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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>                         # Begin Function number 2
>                       logitem_time := proc(fd,secs_in)
>                       global  centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century;
>                       local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int;
>                       secs  :=  (secs_in);
>                       if (secs > 0.0)  then # if number 1
>                     sec_in_millinium  :=   convfloat(sec_in_min *  min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium);
>                     milliniums  :=  convfloat(secs / sec_in_millinium);
>                     millinium_int  :=  floor(milliniums);
>                     centuries  :=  (milliniums - millinium_int)*centuries_in_millinium;
>                     cent_int  :=  floor(centuries);
>                     years  :=  (centuries - cent_int) * years_in_century;
>                     years_int  :=  floor(years);
>                     days  :=  (years - years_int) * days_in_year;
>                     days_int  :=  floor(days);
>                     hours  :=  (days - days_int) * hours_in_day;
>                     hours_int  :=  floor(hours);
>                     minutes  :=  (hours - hours_int) * min_in_hour;
>                     minutes_int  :=  floor(minutes);
>                     seconds  :=  (minutes - minutes_int) * sec_in_min;
>                     sec_int  :=  floor(seconds);
>                     fprintf(fd,"<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,
>   INFO,
>   ALWAYS,
>   glob_max_terms,
>   DEBUGMASSIVE,
>   glob_iolevel,
>   #Top Generate Globals Decl
>   glob_current_iter,
>   glob_small_float,
>   glob_almost_1,
>   glob_html_log,
>   glob_normmax,
>   glob_hmin_init,
>   glob_hmin,
>   glob_not_yet_finished,
>   glob_percent_done,
>   glob_iter,
>   glob_max_rel_trunc_err,
>   glob_not_yet_start_msg,
>   djd_debug2,
>   glob_log10abserr,
>   MAX_UNCHANGED,
>   glob_smallish_float,
>   glob_max_iter,
>   glob_log10_relerr,
>   glob_dump_analytic,
>   years_in_century,
>   hours_in_day,
>   glob_display_flag,
>   glob_log10relerr,
>   glob_orig_start_sec,
>   glob_last_good_h,
>   glob_optimal_done,
>   glob_clock_start_sec,
>   days_in_year,
>   glob_dump,
>   glob_curr_iter_when_opt,
>   glob_optimal_clock_start_sec,
>   glob_h,
>   glob_disp_incr,
>   glob_optimal_expect_sec,
>   glob_max_trunc_err,
>   glob_max_order,
>   glob_abserr,
>   glob_hmax,
>   glob_max_opt_iter,
>   glob_warned2,
>   glob_optimal_start,
>   glob_relerr,
>   glob_large_float,
>   centuries_in_millinium,
>   glob_max_minutes,
>   glob_look_poles,
>   glob_initial_pass,
>   glob_clock_sec,
>   djd_debug,
>   glob_log10normmin,
>   glob_start,
>   glob_max_sec,
>   glob_warned,
>   glob_unchanged_h_cnt,
>   glob_no_eqs,
>   glob_reached_optimal_h,
>   min_in_hour,
>   glob_max_hours,
>   glob_log10_abserr,
>   sec_in_min,
>   #Bottom Generate Globals Decl
>   #BEGIN CONST
>   array_const_2D0,
>   array_const_3D0,
>   array_const_2,
>   array_const_1,
>   array_const_4D0,
>   array_const_0D0,
>   #END CONST
>   array_last_rel_error,
>   array_x1,
>   array_x2,
>   array_type_pole,
>   array_x2_init,
>   array_m1,
>   array_1st_rel_error,
>   array_pole,
>   array_t,
>   array_norms,
>   array_x1_init,
>   array_tmp0,
>   array_tmp1,
>   array_tmp2,
>   array_tmp3,
>   array_tmp4,
>   array_tmp5,
>   array_tmp6,
>   array_tmp7,
>   array_tmp8,
>   array_tmp9,
>   array_tmp10,
>   array_tmp11,
>   array_tmp12,
>   array_tmp13,
>   array_tmp14,
>   array_tmp15,
>   array_tmp16,
>   array_tmp17,
>   array_x2_higher_work2,
>   array_complex_pole,
>   array_x1_higher_work,
>   array_real_pole,
>   array_x2_higher,
>   array_x1_higher_work2,
>   array_poles,
>   array_x2_higher_work,
>   array_x1_higher,
>   glob_last;
>   glob_last;
>   ALWAYS := 1;
>   INFO := 2;
>   DEBUGL := 3;
>   DEBUGMASSIVE := 4;
>   glob_iolevel := INFO;
>   DEBUGL := 3;
>   INFO := 2;
>   ALWAYS := 1;
>   glob_max_terms := 30;
>   DEBUGMASSIVE := 4;
>   glob_iolevel := 5;
>   glob_current_iter := 0;
>   glob_small_float := 0.1e-50;
>   glob_almost_1 := 0.9990;
>   glob_html_log := true;
>   glob_normmax := 0.0;
>   glob_hmin_init := 0.001;
>   glob_hmin := 0.00000000001;
>   glob_not_yet_finished := true;
>   glob_percent_done := 0.0;
>   glob_iter := 0;
>   glob_max_rel_trunc_err := 0.1e-10;
>   glob_not_yet_start_msg := true;
>   djd_debug2 := true;
>   glob_log10abserr := 0.0;
>   MAX_UNCHANGED := 10;
>   glob_smallish_float := 0.1e-100;
>   glob_max_iter := 1000;
>   glob_log10_relerr := 0.1e-10;
>   glob_dump_analytic := false;
>   years_in_century := 100.0;
>   hours_in_day := 24.0;
>   glob_display_flag := true;
>   glob_log10relerr := 0.0;
>   glob_orig_start_sec := 0.0;
>   glob_last_good_h := 0.1;
>   glob_optimal_done := false;
>   glob_clock_start_sec := 0.0;
