.05164667243940437931738490652117         % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012846817922029898839013501196003         
x1[1] (numeric)                   = 0.0012658437812136743417134037384354         
absolute error                    = 1.88380109893155421879463811649e-05          
relative error                    = 1.4663561905872320060945565752337          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence             = 6.634e-05                                    
Order of pole                     = 0.2418                                       
t[1]                              = 0.507                                        
x2[1] (analytic)                  = 0.00083201101378508461244661319002326        
x2[1] (numeric)                   = 0.00084013527057244651425070136660822        
absolute error                    = 8.12425678736190180408817658496e-06          
relative error                    = 0.97646024544820089664076605955721         % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.001284139586869517701405294158948          
x1[1] (numeric)                   = 0.00093355058176335250083126022437346        
absolute error                    = 0.00035058900510616520057403393457454        
relative error                    = 27.301471638362379082855177401818          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence             = 9.349e-05                                    
Order of pole                     = 16.66                                        
t[1]                              = 0.5075                                       
x2[1] (analytic)                  = 0.0008324722882370809511788631756612         
x2[1] (numeric)                   = 0.00097475760317722587637684481428627        
absolute error                    = 0.00014228531494014492519798163862507        
relative error                    = 17.091898066836705402330876169302          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012835976525709478828490588830272         
x1[1] (numeric)                   = -0.0042276610732294209380803045973744        
absolute error                    = 0.0055112587258003688209293634804016         
relative error                    = 429.36029952701606227194060742438          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence             = 0.0003879                                    
Order of pole                     = 181.2                                        
memory used=7.6MB, alloc=4.1MB, time=0.39
t[1]                              = 0.508                                        
x2[1] (analytic)                  = 0.00083293415971170588563803837477598        
x2[1] (numeric)                   = 0.0029566903130173775546846623927067         
absolute error                    = 0.0021237561533056716690466240179307         
relative error                    = 254.97287253061435897550558091988          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012830559891717968507676151575396         
x1[1] (numeric)                   = -0.071374234931290285040166639204913         
absolute error                    = 0.072657290920462081890934254362453          
relative error                    = 5662.8308923106173781827827324822          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5085                                       
x2[1] (analytic)                  = 0.00083339662873853886088515218174166        
x2[1] (numeric)                   = 0.027621181241322226621429206001557          
absolute error                    = 0.026787784612583687760544053819815          
relative error                    = 3214.2900137633994491456764385321          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012825145965366487525520414013697         
x1[1] (numeric)                   = -0.79702669041798808828315607415594          
absolute error                    = 0.79830920501452473703570811555731           
relative error                    = 62245.623337957268431299637299511          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.509                                        
x2[1] (analytic)                  = 0.00083385969584772302873516249155556        
x2[1] (numeric)                   = 0.28466194804950946216278059736196           
absolute error                    = 0.2838280883536617391340454348704            
relative error                    = 34037.871091144999807578029232469          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.001281973474530155426595559729063          
x1[1] (numeric)                   = -7.2459369524189325475208406915529           
absolute error                    = 7.247218925893462702947436251282             
relative error                    = 565317.38525631942268432085639633          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5095                                       
x2[1] (analytic)                  = 0.00083432336156996579481868965658664        
x2[1] (numeric)                   = 2.507444069364568119087605206231             
absolute error                    = 2.5066097460029981532927865165744            
relative error                    = 300436.24108598037252653217188423          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012814326230170363684564948441937         
x1[1] (numeric)                   = -53.733973836266335335003169781186           
absolute error                    = 53.73525526888935237137162627603             
relative error                    = 4193373.4402963575730134931141483          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.51                                         
x2[1] (analytic)                  = 0.00083478762643653936619953115948893        
x2[1] (numeric)                   = 18.27074090657420878808778293205             
absolute error                    = 18.269906118947772248721583400891            
relative error                    = 2188569.3487020859943916190936106          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012808920418620786970381472243591         
x1[1] (numeric)                   = -320.67277136910907078824477319266           
absolute error                    = 320.67405226115093286694181133988            
relative error                    = 25035213.100002991897247058694234          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence             = 2.208e-05                                    
Order of pole                     = 14.46                                        
t[1]                              = 0.5105                                       
x2[1] (analytic)                  = 0.0008352524909792812995485248473563         
x2[1] (numeric)                   = 108.61305294121703039677614533979            
absolute error                    = 108.61221768872605111547659681494            
relative error                    = 13003519.158785748691426003505358          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012803517309301371207855721427719         
x1[1] (numeric)                   = -1514.0299104036562587049614188136           
absolute error                    = 1514.0311907553871888420822043857            
relative error                    = 118251192.55749269390944759295313          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence             = 2.335e-05                                    
Order of pole                     = 24.79                                        
t[1]                              = 0.511                                        
x2[1] (analytic)                  = 0.00083571795573059504987431312643056        
x2[1] (numeric)                   = 520.08173023407345765104498267367            
absolute error                    = 520.08089451611772705599510836054            
relative error                    = 62231628.61942538124675171337096           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012798116900861339038992560756415         
x1[1] (numeric)                   = -5564.5576686600806375497679803704           
absolute error                    = 5564.5589484717707236836718796265            
relative error                    = 434795133.65730115350803289628017          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence             = 1.143e-05                                    
Order of pole                     = 2.49                                         
t[1]                              = 0.5115                                       
x2[1] (analytic)                  = 0.00083618402122345051981156107146395        
x2[1] (numeric)                   = 1986.7401856547279619557898365553            
absolute error                    = 1986.7393494707067385052700249942            
relative error                    = 237595947.66757655590154665218889          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012792719191950588325656820487663         
x1[1] (numeric)                   = -15854.572114661031284015226293769           
absolute error                    = 15854.573393932950479074058859451            
relative error                    = 1239343501.2556936703967511807255          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.512                                        
