|\^/|     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
>  DEBUGL,
>  DEBUGMASSIVE,
>  INFO,
>  ALWAYS,
>  glob_max_terms,
>  glob_iolevel,
>  #Top Generate Globals Decl
>  glob_abserr,
>  glob_not_yet_start_msg,
>  glob_not_yet_finished,
>  hours_in_day,
>  glob_max_opt_iter,
>  glob_warned2,
>  glob_warned,
>  glob_optimal_clock_start_sec,
>  glob_last_good_h,
>  glob_hmax,
>  glob_reached_optimal_h,
>  years_in_century,
>  djd_debug,
>  glob_optimal_expect_sec,
>  glob_log10relerr,
>  glob_normmax,
>  glob_max_order,
>  glob_html_log,
>  glob_optimal_start,
>  glob_max_rel_trunc_err,
>  glob_max_iter,
>  glob_relerr,
>  glob_log10_abserr,
>  glob_initial_pass,
>  days_in_year,
>  glob_dump,
>  glob_log10normmin,
>  glob_curr_iter_when_opt,
>  glob_max_hours,
>  glob_log10_relerr,
>  glob_optimal_done,
>  glob_max_sec,
>  glob_max_trunc_err,
>  glob_dump_analytic,
>  glob_large_float,
>  glob_h,
>  glob_almost_1,
>  min_in_hour,
>  glob_start,
>  glob_no_eqs,
>  glob_look_poles,
>  glob_hmin_init,
>  djd_debug2,
>  glob_percent_done,
>  glob_log10abserr,
>  glob_orig_start_sec,
>  glob_hmin,
>  glob_disp_incr,
>  centuries_in_millinium,
>  glob_display_flag,
>  glob_iter,
>  glob_current_iter,
>  glob_max_minutes,
>  MAX_UNCHANGED,
>  glob_unchanged_h_cnt,
>  glob_small_float,
>  sec_in_min,
>  glob_smallish_float,
>  glob_clock_start_sec,
>  glob_clock_sec,
>  #Bottom Generate Globals Decl
>  #BEGIN CONST
>  array_const_2D0,
>  array_const_3D0,
>  array_const_4D0,
>  array_const_1,
>  array_const_0D0,
>  array_const_2,
>  #END CONST
>  array_x2,
>  array_x1,
>  array_t,
>  array_pole,
>  array_norms,
>  array_tmp10,
>  array_tmp11,
>  array_tmp12,
>  array_tmp13,
>  array_tmp14,
>  array_tmp15,
>  array_tmp16,
>  array_tmp17,
>  array_type_pole,
>  array_x1_init,
>  array_m1,
>  array_tmp0,
>  array_tmp1,
>  array_tmp2,
>  array_tmp3,
>  array_tmp4,
>  array_tmp5,
>  array_tmp6,
>  array_tmp7,
>  array_tmp8,
>  array_tmp9,
>  array_last_rel_error,
>  array_1st_rel_error,
>  array_x2_init,
>  array_complex_pole,
>  array_x1_higher,
>  array_real_pole,
>  array_x1_higher_work,
>  array_poles,
>  array_x1_higher_work2,
>  array_x2_higher_work,
>  array_x2_higher_work2,
>  array_x2_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 DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_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
>  DEBUGL,
>  DEBUGMASSIVE,
>  INFO,
>  ALWAYS,
>  glob_max_terms,
>  glob_iolevel,
>  #Top Generate Globals Decl
>  glob_abserr,
>  glob_not_yet_start_msg,
>  glob_not_yet_finished,
>  hours_in_day,
>  glob_max_opt_iter,
>  glob_warned2,
>  glob_warned,
>  glob_optimal_clock_start_sec,
>  glob_last_good_h,
>  glob_hmax,
>  glob_reached_optimal_h,
>  years_in_century,
>  djd_debug,
>  glob_optimal_expect_sec,
>  glob_log10relerr,
>  glob_normmax,
>  glob_max_order,
>  glob_html_log,
>  glob_optimal_start,
>  glob_max_rel_trunc_err,
>  glob_max_iter,
>  glob_relerr,
>  glob_log10_abserr,
>  glob_initial_pass,
>  days_in_year,
>  glob_dump,
>  glob_log10normmin,
>  glob_curr_iter_when_opt,
>  glob_max_hours,
>  glob_log10_relerr,
>  glob_optimal_done,
>  glob_max_sec,
>  glob_max_trunc_err,
>  glob_dump_analytic,
>  glob_large_float,
>  glob_h,
>  glob_almost_1,
>  min_in_hour,
>  glob_start,
>  glob_no_eqs,
>  glob_look_poles,
>  glob_hmin_init,
>  djd_debug2,
>  glob_percent_done,
>  glob_log10abserr,
>  glob_orig_start_sec,
>  glob_hmin,
>  glob_disp_incr,
>  centuries_in_millinium,
>  glob_display_flag,
>  glob_iter,
>  glob_current_iter,
>  glob_max_minutes,
>  MAX_UNCHANGED,
>  glob_unchanged_h_cnt,
>  glob_small_float,
>  sec_in_min,
>  glob_smallish_float,
>  glob_clock_start_sec,
>  glob_clock_sec,
>  #Bottom Generate Globals Decl
>  #BEGIN CONST
>  array_const_2D0,
>  array_const_3D0,
>  array_const_4D0,
>  array_const_1,
>  array_const_0D0,
>  array_const_2,
>  #END CONST
>  array_x2,
>  array_x1,
>  array_t,
>  array_pole,
>  array_norms,
>  array_tmp10,
>  array_tmp11,
>  array_tmp12,
>  array_tmp13,
>  array_tmp14,
>  array_tmp15,
>  array_tmp16,
>  array_tmp17,
>  array_type_pole,
>  array_x1_init,
>  array_m1,
>  array_tmp0,
>  array_tmp1,
>  array_tmp2,
>  array_tmp3,
>  array_tmp4,
>  array_tmp5,
>  array_tmp6,
>  array_tmp7,
>  array_tmp8,
>  array_tmp9,
>  array_last_rel_error,
>  array_1st_rel_error,
>  array_x2_init,
>  array_complex_pole,
>  array_x1_higher,
>  array_real_pole,
>  array_x1_higher_work,
>  array_poles,
>  array_x1_higher_work2,
>  array_x2_higher_work,
>  array_x2_higher_work2,
>  array_x2_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 DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_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
>  DEBUGL,
>  DEBUGMASSIVE,
>  INFO,
>  ALWAYS,
>  glob_max_terms,
>  glob_iolevel,
>  #Top Generate Globals Decl
>  glob_abserr,
>  glob_not_yet_start_msg,
>  glob_not_yet_finished,
>  hours_in_day,
>  glob_max_opt_iter,
>  glob_warned2,
>  glob_warned,
>  glob_optimal_clock_start_sec,
>  glob_last_good_h,
>  glob_hmax,
>  glob_reached_optimal_h,
>  years_in_century,
>  djd_debug,
>  glob_optimal_expect_sec,
>  glob_log10relerr,
>  glob_normmax,
>  glob_max_order,
>  glob_html_log,
>  glob_optimal_start,
>  glob_max_rel_trunc_err,
>  glob_max_iter,
>  glob_relerr,
>  glob_log10_abserr,
>  glob_initial_pass,
>  days_in_year,
>  glob_dump,
>  glob_log10normmin,
>  glob_curr_iter_when_opt,
>  glob_max_hours,
>  glob_log10_relerr,
>  glob_optimal_done,
>  glob_max_sec,
>  glob_max_trunc_err,
>  glob_dump_analytic,
>  glob_large_float,
>  glob_h,
>  glob_almost_1,
>  min_in_hour,
>  glob_start,
>  glob_no_eqs,
>  glob_look_poles,
>  glob_hmin_init,
>  djd_debug2,
>  glob_percent_done,
>  glob_log10abserr,
>  glob_orig_start_sec,
>  glob_hmin,
>  glob_disp_incr,
>  centuries_in_millinium,
>  glob_display_flag,
>  glob_iter,
>  glob_current_iter,
>  glob_max_minutes,
>  MAX_UNCHANGED,
>  glob_unchanged_h_cnt,
>  glob_small_float,
>  sec_in_min,
>  glob_smallish_float,
>  glob_clock_start_sec,
>  glob_clock_sec,
>  #Bottom Generate Globals Decl
>  #BEGIN CONST
>  array_const_2D0,
>  array_const_3D0,
>  array_const_4D0,
>  array_const_1,
>  array_const_0D0,
>  array_const_2,
>  #END CONST
>  array_x2,
>  array_x1,
>  array_t,
>  array_pole,
>  array_norms,
>  array_tmp10,
>  array_tmp11,
>  array_tmp12,
>  array_tmp13,
>  array_tmp14,
>  array_tmp15,
>  array_tmp16,
>  array_tmp17,
>  array_type_pole,
>  array_x1_init,
>  array_m1,
>  array_tmp0,
>  array_tmp1,
>  array_tmp2,
>  array_tmp3,
>  array_tmp4,
>  array_tmp5,
>  array_tmp6,
>  array_tmp7,
>  array_tmp8,
>  array_tmp9,
>  array_last_rel_error,
>  array_1st_rel_error,
>  array_x2_init,
>  array_complex_pole,
>  array_x1_higher,
>  array_real_pole,
>  array_x1_higher_work,
>  array_poles,
>  array_x1_higher_work2,
>  array_x2_higher_work,
>  array_x2_higher_work2,
>  array_x2_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 DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_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
>  DEBUGL,
>  DEBUGMASSIVE,
>  INFO,
>  ALWAYS,
>  glob_max_terms,
>  glob_iolevel,
>  #Top Generate Globals Decl
>  glob_abserr,
>  glob_not_yet_start_msg,
>  glob_not_yet_finished,
>  hours_in_day,
>  glob_max_opt_iter,
>  glob_warned2,
>  glob_warned,
>  glob_optimal_clock_start_sec,
>  glob_last_good_h,
>  glob_hmax,
>  glob_reached_optimal_h,
>  years_in_century,
>  djd_debug,
>  glob_optimal_expect_sec,
>  glob_log10relerr,
>  glob_normmax,
>  glob_max_order,
>  glob_html_log,
>  glob_optimal_start,
>  glob_max_rel_trunc_err,
>  glob_max_iter,
>  glob_relerr,
>  glob_log10_abserr,
>  glob_initial_pass,
>  days_in_year,
>  glob_dump,
>  glob_log10normmin,
>  glob_curr_iter_when_opt,
>  glob_max_hours,
>  glob_log10_relerr,
>  glob_optimal_done,
>  glob_max_sec,
>  glob_max_trunc_err,
>  glob_dump_analytic,
>  glob_large_float,
>  glob_h,
>  glob_almost_1,
>  min_in_hour,
>  glob_start,
>  glob_no_eqs,
>  glob_look_poles,
>  glob_hmin_init,
>  djd_debug2,
>  glob_percent_done,
>  glob_log10abserr,
>  glob_orig_start_sec,
>  glob_hmin,
>  glob_disp_incr,
>  centuries_in_millinium,
>  glob_display_flag,
>  glob_iter,
>  glob_current_iter,
>  glob_max_minutes,
>  MAX_UNCHANGED,
>  glob_unchanged_h_cnt,
>  glob_small_float,
>  sec_in_min,
>  glob_smallish_float,
>  glob_clock_start_sec,
>  glob_clock_sec,
>  #Bottom Generate Globals Decl
>  #BEGIN CONST
>  array_const_2D0,
>  array_const_3D0,
>  array_const_4D0,
>  array_const_1,
>  array_const_0D0,
>  array_const_2,
>  #END CONST
>  array_x2,
>  array_x1,
>  array_t,
>  array_pole,
>  array_norms,
>  array_tmp10,
>  array_tmp11,
>  array_tmp12,
>  array_tmp13,
>  array_tmp14,
>  array_tmp15,
>  array_tmp16,
>  array_tmp17,
>  array_type_pole,
>  array_x1_init,
>  array_m1,
>  array_tmp0,
>  array_tmp1,
>  array_tmp2,
>  array_tmp3,
>  array_tmp4,
>  array_tmp5,
>  array_tmp6,
>  array_tmp7,
>  array_tmp8,
>  array_tmp9,
>  array_last_rel_error,
>  array_1st_rel_error,
>  array_x2_init,
>  array_complex_pole,
>  array_x1_higher,
>  array_real_pole,
>  array_x1_higher_work,
>  array_poles,
>  array_x1_higher_work2,
>  array_x2_higher_work,
>  array_x2_higher_work2,
>  array_x2_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 DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_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
>     DEBUGL,
>     DEBUGMASSIVE,
>     INFO,
>     ALWAYS,
>     glob_max_terms,
>     glob_iolevel,
>     #Top Generate Globals Decl
>     glob_abserr,
>     glob_not_yet_start_msg,
>     glob_not_yet_finished,
>     hours_in_day,
>     glob_max_opt_iter,
>     glob_warned2,
>     glob_warned,
>     glob_optimal_clock_start_sec,
>     glob_last_good_h,
>     glob_hmax,
>     glob_reached_optimal_h,
>     years_in_century,
>     djd_debug,
>     glob_optimal_expect_sec,
>     glob_log10relerr,
>     glob_normmax,
>     glob_max_order,
>     glob_html_log,
>     glob_optimal_start,
>     glob_max_rel_trunc_err,
>     glob_max_iter,
>     glob_relerr,
>     glob_log10_abserr,
>     glob_initial_pass,
>     days_in_year,
>     glob_dump,
>     glob_log10normmin,
>     glob_curr_iter_when_opt,
>     glob_max_hours,
>     glob_log10_relerr,
>     glob_optimal_done,
>     glob_max_sec,
>     glob_max_trunc_err,
>     glob_dump_analytic,
>     glob_large_float,
>     glob_h,
>     glob_almost_1,
>     min_in_hour,
>     glob_start,
>     glob_no_eqs,
>     glob_look_poles,
>     glob_hmin_init,
>     djd_debug2,
>     glob_percent_done,
>     glob_log10abserr,
>     glob_orig_start_sec,
>     glob_hmin,
>     glob_disp_incr,
>     centuries_in_millinium,
>     glob_display_flag,
>     glob_iter,
>     glob_current_iter,
>     glob_max_minutes,
>     MAX_UNCHANGED,
>     glob_unchanged_h_cnt,
>     glob_small_float,
>     sec_in_min,
>     glob_smallish_float,
>     glob_clock_start_sec,
>     glob_clock_sec,
>     #Bottom Generate Globals Decl
>     #BEGIN CONST
>     array_const_2D0,
>     array_const_3D0,
>     array_const_4D0,
>     array_const_1,
>     array_const_0D0,
>     array_const_2,
>     #END CONST
>     array_x2,
>     array_x1,
>     array_t,
>     array_pole,
>     array_norms,
>     array_tmp10,
>     array_tmp11,
>     array_tmp12,
>     array_tmp13,
>     array_tmp14,
>     array_tmp15,
>     array_tmp16,
>     array_tmp17,
>     array_type_pole,
>     array_x1_init,
>     array_m1,
>     array_tmp0,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_tmp4,
>     array_tmp5,
>     array_tmp6,
>     array_tmp7,
>     array_tmp8,
>     array_tmp9,
>     array_last_rel_error,
>     array_1st_rel_error,
>     array_x2_init,
>     array_complex_pole,
>     array_x1_higher,
>     array_real_pole,
>     array_x1_higher_work,
>     array_poles,
>     array_x1_higher_work2,
>     array_x2_higher_work,
>     array_x2_higher_work2,
>     array_x2_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 DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_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
>     DEBUGL,
>     DEBUGMASSIVE,
>     INFO,
>     ALWAYS,
>     glob_max_terms,
>     glob_iolevel,
>     #Top Generate Globals Decl
>     glob_abserr,
>     glob_not_yet_start_msg,
>     glob_not_yet_finished,
>     hours_in_day,
>     glob_max_opt_iter,
>     glob_warned2,
>     glob_warned,
>     glob_optimal_clock_start_sec,
>     glob_last_good_h,
>     glob_hmax,
>     glob_reached_optimal_h,
>     years_in_century,
>     djd_debug,
>     glob_optimal_expect_sec,
>     glob_log10relerr,
>     glob_normmax,
>     glob_max_order,
>     glob_html_log,
>     glob_optimal_start,
>     glob_max_rel_trunc_err,
>     glob_max_iter,
>     glob_relerr,
>     glob_log10_abserr,
>     glob_initial_pass,
>     days_in_year,
>     glob_dump,
>     glob_log10normmin,
>     glob_curr_iter_when_opt,
>     glob_max_hours,
>     glob_log10_relerr,
>     glob_optimal_done,
>     glob_max_sec,
>     glob_max_trunc_err,
>     glob_dump_analytic,
>     glob_large_float,
>     glob_h,
>     glob_almost_1,
>     min_in_hour,
>     glob_start,
>     glob_no_eqs,
>     glob_look_poles,
>     glob_hmin_init,
>     djd_debug2,
>     glob_percent_done,
>     glob_log10abserr,
>     glob_orig_start_sec,
>     glob_hmin,
>     glob_disp_incr,
>     centuries_in_millinium,
>     glob_display_flag,
>     glob_iter,
>     glob_current_iter,
>     glob_max_minutes,
>     MAX_UNCHANGED,
>     glob_unchanged_h_cnt,
>     glob_small_float,
>     sec_in_min,
>     glob_smallish_float,
>     glob_clock_start_sec,
>     glob_clock_sec,
>     #Bottom Generate Globals Decl
>     #BEGIN CONST
>     array_const_2D0,
>     array_const_3D0,
>     array_const_4D0,
>     array_const_1,
>     array_const_0D0,
>     array_const_2,
>     #END CONST
>     array_x2,
>     array_x1,
>     array_t,
>     array_pole,
>     array_norms,
>     array_tmp10,
>     array_tmp11,
>     array_tmp12,
>     array_tmp13,
>     array_tmp14,
>     array_tmp15,
>     array_tmp16,
>     array_tmp17,
>     array_type_pole,
>     array_x1_init,
>     array_m1,
>     array_tmp0,
>     array_tmp1,
>     array_tmp2,
>     array_tmp3,
>     array_tmp4,
>     array_tmp5,
>     array_tmp6,
>     array_tmp7,