>   days_in_year := 365.0;
>   glob_dump := false;
>   glob_curr_iter_when_opt := 0;
>   glob_optimal_clock_start_sec := 0.0;
>   glob_h := 0.1;
>   glob_disp_incr := 0.1;
>   glob_optimal_expect_sec := 0.1;
>   glob_max_trunc_err := 0.1e-10;
>   glob_max_order := 30;
>   glob_abserr := 0.1e-10;
>   glob_hmax := 1.0;
>   glob_max_opt_iter := 10;
>   glob_warned2 := false;
>   glob_optimal_start := 0.0;
>   glob_relerr := 0.1e-10;
>   glob_large_float := 9.0e100;
>   centuries_in_millinium := 10.0;
>   glob_max_minutes := 0.0;
>   glob_look_poles := false;
>   glob_initial_pass := true;
>   glob_clock_sec := 0.0;
>   djd_debug := true;
>   glob_log10normmin := 0.1;
>   glob_start := 0;
>   glob_max_sec := 10000.0;
>   glob_warned := false;
>   glob_unchanged_h_cnt := 0;
>   glob_no_eqs := 0;
>   glob_reached_optimal_h := false;
>   min_in_hour := 60.0;
>   glob_max_hours := 0.0;
>   glob_log10_abserr := 0.1e-10;
>   sec_in_min := 60.0;
>   #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/complicated2postode.ode#################");
>   omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;");
>   omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
>   omniout_str(ALWAYS,"!");
>   omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
>   omniout_str(ALWAYS,"Digits := 32;");
>   omniout_str(ALWAYS,"max_terms := 30;");
>   omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
>   omniout_str(ALWAYS,"!");
>   omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
>   omniout_str(ALWAYS,"t_start := 0.5;");
>   omniout_str(ALWAYS,"t_end := 5.0;");
>   omniout_str(ALWAYS,"array_x1_init[1] := exact_soln_x1(t_start);");
>   omniout_str(ALWAYS,"array_x2_init[1] := exact_soln_x2(t_start);");
>   omniout_str(ALWAYS,"array_x2_init[2] := exact_soln_x2p(t_start);");
>   omniout_str(ALWAYS,"glob_h := 0.00001 ;");
>   omniout_str(ALWAYS,"glob_look_poles := true;");
>   omniout_str(ALWAYS,"glob_max_iter := 10;");
>   omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
>   omniout_str(ALWAYS,"#BEGIN OVERRIDE  BLOCK");
>   omniout_str(ALWAYS,"glob_h := 0.0002 ;");
>   omniout_str(ALWAYS,"glob_look_poles := true;");
>   omniout_str(ALWAYS,"glob_max_iter := 100;");
>   omniout_str(ALWAYS,"glob_max_minutes := 15;");
>   omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
>   omniout_str(ALWAYS,"!");
>   omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
>   omniout_str(ALWAYS,"exact_soln_x1 := proc(t)");
>   omniout_str(ALWAYS,"local c1,c2,c3;");
>   omniout_str(ALWAYS,"c1 := 0.0001;");
>   omniout_str(ALWAYS,"c2 := 0.0002;");
>   omniout_str(ALWAYS,"c3 := 0.0003;");
>   omniout_str(ALWAYS,"2.0 * c1 + 6.0 * c3 * exp(-t);");
>   omniout_str(ALWAYS,"end;");
>   omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
>   omniout_str(ALWAYS,"local c1,c2,c3;");
>   omniout_str(ALWAYS,"c1 := 0.0001;");
>   omniout_str(ALWAYS,"c2 := 0.0002;");
>   omniout_str(ALWAYS,"c3 := 0.0003;");
>   omniout_str(ALWAYS,"c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
>   omniout_str(ALWAYS,"end;");
>   omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
>   omniout_str(ALWAYS,"local c1,c2,c3;");
>   omniout_str(ALWAYS,"c1 := 0.0001;");
>   omniout_str(ALWAYS,"c2 := 0.0002;");
>   omniout_str(ALWAYS,"c3 := 0.0003;");
>   omniout_str(ALWAYS,"2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
>   omniout_str(ALWAYS,"end;");
>   omniout_str(ALWAYS,"#END USER DEF BLOCK");
>   omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
>   glob_unchanged_h_cnt   :=  0;
>   glob_warned   :=  false;
>   glob_warned2   :=  false;
>   glob_small_float   :=  1.0e-200;
>   glob_smallish_float   :=  1.0e-64;
>   glob_large_float   :=  1.0e100;
>   glob_almost_1   :=  0.99;
>   glob_log10_abserr   :=  -8.0;
>   glob_log10_relerr   :=  -8.0;
>   glob_hmax   :=  0.01;
>   #BEGIN FIRST INPUT BLOCK
>   #BEGIN FIRST INPUT BLOCK
>   Digits := 32;
>   max_terms := 30;
>   #END FIRST INPUT BLOCK
>   #END FIRST INPUT BLOCK
>   #START OF INITS AFTER INPUT BLOCK
>   glob_max_terms := max_terms;
>   glob_html_log := true;
>   #END OF INITS AFTER INPUT BLOCK
>   array_last_rel_error:= Array(1..(max_terms + 1),[]);
>   array_x1:= Array(1..(max_terms + 1),[]);
>   array_x2:= Array(1..(max_terms + 1),[]);
>   array_type_pole:= Array(1..(max_terms + 1),[]);
>   array_x2_init:= Array(1..(max_terms + 1),[]);
>   array_m1:= Array(1..(max_terms + 1),[]);
>   array_1st_rel_error:= Array(1..(max_terms + 1),[]);
>   array_pole:= Array(1..(max_terms + 1),[]);
>   array_t:= Array(1..(max_terms + 1),[]);
>   array_norms:= Array(1..(max_terms + 1),[]);
>   array_x1_init:= 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_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_x2_higher_work2 := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
>   array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
>   array_x1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