x2[1] (analytic)                  = 0.00083665068799138460946718195917937        
x2[1] (numeric)                   = 6066.8819353490434257257619949977            
absolute error                    = 6066.8810986983554343411525278157            
relative error                    = 725139079.63951007926000519258442          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012787324181219691812047754809758         
x1[1] (numeric)                   = -36141.26332918667971989612347285            
absolute error                    = 36141.264607919097841865304677625            
relative error                    = 2826335212.5692210240807686484216          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5125                                       
x2[1] (analytic)                  = 0.00083711795656850176682512429116968        
x2[1] (numeric)                   = 15211.749749532517811688220600317            
absolute error                    = 15211.748912414561243186453775193            
relative error                    = 1817157163.2234813350810091446767          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012781931867319896787342220862856         
x1[1] (numeric)                   = -70878.931477801531185228322335724           
absolute error                    = 70878.932755994717917218001069946            
relative error                    = 5545244137.7202039918003127370626          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=11.4MB, alloc=4.2MB, time=0.60
t[1]                              = 0.513                                        
x2[1] (analytic)                  = 0.00083758582748947453871027492802935        
x2[1] (numeric)                   = 32878.494537382227616276283221484            
absolute error                    = 32878.493699796400126801744511209            
relative error                    = 3925388016.4548946266578527182076          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012776542248903124748506494008434         
x1[1] (numeric)                   = -121734.33181775279400100454885853           
absolute error                    = 121734.33309540701889131702370918            
relative error                    = 9527956056.0180512130722142053005          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5135                                       
x2[1] (analytic)                  = 0.00083805430128954412231203351352064        
x2[1] (numeric)                   = 62646.368155082935618395803327158            
absolute error                    = 62646.367317028634328851681015124            
relative error                    = 7475215773.0868308529493157394242          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012771155324621971063276635049614         
x1[1] (numeric)                   = -170552.50267641655104864202947114           
absolute error                    = 170552.5039535320835108391357988             
relative error                    = 13354508626.538881611119441462666          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.514                                        
x2[1] (analytic)                  = 0.0008385233785045209172681139251402         
x2[1] (numeric)                   = 103632.4288076381813242923338462             
absolute error                    = 103632.42796911480281977141657809            
relative error                    = 12358919336.744057911955317472261          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012765771093129704633307325147448         
x1[1] (numeric)                   = -221043.54767545165413993251032604           
absolute error                    = 221043.54895202876345290297365677            
relative error                    = 17315330765.329968996757319837959          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5145                                       
x2[1] (analytic)                  = 0.00083899305967078507830912904557372        
x2[1] (numeric)                   = 155882.86857296402478674987397618            
absolute error                    = 155882.86773397096511596479566705            
relative error                    = 18579756523.270680690064927943434          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012760389553080267557489084220364         
x1[1] (numeric)                   = -273093.6398686089111403696813386            
absolute error                    = 273093.64114464786644839643708751            
relative error                    = 21401669597.048077416453854448591          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.515                                        
x2[1] (analytic)                  = 0.00083946334532528706846451570820467        
x2[1] (numeric)                   = 219419.15300196709731907392054994            
absolute error                    = 219419.15216250375199378685208542            
relative error                    = 26138026559.989957827440222299193          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012755010703128274795433788656077         
x1[1] (numeric)                   = -326667.77722832612697822616703437           
absolute error                    = 326667.77850382719729105364657775            
relative error                    = 25610937231.41362381315647120084           % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5155                                       
x2[1] (analytic)                  = 0.00083993423600554821283035722907962        
x2[1] (numeric)                   = 294256.15650626590575749397040438            
absolute error                    = 294256.15566633166975194575757402            
relative error                    = 35033237490.796595077068850650458          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012749634541929013831128404207343         
x1[1] (numeric)                   = -381527.82940737843268095211526624           
absolute error                    = 381527.83068234188687385349837908            
relative error                    = 29924609166.453558746528020607702          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.516                                        
x2[1] (analytic)                  = 0.00084040573224966125289966149752755        
x2[1] (numeric)                   = 380334.76495253083110035764661038            
absolute error                    = 380334.76411212509885069639371072            
relative error                    = 45256088757.749950787426925082548          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012744261068138444336756849984992         
x1[1] (numeric)                   = -435372.00163342176086801493735391           
absolute error                    = 435372.00290784786768185937102959            
relative error                    = 34162200584.254250972302650744714          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence             = 5.891e-05                                    
Order of pole                     = 8.19                                         
t[1]                              = 0.5165                                       
x2[1] (analytic)                  = 0.0008408778345962909014556531579845         
x2[1] (numeric)                   = 476858.18875518894526947777528691            
absolute error                    = 476858.18791431111067318687383126            
relative error                    = 56709568060.294132580839540796926          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012738890280413197836689909503695         
x1[1] (numeric)                   = -467234.53771816475593234179387544           
absolute error                    = 467234.53899205378397366157754443            
relative error                    = 36677805421.595843599567037072201          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence             = 5.179e-05                                    
Order of pole                     = 9.925                                        
t[1]                              = 0.517                                        
x2[1] (analytic)                  = 0.0008413505435846743980286389764889         
x2[1] (numeric)                   = 576469.94368900974950143230045822            
absolute error                    = 576469.94284765920591675790242958            
relative error                    = 68517212860.116571420679540453523          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012733522177410577371643104777951         
x1[1] (numeric)                   = -306997.17257629496376740269706476           
absolute error                    = 306997.17384964718150846043422907            
relative error                    = 24109368136.513233364983584771228          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Complex estimate of poles used
Complex estimate of poles used
Radius of convergence             = 5.833e-05                                    
Order of pole                     = 3.058                                        
t[1]                              = 0.5175                                       