>     array_tmp8,
>     array_tmp9,
>     array_last_rel_error,
>     array_1st_rel_error,
>     array_x2_init,
>     array_complex_pole,
>     array_x1_higher,
>     array_real_pole,
>     array_x1_higher_work,
>     array_poles,
>     array_x1_higher_work2,
>     array_x2_higher_work,
>     array_x2_higher_work2,
>     array_x2_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 DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_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
>   DEBUGL,
>   DEBUGMASSIVE,
>   INFO,
>   ALWAYS,
>   glob_max_terms,
>   glob_iolevel,
>   #Top Generate Globals Decl
>   glob_abserr,
>   glob_not_yet_start_msg,
>   glob_not_yet_finished,
>   hours_in_day,
>   glob_max_opt_iter,
>   glob_warned2,
>   glob_warned,
>   glob_optimal_clock_start_sec,
>   glob_last_good_h,
>   glob_hmax,
>   glob_reached_optimal_h,
>   years_in_century,
>   djd_debug,
>   glob_optimal_expect_sec,
>   glob_log10relerr,
>   glob_normmax,
>   glob_max_order,
>   glob_html_log,
>   glob_optimal_start,
>   glob_max_rel_trunc_err,
>   glob_max_iter,
>   glob_relerr,
>   glob_log10_abserr,
>   glob_initial_pass,
>   days_in_year,
>   glob_dump,
>   glob_log10normmin,
>   glob_curr_iter_when_opt,
>   glob_max_hours,
>   glob_log10_relerr,
>   glob_optimal_done,
>   glob_max_sec,
>   glob_max_trunc_err,
>   glob_dump_analytic,
>   glob_large_float,
>   glob_h,
>   glob_almost_1,
>   min_in_hour,
>   glob_start,
>   glob_no_eqs,
>   glob_look_poles,
>   glob_hmin_init,
>   djd_debug2,
>   glob_percent_done,
>   glob_log10abserr,
>   glob_orig_start_sec,
>   glob_hmin,
>   glob_disp_incr,
>   centuries_in_millinium,
>   glob_display_flag,
>   glob_iter,
>   glob_current_iter,
>   glob_max_minutes,
>   MAX_UNCHANGED,
>   glob_unchanged_h_cnt,
>   glob_small_float,
>   sec_in_min,
>   glob_smallish_float,
>   glob_clock_start_sec,
>   glob_clock_sec,
>   #Bottom Generate Globals Decl
>   #BEGIN CONST
>   array_const_2D0,
>   array_const_3D0,
>   array_const_4D0,
>   array_const_1,
>   array_const_0D0,
>   array_const_2,
>   #END CONST
>   array_x2,
>   array_x1,
>   array_t,
>   array_pole,
>   array_norms,
>   array_tmp10,
>   array_tmp11,
>   array_tmp12,
>   array_tmp13,
>   array_tmp14,
>   array_tmp15,
>   array_tmp16,
>   array_tmp17,
>   array_type_pole,
>   array_x1_init,
>   array_m1,
>   array_tmp0,
>   array_tmp1,
>   array_tmp2,
>   array_tmp3,
>   array_tmp4,
>   array_tmp5,
>   array_tmp6,
>   array_tmp7,
>   array_tmp8,
>   array_tmp9,
>   array_last_rel_error,
>   array_1st_rel_error,
>   array_x2_init,
>   array_complex_pole,
>   array_x1_higher,
>   array_real_pole,
>   array_x1_higher_work,
>   array_poles,
>   array_x1_higher_work2,
>   array_x2_higher_work,
>   array_x2_higher_work2,
>   array_x2_higher,
>   glob_last;
>   glob_last;
>   ALWAYS := 1;
>   INFO := 2;
>   DEBUGL := 3;
>   DEBUGMASSIVE := 4;
>   glob_iolevel := INFO;
>   DEBUGL := 3;
>   DEBUGMASSIVE := 4;
>   INFO := 2;
>   ALWAYS := 1;
>   glob_max_terms := 30;
>   glob_iolevel := 5;
>   glob_abserr := 0.1e-10;
>   glob_not_yet_start_msg := true;
>   glob_not_yet_finished := true;
>   hours_in_day := 24.0;
>   glob_max_opt_iter := 10;
>   glob_warned2 := false;
>   glob_warned := false;
>   glob_optimal_clock_start_sec := 0.0;
>   glob_last_good_h := 0.1;
>   glob_hmax := 1.0;
>   glob_reached_optimal_h := false;
>   years_in_century := 100.0;
>   djd_debug := true;
>   glob_optimal_expect_sec := 0.1;
>   glob_log10relerr := 0.0;
>   glob_normmax := 0.0;
>   glob_max_order := 30;
>   glob_html_log := true;
>   glob_optimal_start := 0.0;
>   glob_max_rel_trunc_err := 0.1e-10;
>   glob_max_iter := 1000;
>   glob_relerr := 0.1e-10;
>   glob_log10_abserr := 0.1e-10;
>   glob_initial_pass := true;
>   days_in_year := 365.0;
>   glob_dump := false;
>   glob_log10normmin := 0.1;
>   glob_curr_iter_when_opt := 0;
>   glob_max_hours := 0.0;
>   glob_log10_relerr := 0.1e-10;
>   glob_optimal_done := false;
>   glob_max_sec := 10000.0;
>   glob_max_trunc_err := 0.1e-10;
>   glob_dump_analytic := false;
>   glob_large_float := 9.0e100;
>   glob_h := 0.1;
>   glob_almost_1 := 0.9990;
>   min_in_hour := 60.0;
>   glob_start := 0;
>   glob_no_eqs := 0;
>   glob_look_poles := false;
>   glob_hmin_init := 0.001;
>   djd_debug2 := true;
>   glob_percent_done := 0.0;
>   glob_log10abserr := 0.0;
>   glob_orig_start_sec := 0.0;
>   glob_hmin := 0.00000000001;
>   glob_disp_incr := 0.1;
>   centuries_in_millinium := 10.0;
>   glob_display_flag := true;
>   glob_iter := 0;
>   glob_current_iter := 0;
>   glob_max_minutes := 0.0;
>   MAX_UNCHANGED := 10;
>   glob_unchanged_h_cnt := 0;
>   glob_small_float := 0.1e-50;
>   sec_in_min := 60.0;
>   glob_smallish_float := 0.1e-100;
>   glob_clock_start_sec := 0.0;
>   glob_clock_sec := 0.0;
>   #Write Set Defaults
>   glob_orig_start_sec   :=  elapsed_time_seconds();
>   MAX_UNCHANGED   := 10;
>   glob_curr_iter_when_opt   :=  0;
>   glob_display_flag   :=   true;
>   glob_max_order   := 2;
>   glob_no_eqs   := 2;
>   glob_iter   :=  -1;
>   opt_iter   :=  -1;
>   glob_max_iter   :=  50000;
>   glob_max_hours   :=  0.0;
>   glob_max_minutes   :=  15.0;
>   omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
>   omniout_str(ALWAYS,"##############temp/complicatedrevpostode.ode#################");
>   omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
>   omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;");
>   omniout_str(ALWAYS,"!");
>   omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>   omniout_str(ALWAYS,"Digits := 32;");
>   omniout_str(ALWAYS,"max_terms := 30;");
>   omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>   omniout_str(ALWAYS,"!");
>   omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>   omniout_str(ALWAYS,"t_start := 0.5;");
>   omniout_str(ALWAYS,"t_end := 5.0;");
>   omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);");
>   omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);");
>   omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);");
>   omniout_str(ALWAYS,"glob_h := 0.00001 ;");
>   omniout_str(ALWAYS,"glob_look_poles := true;");
>   omniout_str(ALWAYS,"glob_max_iter := 10;");
>   omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
>   omniout_str(ALWAYS,"#BEGIN OVERRIDE  BLOCK");
>   omniout_str(ALWAYS,"glob_h := 0.00005 ;");
>   omniout_str(ALWAYS,"glob_look_poles := true;");
>   omniout_str(ALWAYS,"glob_max_iter := 100;");
>   omniout_str(ALWAYS,"glob_max_minutes := 15;");
>   omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>   omniout_str(ALWAYS,"!");
>   omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>   omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
>   omniout_str(ALWAYS,"local c1,c2,c3;");
>   omniout_str(ALWAYS,"c1 := 0.0001;");
>   omniout_str(ALWAYS,"c2 := 0.0002;");
>   omniout_str(ALWAYS,"c3 := 0.0003;");
>   omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);");
>   omniout_str(ALWAYS,"end;");
>   omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
>   omniout_str(ALWAYS,"local c1,c2,c3;");
>   omniout_str(ALWAYS,"c1 := 0.0001;");
>   omniout_str(ALWAYS,"c2 := 0.0002;");
>   omniout_str(ALWAYS,"c3 := 0.0003;");
>   omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
>   omniout_str(ALWAYS,"end;");
>   omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
>   omniout_str(ALWAYS,"local c1,c2,c3;");
>   omniout_str(ALWAYS,"c1 := 0.0001;");
>   omniout_str(ALWAYS,"c2 := 0.0002;");
>   omniout_str(ALWAYS,"c3 := 0.0003;");
>   omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
>   omniout_str(ALWAYS,"end;");
>   omniout_str(ALWAYS,"#END USER DEF BLOCK");
>   omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>   glob_unchanged_h_cnt   :=  0;
>   glob_warned   :=  false;
>   glob_warned2   :=  false;
>   glob_small_float   :=  1.0e-200;
>   glob_smallish_float   :=  1.0e-64;
>   glob_large_float   :=  1.0e100;
>   glob_almost_1   :=  0.99;
>   glob_log10_abserr   :=  -8.0;
>   glob_log10_relerr   :=  -8.0;
>   glob_hmax   :=  0.01;
>   #BEGIN FIRST INPUT BLOCK
>   #BEGIN FIRST INPUT BLOCK
>   Digits := 32;
>   max_terms := 30;
>   #END FIRST INPUT BLOCK
>   #END FIRST INPUT BLOCK
>   #START OF INITS AFTER INPUT BLOCK
>   glob_max_terms := max_terms;
>   glob_html_log := true;
>   #END OF INITS AFTER INPUT BLOCK
>   array_x2:= Array(1..(max_terms + 1),[]);
>   array_x1:= Array(1..(max_terms + 1),[]);
>   array_t:= Array(1..(max_terms + 1),[]);
>   array_pole:= Array(1..(max_terms + 1),[]);
>   array_norms:= Array(1..(max_terms + 1),[]);
>   array_tmp10:= Array(1..(max_terms + 1),[]);
>   array_tmp11:= Array(1..(max_terms + 1),[]);
>   array_tmp12:= Array(1..(max_terms + 1),[]);
>   array_tmp13:= Array(1..(max_terms + 1),[]);
>   array_tmp14:= Array(1..(max_terms + 1),[]);
>   array_tmp15:= Array(1..(max_terms + 1),[]);
>   array_tmp16:= Array(1..(max_terms + 1),[]);
>   array_tmp17:= Array(1..(max_terms + 1),[]);
>   array_type_pole:= Array(1..(max_terms + 1),[]);
>   array_x1_init:= Array(1..(max_terms + 1),[]);
>   array_m1:= Array(1..(max_terms + 1),[]);
>   array_tmp0:= Array(1..(max_terms + 1),[]);
>   array_tmp1:= Array(1..(max_terms + 1),[]);
>   array_tmp2:= Array(1..(max_terms + 1),[]);
>   array_tmp3:= Array(1..(max_terms + 1),[]);
>   array_tmp4:= Array(1..(max_terms + 1),[]);
>   array_tmp5:= Array(1..(max_terms + 1),[]);
>   array_tmp6:= Array(1..(max_terms + 1),[]);
>   array_tmp7:= Array(1..(max_terms + 1),[]);
>   array_tmp8:= Array(1..(max_terms + 1),[]);
>   array_tmp9:= Array(1..(max_terms + 1),[]);
>   array_last_rel_error:= Array(1..(max_terms + 1),[]);
>   array_1st_rel_error:= Array(1..(max_terms + 1),[]);
>   array_x2_init:= Array(1..(max_terms + 1),[]);
>   array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
>   array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
>   array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
>   array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
>   array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
>   array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
>   array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
>   array_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
>   array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
>   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_t[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_pole[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_norms[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_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_x1_init[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_m1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp0[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp2[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp3[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp4[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp5[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp6[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp7[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp8[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp9[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_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_1st_rel_error[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_x2_init[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   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[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=2 do # do number 2
>  term := 1;
>  while term <= 3 do # do number 3
>   array_real_pole[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=2 do # do number 2
>  term := 1;
>  while term <= max_terms do # do number 3
>   array_x1_higher_work[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=2 do # do number 2
>  term := 1;
>  while term <= 3 do # do number 3
>   array_poles[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=2 do # do number 2
>  term := 1;
>  while term <= max_terms do # do number 3
>   array_x1_higher_work2[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=3 do # do number 2
>  term := 1;
>  while term <= max_terms do # do number 3
>   array_x2_higher_work[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=3 do # do number 2
>  term := 1;
>  while term <= max_terms do # do number 3
>   array_x2_higher_work2[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=3 do # do number 2
>  term := 1;
>  while term <= max_terms do # do number 3
>   array_x2_higher[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_t := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_t[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp17 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp17[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp16 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp16[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp15 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp15[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp14 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp14[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp13 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp13[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp12 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp12[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp11 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp11[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp10 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp10[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp9 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp9[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp8 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp8[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp7 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp7[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp6 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp6[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp5 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp5[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp4 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp4[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp3 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp3[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp2 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp2[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp1 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_tmp0 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_tmp0[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_const_2D0[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_const_2D0[1]   := 2.0;