>   array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]);
>   array_x2_higher := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
>   array_x1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
>   array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]);
>   array_x2_higher_work := Array(1..(3+ 1) ,(1..max_terms+ 1),[]);
>   array_x1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]);
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_last_rel_error[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_x1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_x2[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_type_pole[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_x2_init[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_m1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_1st_rel_error[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_pole[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   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_norms[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_x1_init[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp0[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp2[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp3[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp4[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp5[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp6[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp7[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp8[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp9[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp10[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp11[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp12[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp13[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp14[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp15[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp16[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_tmp17[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=3 do # do number 2
>  term := 1;
>  while term <= max_terms do # do number 3
>   array_x2_higher_work2[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=2 do # do number 2
>  term := 1;
>  while term <= 3 do # do number 3
>   array_complex_pole[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=2 do # do number 2
>  term := 1;
>  while term <= max_terms do # do number 3
>   array_x1_higher_work[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=2 do # do number 2
>  term := 1;
>  while term <= 3 do # do number 3
>   array_real_pole[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=3 do # do number 2
>  term := 1;
>  while term <= max_terms do # do number 3
>   array_x2_higher[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=2 do # do number 2
>  term := 1;
>  while term <= max_terms do # do number 3
>   array_x1_higher_work2[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=2 do # do number 2
>  term := 1;
>  while term <= 3 do # do number 3
>   array_poles[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   ord := 1;
>   while ord <=3 do # do number 2
>  term := 1;
>  while term <= max_terms do # do number 3
>   array_x2_higher_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 <= max_terms do # do number 3
>   array_x1_higher[ord,term] := 0.0;
>   term := term + 1;
>   od;# end do number 3
>  ;
>  ord := ord + 1;
>  od;# end do number 2
>   ;
>   #BEGIN ARRAYS DEFINED AND INITIALIZATED
>   array_x2 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_x2[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_x1 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_x1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_t := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_t[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_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_2 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_const_2[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_const_2[1]   := 2;
>   array_const_1 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_const_1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_const_1[1]   := 1;
>   array_const_4D0 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_const_4D0[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_const_4D0[1]   := 4.0;
>   array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms + 1 do # do number 2
>  array_const_0D0[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_const_0D0[1]   := 0.0;
>   array_m1 := Array(1..(max_terms+1 + 1),[]);
>   term := 1;
>   while term <= max_terms do # do number 2
>  array_m1[term] := 0.0;
>  term := term + 1;
>  od;# end do number 2
>   ;
>   array_m1[1]   :=  -1.0;
>   #END ARRAYS DEFINED AND INITIALIZATED
>   #TOP SECOND INPUT BLOCK
>   #BEGIN SECOND INPUT BLOCK
>   #BEGIN SECOND INPUT BLOCK
>   t_start := 0.5;