x2[1] (analytic)                  = 0.00084182385975462206491700604678574        
x2[1] (numeric)                   = 620067.80837159484771196542070457            
absolute error                    = 620067.80752977098795734335578756            
relative error                    = 73657666071.67806433929706136264           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012728156757788557163002449507755         
x1[1] (numeric)                   = 1261994.6473790096816609829587652            
absolute error                    = 1261994.646106194005882127242465             
relative error                    = 99149835292.055139563525419337414          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Complex estimate of poles used
NO POLE
Radius of convergence             = 0.0002122                                    
Order of pole                     = 220.4                                        
memory used=15.2MB, alloc=4.3MB, time=0.82
t[1]                              = 0.518                                        
x2[1] (analytic)                  = 0.00084229778364651786377291305301299        
x2[1] (numeric)                   = 188284.92344411469103950882168391            
absolute error                    = 188284.922601816907392990957911              
relative error                    = 22353724093.477293161787959783597          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012722794020205782277317997435378         
x1[1] (numeric)                   = 11878872.85536794496150553458646             
absolute error                    = 11878872.854095665559484956358728            
relative error                    = 933668566450.90392775379219179893          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5185                                       
x2[1] (analytic)                  = 0.00084277231580131995275323536853887        
x2[1] (numeric)                   = -3347530.2662970999244732668515231           
absolute error                    = 3347530.2671398722402745868042763            
relative error                    = 397204583536.53829494220070911194          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012717433963321568290965101996664         
x1[1] (numeric)                   = 73857883.680816429683939586531192            
absolute error                    = 73857883.679544686287607429702095            
relative error                    = 5807608979339.5959931140721636703          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.519                                        
x2[1] (analytic)                  = 0.00084324745676056124423632533367627        
x2[1] (numeric)                   = -24644953.788113455395681978809988           
absolute error                    = 24644953.788956702852442540054224            
relative error                    = 2922624146846.9199006788723729987          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012712076585795900954973303432135         
x1[1] (numeric)                   = 399647354.74102577365802095393804            
absolute error                    = 399647354.73975456599944136384254            
relative error                    = 31438400488108.191571921912348935          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5195                                       
x2[1] (analytic)                  = 0.00084372320706634996310514961872029        
x2[1] (numeric)                   = -138417628.69509355196896110428911           
absolute error                    = 138417628.69593727517602745425222            
relative error                    = 16405573242108.55603296213816145           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.001270672188628943586002275956513          
x1[1] (numeric)                   = 2023833770.226769303288659067818             
absolute error                    = 2023833770.225498631100030124232             
relative error                    = 159272689552544.39439308677768454          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.52                                         
x2[1] (analytic)                  = 0.00084419956726137020559736614303792        
x2[1] (numeric)                   = -714538675.17055883365270177417509           
absolute error                    = 714538675.17140303321996314438069            
relative error                    = 84640966766828.105274532339936869          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.00127013698634634981016081364961           
x1[1] (numeric)                   = 10294794729.232272591356107920747            
absolute error                    = 10294794729.231002454369761570937            
relative error                    = 810526332190734.74343528375714892          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence             = 8.940e-05                                    
Order of pole                     = 48.06                                        
t[1]                              = 0.5205                                       
x2[1] (analytic)                  = 0.00084467653788888249872290358578525        
x2[1] (numeric)                   = -3669290420.36856066090184157666             
absolute error                    = 3669290420.3694053374397304591587            
relative error                    = 434401839731471.48160176299358999          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012696020515980081945369875504003         
x1[1] (numeric)                   = 55076245329.58287825691947904998             
absolute error                    = 55076245329.581608654867881041785            
relative error                    = 4338071544564603.5218553916967252          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence             = 0.0001756                                    
Order of pole                     = 150.1                                        
t[1]                              = 0.521                                        
x2[1] (analytic)                  = 0.00084515411949272436024960708923766        
x2[1] (numeric)                   = -19537669223.346100813204834136139           
absolute error                    = 19537669223.346945967324326860499            
relative error                    = 2311728567929572.638133937372319           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012690673842501850492592752487639         
x1[1] (numeric)                   = 300833239754.18482972996587592729            
absolute error                    = 300833239754.18356066258162574224            
relative error                    = 23705064324218502.947995760702528          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5215                                       
x2[1] (analytic)                  = 0.0008456323126173108592575143216941         
x2[1] (numeric)                   = -105403371939.89467105397520881226           
absolute error                    = 105403371939.89551668628782612312            
relative error                    = 12464444696260748.611285672794685          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012685329841692135345871646321545         
x1[1] (numeric)                   = 1552077303866.2771059734752098387            
absolute error                    = 1552077303866.2758374404910406252            
relative error                    = 122352144030591438.6758388546332           % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.522                                        
x2[1] (analytic)                  = 0.00084611111780763517726232663345645        
x2[1] (numeric)                   = -539909657956.70839967033883755136           
absolute error                    = 539909657956.70924578145664518654            
relative error                    = 63810727290249203.20465103361347           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012679988512214936274944432542899         
x1[1] (numeric)                   = 7085923949862.3696601146614305768            
absolute error                    = 7085923949862.3683921158102090832            
relative error                    = 558827316210604476.17165068141325          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence             = 2.933e-05                                    
Order of pole                     = 22.77                                        
t[1]                              = 0.5225                                       
x2[1] (analytic)                  = 0.00084659053560926916990864060649109        
x2[1] (numeric)                   = -2479016948111.2995284789681549156           
absolute error                    = 2479016948111.3003750695037641848            
relative error                    = 292823607616545867.90857989501126          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012674649852734920882691918827657         
x1[1] (numeric)                   = 27637356319596.592213740971466365            
absolute error                    = 27637356319596.590946275986192873            
relative error                    = 2180522274043967774.2906852551271          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence             = 1.641e-05                                    