>   array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_const_3D0[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_const_3D0[1]   := 3.0;
>   array_const_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_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_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_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_m1 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_m1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_m1[1]   :=  -1.0;
>   #END ARRAYS DEFINED AND INITIALIZATED
>   #TOP SECOND INPUT BLOCK
>   #BEGIN SECOND INPUT BLOCK
>   #BEGIN SECOND INPUT BLOCK
>   t_start := 0.5;
>   t_end := 5.0;
>   array_x1_init[1] := exact_soln_x1(t_start);
>   array_x2_init[1] := exact_soln_x2(t_start);
>   array_x2_init[2] := exact_soln_x2p(t_start);
>   glob_h := 0.00001 ;
>   glob_look_poles := true;
>   glob_max_iter := 10;
>   #END SECOND INPUT BLOCK
>   #BEGIN OVERRIDE  BLOCK
>   glob_h := 0.00005 ;
>   glob_look_poles := true;
>   glob_max_iter := 100;
>   glob_max_minutes := 15;
>   #END OVERRIDE BLOCK
>   #END SECOND INPUT BLOCK
>   #BEGIN INITS AFTER SECOND INPUT BLOCK
>   glob_last_good_h := glob_h;
>   glob_max_terms   := max_terms;
>   glob_max_sec   := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
>   glob_abserr   :=  10.0 ^ (glob_log10_abserr);
>   glob_relerr   :=  10.0 ^ (glob_log10_relerr);
>   chk_data();
>   #AFTER INITS AFTER SECOND INPUT BLOCK
>   if glob_html_log  then # if number 3
>       html_log_file := fopen("html/entry.html",WRITE,TEXT);
>       fi;# end if 3
>     ;
>     #BEGIN SOLUTION CODE
>     omniout_str(ALWAYS,"START of Soultion");
>     #Start Series -- INITIALIZE FOR SOLUTION
>     array_t[1]   := t_start;
>     array_t[2]   :=  glob_h;
>     order_diff := 2;
>     #Start Series array_x2
>     term_no   :=  1;
>     while (term_no <= order_diff) do # do number 2
>       array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
>       term_no   :=  term_no + 1;
>       od;# end do number 2
>     ;
>     rows   :=  order_diff;
>     r_order   :=  1;
>     while (r_order <= rows) do # do number 2
>       term_no   :=  1;
>       while (term_no <= (rows - r_order + 1)) do # do number 3
>         it  := term_no + r_order - 1;
>         array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
>         term_no   :=  term_no + 1;
>         od;# end do number 3
>       ;
>       r_order   :=  r_order + 1;
>       od;# end do number 2
>     ;
>     order_diff := 1;
>     #Start Series array_x1
>     term_no   :=  1;
>     while (term_no <= order_diff) do # do number 2
>       array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
>       term_no   :=  term_no + 1;
>       od;# end do number 2
>     ;
>     rows   :=  order_diff;
>     r_order   :=  1;
>     while (r_order <= rows) do # do number 2
>       term_no   :=  1;
>       while (term_no <= (rows - r_order + 1)) do # do number 3
>         it  := term_no + r_order - 1;
>         array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
>         term_no   :=  term_no + 1;
>         od;# end do number 3
>       ;
>       r_order   :=  r_order + 1;
>       od;# end do number 2
>     ;
>     current_iter   :=  1;
>     glob_clock_start_sec   := elapsed_time_seconds();
>     start_array_x2();
>     if (abs(array_x2_higher[1,1]) > glob_small_float)  then # if number 3
>       tmp   :=  abs(array_x2_higher[1,1]);
>       log10norm   :=  (log10(tmp));
>       if (log10norm < glob_log10normmin)  then # if number 4
>         glob_log10normmin   :=  log10norm;
>         fi;# end if 4
>       fi;# end if 3
>     ;
>     display_alot(current_iter)
>     ;
>     start_array_x1();
>     if (abs(array_x1_higher[1,1]) > glob_small_float)  then # if number 3
>       tmp   :=  abs(array_x1_higher[1,1]);
>       log10norm   :=  (log10(tmp));
>       if (log10norm < glob_log10normmin)  then # if number 4
>         glob_log10normmin   :=  log10norm;
>         fi;# end if 4
>       fi;# end if 3
>     ;
>     display_alot(current_iter)
>     ;
>     glob_clock_sec   :=  elapsed_time_seconds();
>     glob_current_iter   :=  0;
>     glob_iter   :=  0;
>     omniout_str(DEBUGL," ");
>     glob_reached_optimal_h   :=  true;
>     glob_optimal_clock_start_sec := elapsed_time_seconds();
>     while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
>       #left paren 0001C
>       omniout_str(INFO," ");
>       omniout_str(INFO,"TOP MAIN SOLVE Loop");
>       glob_iter   :=  glob_iter + 1;
>       glob_clock_sec   := elapsed_time_seconds();
>       glob_current_iter   :=  glob_current_iter + 1;
>       atomall();
>       if (glob_look_poles)  then # if number 3
>         #left paren 0004C
>         check_for_pole();
>         fi;# end if 3
>       ;#was right paren 0004C
>       array_t[1]   := array_t[1] + glob_h;
>       array_t[2]   :=  glob_h;
>       order_diff := 2;
>       #Jump Series array_x2
>       #START PART 1  SUM AND ADJUST
>       #START SUM AND ADJUST EQ =1
>       #sum_and_adjust array_x2
>       order_diff := 2;
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 2;
>       ord := 3;
>       calc_term := 1;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 3;
>       calc_term := 1;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 2;
>       ord := 2;
>       calc_term := 2;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 2;
>       calc_term := 2;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 2;
>       ord := 2;
>       calc_term := 1;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 2;
>       calc_term := 1;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 2;
>       ord := 1;
>       calc_term := 3;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 3;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 2;
>       ord := 1;
>       calc_term := 2;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 2;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 2;
>       ord := 1;
>       calc_term := 1;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 1;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #END SUM AND ADJUST EQ =1
>       #END PART 1
>       #START PART 2  MOVE TERMS to REGULAR Array
>       term_no := glob_max_terms;
>       while (term_no >= 1) do # do number 3
>         array_x2[term_no] := array_x2_higher_work2[1,term_no];
>         ord := 1;
>         while ord <= order_diff  do # do number 4
>           array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no];
>           ord := ord + 1;
>           od;# end do number 4
>         ;
>         term_no   :=  term_no - 1;
>         od;# end do number 3
>       ;
>       #END PART 2 HEVE MOVED TERMS to REGULAR Array
>       order_diff := 1;
>       #Jump Series array_x1
>       #START PART 1  SUM AND ADJUST
>       #START SUM AND ADJUST EQ =2
>       #sum_and_adjust array_x1
>       order_diff := 1;
>       #BEFORE ADJUST SUBSERIES EQ =2
>       order_diff := 1;
>       ord := 2;
>       calc_term := 1;
>       #adjust_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =2
>       #BEFORE SUM SUBSERIES EQ =2
>       order_diff := 1;
>       temp_sum := 0.0;
>       ord := 2;
>       calc_term := 1;
>       #sum_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x1_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =2
>       #BEFORE ADJUST SUBSERIES EQ =2
>       order_diff := 1;
>       ord := 1;
>       calc_term := 2;
>       #adjust_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =2
>       #BEFORE SUM SUBSERIES EQ =2
>       order_diff := 1;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 2;
>       #sum_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x1_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =2
>       #BEFORE ADJUST SUBSERIES EQ =2
>       order_diff := 1;
>       ord := 1;
>       calc_term := 1;
>       #adjust_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =2
>       #BEFORE SUM SUBSERIES EQ =2
>       order_diff := 1;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 1;
>       #sum_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x1_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =2
>       #END SUM AND ADJUST EQ =2
>       #END PART 1
>       #START PART 2  MOVE TERMS to REGULAR Array
>       term_no := glob_max_terms;
>       while (term_no >= 1) do # do number 3
>         array_x1[term_no] := array_x1_higher_work2[1,term_no];
>         ord := 1;
>         while ord <= order_diff  do # do number 4
>           array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no];
>           ord := ord + 1;
>           od;# end do number 4
>         ;
>         term_no   :=  term_no - 1;
>         od;# end do number 3
>       ;
>       #END PART 2 HEVE MOVED TERMS to REGULAR Array
>       display_alot(current_iter)
>       ;
>       od;# end do number 2
>     ;#right paren 0001C
>     omniout_str(ALWAYS,"Finished!");
>     if (glob_iter >= glob_max_iter)  then # if number 3
>       omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
>       fi;# end if 3
>     ;
>     if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec  )) then # if number 3
>       omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
>       fi;# end if 3
>     ;
>     glob_clock_sec   := elapsed_time_seconds();
>     omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
>     omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;");
>     omniout_int(INFO,"Iterations                       ",32,glob_iter,4," ")
>     ;
>     prog_report(t_start,t_end);
>     if glob_html_log  then # if number 3
>       logstart(html_log_file);
>       logitem_str(html_log_file,"2012-06-02T02:11:39-05:00")
>       ;
>       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 DEBUGL, DEBUGMASSIVE, INFO, ALWAYS, glob_max_terms, glob_iolevel,
glob_abserr, glob_not_yet_start_msg, glob_not_yet_finished, hours_in_day,
glob_max_opt_iter, glob_warned2, glob_warned, glob_optimal_clock_start_sec,
glob_last_good_h, glob_hmax, glob_reached_optimal_h, years_in_century,
djd_debug, glob_optimal_expect_sec, glob_log10relerr, glob_normmax,
glob_max_order, glob_html_log, glob_optimal_start, glob_max_rel_trunc_err,
glob_max_iter, glob_relerr, glob_log10_abserr, glob_initial_pass,
days_in_year, glob_dump, glob_log10normmin, glob_curr_iter_when_opt,
glob_max_hours, glob_log10_relerr, glob_optimal_done, glob_max_sec,
glob_max_trunc_err, glob_dump_analytic, glob_large_float, glob_h,
glob_almost_1, min_in_hour, glob_start, glob_no_eqs, glob_look_poles,
glob_hmin_init, djd_debug2, glob_percent_done, glob_log10abserr,
glob_orig_start_sec, glob_hmin, glob_disp_incr, centuries_in_millinium,
glob_display_flag, glob_iter, glob_current_iter, glob_max_minutes,
MAX_UNCHANGED, glob_unchanged_h_cnt, glob_small_float, sec_in_min,
glob_smallish_float, glob_clock_start_sec, glob_clock_sec, array_const_2D0,
array_const_3D0, array_const_4D0, array_const_1, array_const_0D0,
array_const_2, array_x2, array_x1, array_t, array_pole, array_norms,
array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_type_pole, array_x1_init,
array_m1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_tmp6, array_tmp7, array_tmp8, array_tmp9,
array_last_rel_error, array_1st_rel_error, array_x2_init,
array_complex_pole, array_x1_higher, array_real_pole, array_x1_higher_work,
array_poles, array_x1_higher_work2, array_x2_higher_work,
array_x2_higher_work2, array_x2_higher, glob_last;
    glob_last;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    glob_iolevel := INFO;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    INFO := 2;
    ALWAYS := 1;
    glob_max_terms := 30;
    glob_iolevel := 5;
    glob_abserr := 0.1*10^(-10);
    glob_not_yet_start_msg := true;
    glob_not_yet_finished := true;
    hours_in_day := 24.0;
    glob_max_opt_iter := 10;
    glob_warned2 := false;
    glob_warned := false;
    glob_optimal_clock_start_sec := 0.;
    glob_last_good_h := 0.1;
    glob_hmax := 1.0;
    glob_reached_optimal_h := false;
    years_in_century := 100.0;
    djd_debug := true;
    glob_optimal_expect_sec := 0.1;
    glob_log10relerr := 0.;
    glob_normmax := 0.;
    glob_max_order := 30;
    glob_html_log := true;
    glob_optimal_start := 0.;
    glob_max_rel_trunc_err := 0.1*10^(-10);
    glob_max_iter := 1000;
    glob_relerr := 0.1*10^(-10);
    glob_log10_abserr := 0.1*10^(-10);
    glob_initial_pass := true;
    days_in_year := 365.0;
    glob_dump := false;
    glob_log10normmin := 0.1;
    glob_curr_iter_when_opt := 0;
    glob_max_hours := 0.;
    glob_log10_relerr := 0.1*10^(-10);
    glob_optimal_done := false;
    glob_max_sec := 10000.0;
    glob_max_trunc_err := 0.1*10^(-10);
    glob_dump_analytic := false;
    glob_large_float := 0.90*10^101;
    glob_h := 0.1;
    glob_almost_1 := 0.9990;
    min_in_hour := 60.0;
    glob_start := 0;
    glob_no_eqs := 0;
    glob_look_poles := false;
    glob_hmin_init := 0.001;
    djd_debug2 := true;
    glob_percent_done := 0.;
    glob_log10abserr := 0.;
    glob_orig_start_sec := 0.;
    glob_hmin := 0.1*10^(-10);
    glob_disp_incr := 0.1;
    centuries_in_millinium := 10.0;
    glob_display_flag := true;
    glob_iter := 0;
    glob_current_iter := 0;
    glob_max_minutes := 0.;
    MAX_UNCHANGED := 10;
    glob_unchanged_h_cnt := 0;
    glob_small_float := 0.1*10^(-50);
    sec_in_min := 60.0;
    glob_smallish_float := 0.1*10^(-100);
    glob_clock_start_sec := 0.;
    glob_clock_sec := 0.;
    glob_orig_start_sec := elapsed_time_seconds();
    MAX_UNCHANGED := 10;
    glob_curr_iter_when_opt := 0;
    glob_display_flag := true;
    glob_max_order := 2;
    glob_no_eqs := 2;
    glob_iter := -1;
    opt_iter := -1;