>   t_end := 5.0;
>   array_x1_init[1] := exact_soln_x1(t_start);
>   array_x2_init[1] := exact_soln_x2(t_start);
>   array_x2_init[2] := exact_soln_x2p(t_start);
>   glob_h := 0.00001 ;
>   glob_look_poles := true;
>   glob_max_iter := 10;
>   #END SECOND INPUT BLOCK
>   #BEGIN OVERRIDE  BLOCK
>   glob_h := 0.0002 ;
>   glob_look_poles := true;
>   glob_max_iter := 100;
>   glob_max_minutes := 15;
>   #END OVERRIDE BLOCK
>   #END SECOND INPUT BLOCK
>   #BEGIN INITS AFTER SECOND INPUT BLOCK
>   glob_last_good_h := glob_h;
>   glob_max_terms   := max_terms;
>   glob_max_sec   := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
>   glob_abserr   :=  10.0 ^ (glob_log10_abserr);
>   glob_relerr   :=  10.0 ^ (glob_log10_relerr);
>   chk_data();
>   #AFTER INITS AFTER SECOND INPUT BLOCK
>   if glob_html_log  then # if number 3
>       html_log_file := fopen("html/entry.html",WRITE,TEXT);
>       fi;# end if 3
>     ;
>     #BEGIN SOLUTION CODE
>     omniout_str(ALWAYS,"START of Soultion");
>     #Start Series -- INITIALIZE FOR SOLUTION
>     array_t[1]   := t_start;
>     array_t[2]   :=  glob_h;
>     order_diff := 1;
>     #Start Series array_x1
>     term_no   :=  1;
>     while (term_no <= order_diff) do # do number 2
>       array_x1[term_no] := array_x1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
>       term_no   :=  term_no + 1;
>       od;# end do number 2
>     ;
>     rows   :=  order_diff;
>     r_order   :=  1;
>     while (r_order <= rows) do # do number 2
>       term_no   :=  1;
>       while (term_no <= (rows - r_order + 1)) do # do number 3
>         it  := term_no + r_order - 1;
>         array_x1_higher[r_order,term_no] := array_x1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
>         term_no   :=  term_no + 1;
>         od;# end do number 3
>       ;
>       r_order   :=  r_order + 1;
>       od;# end do number 2
>     ;
>     order_diff := 2;
>     #Start Series array_x2
>     term_no   :=  1;
>     while (term_no <= order_diff) do # do number 2
>       array_x2[term_no] := array_x2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1);
>       term_no   :=  term_no + 1;
>       od;# end do number 2
>     ;
>     rows   :=  order_diff;
>     r_order   :=  1;
>     while (r_order <= rows) do # do number 2
>       term_no   :=  1;
>       while (term_no <= (rows - r_order + 1)) do # do number 3
>         it  := term_no + r_order - 1;
>         array_x2_higher[r_order,term_no] := array_x2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1)));
>         term_no   :=  term_no + 1;
>         od;# end do number 3
>       ;
>       r_order   :=  r_order + 1;
>       od;# end do number 2
>     ;
>     current_iter   :=  1;
>     glob_clock_start_sec   := elapsed_time_seconds();
>     start_array_x1();
>     if (abs(array_x1_higher[1,1]) > glob_small_float)  then # if number 3
>       tmp   :=  abs(array_x1_higher[1,1]);
>       log10norm   :=  (log10(tmp));
>       if (log10norm < glob_log10normmin)  then # if number 4
>         glob_log10normmin   :=  log10norm;
>         fi;# end if 4
>       fi;# end if 3
>     ;
>     display_alot(current_iter)
>     ;
>     start_array_x2();
>     if (abs(array_x2_higher[1,1]) > glob_small_float)  then # if number 3
>       tmp   :=  abs(array_x2_higher[1,1]);
>       log10norm   :=  (log10(tmp));
>       if (log10norm < glob_log10normmin)  then # if number 4
>         glob_log10normmin   :=  log10norm;
>         fi;# end if 4
>       fi;# end if 3
>     ;
>     display_alot(current_iter)
>     ;
>     glob_clock_sec   :=  elapsed_time_seconds();
>     glob_current_iter   :=  0;
>     glob_iter   :=  0;
>     omniout_str(DEBUGL," ");
>     glob_reached_optimal_h   :=  true;
>     glob_optimal_clock_start_sec := elapsed_time_seconds();
>     while ((glob_current_iter < glob_max_iter) and (array_t[1] <= t_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
>       #left paren 0001C
>       omniout_str(INFO," ");
>       omniout_str(INFO,"TOP MAIN SOLVE Loop");
>       glob_iter   :=  glob_iter + 1;
>       glob_clock_sec   := elapsed_time_seconds();
>       glob_current_iter   :=  glob_current_iter + 1;
>       sub_iter := 1;
>       while sub_iter <= 3 do # do number 3
>         atomall()
>         ;
>         sub_iter := sub_iter + 1;
>         od;# end do number 3
>       ;
>       if (glob_look_poles)  then # if number 3
>         #left paren 0004C
>         check_for_pole();
>         fi;# end if 3
>       ;#was right paren 0004C
>       array_t[1]   := array_t[1] + glob_h;
>       array_t[2]   :=  glob_h;
>       order_diff := 1;
>       #Jump Series array_x1
>       #START PART 1  SUM AND ADJUST
>       #START SUM AND ADJUST EQ =1
>       #sum_and_adjust array_x1
>       order_diff := 1;
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 1;
>       ord := 2;
>       calc_term := 1;
>       #adjust_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 1;