Order of pole                     = 5.849                                        
memory used=19.0MB, alloc=4.3MB, time=1.05
t[1]                              = 0.523                                        
x2[1] (analytic)                  = 0.00084707056656836392923350586605222        
x2[1] (numeric)                   = -9876927113559.9329291230856873854           
absolute error                    = 9876927113559.9337761936522557493            
relative error                    = 1166009952815755587.6066500023345          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012669313861917424271304738755899         
x1[1] (numeric)                   = 90912034949970.810295004385933822            
absolute error                    = 90912034949970.80902807299974208             
relative error                    = 7175766260179445947.9588024969319          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence             = 1.753e-05                                    
Order of pole                     = 14.09                                        
t[1]                              = 0.5235                                       
x2[1] (analytic)                  = 0.00084755121123165034650087559078626        
x2[1] (numeric)                   = -33736028236628.631002810566059793           
absolute error                    = 33736028236628.631850361777291443            
relative error                    = 3980411778021516410.1055448275556          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012663980538428448708617120408105         
x1[1] (numeric)                   = 252817726183951.98016365082859896            
absolute error                    = 252817726183951.97889725277475612            
relative error                    = 19963527693112333748.415673260533          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence             = 2.648e-05                                    
Order of pole                     = 43.09                                        
t[1]                              = 0.524                                        
x2[1] (analytic)                  = 0.00084803247014643967560751672664236        
x2[1] (numeric)                   = -98968383520029.418529647296942646           
absolute error                    = 98968383520029.419377679767089086            
relative error                    = 11670353082463858038.533343463937          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012658649880934663294607446375807         
x1[1] (numeric)                   = 602836385208340.2733569129272233             
absolute error                    = 602836385208340.27209104793912983            
relative error                    = 47622486669473259955.836527631358          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence             = 9.320e-06                                    
Order of pole                     = 1.999                                        
t[1]                              = 0.5245                                       
x2[1] (analytic)                  = 0.00084851434386062409706094747929037        
x2[1] (numeric)                   = -252257466810436.31693075351611337           
absolute error                    = 252257466810436.31777926785997399            
relative error                    = 29729310840250428718.789521947627          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012653321888103403628065521811756         
x1[1] (numeric)                   = 1257065426902727.9617955410585566            
absolute error                    = 1257065426902727.9605302088697463            
relative error                    = 99346672598648993931.866929669829          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.525                                        
x2[1] (analytic)                  = 0.00084899683292267728252997022968994        
x2[1] (numeric)                   = -567682466997653.49630835881567671           
absolute error                    = 567682466997653.49715735564859939            
relative error                    = 66865086533173840367.375384656374          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012647996558602671473426467186411         
x1[1] (numeric)                   = 2325313226126924.932296195330972             
absolute error                    = 2325313226126924.9310313956751117            
relative error                    = 183848344309149738343.84751172721          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5255                                       
x2[1] (analytic)                  = 0.00084947993788165495996836858796728        
x2[1] (numeric)                   = -1143608882669246.2465899976255879           
absolute error                    = 1143608882669246.2474394775634696            
relative error                    = 134624589901564899847.0996455185           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012642673891101134427771152459227         
x1[1] (numeric)                   = 3842454069120740.3537794256811757            
absolute error                    = 3842454069120740.3525151582920656            
relative error                    = 303927325992751325354.64881396242          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.526                                        
x2[1] (analytic)                  = 0.00084996365928719547931233787183942        
x2[1] (numeric)                   = -2083195019788801.6805069534403201           
absolute error                    = 2083195019788801.6813569170996073            
relative error                    = 245092245653870694687.41963847191          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012637353884268125587993089414852         
x1[1] (numeric)                   = 5773450524804747.6324641370814927            
absolute error                    = 5773450524804747.6312004016930659            
relative error                    = 456855966658649032773.4103175112           % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5265                                       
x2[1] (analytic)                  = 0.00085044799768952037875221886747711        
x2[1] (numeric)                   = -3477964265445560.6718763872569579           
absolute error                    = 3477964265445560.6727268352546474            
relative error                    = 408956723385136119582.03961223177          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012632036536773643218131698955945         
x1[1] (numeric)                   = 8144018458460057.2496789527346866            
absolute error                    = 8144018458460057.2484157490810092            
relative error                    = 644711439422429534338.91657730931          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.527                                        
x2[1] (analytic)                  = 0.00085093295363943495157910530292247        
x2[1] (numeric)                   = -5422665950536506.384947945965288            
absolute error                    = 5422665950536506.3857988789189274            
relative error                    = 637261246887172230634.42537363941          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012626721847288350416871870185942         
x1[1] (numeric)                   = 10954550959757925.31064718870528             
absolute error                    = 10954550959757925.309384516520551            
relative error                    = 867568882267765176701.095977327            % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5275                                       
x2[1] (analytic)                  = 0.00085141852768832881360689603697165        
x2[1] (numeric)                   = -8008567209085095.6579374860166112           
absolute error                    = 8008567209085095.6587889045442995            
relative error                    = 940614627077591671388.75148164739          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012621409814483574785209728156648         
x1[1] (numeric)                   = 14146764073110436.394938574383196            
absolute error                    = 14146764073110436.393676433401748            
relative error                    = 1120854506829851631999.6922427507          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=22.8MB, alloc=4.3MB, time=1.27
t[1]                              = 0.528                                        
x2[1] (analytic)                  = 0.00085190472038817647117036353980059        
x2[1] (numeric)                   = -11306312433891356.482079617493049           
absolute error                    = 11306312433891356.482931522213437            
relative error                    = 1327180395096244385074.1937672672          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012616100437031308094284527197097         
x1[1] (numeric)                   = 17313099310742399.937189175909267            
absolute error                    = 17313099310742399.935927565865564            