    glob_max_iter := 50000;
    glob_max_hours := 0.;
    glob_max_minutes := 15.0;
    omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
    omniout_str(ALWAYS,
        "##############temp/complicatedrevpostode.ode#################");
    omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \
        diff(x1,t,2) - diff (x1,t,1) + x1;");
    omniout_str(ALWAYS,
        "diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits := 32;");
    omniout_str(ALWAYS, "max_terms := 30;");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "t_start := 0.5;");
    omniout_str(ALWAYS, "t_end := 5.0;");
    omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);");
    omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);");
    omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);");
    omniout_str(ALWAYS, "glob_h := 0.00001 ;");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "glob_max_iter := 10;");
    omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN OVERRIDE  BLOCK");
    omniout_str(ALWAYS, "glob_h := 0.00005 ;");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "glob_max_iter := 100;");
    omniout_str(ALWAYS, "glob_max_minutes := 15;");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := 0.0001;");
    omniout_str(ALWAYS, "c2 := 0.0002;");
    omniout_str(ALWAYS, "c3 := 0.0003;");
    omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := 0.0001;");
    omniout_str(ALWAYS, "c2 := 0.0002;");
    omniout_str(ALWAYS, "c3 := 0.0003;");
    omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := 0.0001;");
    omniout_str(ALWAYS, "c2 := 0.0002;");
    omniout_str(ALWAYS, "c3 := 0.0003;");
    omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := 0.10*10^(-199);
    glob_smallish_float := 0.10*10^(-63);
    glob_large_float := 0.10*10^101;
    glob_almost_1 := 0.99;
    glob_log10_abserr := -8.0;
    glob_log10_relerr := -8.0;
    glob_hmax := 0.01;
    Digits := 32;
    max_terms := 30;
    glob_max_terms := max_terms;
    glob_html_log := true;
    array_x2 := Array(1 .. max_terms + 1, []);
    array_x1 := Array(1 .. max_terms + 1, []);
    array_t := Array(1 .. max_terms + 1, []);
    array_pole := Array(1 .. max_terms + 1, []);
    array_norms := Array(1 .. max_terms + 1, []);
    array_tmp10 := Array(1 .. max_terms + 1, []);
    array_tmp11 := Array(1 .. max_terms + 1, []);
    array_tmp12 := Array(1 .. max_terms + 1, []);
    array_tmp13 := Array(1 .. max_terms + 1, []);
    array_tmp14 := Array(1 .. max_terms + 1, []);
    array_tmp15 := Array(1 .. max_terms + 1, []);
    array_tmp16 := Array(1 .. max_terms + 1, []);
    array_tmp17 := Array(1 .. max_terms + 1, []);
    array_type_pole := Array(1 .. max_terms + 1, []);
    array_x1_init := Array(1 .. max_terms + 1, []);
    array_m1 := Array(1 .. max_terms + 1, []);
    array_tmp0 := Array(1 .. max_terms + 1, []);
    array_tmp1 := Array(1 .. max_terms + 1, []);
    array_tmp2 := Array(1 .. max_terms + 1, []);
    array_tmp3 := Array(1 .. max_terms + 1, []);
    array_tmp4 := Array(1 .. max_terms + 1, []);
    array_tmp5 := Array(1 .. max_terms + 1, []);
    array_tmp6 := Array(1 .. max_terms + 1, []);
    array_tmp7 := Array(1 .. max_terms + 1, []);
    array_tmp8 := Array(1 .. max_terms + 1, []);
    array_tmp9 := Array(1 .. max_terms + 1, []);
    array_last_rel_error := Array(1 .. max_terms + 1, []);
    array_1st_rel_error := Array(1 .. max_terms + 1, []);
    array_x2_init := Array(1 .. max_terms + 1, []);
    array_complex_pole := Array(1 .. 3, 1 .. 4, []);
    array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
    array_real_pole := Array(1 .. 3, 1 .. 4, []);
    array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
    array_poles := Array(1 .. 3, 1 .. 4, []);
    array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
    array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
    array_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
    array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
    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_t[term] := 0.; term := term + 1 end do
    ;
    term := 1;
    while term <= max_terms do array_pole[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_norms[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_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_x1_init[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_m1[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp7[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do
        array_last_rel_error[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do
        array_1st_rel_error[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_x2_init[term] := 0.; term := term + 1
    end do;
    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[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do
            array_real_pole[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= max_terms do
            array_x1_higher_work[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= max_terms do
            array_x1_higher_work2[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= max_terms do
            array_x2_higher_work[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= max_terms do
            array_x2_higher_work2[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= max_terms do
            array_x2_higher[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_t := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1
    end do;
    array_tmp17 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp17[term] := 0.; term := term + 1
    end do;
    array_tmp16 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp16[term] := 0.; term := term + 1
    end do;
    array_tmp15 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp15[term] := 0.; term := term + 1
    end do;
    array_tmp14 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp14[term] := 0.; term := term + 1
    end do;
    array_tmp13 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp13[term] := 0.; term := term + 1
    end do;
    array_tmp12 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp12[term] := 0.; term := term + 1
    end do;
    array_tmp11 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp11[term] := 0.; term := term + 1
    end do;
    array_tmp10 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_tmp10[term] := 0.; term := term + 1
    end do;
    array_tmp9 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1
    end do;
    array_tmp8 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
    end do;
    array_tmp7 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1
    end do;
    array_tmp6 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
    end do;
    array_tmp5 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
    end do;
    array_tmp4 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
    end do;
    array_tmp3 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
    end do;
    array_tmp2 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
    end do;
    array_tmp1 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
    end do;
    array_tmp0 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
    end do;
    array_const_2D0 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_const_2D0[term] := 0.; term := term + 1
    end do;
    array_const_2D0[1] := 2.0;
    array_const_3D0 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_const_3D0[term] := 0.; term := term + 1
    end do;
    array_const_3D0[1] := 3.0;
    array_const_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_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_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_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_m1 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms do array_m1[term] := 0.; term := term + 1
    end do;
    array_m1[1] := -1.0;
    t_start := 0.5;
    t_end := 5.0;
    array_x1_init[1] := exact_soln_x1(t_start);
    array_x2_init[1] := exact_soln_x2(t_start);
    array_x2_init[2] := exact_soln_x2p(t_start);
    glob_h := 0.00001;
    glob_look_poles := true;
    glob_max_iter := 10;
    glob_h := 0.00005;
    glob_look_poles := true;
    glob_max_iter := 100;
    glob_max_minutes := 15;
    glob_last_good_h := glob_h;
    glob_max_terms := max_terms;
    glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
         + convfloat(3600.0)*convfloat(glob_max_hours);
    glob_abserr := 10.0^glob_log10_abserr;
    glob_relerr := 10.0^glob_log10_relerr;
    chk_data();
    if glob_html_log then
        html_log_file := fopen("html/entry.html", WRITE, TEXT)
    end if;
    omniout_str(ALWAYS, "START of Soultion");
    array_t[1] := t_start;
    array_t[2] := glob_h;
    order_diff := 2;
    term_no := 1;
    while term_no <= order_diff do
        array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/
            factorial_1(term_no - 1);
        term_no := term_no + 1
    end do;
    rows := order_diff;
    r_order := 1;
    while r_order <= rows do
        term_no := 1;
        while term_no <= rows - r_order + 1 do
            it := term_no + r_order - 1;
            array_x2_higher[r_order, term_no] := array_x2_init[it]*
                glob_h^(term_no - 1)/factorial_1(term_no - 1);
            term_no := term_no + 1
        end do;
        r_order := r_order + 1
    end do;
    order_diff := 1;
    term_no := 1;
    while term_no <= order_diff do
        array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/
            factorial_1(term_no - 1);
        term_no := term_no + 1
    end do;
    rows := order_diff;
    r_order := 1;
    while r_order <= rows do
        term_no := 1;
        while term_no <= rows - r_order + 1 do
            it := term_no + r_order - 1;
            array_x1_higher[r_order, term_no] := array_x1_init[it]*
                glob_h^(term_no - 1)/factorial_1(term_no - 1);
            term_no := term_no + 1
        end do;
        r_order := r_order + 1
    end do;
    current_iter := 1;
    glob_clock_start_sec := elapsed_time_seconds();
    start_array_x2();
    if glob_small_float < abs(array_x2_higher[1, 1]) then
        tmp := abs(array_x2_higher[1, 1]);
        log10norm := log10(tmp);
        if log10norm < glob_log10normmin then
            glob_log10normmin := log10norm
        end if
    end if;
    display_alot(current_iter);
    start_array_x1();
    if glob_small_float < abs(array_x1_higher[1, 1]) then
        tmp := abs(array_x1_higher[1, 1]);
        log10norm := log10(tmp);
        if log10norm < glob_log10normmin then
            glob_log10normmin := log10norm
        end if
    end if;
    display_alot(current_iter);
    glob_clock_sec := elapsed_time_seconds();
    glob_current_iter := 0;
    glob_iter := 0;
    omniout_str(DEBUGL, " ");
    glob_reached_optimal_h := true;
    glob_optimal_clock_start_sec := elapsed_time_seconds();
    while glob_current_iter < glob_max_iter and array_t[1] <= t_end and
    convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
    convfloat(glob_max_sec) do
        omniout_str(INFO, " ");
        omniout_str(INFO, "TOP MAIN SOLVE Loop");
        glob_iter := glob_iter + 1;
        glob_clock_sec := elapsed_time_seconds();
        glob_current_iter := glob_current_iter + 1;
        atomall();
        if glob_look_poles then check_for_pole() end if;
        array_t[1] := array_t[1] + glob_h;
        array_t[2] := glob_h;
        order_diff := 2;
        order_diff := 2;
        order_diff := 2;
        ord := 3;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 3;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 2;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 2;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 2;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 2;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 1;
        calc_term := 3;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 1;
        calc_term := 3;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 1;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 1;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 1;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 1;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        term_no := glob_max_terms;
        while 1 <= term_no do
            array_x2[term_no] := array_x2_higher_work2[1, term_no];
            ord := 1;
            while ord <= order_diff do
                array_x2_higher[ord, term_no] :=
                    array_x2_higher_work2[ord, term_no];
                ord := ord + 1
            end do;
            term_no := term_no - 1
        end do;
        order_diff := 1;
        order_diff := 1;
        order_diff := 1;
        ord := 2;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 1;
        temp_sum := 0.;
        ord := 2;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x1_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x1_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 1;
        ord := 1;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 1;
        temp_sum := 0.;
        ord := 1;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x1_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x1_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 1;
        ord := 1;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 1;
        temp_sum := 0.;
        ord := 1;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x1_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x1_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        term_no := glob_max_terms;
        while 1 <= term_no do
            array_x1[term_no] := array_x1_higher_work2[1, term_no];
            ord := 1;
            while ord <= order_diff do
                array_x1_higher[ord, term_no] :=
                    array_x1_higher_work2[ord, term_no];
                ord := ord + 1
            end do;
            term_no := term_no - 1
        end do;
        display_alot(current_iter)
    end do;
    omniout_str(ALWAYS, "Finished!");
    if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
        "Maximum Iterations Reached before Solution Completed!")