>       temp_sum := 0.0;
>       ord := 2;
>       calc_term := 1;
>       #sum_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x1_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 1;
>       ord := 1;
>       calc_term := 2;
>       #adjust_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 1;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 2;
>       #sum_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x1_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #BEFORE ADJUST SUBSERIES EQ =1
>       order_diff := 1;
>       ord := 1;
>       calc_term := 1;
>       #adjust_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =1
>       #BEFORE SUM SUBSERIES EQ =1
>       order_diff := 1;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 1;
>       #sum_subseriesarray_x1
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x1_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =1
>       #END SUM AND ADJUST EQ =1
>       #END PART 1
>       #START PART 2  MOVE TERMS to REGULAR Array
>       term_no := glob_max_terms;
>       while (term_no >= 1) do # do number 3
>         array_x1[term_no] := array_x1_higher_work2[1,term_no];
>         ord := 1;
>         while ord <= order_diff  do # do number 4
>           array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no];
>           ord := ord + 1;
>           od;# end do number 4
>         ;
>         term_no   :=  term_no - 1;
>         od;# end do number 3
>       ;
>       #END PART 2 HEVE MOVED TERMS to REGULAR Array
>       order_diff := 2;
>       #Jump Series array_x2
>       #START PART 1  SUM AND ADJUST
>       #START SUM AND ADJUST EQ =2
>       #sum_and_adjust array_x2
>       order_diff := 2;
>       #BEFORE ADJUST SUBSERIES EQ =2
>       order_diff := 2;
>       ord := 3;
>       calc_term := 1;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =2
>       #BEFORE SUM SUBSERIES EQ =2
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 3;
>       calc_term := 1;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =2
>       #BEFORE ADJUST SUBSERIES EQ =2
>       order_diff := 2;
>       ord := 2;
>       calc_term := 2;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =2
>       #BEFORE SUM SUBSERIES EQ =2
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 2;
>       calc_term := 2;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =2
>       #BEFORE ADJUST SUBSERIES EQ =2
>       order_diff := 2;
>       ord := 2;
>       calc_term := 1;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =2
>       #BEFORE SUM SUBSERIES EQ =2
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 2;
>       calc_term := 1;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =2
>       #BEFORE ADJUST SUBSERIES EQ =2
>       order_diff := 2;
>       ord := 1;
>       calc_term := 3;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =2
>       #BEFORE SUM SUBSERIES EQ =2
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 3;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =2
>       #BEFORE ADJUST SUBSERIES EQ =2
>       order_diff := 2;
>       ord := 1;
>       calc_term := 2;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =2
>       #BEFORE SUM SUBSERIES EQ =2
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 2;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =2
>       #BEFORE ADJUST SUBSERIES EQ =2
>       order_diff := 2;
>       ord := 1;
>       calc_term := 1;
>       #adjust_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii  - 1);
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       #AFTER ADJUST SUBSERIES EQ =2
>       #BEFORE SUM SUBSERIES EQ =2
>       order_diff := 2;
>       temp_sum := 0.0;
>       ord := 1;
>       calc_term := 1;
>       #sum_subseriesarray_x2
>       iii  := glob_max_terms;
>       while (iii >= calc_term)   do # do number 3
>         temp_sum := temp_sum + array_x2_higher_work[ord,iii];
>         iii  := iii - 1;
>         od;# end do number 3
>       ;
>       array_x2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!);
>       #AFTER SUM SUBSERIES EQ =2
>       #END SUM AND ADJUST EQ =2
>       #END PART 1
>       #START PART 2  MOVE TERMS to REGULAR Array
>       term_no := glob_max_terms;
>       while (term_no >= 1) do # do number 3
>         array_x2[term_no] := array_x2_higher_work2[1,term_no];
>         ord := 1;
>         while ord <= order_diff  do # do number 4
>           array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no];
>           ord := ord + 1;
>           od;# end do number 4
>         ;
>         term_no   :=  term_no - 1;
>         od;# end do number 3
>       ;
>       #END PART 2 HEVE MOVED TERMS to REGULAR Array
>       display_alot(current_iter)
>       ;
>       od;# end do number 2
>     ;#right paren 0001C
>     omniout_str(ALWAYS,"Finished!");
>     if (glob_iter >= glob_max_iter)  then # if number 3
>       omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!")