relative error                    = 1372301956310070534427.57631202            % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5285                                       
x2[1] (analytic)                  = 0.00085239153229153788969981081555131        
x2[1] (numeric)                   = -15264033454585309.11309229419851            
absolute error                    = 15264033454585309.113944685730802            
relative error                    = 1790730301314707544898.1259684695          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012610793713604205953376586781657         
x1[1] (numeric)                   = 18004946230276114.220297882065746            
absolute error                    = 18004946230276114.219036802694386            
relative error                    = 1427740920926557753671.6309194429          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.529                                        
x2[1] (analytic)                  = 0.00085287896395155906287288949160932        
x2[1] (numeric)                   = -19113596354839399.574120570278964           
absolute error                    = 19113596354839399.574973449242916            
relative error                    = 2241067861057597130338.442742282           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.001260548964287558747807118693686          
x1[1] (numeric)                   = 2042666771743193.788191180270508             
absolute error                    = 2042666771743193.7869306313062204            
relative error                    = 162045809374622347999.41152674923          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5295                                       
x2[1] (analytic)                  = 0.00085336701592197258234415237438934        
x2[1] (numeric)                   = -17987895330910443.749807441534256           
absolute error                    = 17987895330910443.750660808550178            
relative error                    = 2107873282573082580978.2801471705          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012600188223519434958588340227923         
x1[1] (numeric)                   = -108901538913097309.64439232558523           
absolute error                    = 108901538913097309.64565234440758            
relative error                    = 8642850168684175467034.7395786238          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.53                                         
x2[1] (analytic)                  = 0.00085385568875709820805291434710783        
x2[1] (numeric)                   = 15344082959924377.581050451541882            
absolute error                    = 15344082959924377.580196595853125            
relative error                    = 1797034693562767496273.1761538882          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012594889454210393528278357407412         
x1[1] (numeric)                   = -718905094756948492.63409768210465           
absolute error                    = 718905094756948492.63535717105007            
relative error                    = 57079111124442856666528.484007099          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Complex estimate of poles used
NO POLE
Radius of convergence             = 3.405e-05                                    
Order of pole                     = 0.8958                                       
t[1]                              = 0.5305                                       
x2[1] (analytic)                  = 0.00085434498301184343910999606125632        
x2[1] (numeric)                   = 222084264026351986.4448387340419             
absolute error                    = 222084264026351986.44398438905889            
relative error                    = 25994682293730204075499.267589827          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012589593333623770832283123849924         
x1[1] (numeric)                   = -3765520673759440461.8216602301546           
absolute error                    = 3765520673759440461.822919189488             
relative error                    = 299097879810195448860381.05906417          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
Complex estimate of poles used
Radius of convergence             = 3.494e-05                                    
Order of pole                     = 7.26                                         
t[1]                              = 0.531                                        
x2[1] (analytic)                  = 0.00085483489924170408526392545030159        
x2[1] (numeric)                   = 1285339260339291775.6822076965355            
absolute error                    = 1285339260339291775.6813528616363            
relative error                    = 150361112008818772536773.92109143          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012584299860435536696363003938124         
x1[1] (numeric)                   = -18071379967188571349.42098905618            
absolute error                    = 18071379967188571349.422247486166            
relative error                    = 1436025855042135764287592.0547221          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5315                                       
x2[1] (analytic)                  = 0.00085532543800276483894717267152565        
x2[1] (numeric)                   = 6351655586891070163.5136894639149            
absolute error                    = 6351655586891070163.5128341384769            
relative error                    = 742601038702012559665353.02454215          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012579009033322322795889290606847         
x1[1] (numeric)                   = -83502646910879873177.811270178195           
absolute error                    = 83502646910879873177.812528079098            
relative error                    = 6638253195436767506774580.0956509          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.532                                        
x2[1] (analytic)                  = 0.00085581659985169984790299465988337        
x2[1] (numeric)                   = 29742630237525221173.664039171158            
absolute error                    = 29742630237525221173.663183354558            
relative error                    = 3475350938820206560826028.9283272          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.001257372085096142232500211729337          
x1[1] (numeric)                   = -385256236150103136964.09718339762           
absolute error                    = 385256236150103136964.09844076971            
relative error                    = 30639795547922105610514301.153646          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5325                                       
x2[1] (analytic)                  = 0.00085630838534577328839346605629603        
x2[1] (numeric)                   = 137808832960151368013.39321742939            
absolute error                    = 137808832960151368013.392361121              
relative error                    = 16093364880983246596523444.58971           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012568435312030789665933749583355         
x1[1] (numeric)                   = -1795421850745076614064.9587631391           
absolute error                    = 1795421850745076614064.9600199826            
relative error                    = 142851660224280928309127053.18287          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence             = 2.571e-05                                    
Order of pole                     = 2.427                                        
t[1]                              = 0.533                                        
x2[1] (analytic)                  = 0.0008568007950428399389892738519192         
x2[1] (numeric)                   = 640363503434935418571.29485019612            
absolute error                    = 640363503434935418571.29399339532            
relative error                    = 74738901637330684165460903.001863          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012563152415209040058497173883259         
x1[1] (numeric)                   = -8246620078116664779998.04418466             
absolute error                    = 8246620078116664779998.0454409752            
relative error                    = 656413279531119030019866121.8684           % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.3MB, time=1.49
Real estimate of pole used
Real estimate of pole used
Radius of convergence             = 2.429e-05                                    
Order of pole                     = 4.517                                        
t[1]                              = 0.5335                                       
x2[1] (analytic)                  = 0.0008572938295013457549418536696203         
x2[1] (numeric)                   = 2929263808068270633725.6520374488            
absolute error                    = 2929263808068270633725.651180155             
relative error                    = 341687261387628167982730442.4305           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012557872159175449269739900491366         
x1[1] (numeric)                   = -35762673403417546591916.963266106           