    end if;
    if convfloat(glob_max_sec) <=
    elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
        omniout_str(ALWAYS,
        "Maximum Time Reached before Solution Completed!")
    end if;
    glob_clock_sec := elapsed_time_seconds();
    omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
        ff(x1,t,2) - diff (x1,t,1) + x1;");
    omniout_str(INFO,
        "diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;");
    omniout_int(INFO, "Iterations                       ", 32, glob_iter, 4,
        " ");
    prog_report(t_start, t_end);
    if glob_html_log then
        logstart(html_log_file);
        logitem_str(html_log_file, "2012-06-02T02:11:39-05:00");
        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 := 0.00005 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1]                              = 0.5                                          
x2[1] (analytic)                  = 0.00082561556360559907415319735476789        
x2[1] (numeric)                   = 0.00082561556360559907415319735476789        
absolute error                    = 0                                            
relative error                    = 0                                          % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012917551874827401624868391629841         
x1[1] (numeric)                   = 0.0012917551874827401624868391629841         
absolute error                    = 0                                            
relative error                    = 0                                          % 
h                                 = 5e-05                                        
t[1]                              = 0.5                                          
x2[1] (analytic)                  = 0.00082561556360559907415319735476789        
x2[1] (numeric)                   = 0.00082561556360559907415319735476789        
absolute error                    = 0                                            
relative error                    = 0                                          % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012917551874827401624868391629841         
x1[1] (numeric)                   = 0.0012917551874827401624868391629841         
absolute error                    = 0                                            
relative error                    = 0                                          % 
h                                 = 5e-05                                        
 
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50005                                      
x2[1] (analytic)                  = 0.00082566083422809021229815693339498        
x2[1] (numeric)                   = 0.0008256608342280902112128809789913         
absolute error                    = 1.08527595440368e-21                         
relative error                    = 1.3144331296982299010145367931419e-16      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012917006010880372652167092040327         
x1[1] (numeric)                   = 0.001291700601088095146219364060659          
absolute error                    = 5.78810026548566263e-17                      
relative error                    = 4.4809921591816061521273028438937e-12      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5001                                       
x2[1] (analytic)                  = 0.00082570611074256394598966051590164        
x2[1] (numeric)                   = 0.00082570611347206562644713699489435        
absolute error                    = 2.72950168045747647899271e-12                
relative error                    = 3.3056576001391273795257349110012e-07      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.001291646017422585871235266471237          
x1[1] (numeric)                   = 0.0012916460119643116371280973748446         
absolute error                    = 5.4582742341071690963924e-12                 
relative error                    = 4.2258282536254619845612697292069e-07      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50015                                      
x2[1] (analytic)                  = 0.00082575139314954126995470805844824        
x2[1] (numeric)                   = 0.00082575140406802564281686871319886        
absolute error                    = 1.091848437286216065475062e-11               
relative error                    = 1.3222483744432331394992543106801e-06      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012915914364862495213788540506512         
x1[1] (numeric)                   = 0.001291591414653326414540770995122          
absolute error                    = 2.18329231068380830555292e-11                
relative error                    = 1.6903892740442863466810236789852e-06      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5002                                       
x2[1] (analytic)                  = 0.0008257966814495432344339416603249         
x2[1] (numeric)                   = 0.00082579670601776504825521809306856        
absolute error                    = 2.456822181382127643274366e-11               
relative error                    = 2.9750933087665129214883467185353e-06      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012915368582788917633066026400632         
x1[1] (numeric)                   = 0.0012915368091547605399638597636327         
absolute error                    = 4.91241312233427428764305e-11                
relative error                    = 3.8035407900635369168021387272216e-06      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50025                                      
x2[1] (analytic)                  = 0.00082584197564309094518702663178858        
x2[1] (numeric)                   = 0.00082584201932344272793081978780986        
absolute error                    = 4.368035178274379315602128e-11               
relative error                    = 5.2891900715908138154263162587966e-06      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012914822828003761515000894181426         
x1[1] (numeric)                   = 0.0012914821954673861157167421604024         
absolute error                    = 8.73329900357833472577402e-11                
relative error                    = 6.7622290447853065221893849845794e-06      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=3.8MB, alloc=2.9MB, time=0.17
t[1]                              = 0.5003                                       
x2[1] (analytic)                  = 0.00082588727573070556349803310856235        
x2[1] (numeric)                   = 0.00082588734398721787879028945562029        
absolute error                    = 6.825651231529225634705794e-11               
relative error                    = 8.2646281545992046697870150154137e-06      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012914277100505662472629969306448         
x1[1] (numeric)                   = 0.0012914275735899751963934017782433         
absolute error                    = 1.364605910508695951524015e-10               
relative error                    = 1.0566645735480342058201119878555e-05      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50035                                      
x2[1] (analytic)                  = 0.00082593258171290830618081821305085        
x2[1] (numeric)                   = 0.00082593268001125006720421780581691        
absolute error                    = 9.829834176102339959276606e-11               
relative error                    = 1.1901497039523694324166328783172e-05      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012913731400293256187207719936699         
x1[1] (numeric)                   = 0.0012913729435212996524334089100879         
absolute error                    = 1.965080259662873630835820e-10               
relative error                    = 1.5216982595892066392731728962904e-05      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5004                                       
x2[1] (analytic)                  = 0.00082597789359022044558440876232671        
x2[1] (numeric)                   = 0.00082597802739769922901785675780158        
absolute error                    = 1.3380747878343344799547487e-10              
relative error                    = 1.6199886198142885101723757319479e-05      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012913185727365178408202846139762         
x1[1] (numeric)                   = 0.0012913183052601311701163150872154         
absolute error                    = 2.674763866707039695267608e-10               
relative error                    = 2.0713431396241535032098315877769e-05      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50045                                      
x2[1] (analytic)                  = 0.00082602321136316330959838452294175        
x2[1] (numeric)                   = 0.00082602338614872566961108883300895        
absolute error                    = 1.7478556236001270431006720e-10              
relative error                    = 2.1159885092280750123100989569948e-05      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012912640081720064953294869263476         
x1[1] (numeric)                   = 0.0012912636588052412515340347370404         
absolute error                    = 3.493667652437954521893072e-10               
relative error                    = 2.7056183943234097981506726047895e-05      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5005                                       
x2[1] (analytic)                  = 0.00082606853503225828165826201261726        
x2[1] (numeric)                   = 0.00082606875626649006395840449911754        
absolute error                    = 2.2123423178230014248650028e-10              
relative error                    = 2.6781583173805411188280210146852e-05      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012912094463356551708370721480129         
x1[1] (numeric)                   = 0.001291209004155401214563226252667          
absolute error                    = 4.421802539562738458953459e-10               
relative error                    = 3.4245432080066062523454204021962e-05      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50055                                      
x2[1] (analytic)                  = 0.00082611386459802680075087884886784        
x2[1] (numeric)                   = 0.00082611413775315345668888896468016        
absolute error                    = 2.7315512665593801011581232e-10              
relative error                    = 3.3065069884627917407609282961215e-05      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012911548872273274627521335501181         
x1[1] (numeric)                   = 0.0012911543413093821928376689204337         
absolute error                    = 5.459179452699144646296844e-10               
relative error                    = 4.2281367686431357189388814628772e-05      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5006                                       
x2[1] (analytic)                  = 0.00082615920006099036141977864461309        
x2[1] (numeric)                   = 0.00082615953061087726214621842539718        
absolute error                    = 3.3054988690072643978078409e-10              
relative error                    = 4.0010434656701024581949552109456e-05      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012911003308468869733038234462486         
x1[1] (numeric)                   = 0.0012910996702659551357206357053896         
absolute error                    = 6.605809318375831877408590e-10               
relative error                    = 5.1164182678528196924791464428897e-05      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
Complex estimate of poles used
NO POLE
Radius of convergence             = 9.530e-05                                    
Order of pole                     = 1.45                                         
t[1]                              = 0.50065                                      
x2[1] (analytic)                  = 0.0008262045414216705137705964508309         
x2[1] (numeric)                   = 0.00082620493484182326444866576350163        
absolute error                    = 3.9342015275067806931267073e-10              
relative error                    = 4.7617766912017975331931690868870e-05      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012910457771941973115410121980021         
x1[1] (numeric)                   = 0.0012910449910238908082772618940204         
absolute error                    = 7.861703065032637503039817e-10               
relative error                    = 6.0894069009065749447894853936796e-05      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence             = 6.634e-05                                    
Order of pole                     = 0.243                                        
t[1]                              = 0.5007                                       
x2[1] (analytic)                  = 0.00082624988868058886347644474630742        
x2[1] (numeric)                   = 0.00082625035044815361754911570174268        
absolute error                    = 4.6176756475407267095543526e-10              
relative error                    = 5.5887156062611279976306896949143e-05      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012909912262691220933319472376107         
x1[1] (numeric)                   = 0.0012909903035819597912469095932504         
absolute error                    = 9.226871623020850376443603e-10               
relative error                    = 7.1471218667270802802276184754481e-05      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
Real estimate of pole used
Real estimate of pole used
Radius of convergence             = 9.350e-05                                    
Order of pole                     = 16.66                                        
t[1]                              = 0.50075                                      
x2[1] (analytic)                  = 0.00082629524183826707178329997453724        
x2[1] (numeric)                   = 0.00082629577743203084529508941356178        
absolute error                    = 5.3559376377351178943902454e-10              
relative error                    = 6.4818691510551498159393858391484e-05      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012909366780715249413639121076118         
x1[1] (numeric)                   = 0.0012909356079389324810155280827534         
absolute error                    = 1.0701325924603483840248584e-09              
relative error                    = 8.2895823678894434103714976133245e-05      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence             = 0.0003883                                    
Order of pole                     = 181.4                                        
t[1]                              = 0.5008                                       
x2[1] (analytic)                  = 0.00082634060089522685551538962782877        
x2[1] (numeric)                   = 0.00082634121579561784148877859176918        
absolute error                    = 6.1490039098597338896394041e-10              
relative error                    = 7.4412462647946021227707970268687e-05      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012908821326012694851428855175656         
x1[1] (numeric)                   = 0.0012908809040935790895880100038865         
absolute error                    = 1.2285076903955548755136791e-09              
relative error                    = 9.5168076106218679482770050054311e-05      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.2MB, time=0.40
NO POLE
NO POLE
t[1]                              = 0.50085                                      
x2[1] (analytic)                  = 0.00082638596585198998708057987866837        
x2[1] (numeric)                   = 0.00082638666554107786994708898284107        
absolute error                    = 6.9968908788286650910417270e-10              
relative error                    = 8.4668558856937855356441671362775e-05      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012908275898582193609932004178204         
x1[1] (numeric)                   = 0.0012908261920446696445605432805914         
absolute error                    = 1.3978135497164326571372290e-09              
relative error                    = 0.00010828816804806320523134541790187      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5009                                       
x2[1] (analytic)                  = 0.00082643133670907829447576375839823        
x2[1] (numeric)                   = 0.00082643212667057456456169342423452        
absolute error                    = 7.8996149627008592966583629e-10              
relative error                    = 9.5587069509704405430127772053782e-05      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012907730498422382120572030903234         
x1[1] (numeric)                   = 0.0012907714717909739890929581838272         
absolute error                    = 1.5780512642229642449064962e-09              
relative error                    = 0.00012225629163979198019899719555733      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50095                                      
x2[1] (analytic)                  = 0.00082647671346701366129224988326191        
x2[1] (numeric)                   = 0.00082647759918627192935909458690167        
absolute error                    = 8.8571925826806684470363976e-10              
relative error                    = 0.00010716808396845625970175393146151      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012907185125531896882949122564762         
x1[1] (numeric)                   = 0.0012907167433312617818810668579742         
absolute error                    = 1.7692219279064138453985020e-09              
relative error                    = 0.00013707263905331994964691660082604      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.501                                        
x2[1] (analytic)                  = 0.00082652209612631802672115172787186        
x2[1] (numeric)                   = 0.00082652308309033433856069834427694        
absolute error                    = 9.8696401631183954661640508e-10              
relative error                    = 0.00011941169158543597534158781585741      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012906639779909374464836782020351         
x1[1] (numeric)                   = 0.001290662006664302497128986429335          
absolute error                    = 1.9713266349493546917727001e-09              
relative error                    = 0.00015273740249711971124783660771257      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
Real estimate of pole used
NO POLE
Radius of convergence             = 2.210e-05                                    
Order of pole                     = 14.49                                        
t[1]                              = 0.50105                                      
x2[1] (analytic)                  = 0.0008265674846875133855587774461534         
x2[1] (numeric)                   = 0.00082656857838492653664290094548412        
absolute error                    = 1.09369741315108412349933072e-09             
relative error                    = 0.00013231798170291686525991667208559      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012906094461553451502178419190542         
x1[1] (numeric)                   = 0.0012906072617888654245214289948781         
absolute error                    = 2.1843664797256964129241761e-09              
relative error                    = 0.00016925077421622819452641104815716      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence             = 2.336e-05                                    
Order of pole                     = 24.84                                        
t[1]                              = 0.5011                                       
x2[1] (analytic)                  = 0.00082661287915112178821202023981947        
x2[1] (numeric)                   = 0.00082661408507221363839719704923771        
absolute error                    = 1.20592109185018517680941824e-09             
relative error                    = 0.00014588704365320178705696758450004      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012905549170462764699083942648711         