>       fi;# end if 3
>     ;
>     if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec  )) then # if number 3
>       omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!")
>       fi;# end if 3
>     ;
>     glob_clock_sec   := elapsed_time_seconds();
>     omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;");
>     omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
>     omniout_int(INFO,"Iterations                       ",32,glob_iter,4," ")
>     ;
>     prog_report(t_start,t_end);
>     if glob_html_log  then # if number 3
>       logstart(html_log_file);
>       logitem_str(html_log_file,"2012-06-02T02:04:48-05:00")
>       ;
>       logitem_str(html_log_file,"Maple")
>       ;
>       logitem_str(html_log_file,"<a href=\"complicated2.ode.txt\">complicated2</a>")
>       ;
>       logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;")
>       ;
>       logitem_float(html_log_file,t_start)
>       ;
>       logitem_float(html_log_file,t_end)
>       ;
>       logitem_float(html_log_file,array_t[1])
>       ;
>       logitem_float(html_log_file,glob_h)
>       ;
>       logitem_integer(html_log_file,Digits)
>       ;
>       ;
>       logitem_integer(html_log_file,glob_max_terms)
>       ;
>       logitem_float(html_log_file,array_1st_rel_error[1])
>       ;
>       logitem_float(html_log_file,array_last_rel_error[1])
>       ;
>       logitem_integer(html_log_file,glob_iter)
>       ;
>       logitem_pole(html_log_file,array_type_pole[1])
>       ;
>       if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 4
>         logitem_float(html_log_file,array_pole[1])
>         ;
>         logitem_float(html_log_file,array_pole[2])
>         ;
>         0;
>         else
>         logitem_str(html_log_file,"NA")
>         ;
>         logitem_str(html_log_file,"NA")
>         ;
>         0;
>         fi;# end if 4
>       ;
>       logitem_time(html_log_file,convfloat(glob_clock_sec))
>       ;
>       if glob_percent_done < 100.0  then # if number 4
>         logitem_time(html_log_file,convfloat(glob_optimal_expect_sec))
>         ;
>         0
>         else
>         logitem_str(html_log_file,"Done")
>         ;
>         0
>         fi;# end if 4
>       ;
>       log_revs(html_log_file,"<td> 076 </td>")
>       ;
>       logitem_str(html_log_file,"<a href=\"diffeq.complicated2.mxt.txt\">complicated2 diffeq.mxt</a>")
>       ;
>       logitem_str(html_log_file,"<a href=\"results.complicated2.mxt.txt\">complicated2 maple results</a>")
>       ;
>       logitem_str(html_log_file,"sub iter tot order")
>       ;
>       logend(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;")
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       ;
>       logditto(html_log_file)
>       ;
>       logitem_float(html_log_file,array_1st_rel_error[2])
>       ;
>       logitem_float(html_log_file,array_last_rel_error[2])
>       ;
>       logditto(html_log_file)
>       ;
>       logitem_pole(html_log_file,array_type_pole[2])
>       ;
>       if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 4
>         logitem_float(html_log_file,array_pole[1])
>         ;
>         logitem_float(html_log_file,array_pole[2])
>         ;
>         0;
>         else
>         logitem_str(html_log_file,"NA")
>         ;
>         logitem_str(html_log_file,"NA")
>         ;
>         0;
>         fi;# end if 4
>       ;
>       logditto(html_log_file)
>       ;
>       if glob_percent_done < 100.0  then # if number 4
>         logditto(html_log_file)
>         ;
>         0
>         else
>         logditto(html_log_file)
>         ;
>         0
>         fi;# end if 4
>       ;
>       logditto(html_log_file);
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logditto(html_log_file)
>       ;
>       logend(html_log_file)
>       ;
>       ;
>       fi;# end if 3
>     ;
>     if glob_html_log  then # if number 3
>       fclose(html_log_file);
>       fi;# end if 3
>     ;
>     ;;
>     #END OUTFILEMAIN
>     # End Function number 8
>     end;
mainprog := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum,
current_iter, t_start, t_end, it, log10norm, max_terms, opt_iter, tmp;
global DEBUGL, INFO, ALWAYS, glob_max_terms, DEBUGMASSIVE, glob_iolevel,
glob_current_iter, glob_small_float, glob_almost_1, glob_html_log,
glob_normmax, glob_hmin_init, glob_hmin, glob_not_yet_finished,
glob_percent_done, glob_iter, glob_max_rel_trunc_err,
glob_not_yet_start_msg, djd_debug2, glob_log10abserr, MAX_UNCHANGED,
glob_smallish_float, glob_max_iter, glob_log10_relerr, glob_dump_analytic,
years_in_century, hours_in_day, glob_display_flag, glob_log10relerr,
glob_orig_start_sec, glob_last_good_h, glob_optimal_done,
glob_clock_start_sec, days_in_year, glob_dump, glob_curr_iter_when_opt,
glob_optimal_clock_start_sec, glob_h, glob_disp_incr,
glob_optimal_expect_sec, glob_max_trunc_err, glob_max_order, glob_abserr,