absolute error                    = 35762673403417546591916.964521893            
relative error                    = 2847829070889803207868863386.2084          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence             = 1.892e-05                                    
Order of pole                     = 1.236                                        
t[1]                              = 0.534                                        
x2[1] (analytic)                  = 0.00085778748928032844313844618417794        
x2[1] (numeric)                   = 12723863803503612966944.951632938            
absolute error                    = 12723863803503612966944.950775151            
relative error                    = 1483335203941800844242717190.5161          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012552594542609953263762898480893         
x1[1] (numeric)                   = -141117242592842936818788.89456958           
absolute error                    = 141117242592842936818788.89582484            
relative error                    = 11242077652856430074514325141.094          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence             = 1.866e-05                                    
Order of pole                     = 5.517                                        
t[1]                              = 0.5345                                       
x2[1] (analytic)                  = 0.00085828177493941803764065276357102        
x2[1] (numeric)                   = 50779986657453412314765.535427761            
absolute error                    = 50779986657453412314765.534569479            
relative error                    = 5916470341111195813265341939.6841          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012547319564193147871704579849903         
x1[1] (numeric)                   = -495641417760753719092253.69124579           
absolute error                    = 495641417760753719092253.69250052            
relative error                    = 39501776871546971859763274487.862          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.535                                        
x2[1] (analytic)                  = 0.00085877668703883747580706999516187        
x2[1] (numeric)                   = 182383357543139051085790.50228507            
absolute error                    = 182383357543139051085790.50142629            
relative error                    = 21237576694357902658704953336.843          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012542047222606288461889750434006         
x1[1] (numeric)                   = -1535719195009533818024684.5854046           
absolute error                    = 1535719195009533818024684.5866588            
relative error                    = 122445655621635039464433727918.77          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5355                                       
x2[1] (analytic)                  = 0.00085927222613940317500058334259466        
x2[1] (numeric)                   = 584245456741016598193136.96504788            
absolute error                    = 584245456741016598193136.96418861            
relative error                    = 67993057260323007064385442457.088          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012536777516531289610143445119101         
x1[1] (numeric)                   = -4198711795327422341311473.4711808           
absolute error                    = 4198711795327422341311473.4724345            
relative error                    = 334911566372690449664417273467.94          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.536                                        
x2[1] (analytic)                  = 0.00085976839280252560988090076182799        
x2[1] (numeric)                   = 1668425598384868693675922.6702196            
absolute error                    = 1668425598384868693675922.6693598            
relative error                    = 194055237707264506388118823155.96          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012531510444650724770269564932605         
x1[1] (numeric)                   = -10192002055401215155408126.657669           
absolute error                    = 10192002055401215155408126.658922            
relative error                    = 813309943794671127760374112640.25          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5365                                       
x2[1] (analytic)                  = 0.00086026518759020989028290768790106        
x2[1] (numeric)                   = 4268486192558119422841828.4549432            
absolute error                    = 4268486192558119422841828.4540829            
relative error                    = 496182602078212497922821794812.39          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012526246005647825944694233632835         
x1[1] (numeric)                   = -22167475421752186535981459.684403           
absolute error                    = 22167475421752186535981459.685656            
relative error                    = 1769682266479305062146659587218.1          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.537                                        
x2[1] (analytic)                  = 0.00086076261106505633968142538779503        
x2[1] (numeric)                   = 9860486575201215305245918.1652836            
absolute error                    = 9860486575201215305245918.1644228            
relative error                    = 1145552379767104086940409493799.1          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012520984198206483355273791457368         
x1[1] (numeric)                   = -43616353299197776755066837.27431            
absolute error                    = 43616353299197776755066837.275562            
relative error                    = 3483460453966982967720870999439.9          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5375                                       
x2[1] (analytic)                  = 0.00086126066379026107424295525909657        
x2[1] (numeric)                   = 20746770079766820496572179.259105            
absolute error                    = 20746770079766820496572179.258244            
relative error                    = 2408883971138752467205705142867.6          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012515725021011245114267343732391         
x1[1] (numeric)                   = -78373412687484705812691783.212034           
absolute error                    = 78373412687484705812691783.213286            
relative error                    = 6261995414241874542596428532082.4          % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence             = 1.075e-05                                    
Order of pole                     = 5.3                                          
t[1]                              = 0.538                                        
x2[1] (analytic)                  = 0.0008617593463296165824649922390997         
x2[1] (numeric)                   = 40109271495240072886557707.694415            
absolute error                    = 40109271495240072886557707.693553            
relative error                    = 4654347140657360843460562778174.5          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012510468472747316895473782086164         
x1[1] (numeric)                   = -130067846758286330612327713.40792           
absolute error                    = 130067846758286330612327713.40917            
relative error                    = 10396720717663360541379379539772           % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.4MB, time=1.72
NO POLE
Real estimate of pole used
Radius of convergence             = 2.379e-05                                    
Order of pole                     = 55.5                                         
t[1]                              = 0.5385                                       
x2[1] (analytic)                  = 0.00086225865924751230540349107449532        
x2[1] (numeric)                   = 71929005099412812142317827.907436            
absolute error                    = 71929005099412812142317827.906574            
relative error                    = 8341928994042785411336794486985.9          % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012505214552100561605533196050853         
x1[1] (numeric)                   = -202126520914098477766037860.72774           
absolute error                    = 202126520914098477766037860.72899            
relative error                    = 16163378890620177696408685049607           % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.539                                        
x2[1] (analytic)                  = 0.00086275860310893521748906978789598        
x2[1] (numeric)                   = 120907492932658273039663591.83428            
absolute error                    = 120907492932658273039663591.83342            
relative error                    = 14014058219410421600780489479826           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012499963257757499055392592878095         
x1[1] (numeric)                   = -297555576985738024336133006.19522           