x1[1] (numeric)                   = 0.0012905525087037196691959618481976         
absolute error                    = 2.4083425568007124324166735e-09              
relative error                    = 0.00018661294649225334348077323939715      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
Real estimate of pole used
Radius of convergence             = 1.141e-05                                    
Order of pole                     = 2.46                                         
t[1]                              = 0.50115                                      
x2[1] (analytic)                  = 0.00082665827951766534070374927443031        
x2[1] (numeric)                   = 0.00082665960315436112899031384330714        
absolute error                    = 1.32363669578828656456887683e-09             
relative error                    = 0.00016011896675862193473133214038365      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012905003906635950827826351381346         
x1[1] (numeric)                   = 0.001290497747407634151715323712609          
absolute error                    = 2.6432559609310673114255256e-09              
relative error                    = 0.00020482411164338079573977004314158      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5012                                       
x2[1] (analytic)                  = 0.00082670368578766620467820114309252        
x2[1] (numeric)                   = 0.00082670513263353486402435507813827        
absolute error                    = 1.44684586865934615393504575e-09             
relative error                    = 0.00017501384033153563118979833302682      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012904458670071646728838326718726         
x1[1] (numeric)                   = 0.0012904429778993776080398574894025         
absolute error                    = 2.8891077870648439751824701e-09              
relative error                    = 0.0002238844620243805535657308320619       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50125                                      
x2[1] (analytic)                  = 0.00082674909796164659740637187785192        
x2[1] (numeric)                   = 0.00082675067351190106959692671965234        
absolute error                    = 1.57555025447219055484180042e-09             
relative error                    = 0.00019057175367432711813593685869316      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012903913460768489310708824436005         
x1[1] (numeric)                   = 0.0012903882001777185894998475956791         
absolute error                    = 3.1458991303415710348479214e-09              
relative error                    = 0.00024379419002661366312352445869106      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5013                                       
x2[1] (analytic)                  = 0.00082679451604012879179140950883443        
x2[1] (numeric)                   = 0.00082679622579162634236126301599356        
absolute error                    = 1.70975149755056985350715913e-09             
relative error                    = 0.00020679279607940534561175300696596      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012903368278725115550179667024679         
x1[1] (numeric)                   = 0.0012903334142414254627683205900583         
absolute error                    = 3.4136310860922496461124096e-09              
relative error                    = 0.00026455348807803885871951801637687      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
memory used=11.4MB, alloc=4.3MB, time=0.62
NO POLE
t[1]                              = 0.50135                                      
x2[1] (analytic)                  = 0.00082683994002363511637400717118929        
x2[1] (numeric)                   = 0.00082684178947487764958623358631015        
absolute error                    = 1.84945124253321222641512086e-09             
relative error                    = 0.00022367705682920274675308798412464      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012902823123940162492142136134444         
x1[1] (numeric)                   = 0.0012902786200892664098346456101133         
absolute error                    = 3.6923047498393795680033311e-09              
relative error                    = 0.00028616254864321914591847241354952      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5014                                       
x2[1] (analytic)                  = 0.00082688536991268795533779675988916        
x2[1] (numeric)                   = 0.00082688736456382232921608864264273        
absolute error                    = 1.99465113437387829188275357e-09             
relative error                    = 0.00024122462519617398048417150809564      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012902277996412267249633565185424         
x1[1] (numeric)                   = 0.0012902238177200094279729425426769         
absolute error                    = 3.9819212172969904139758655e-09              
relative error                    = 0.0003086215642233287879403327220334       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50145                                      
x2[1] (analytic)                  = 0.00082693080570780974851474313244131        
x2[1] (numeric)                   = 0.00082693295106062808993114507299581        
absolute error                    = 2.14535281834141640194055450e-09             
relative error                    = 0.0002594355904427947876085798671822       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012901732896140067003833932150759         
x1[1] (numeric)                   = 0.0012901690071324223297169055925665         
absolute error                    = 4.2824815843706664876225094e-09              
relative error                    = 0.00033193072735615979575782052203881      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5015                                       
x2[1] (analytic)                  = 0.00082697624740952299139053885956424        
x2[1] (numeric)                   = 0.00082697854896746301120785883420776        
absolute error                    = 2.30155794001981731997464352e-09             
relative error                    = 0.00027831004182156077227291004636589      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012901187823122199004062452509559         
x1[1] (numeric)                   = 0.0012901141883252727428317147811532         
absolute error                    = 4.5939869471575745304698027e-09              
relative error                    = 0.00035609023061612864474084966933865      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50155                                      
x2[1] (analytic)                  = 0.00082702169501835023510999952388432        
x2[1] (numeric)                   = 0.0008270241582864955433790033090115         
absolute error                    = 2.46326814530826900378512718e-09             
relative error                    = 0.00029784806857498619584955683714112      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012900642777357300567774172370197         
x1[1] (numeric)                   = 0.0012900593612973281102863389190148         
absolute error                    = 4.9164384019464910783180049e-09              
relative error                    = 0.00038110026661428296183864119182014      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5016                                       
x2[1] (analytic)                  = 0.00082706714853481408648245956670656        
x2[1] (numeric)                   = 0.00082706977901989450769385489220588        
absolute error                    = 2.63048508042121139532549932e-09             
relative error                    = 0.00031804975993560277129593468950195      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.001290009775884400908055656176395          
x1[1] (numeric)                   = 0.0012900045260473556902258254181453         
absolute error                    = 5.2498370452178298307582497e-09              
relative error                    = 0.00040696102799830821465741053608137      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50165                                      
x2[1] (analytic)                  = 0.00082711260795943720798716868291399        
x2[1] (numeric)                   = 0.00082711541116982909637838805970475        
absolute error                    = 2.80321039188839121937679076e-09             
relative error                    = 0.00033891520512595845826254094678894      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012899552767580961996126108108966         
x1[1] (numeric)                   = 0.0012899496825741225559435859508189         
absolute error                    = 5.5941839736436690248600777e-09              
relative error                    = 0.00043367270745253440173574659510224      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5017                                       
x2[1] (analytic)                  = 0.00082715807329274231777868876405026        
x2[1] (numeric)                   = 0.000827161054738468872695479921465          
absolute error                    = 2.98144572655491679115741474e-09             
relative error                    = 0.00036044449335861625894978717254087      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012899007803566796836324909844552         
x1[1] (numeric)                   = 0.0012898948308763955958536779527188         
absolute error                    = 5.9494802840877788130317364e-09              
relative error                    = 0.00046123549769794274401802974202934      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50175                                      
x2[1] (analytic)                  = 0.0008272035445352521896922913896394         
x2[1] (numeric)                   = 0.00082720670972798377100512425976157        
absolute error                    = 3.16519273158131283287012217e-09             
relative error                    = 0.00038263771383615301471358170812616      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012898462866800151191117270235781         
x1[1] (numeric)                   = 0.0012898399709529415134630819697096         
absolute error                    = 6.3157270736056486450538685e-09              
relative error                    = 0.00048964959149217237752609908408452      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5018                                       
x2[1] (analytic)                  = 0.00082724902168748965324935586679766        
x2[1] (numeric)                   = 0.00082725237614054409682465505427742        
absolute error                    = 3.35445305444357529918747976e-09             
relative error                    = 0.0004054949557511582034196463826453       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012897917957279662718586291348401         
x1[1] (numeric)                   = 0.0012897851028025268273439748476288         
absolute error                    = 6.6929254394445146542872113e-09              
relative error                    = 0.00051891518162952704722937931891312      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50185                                      
x2[1] (analytic)                  = 0.00082729450474997759366276781819127        
x2[1] (numeric)                   = 0.00082729805397832052688897949547691        
absolute error                    = 3.54922834293322621167728564e-09             
relative error                    = 0.00042901630828623273754655038521288      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012897373075003969144930468194044         
x1[1] (numeric)                   = 0.0012897302264239178711059987644746         
absolute error                    = 7.0810764790433870480549298e-09              
relative error                    = 0.00054903246094098180211367758897854      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.4MB, time=0.84
NO POLE
NO POLE
t[1]                              = 0.5019                                       
x2[1] (analytic)                  = 0.00082733999372323895184231831839524        
x2[1] (numeric)                   = 0.00082734374324348410921082048773105        
absolute error                    = 3.74952024515736850216933581e-09             
relative error                    = 0.00045320186061398776303744405863382      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012896828219971708264460283045716         
x1[1] (numeric)                   = 0.0012896753418158807933685261043666         
absolute error                    = 7.4801812900330775022002050e-09              
relative error                    = 0.00058000162229418969144886067311321      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50195                                      
x2[1] (analytic)                  = 0.00082738548860779672440010357870682        
x2[1] (numeric)                   = 0.00082738944393820626314096864366339        
absolute error                    = 3.95533040953874086506495657e-09             
relative error                    = 0.00047805170189704345890047549475362      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012896283392181517939594799923581         
x1[1] (numeric)                   = 0.0012896204489771815577329201726557         
absolute error                    = 7.8902409702362265598197024e-09              
relative error                    = 0.00061182285859348846225562315449888      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.502                                        
x2[1] (analytic)                  = 0.0008274309894041739636559251804687         
x2[1] (numeric)                   = 0.00082743515606465877942854377118556        
absolute error                    = 4.16666048481577261859071686e-09             
relative error                    = 0.0005035659212880278375578725667491       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012895738591632036100858259251            
x1[1] (numeric)                   = 0.0012895655479065859427547917515594         
absolute error                    = 8.3112566176673310341735406e-09              
relative error                    = 0.00064449636277990725797155683773415      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50205                                      
x2[1] (analytic)                  = 0.00082747649611289377764269085695601        
x2[1] (numeric)                   = 0.0008274808796250138202812658546917         
absolute error                    = 4.38351212004263857499773569e-09             
relative error                    = 0.00052974460792957554594367308720935      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012895193818321900746876672680847         
x1[1] (numeric)                   = 0.0012895106386028595419162514956996         
absolute error                    = 8.7432293305327714157723851e-09              
relative error                    = 0.00067802232783117331831673211962611      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5021                                       
x2[1] (analytic)                  = 0.00082752200873447933011181582388164        
x2[1] (numeric)                   = 0.00082752661462144391942573553188116        
absolute error                    = 4.60588696458931391970799952e-09             
relative error                    = 0.00055658785095432666735008564466675      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012894649072249749944374418092067         
x1[1] (numeric)                   = 0.0012894557210647677635981581669182         
absolute error                    = 9.1861602072308392836422885e-09              
relative error                    = 0.00071240094676171868035900174476368      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50215                                      
x2[1] (analytic)                  = 0.00082756752726945384053862465857453        
x2[1] (numeric)                   = 0.00082757236105612198216772406767919        
absolute error                    = 4.83378666814162909940910466e-09             
relative error                    = 0.00058409573948492552402246359913447      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012894104353414221828170834756492         
x1[1] (numeric)                   = 0.0012894007952910758310523627077468         
absolute error                    = 9.6400503463517647207679024e-09              
relative error                    = 0.00074763241262268688077923772367162      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5022                                       
x2[1] (analytic)                  = 0.0008276130517183405841277537278848         
x2[1] (numeric)                   = 0.00082761811893122128545247282672549        
absolute error                    = 5.06721288070132471909884069e-09             
relative error                    = 0.00061226836263401948050287473211411      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012893559661813954601176818675888         
x1[1] (numeric)                   = 0.0012893458612805487823739481529073         
absolute error                    = 1.01049008466777437337146815e-08             
relative error                    = 0.00078371691850193965933671184794605      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50225                                      
x2[1] (analytic)                  = 0.00082765858208166289181855416487103        
x2[1] (numeric)                   = 0.00082766388824891547792500224590075        
absolute error                    = 5.30616725258610644808102972e-09             
relative error                    = 0.00064110580950425774772224880647601      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012893014997447586534391418089226         
x1[1] (numeric)                   = 0.0012892909190319514704734653782179         
absolute error                    = 1.05807128071829656764307047e-08             
relative error                    = 0.00082065465752406366353483059904026      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5023                                       
x2[1] (analytic)                  = 0.00082770411835994415029049539432325        
x2[1] (numeric)                   = 0.0008277096690113785799904303083615         
absolute error                    = 5.55065143442969993491403825e-09             
relative error                    = 0.00067060816918829018784108542859691      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012892470360313755966898429150187         
x1[1] (numeric)                   = 0.0012892359685440485630491646862818         
absolute error                    = 1.10674873270336406782287369e-08             
relative error                    = 0.00085844582285037715448743519091747      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50235                                      
x2[1] (analytic)                  = 0.00082774966055370780196856920717682        
x2[1] (numeric)                   = 0.00082775546122078498387430052055384        
absolute error                    = 5.80066707718190573131337702e-09             
relative error                    = 0.00070077553076876611983870434215         % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012891925750411101305862991774863         
x1[1] (numeric)                   = 0.0012891810098156045425592232283333         
absolute error                    = 1.15652255055880270759491530e-08             
relative error                    = 0.00089709060767893671398587734498348      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=19.0MB, alloc=4.4MB, time=1.06
t[1]                              = 0.5024                                       
x2[1] (analytic)                  = 0.00082779520866347734502869438387111        
x2[1] (numeric)                   = 0.00082780126487930945368291939367687        
absolute error                    = 6.05621583210865422500980576e-09             
relative error                    = 0.00073160798331833312585102036918086      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012891381167738261026528185659675         
x1[1] (numeric)                   = 0.0012891260428453837061939682616174         
absolute error                    = 1.20739284423964588503043501e-08             