glob_hmax, glob_max_opt_iter, glob_warned2, glob_optimal_start, glob_relerr,
glob_large_float, centuries_in_millinium, glob_max_minutes, glob_look_poles,
glob_initial_pass, glob_clock_sec, djd_debug, glob_log10normmin, glob_start,
glob_max_sec, glob_warned, glob_unchanged_h_cnt, glob_no_eqs,
glob_reached_optimal_h, min_in_hour, glob_max_hours, glob_log10_abserr,
sec_in_min, array_const_2D0, array_const_3D0, array_const_2, array_const_1,
array_const_4D0, array_const_0D0, array_last_rel_error, array_x1, array_x2,
array_type_pole, array_x2_init, array_m1, array_1st_rel_error, array_pole,
array_t, array_norms, array_x1_init, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7, array_tmp8,
array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13, array_tmp14,
array_tmp15, array_tmp16, array_tmp17, array_x2_higher_work2,
array_complex_pole, array_x1_higher_work, array_real_pole, array_x2_higher,
array_x1_higher_work2, array_poles, array_x2_higher_work, array_x1_higher,
glob_last;
    glob_last;
    ALWAYS := 1;
    INFO := 2;
    DEBUGL := 3;
    DEBUGMASSIVE := 4;
    glob_iolevel := INFO;
    DEBUGL := 3;
    INFO := 2;
    ALWAYS := 1;
    glob_max_terms := 30;
    DEBUGMASSIVE := 4;
    glob_iolevel := 5;
    glob_current_iter := 0;
    glob_small_float := 0.1*10^(-50);
    glob_almost_1 := 0.9990;
    glob_html_log := true;
    glob_normmax := 0.;
    glob_hmin_init := 0.001;
    glob_hmin := 0.1*10^(-10);
    glob_not_yet_finished := true;
    glob_percent_done := 0.;
    glob_iter := 0;
    glob_max_rel_trunc_err := 0.1*10^(-10);
    glob_not_yet_start_msg := true;
    djd_debug2 := true;
    glob_log10abserr := 0.;
    MAX_UNCHANGED := 10;
    glob_smallish_float := 0.1*10^(-100);
    glob_max_iter := 1000;
    glob_log10_relerr := 0.1*10^(-10);
    glob_dump_analytic := false;
    years_in_century := 100.0;
    hours_in_day := 24.0;
    glob_display_flag := true;
    glob_log10relerr := 0.;
    glob_orig_start_sec := 0.;
    glob_last_good_h := 0.1;
    glob_optimal_done := false;
    glob_clock_start_sec := 0.;
    days_in_year := 365.0;
    glob_dump := false;
    glob_curr_iter_when_opt := 0;
    glob_optimal_clock_start_sec := 0.;
    glob_h := 0.1;
    glob_disp_incr := 0.1;
    glob_optimal_expect_sec := 0.1;
    glob_max_trunc_err := 0.1*10^(-10);
    glob_max_order := 30;
    glob_abserr := 0.1*10^(-10);
    glob_hmax := 1.0;
    glob_max_opt_iter := 10;
    glob_warned2 := false;
    glob_optimal_start := 0.;
    glob_relerr := 0.1*10^(-10);
    glob_large_float := 0.90*10^101;
    centuries_in_millinium := 10.0;
    glob_max_minutes := 0.;
    glob_look_poles := false;
    glob_initial_pass := true;
    glob_clock_sec := 0.;
    djd_debug := true;
    glob_log10normmin := 0.1;
    glob_start := 0;
    glob_max_sec := 10000.0;
    glob_warned := false;
    glob_unchanged_h_cnt := 0;
    glob_no_eqs := 0;
    glob_reached_optimal_h := false;
    min_in_hour := 60.0;
    glob_max_hours := 0.;
    glob_log10_abserr := 0.1*10^(-10);
    sec_in_min := 60.0;
    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/complicated2postode.ode#################");
    omniout_str(ALWAYS,
        "diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;");
    omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \
        diff(x1,t,2) - diff (x1,t,1) + x1;");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "Digits := 32;");
    omniout_str(ALWAYS, "max_terms := 30;");
    omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "t_start := 0.5;");
    omniout_str(ALWAYS, "t_end := 5.0;");
    omniout_str(ALWAYS, "array_x1_init[1] := exact_soln_x1(t_start);");
    omniout_str(ALWAYS, "array_x2_init[1] := exact_soln_x2(t_start);");
    omniout_str(ALWAYS, "array_x2_init[2] := exact_soln_x2p(t_start);");
    omniout_str(ALWAYS, "glob_h := 0.00001 ;");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "glob_max_iter := 10;");
    omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
    omniout_str(ALWAYS, "#BEGIN OVERRIDE  BLOCK");
    omniout_str(ALWAYS, "glob_h := 0.0002 ;");
    omniout_str(ALWAYS, "glob_look_poles := true;");
    omniout_str(ALWAYS, "glob_max_iter := 100;");
    omniout_str(ALWAYS, "glob_max_minutes := 15;");
    omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
    omniout_str(ALWAYS, "!");
    omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
    omniout_str(ALWAYS, "exact_soln_x1 := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := 0.0001;");
    omniout_str(ALWAYS, "c2 := 0.0002;");
    omniout_str(ALWAYS, "c3 := 0.0003;");
    omniout_str(ALWAYS, "2.0 * c1 + 6.0 * c3 * exp(-t);");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := 0.0001;");
    omniout_str(ALWAYS, "c2 := 0.0002;");
    omniout_str(ALWAYS, "c3 := 0.0003;");
    omniout_str(ALWAYS, "c1 + c2 * exp(2.0 * t) + c3 * exp(-t);");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