absolute error                    = 297555576985738024336133006.19647            
relative error                    = 23804516129363381364222717535831           % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5395                                       
x2[1] (analytic)                  = 0.00086325917847947040793253526412643        
x2[1] (numeric)                   = 192308673450003218871655425.54034            
absolute error                    = 192308673450003218871655425.53948            
relative error                    = 22277049378001673483930047710717           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.00124947145884053056319358434347           
x1[1] (numeric)                   = -415629000878842632890159052.17812           
absolute error                    = 415629000878842632890159052.17937            
relative error                    = 33264385347748000129495445976399           % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.54                                         
x2[1] (analytic)                  = 0.0008637603859253016627203164664802         
x2[1] (numeric)                   = 290865692974287213597128303.72334            
absolute error                    = 290865692974287213597128303.72248            
relative error                    = 33674349705526017595914875299130           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012489468542731813969777772086            
x1[1] (numeric)                   = -536102802344475537820118662.54725           
absolute error                    = 536102802344475537820118662.5485             
relative error                    = 42924388696783897990752560341220           % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5405                                       
x2[1] (analytic)                  = 0.00086426222601321204720039138099847        
x2[1] (numeric)                   = 415187277955386869767468266.15947            
absolute error                    = 415187277955386869767468266.15861            
relative error                    = 48039502995591973026582006752710           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012484225119425512623222308515348         
x1[1] (numeric)                   = -538074289419639065437490538.82957           
absolute error                    = 538074289419639065437490538.83082            
relative error                    = 43100335365019408112017392440708           % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.541                                        
x2[1] (analytic)                  = 0.00086476469931058448925929437526969        
x2[1] (numeric)                   = 529141281251122906684572608.06398            
absolute error                    = 529141281251122906684572608.06312            
relative error                    = 61189047341198095843790295326581           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012478984317175545738384619469313         
x1[1] (numeric)                   = 204711289248724974096275110.08614            
absolute error                    = 204711289248724974096275110.08489            
relative error                    = 16404483253253954463701608649431           % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5415                                       
x2[1] (analytic)                  = 0.00086526780638540236309079124728038        
x2[1] (numeric)                   = 419260389777346543480887562.97793            
absolute error                    = 419260389777346543480887562.97706            
relative error                    = 48454407604597981720254004660189           % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012473746134671712725477138459096         
x1[1] (numeric)                   = 4750968485575437052379217715.5397            
absolute error                    = 4750968485575437052379217715.5385            
relative error                    = 3.8087743924575824861746350362290e+32      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.542                                        
x2[1] (analytic)                  = 0.00086577154780625007355680982946525        
x2[1] (numeric)                   = -985949291504139513066319861.76797           
absolute error                    = 985949291504139513066319861.76884            
relative error                    = 1.1388099943944841505845153696078e+32      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.001246851057060446793125941148968          
x1[1] (numeric)                   = 27277593319232498764647040083.267            
absolute error                    = 27277593319232498764647040083.266            
relative error                    = 2.1877186665375777107038593297225e+33      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5425                                       
x2[1] (analytic)                  = 0.00086627592414231364114121460331367        
x2[1] (numeric)                   = -8705373054671661504687875118.8928           
absolute error                    = 8705373054671661504687875118.8937            
relative error                    = 1.0049191963046550519046504639269e+33      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.001246327762366492031165167692916          
x1[1] (numeric)                   = 130532858148116032968558032915.75            
absolute error                    = 130532858148116032968558032915.75            
relative error                    = 1.0473397294806618171988014479698e+34      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.543                                        
x2[1] (analytic)                  = 0.00086678093596338128749701437068642        
x2[1] (numeric)                   = -45151246610410039488571296780.181           
absolute error                    = 45151246610410039488571296780.182            
relative error                    = 5.2090724123075931078514805393601e+33      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012458047292544833104512097671668         
x1[1] (numeric)                   = 584623185719748405509133831935.52            
absolute error                    = 584623185719748405509133831935.52            
relative error                    = 4.6927353219280172079807323532392e+34      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.4MB, time=1.95
NO POLE
NO POLE
t[1]                              = 0.5435                                       
x2[1] (analytic)                  = 0.00086728658383984402158759261938419        
x2[1] (numeric)                   = -207518090832129601586848865412.37           
absolute error                    = 207518090832129601586848865412.37            
relative error                    = 2.3927280174606110505448249705755e+34      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012452819575936623502577563788178         
x1[1] (numeric)                   = 2545395928331854489330323895330.1            
absolute error                    = 2545395928331854489330323895330.1            
relative error                    = 2.0440318056566764851814004107771e+35      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.544                                        
x2[1] (analytic)                  = 0.00086779286834269622642255081248739        
x2[1] (numeric)                   = -912990149949592070479114926650.21           
absolute error                    = 912990149949592070479114926650.21            
relative error                    = 1.0520830295519865765576263264702e+35      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.00124475944725333623265679839004           
x1[1] (numeric)                   = 10961655244938662791203701285890             
absolute error                    = 10961655244938662791203701285890             
relative error                    = 8.8062438643277251196936442279076e+35      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5445                                       
x2[1] (analytic)                  = 0.00086829979004353624638875542355646        
x2[1] (numeric)                   = -3945118565748965115872734800241.6           
absolute error                    = 3945118565748965115872734800241.6            
relative error                    = 4.5434982375743270157128828445586e+35      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012442371981028773698453983553836         
x1[1] (numeric)                   = 46619953460160700019367928449448             
absolute error                    = 46619953460160700019367928449448             
relative error                    = 3.7468702536175114779783834926941e+36      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.545                                        
x2[1] (analytic)                  = 0.00086880734951456697517718013294248        
x2[1] (numeric)                   = -16783756667081145726045549389798            
absolute error                    = 16783756667081145726045549389798             
relative error                    = 1.9318156869251643703391909238176e+36      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012437152100117234714887928906918         