relative error                    = 0.00093658920524454395276708177356707      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50245                                      
x2[1] (analytic)                  = 0.00082784076268977633340312186670805        
x2[1] (numeric)                   = 0.0008278470799891271254637034310668         
absolute error                    = 6.31729935079206058156435875e-09             
relative error                    = 0.00076310561589963585825682499586731      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012890836612293873672211626469477         
x1[1] (numeric)                   = 0.0012890710676321501658480962416781         
absolute error                    = 1.25935972372013730664052696e-08             
relative error                    = 0.00097694180881875221998280604355632      % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5025                                       
x2[1] (analytic)                  = 0.00082788632263312837678584048126422        
x2[1] (numeric)                   = 0.000827892906552413507265535622973          
absolute error                    = 6.58391928513047969514170878e-09             
relative error                    = 0.00079526851756531484751255670592886      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012890292084076577854302062195851         
x1[1] (numeric)                   = 0.0012890160841746678480928877489317         
absolute error                    = 1.31242329899373373184706534e-08             
relative error                    = 0.0010181486117098733138703087145388       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50255                                      
x2[1] (analytic)                  = 0.00082793188849405714063798320691191        
x2[1] (numeric)                   = 0.00082793874457134447919913145019748        
absolute error                    = 6.85607728733856114824328557e-09             
relative error                    = 0.00082809677735800531073554188242706      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012889747583085012252255969685576         
x1[1] (numeric)                   = 0.0012889610924717004941484182488993         
absolute error                    = 1.36658368007310771787196583e-08             
relative error                    = 0.0010602098072629841936246366669017       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5026                                       
x2[1] (analytic)                  = 0.00082797746027308634619323399650282        
x2[1] (numeric)                   = 0.00082798459404809629349741439806942        
absolute error                    = 7.13377500994730418040156660e-09             
relative error                    = 0.00086159048431033596103568822964852      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.001288920310931781561359415133927          
x1[1] (numeric)                   = 0.0012889060925220116598557646854744         
absolute error                    = 1.42184097699015036504484526e-08             
relative error                    = 0.0011031255888599336924727425564524       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50265                                      
x2[1] (analytic)                  = 0.00082802303797073977046323514526932        
x2[1] (numeric)                   = 0.00082803045498484557457590098222676        
absolute error                    = 7.41701410580411266583695744e-09             
relative error                    = 0.00089574972744492781759561246550527      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012888658662773626753898331980192         
x1[1] (numeric)                   = 0.001288851084324364715649207906601          
absolute error                    = 1.47819529979597406252914182e-08             
relative error                    = 0.0011468961499193492319496433066746       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5027                                       
x2[1] (analytic)                  = 0.00082806862158754124624299520899781        
x2[1] (numeric)                   = 0.00082807632738376931909309528767692        
absolute error                    = 7.70579622807285010007867911e-09             
relative error                    = 0.00093057459577439301649918399069987      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012888114243451084556807755893193         
x1[1] (numeric)                   = 0.0012887960678775228465284309217365         
absolute error                    = 1.53564675856091523446675828e-08             
relative error                    = 0.0011915216838966435373768306794499       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50275                                      
x2[1] (analytic)                  = 0.00082811421112401466211629747152829        
x2[1] (numeric)                   = 0.00082812221124704489601089302260907        
absolute error                    = 8.00012303023389459555108078e-09             
relative error                    = 0.00096606517830133362230846623777141      % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012887569851348827974015784033818         
x1[1] (numeric)                   = 0.0012887410431802490520307129904753         
absolute error                    = 1.59419546337453708654129065e-08             
relative error                    = 0.0012370023842840213545431449706798       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5028                                       
x2[1] (analytic)                  = 0.00082815980658068396246110896163522        
x2[1] (numeric)                   = 0.0008281681065768500466549950884305         
absolute error                    = 8.29999616608419388612679528e-09             
relative error                    = 0.0010022215640183404403890372043692       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012887025486465496025266491407532         
x1[1] (numeric)                   = 0.0012886860102313061462031195417074         
absolute error                    = 1.65384152434563235295990458e-08             
relative error                    = 0.001283338444610486167588322805248        % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50285                                      
x2[1] (analytic)                  = 0.0008282054079580731474549900193436         
x2[1] (numeric)                   = 0.00082821401337536288477533066749994        
absolute error                    = 8.60541728973732034064815634e-09             
relative error                    = 0.001039043841907991829983670752911        % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012886481148799727798351264619085         
x1[1] (numeric)                   = 0.0012886309690294567575746879226867         
absolute error                    = 1.71458505160222604385392218e-08             
relative error                    = 0.0013305300584418469180894303294862       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5029                                       
x2[1] (analytic)                  = 0.0008282510152567062730805044117353         
x2[1] (numeric)                   = 0.00082825993164476189660648983003084        
absolute error                    = 8.91638805562352598541829554e-09             
relative error                    = 0.0010765321009428525180343600479695       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012885936838350162449105399591989         
x1[1] (numeric)                   = 0.0012885759195734633291286089773842         
absolute error                    = 1.77642615529157819309818147e-08             
relative error                    = 0.0013785774193807247253503927635229       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.4MB, time=1.29
NO POLE
NO POLE
t[1]                              = 0.50295                                      
x2[1] (analytic)                  = 0.00082829662847710745113062999829971        
x2[1] (numeric)                   = 0.00082830586138722594092816566163796        
absolute error                    = 9.23291011848979753566333825e-09             
relative error                    = 0.0011146864300854724137526645624312       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012885392555115439201404699458103         
x1[1] (numeric)                   = 0.0012885208618620881182744044535006         
absolute error                    = 1.83936494558018660654923097e-08             
relative error                    = 0.0014274807210665596078948315375385       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.503                                        
x2[1] (analytic)                  = 0.0008283422476198008492141699458837         
x2[1] (numeric)                   = 0.00082835180260493424912560591300064        
absolute error                    = 9.55498513339991143596711694e-09             
relative error                    = 0.0011535069182883854239383618775362       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012884848299094197347162072617323         
x1[1] (numeric)                   = 0.0012884657958940931968201002375121         
absolute error                    = 1.90340153265378961070242202e-08             
relative error                    = 0.0014772401571756172061624203269484       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50305                                      
x2[1] (analytic)                  = 0.00082838787268531069076116449329504        
x2[1] (numeric)                   = 0.00082839775530006642525007417311659        
absolute error                    = 9.88261475573448890967982155e-09             
relative error                    = 0.0011929936544941082690463855628223       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012884304070285076246324130967366         
x1[1] (numeric)                   = 0.001288410721668240450944395417125          
absolute error                    = 1.96853602671736880176796116e-08             
relative error                    = 0.0015278559214209955064089711286707       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5031                                       
x2[1] (analytic)                  = 0.00082843350367416125502830326561401        
x2[1] (numeric)                   = 0.00082844371947480244607932056762007        
absolute error                    = 1.021580064119105101730200606e-08            
relative error                    = 0.0012331467276351393000020302583507       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012883759868686715326867788303632         
x1[1] (numeric)                   = 0.0012883556391832915811688271705125         
absolute error                    = 2.03476853799515179516598507e-08             
relative error                    = 0.0015793282075526315658104616814499       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50315                                      
x2[1] (analytic)                  = 0.0008284791405868768771043381382677         
x2[1] (numeric)                   = 0.00082848969513132266117806198363867        
absolute error                    = 1.055454444578407372384537097e-08            
relative error                    = 0.0012739662266339573157644050531797       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012883215694297754084796858889148         
x1[1] (numeric)                   = 0.0012883005484380081023299314817082         
absolute error                    = 2.10209917673061497544072066e-08             
relative error                    = 0.0016316572093573082387712156319767       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5032                                       
x2[1] (analytic)                  = 0.00082852478342398194791549665092172        
x2[1] (numeric)                   = 0.00082853568227180779295847182266308        
absolute error                    = 1.089884782584504297517174136e-08            
relative error                    = 0.0013154522404030203816381161520137       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012882671547116832084138656194575         
x1[1] (numeric)                   = 0.0012882454494311513435513996815309         
absolute error                    = 2.17052805318648624659379266e-08             
relative error                    = 0.0016848431206586609044364466911856       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50325                                      
x2[1] (analytic)                  = 0.00082857043218600091423089597124342        
x2[1] (numeric)                   = 0.00082858168089843893674067928290445        
absolute error                    = 1.124871243802250978331166103e-08            
relative error                    = 0.0013576048578447646483331598249433       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012882127427142588956940591808277         
x1[1] (numeric)                   = 0.0012881903421614824482162308134136         
absolute error                    = 2.24005527764474778283674141e-08             
relative error                    = 0.0017388861353171841954093783256838       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5033                                       
x2[1] (analytic)                  = 0.00082861608687345827866795740859187        
x2[1] (numeric)                   = 0.00082862769101339756081327817261424        
absolute error                    = 1.160413993928214532076402237e-08            
relative error                    = 0.0014004241678516031717730064354027       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012881583334373664403266774516441         
x1[1] (numeric)                   = 0.0012881352266277623739388798235123         
absolute error                    = 2.31068096040663877976281318e-08             
relative error                    = 0.0017937864472302387276731502710021       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50335                                      
x2[1] (analytic)                  = 0.0008286617474868785996978214776885         
x2[1] (numeric)                   = 0.00082867371261886550649384525584157        
absolute error                    = 1.196513198690679602377815307e-08            
relative error                    = 0.0014439102593059247336508564205295       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012881039268808698191194609553229         
x1[1] (numeric)                   = 0.0012880801028287518925374015744666         
absolute error                    = 2.38240521179265820593808563e-08             
relative error                    = 0.0018495442503320578317177233996107       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5034                                       
x2[1] (analytic)                  = 0.00082870741402678649165076351232339        
x2[1] (numeric)                   = 0.00082871974571702498818946813210342        
absolute error                    = 1.233169023849653870461978003e-08            
relative error                    = 0.001488063221080092662734048910417        % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012880495230446330156811398020981         
x1[1] (numeric)                   = 0.0012880249707632115900055906821877         
absolute error                    = 2.45522814214256755491199104e-08             
relative error                    = 0.0019061597385937542848719945211174       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=26.7MB, alloc=4.5MB, time=1.52
t[1]                              = 0.50345                                      
x2[1] (analytic)                  = 0.00082875308649370662472160982915166        
x2[1] (numeric)                   = 0.00082876579031005859345728265144321        
absolute error                    = 1.270381635196873567282229155e-08            
relative error                    = 0.0015328831420364436569166036625088       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012879951219285200204210936480425         
x1[1] (numeric)                   = 0.0012879698304299018664851171750458         
absolute error                    = 2.52914986181539359764729967e-08             
relative error                    = 0.0019636331060233270448413325114024       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5035                                       
x2[1] (analytic)                  = 0.00082879876488816372497515444163463        
x2[1] (numeric)                   = 0.00082881184640014928306501986635347        
absolute error                    = 1.308151198555808986542471884e-08            
relative error                    = 0.0015783701110272866060198768854226       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012879407235323948305490116710912         
x1[1] (numeric)                   = 0.001287914681827582936237657974832          
absolute error                    = 2.60417048118943113536962592e-08             
relative error                    = 0.002021964546665667984450747437023        % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50355                                      
x2[1] (analytic)                  = 0.00082884444921068257435157632418004        
x2[1] (numeric)                   = 0.00082885791398948039105156252203858        
absolute error                    = 1.346477879781669998619785854e-08            
relative error                    = 0.0016245242168949014153413115078029       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012878863278561214500745525640661         
x1[1] (numeric)                   = 0.0012878595249550148276170241988667         
absolute error                    = 2.68029011066224575283651994e-08             
relative error                    = 0.0020811542546025686275939043546676       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5036                                       
x2[1] (analytic)                  = 0.00082889013946178801067185722653652        
x2[1] (numeric)                   = 0.00082890399308023562478751108649386        
absolute error                    = 1.385361844761411565385995734e-08            
relative error                    = 0.0016713455484715378299512622783016       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012878319348995638898070045446997         
x1[1] (numeric)                   = 0.0012878043598109573830412842826292         
absolute error                    = 2.75750886065067657202620705e-08             
relative error                    = 0.0021412024239527268863881932692266       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50365                                      
x2[1] (analytic)                  = 0.00082893583564200492764320003849618        
x2[1] (numeric)                   = 0.00082895008367459906503575932187736        
absolute error                    = 1.424803259413739255928338118e-08            
relative error                    = 0.0017188341945794142597378761534084       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012877775446625861673549453826583         
x1[1] (numeric)                   = 0.0012877491863941702589648829222811         
absolute error                    = 2.83582684159083900624603772e-08             
relative error                    = 0.0022021092488717537995360670657894       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5037                                       
x2[1] (analytic)                  = 0.00082898153775185827486444770496057        
x2[1] (numeric)                   = 0.00082899618577475516601207939865101        
absolute error                    = 1.464802289689114763169369044e-08            
relative error                    = 0.0017669902440307166052000082036702       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012877231571450523071259024435631         
x1[1] (numeric)                   = 0.0012876940047034129258507558364565         
absolute error                    = 2.91524416393812751466071066e-08             
relative error                    = 0.0022638749235521802718928591045642       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50375                                      
x2[1] (analytic)                  = 0.00082902724579187305783150269142413        
x2[1] (numeric)                   = 0.00082904229938288875544571655396807        
absolute error                    = 1.505359101569761421386254394e-08            
relative error                    = 0.0018158137856275970839881533418888       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012876687723468263403260127500097         
x1[1] (numeric)                   = 0.0012876388147374446681424403466929         
absolute error                    = 2.99576093816721835724033168e-08             
relative error                    = 0.002326499642223463815241292282096        % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5038                                       
x2[1] (analytic)                  = 0.0008290729597625743379427469999303         
x2[1] (numeric)                   = 0.00082908842450118503463999329578393        
absolute error                    = 1.546473861069669724629585363e-08            
relative error                    = 0.0018653049081621730581933739664325       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012876143902677723049596830595824         
x1[1] (numeric)                   = 0.001287583616495024584236181775875          
absolute error                    = 3.07737727477207235012837074e-08             
relative error                    = 0.00238998359915199529027289120475         % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50385                                      
x2[1] (analytic)                  = 0.00082911867966448723250446273555416        
x2[1] (numeric)                   = 0.00082913456113182957853292315416763        
absolute error                    = 1.588146734234602846041861347e-08            
relative error                    = 0.0019154637004165258623842037111808       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012875600109077542458292499598661         
x1[1] (numeric)                   = 0.0012875284099749115864530356640648         
absolute error                    = 3.16009328426593762142958013e-08             
relative error                    = 0.0024543269886411056497765095532075       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5039                                       
x2[1] (analytic)                  = 0.00082916440549813691473625322346704        
x2[1] (numeric)                   = 0.00082918070927700833575783398129162        
absolute error                    = 1.630377887142102158075782458e-08            
relative error                    = 0.0019662902511626996323915072253026       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012875056342666362145346399804511         
x1[1] (numeric)                   = 0.0012874731951758644010109658010907         
absolute error                    = 3.24390907718135236741793604e-08             
relative error                    = 0.0025195300050310726830341842176367       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50395                                      
x2[1] (analytic)                  = 0.00082921013726404861377646467663714        
x2[1] (numeric)                   = 0.00082922686893890762870400080157761        
absolute error                    = 1.673167485901492753612494047e-08            
relative error                    = 0.0020177846491627001348412760177397       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012874512603442822694730297219339         
x1[1] (numeric)                   = 0.0012874179720966415679969380752684         
absolute error                    = 3.32882476407014760916466655e-08             
relative error                    = 0.0025855928426991277614245284101548       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=30.5MB, alloc=4.5MB, time=1.74
t[1]                              = 0.504                                        
x2[1] (analytic)                  = 0.00082925587496274761468760841422102        
x2[1] (numeric)                   = 0.00082927304011971415357728821347647        
absolute error                    = 1.716515696653888967979925545e-08            
relative error                    = 0.0020699469831684935974353402186172       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012873968891405564758385060019091         
x1[1] (numeric)                   = 0.001287362740736001441339010137626          
absolute error                    = 3.41484045550344994958642831e-08             
relative error                    = 0.0026525156960594625852338753999593       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50405                                      
x2[1] (analytic)                  = 0.00082930161859475925846178363070083        
x2[1] (numeric)                   = 0.00082931922282161498046080234436041        
absolute error                    = 1.760422685572199901871365958e-08            
relative error                    = 0.0021227773419220055399799760441893       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012873425206553229056217260179551         
x1[1] (numeric)                   = 0.0012873075010927021887784168810059         
absolute error                    = 3.50195626207168433091369492e-08             
relative error                    = 0.0027202987595632359316753851202108       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5041                                       
x2[1] (analytic)                  = 0.00082934736816060894202610071582133        
x2[1] (numeric)                   = 0.00082936541704679755337555236000599        
absolute error                    = 1.804888618861134945164418466e-08            
relative error                    = 0.0021762758141551196061623887924326       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012872881548884456376095775276106         
x1[1] (numeric)                   = 0.0012872522531655017918416517334163         
absolute error                    = 3.59017229438457679257941943e-08             
relative error                    = 0.0027889422276985804041163254665201       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50415                                      
x2[1] (analytic)                  = 0.00082939312366082211824810512538206        
x2[1] (numeric)                   = 0.00082941162279744969034112153014651        
absolute error                    = 1.849913662757209301640476445e-08            
relative error                    = 0.0022304424885896763960750509414606       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012872337918397887573848390453416         
x1[1] (numeric)                   = 0.0012871969969531580458125437650045         
absolute error                    = 3.67948866307115722952803371e-08             
relative error                    = 0.002858446294990609182513740392183        % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5042                                       
x2[1] (analytic)                  = 0.00082943888509592429594120180293885        
x2[1] (numeric)                   = 0.00082945784007575958343634785157286        
absolute error                    = 1.895497983528749514604863401e-08            
relative error                    = 0.0022852774539374722994878750309954       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012871794315092163573258400564985         
x1[1] (numeric)                   = 0.0012871417324544285597043306080238         
absolute error                    = 3.76990547877976215094484747e-08             
relative error                    = 0.0029288111560014227750587169576382       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50425                                      
x2[1] (analytic)                  = 0.00082948465246644103987008015246953        
x2[1] (numeric)                   = 0.00082950406888391579886001423026184        
absolute error                    = 1.941641747475898993407779231e-08            
relative error                    = 0.0023407807989002583298682008209635       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012871250738965925366061212482615         
x1[1] (numeric)                   = 0.0012870864596680707562317271891667         
absolute error                    = 3.86142285217803743940590948e-08             
relative error                    = 0.0030000370053301157710294633419651       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5043                                       
x2[1] (analytic)                  = 0.00082953042577289797075613956205843        
x2[1] (numeric)                   = 0.00082955030922410727699154822401139        
absolute error                    = 1.988345120930623540866195296e-08            
relative error                    = 0.0023969526121697389591485762087669       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012870707190017814011940947575749         
x1[1] (numeric)                   = 0.0012870311785928418717829902736363         
absolute error                    = 3.95404089395294111044839386e-08             
relative error                    = 0.0030721240376127835948534101018352       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50435                                      
x2[1] (analytic)                  = 0.00082957620501582076528291547865441        
x2[1] (numeric)                   = 0.00082959656109852333245173134706231        
absolute error                    = 2.035608270256716881586840790e-08            
relative error                    = 0.0024537929824275709532423112886725       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012870163668246470638527044360674         
x1[1] (numeric)                   = 0.0012869758892274989563919788203279         
absolute error                    = 4.04775971481074607256157395e-08             
relative error                    = 0.0031450724475225292613785467126817       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5044                                       
x2[1] (analytic)                  = 0.00082962199019573515610150603395714        
x2[1] (numeric)                   = 0.00082964282450935365416341793818631        
absolute error                    = 2.083431361849806191190422917e-08            
relative error                    = 0.0025113019983453622083067848736265       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.00128696201736505364413908613196           
x1[1] (numeric)                   = 0.0012869205915707988737102101474927         
absolute error                    = 4.14257942547704288759844673e-08             
relative error                    = 0.003218882429769470132354205813243        % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50445                                      
x2[1] (analytic)                  = 0.00082966778131316693183599922148616        
x2[1] (numeric)                   = 0.00082968909945878830541226359372039        
absolute error                    = 2.131814562137357626437223423e-08            
relative error                    = 0.0025694797485846705877544827451191       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012869076706228652684042279889585         
x1[1] (numeric)                   = 0.0012868652856214983009789119082553         
absolute error                    = 4.23850013669674253160807032e-08             
relative error                    = 0.0032935541791007446741215072618302       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5045                                       
x2[1] (analytic)                  = 0.00082971357836864193708890062488759        
x2[1] (numeric)                   = 0.0008297353859490177239074631670279         
absolute error                    = 2.180758037578681856254214031e-08            
relative error                    = 0.0026283263217970027600117468010614       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012868533265979460697926307621308         
x1[1] (numeric)                   = 0.0012868099713783537290010698753567         
absolute error                    = 4.33552195923407915608867741e-08             
relative error                    = 0.0033690878903005192165136743903105       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.5MB, time=1.97
NO POLE
NO POLE
t[1]                              = 0.50455                                      
x2[1] (analytic)                  = 0.00082975938136268607244656169753319        
x2[1] (numeric)                   = 0.0008297816839822327218424983358667         
absolute error                    = 2.230261954664939593663833351e-08            
relative error                    = 0.0026878418066238130370252142037215       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012867989852901601882419681507683         
x1[1] (numeric)                   = 0.0012867546488401214621134715344945         
absolute error                    = 4.43364500387261284966162738e-08             
relative error                    = 0.0034454837581899947129664348009221       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5046                                       
x2[1] (analytic)                  = 0.00082980519029582529448460859346626        
x2[1] (numeric)                   = 0.00082982799356062448595589473914524        
absolute error                    = 2.280326479919147128614567898e-08            
relative error                    = 0.0027480262916965022135159256064519       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012867446466993717704827471482299         
x1[1] (numeric)                   = 0.0012866993180055576181587454856319         
absolute error                    = 4.53286938141523240016625980e-08             
relative error                    = 0.0035227419776274135018387180256803       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50465                                      
x2[1] (analytic)                  = 0.00082985100516858561577337154974936        
x2[1] (numeric)                   = 0.00082987431468638457759198868454745        
absolute error                    = 2.330951779896181861713479809e-08            
relative error                    = 0.0028088798656364164069810813904913       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.001286690310825444970037968408768          
x1[1] (numeric)                   = 0.0012866439788734181284573966516463         
absolute error                    = 4.63319520268415805717571217e-08             
relative error                    = 0.0036008627435080660689438625292823       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5047                                       
x2[1] (analytic)                  = 0.00082989682598149310488331482026843        
x2[1] (numeric)                   = 0.00082992064736170493276170342850761        
absolute error                    = 2.382138021182787838860823918e-08            
relative error                    = 0.002870402617054845898443424828277        % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012866359776682439472227866313365         
x1[1] (numeric)                   = 0.00128658863144245873777983729369           
absolute error                    = 4.73462257852094429493376465e-08             
relative error                    = 0.0036798462507642978112915444799932       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50475                                      
x2[1] (analytic)                  = 0.00082994265273507388639046716104801        
x2[1] (numeric)                   = 0.00082996699158877786220333503001671        
absolute error                    = 2.433885370397581286786896870e-08            
relative error                    = 0.0029325946345530239739482310194129       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.001286581647227632869144170960378          
x1[1] (numeric)                   = 0.001286533275711435004318413832633          
absolute error                    = 4.83715161978648257571277450e-08             
relative error                    = 0.0037596926943655158020406407187338       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5048                                       
x2[1] (analytic)                  = 0.00082998848542985414088185286713247        
x2[1] (numeric)                   = 0.00083001334736979605144334777974179        
absolute error                    = 2.486193994191056149491260932e-08            
relative error                    = 0.0029954560067221257668078803209419       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012865273195034759097005654035915         
x1[1] (numeric)                   = 0.0012864779116791022996594294759595         
absolute error                    = 4.94078243736100411359276320e-08             
relative error                    = 0.0038404022693181955566632385799424       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50485                                      
x2[1] (analytic)                  = 0.00083003432406636010496092336108762        
x2[1] (numeric)                   = 0.00083005971470695256085717920594029        
absolute error                    = 2.539064059245589625584485267e-08            
relative error                    = 0.0030589868221432671005939950269432       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012864729944956372495815492666783         
x1[1] (numeric)                   = 0.0012864225393442158087551626494895         
absolute error                    = 5.04551514214408263866171888e-08             
relative error                    = 0.0039219751706658878003200049826118       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5049                                       
x2[1] (analytic)                  = 0.00083008016864511807125298933317795        
x2[1] (numeric)                   = 0.00083010609360244082573005465865133        
absolute error                    = 2.592495732275447706532547338e-08            
relative error                    = 0.0031231871693875033328771178364244       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.001286418672203981076267497605066          
x1[1] (numeric)                   = 0.001286367158705530529895881233296          
absolute error                    = 5.15134984505463716163717700e-08             
relative error                    = 0.0040044115934892252364471274798989       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.50495                                      
x2[1] (analytic)                  = 0.00083012601916665438841065343327373        
x2[1] (numeric)                   = 0.00083015248405845465631781147364636        
absolute error                    = 2.646489180026790715804037263e-08            
relative error                    = 0.0031880571370158281997139107372988       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012863643526283715840292416926091         
x1[1] (numeric)                   = 0.0012863117697618012746818526011888         
absolute error                    = 5.25828665703093473890914203e-08             
relative error                    = 0.0040877117329059293165550398371083       % 
h                                 = 5e-05                                        
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.505                                        
x2[1] (analytic)                  = 0.00083017187563149546111924351454314        
x2[1] (numeric)                   = 0.00083019888607718823790773271762169        
absolute error                    = 2.701044569277678848920307855e-08            
relative error                    = 0.0032535968135791726608818527326769       % 
h                                 = 5e-05                                        
x1[1] (analytic)                  = 0.0012863100357686729739277295072664         
x1[1] (numeric)                   = 0.0012862563725117826679953494631352         
absolute error                    = 5.36632568903059323800441312e-08             
relative error                    = 0.0041718757840708170112391449234859       % 
h                                 = 5e-05                                        
Finished!
Maximum Iterations Reached before Solution Completed!
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;
Iterations                        = 100                                 
Total Elapsed Time               = 2 Seconds
Elapsed Time(since restart)      = 2 Seconds
Expected Time Remaining          = 31 Minutes 43 Seconds
Optimized Time Remaining         = 31 Minutes 32 Seconds
Time to Timeout                  = 14 Minutes 57 Seconds
Percent Done                     = 0.1122                                     % 
> quit
memory used=37.9MB, alloc=4.5MB, time=2.18