x1[1] (numeric)                   = 1.9221053940026504163281784232491e+32        
absolute error                    = 1.9221053940026504163281784232491e+32        
relative error                    = 1.5454546012865214725264734071068e+37      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5455                                       
x2[1] (analytic)                  = 0.00086931554732859644430613519421227        
x2[1] (numeric)                   = -69306410025358255599689310210776            
absolute error                    = 69306410025358255599689310210776             
relative error                    = 7.9725262292083242690627686030830e+36      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012431934828493775120798194093974         
x1[1] (numeric)                   = 7.4908479576498000050282007092093e+32        
absolute error                    = 7.4908479576498000050282007092093e+32        
relative error                    = 6.0254884384375220092429845679213e+37      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.546                                        
x2[1] (analytic)                  = 0.00086982438405903841224147657403825        
x2[1] (numeric)                   = -2.7188658327054042462173549028549e+32       
absolute error                    = 2.7188658327054042462173549028549e+32        
relative error                    = 3.1257640996655068441168175409119e+37      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012426720164854076983146590660609         
x1[1] (numeric)                   = 2.7004216694331248949338790337014e+33        
absolute error                    = 2.7004216694331248949338790337014e+33        
relative error                    = 2.1730767520384048870911580973362e+38      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5465                                       
x2[1] (analytic)                  = 0.00087033386027991295411438806384394        
x2[1] (numeric)                   = -9.9371235913063686281182502530752e+32       
absolute error                    = 9.9371235913063686281182502530752e+32        
relative error                    = 1.1417599664696987173493939370637e+38      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012421508107894474364848877510829         
x1[1] (numeric)                   = 8.8807163496302727770740507216938e+33        
absolute error                    = 8.8807163496302727770740507216938e+33        
relative error                    = 7.1494670956952033112182383141392e+38      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.547                                        
x2[1] (analytic)                  = 0.00087084397656584705203733015703041        
x2[1] (numeric)                   = -3.3394526341078264781359786607001e+33       
absolute error                    = 3.3394526341078264781359786607001e+33        
relative error                    = 3.8347312767516406289416826073554e+38      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012416298656311952998858269846059         
x1[1] (numeric)                   = 2.6470686020963982056373154837874e+34        
absolute error                    = 2.6470686020963982056373154837874e+34        
relative error                    = 2.1319305175948982857691308171267e+39      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5475                                       
x2[1] (analytic)                  = 0.00087135473349207518601875008173811        
x2[1] (numeric)                   = -1.0251283111682724443985606430305e+34       
absolute error                    = 1.0251283111682724443985606430305e+34        
relative error                    = 1.1764764357908842430194100899068e+39      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012411091808804149962411865616909         
x1[1] (numeric)                   = 7.1449126130885238003843349547687e+34        
absolute error                    = 7.1449126130885238003843349547687e+34        
relative error                    = 5.7568767705191602563980182995254e+39      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Complex estimate of poles used
NO POLE
Radius of convergence             = 2.986e-05                                    
Order of pole                     = 13.6                                         
t[1]                              = 0.548                                        
x2[1] (analytic)                  = 0.0008718661316344399254771479758239         
x2[1] (numeric)                   = -2.8705751586349402910833012132160e+34       
absolute error                    = 2.8705751586349402910833012132160e+34        
relative error                    = 3.2924494420417839495557080776440e+39      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012405887564069353351439908049313         
x1[1] (numeric)                   = 1.7514604516937132731553704125369e+35        
absolute error                    = 1.7514604516937132731553704125369e+35        
relative error                    = 1.4117977796013515300293051846156e+40      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=38.1MB, alloc=4.4MB, time=2.17
t[1]                              = 0.5485                                       
x2[1] (analytic)                  = 0.00087237817156939252135509478805287        
x2[1] (numeric)                   = -7.3485407107571281218361097772725e+34       
absolute error                    = 7.3485407107571281218361097772725e+34        
relative error                    = 8.4235724256342138340678323475737e+39      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012400685920806501955137802847337         
x1[1] (numeric)                   = 3.9195023143625767086919112068635e+35        
absolute error                    = 3.9195023143625767086919112068635e+35        
relative error                    = 3.1607141245197060007356673974240e+40      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.549                                        
x2[1] (analytic)                  = 0.00087289085387399349883379808742284        
x2[1] (numeric)                   = -1.7274041392085438298117672105502e+35       
absolute error                    = 1.7274041392085438298117672105502e+35        
relative error                    = 1.9789463156156564919607261785595e+40      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012395486877715184930700808715671         
x1[1] (numeric)                   = 8.0589824057327805400642895321993e+35        
absolute error                    = 8.0589824057327805400642895321993e+35        
relative error                    = 6.5015456716116208680040213149204e+40      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5495                                       
x2[1] (analytic)                  = 0.00087340417912591325064881256105309        
x2[1] (numeric)                   = -3.7497619106324116753806784082608e+35       
absolute error                    = 3.7497619106324116753806784082608e+35        
relative error                    = 4.2932722332346795567299580548735e+40      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.001239029043349564147822131988547          
x1[1] (numeric)                   = 1.5334208008869407782062369054791e+36        
absolute error                    = 1.5334208008869407782062369054791e+36        
relative error                    = 1.2375987545388963285424098868184e+41      % 
h                                 = 0.0005                                       
 
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence             = 0.0001338                                    
Order of pole                     = 326.5                                        
t[1]                              = 0.55                                         
x2[1] (analytic)                  = 0.00087391814790343263100749258018221        
x2[1] (numeric)                   = -7.5645094059719809573560874690152e+35       
absolute error                    = 7.5645094059719809573560874690152e+35        
relative error                    = 8.6558557275868061860501280818240e+40      % 
h                                 = 0.0005                                       
x1[1] (analytic)                  = 0.0012385096586848760515748659367868         
x1[1] (numeric)                   = 2.7212753786517590928930158332142e+36        
absolute error                    = 2.7212753786517590928930158332142e+36        
relative error                    = 2.1972177282342494988679742744605e+41      % 
h                                 = 0.0005                                       
Finished!
Maximum Iterations Reached before Solution Completed!
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;
Iterations                        = 100                                 
Total Elapsed Time               = 2 Seconds
Elapsed Time(since restart)      = 2 Seconds
Expected Time Remaining          = 3 Minutes 14 Seconds
Optimized Time Remaining         = 3 Minutes 13 Seconds
Time to Timeout                  = 14 Minutes 57 Seconds
Percent Done                     = 1.122                                      % 
> quit
memory used=39.5MB, alloc=4.4MB, time=2.24