    omniout_str(ALWAYS, "local c1,c2,c3;");
    omniout_str(ALWAYS, "c1 := 0.0001;");
    omniout_str(ALWAYS, "c2 := 0.0002;");
    omniout_str(ALWAYS, "c3 := 0.0003;");
    omniout_str(ALWAYS, "2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);");
    omniout_str(ALWAYS, "end;");
    omniout_str(ALWAYS, "#END USER DEF BLOCK");
    omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
    glob_unchanged_h_cnt := 0;
    glob_warned := false;
    glob_warned2 := false;
    glob_small_float := 0.10*10^(-199);
    glob_smallish_float := 0.10*10^(-63);
    glob_large_float := 0.10*10^101;
    glob_almost_1 := 0.99;
    glob_log10_abserr := -8.0;
    glob_log10_relerr := -8.0;
    glob_hmax := 0.01;
    Digits := 32;
    max_terms := 30;
    glob_max_terms := max_terms;
    glob_html_log := true;
    array_last_rel_error := Array(1 .. max_terms + 1, []);
    array_x1 := Array(1 .. max_terms + 1, []);
    array_x2 := Array(1 .. max_terms + 1, []);
    array_type_pole := Array(1 .. max_terms + 1, []);
    array_x2_init := Array(1 .. max_terms + 1, []);
    array_m1 := Array(1 .. max_terms + 1, []);
    array_1st_rel_error := Array(1 .. max_terms + 1, []);
    array_pole := Array(1 .. max_terms + 1, []);
    array_t := Array(1 .. max_terms + 1, []);
    array_norms := Array(1 .. max_terms + 1, []);
    array_x1_init := 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_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_x2_higher_work2 := Array(1 .. 4, 1 .. max_terms + 1, []);
    array_complex_pole := Array(1 .. 3, 1 .. 4, []);
    array_x1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []);
    array_real_pole := Array(1 .. 3, 1 .. 4, []);
    array_x2_higher := Array(1 .. 4, 1 .. max_terms + 1, []);
    array_x1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []);
    array_poles := Array(1 .. 3, 1 .. 4, []);
    array_x2_higher_work := Array(1 .. 4, 1 .. max_terms + 1, []);
    array_x1_higher := Array(1 .. 3, 1 .. max_terms + 1, []);
    term := 1;
    while term <= max_terms do
        array_last_rel_error[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_x1[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_x2[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do
        array_type_pole[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_x2_init[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_m1[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do
        array_1st_rel_error[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_pole[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_t[term] := 0.; term := term + 1 end do
    ;
    term := 1;
    while term <= max_terms do array_norms[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_x1_init[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp7[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp10[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp11[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp12[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp13[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp14[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp15[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp16[term] := 0.; term := term + 1
    end do;
    term := 1;
    while term <= max_terms do array_tmp17[term] := 0.; term := term + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= max_terms do
            array_x2_higher_work2[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do
            array_complex_pole[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= max_terms do
            array_x1_higher_work[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do
            array_real_pole[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= max_terms do
            array_x2_higher[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= max_terms do
            array_x1_higher_work2[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 3 do
        term := 1;
        while term <= max_terms do
            array_x2_higher_work[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    ord := 1;
    while ord <= 2 do
        term := 1;
        while term <= max_terms do
            array_x1_higher[ord, term] := 0.; term := term + 1
        end do;
        ord := ord + 1
    end do;
    array_x2 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_x2[term] := 0.; term := term + 1
    end do;
    array_x1 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_x1[term] := 0.; term := term + 1
    end do;
    array_t := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do array_t[term] := 0.; term := term + 1
    end do;
    array_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_2 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_const_2[term] := 0.; term := term + 1
    end do;
    array_const_2[1] := 2;
    array_const_1 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_const_1[term] := 0.; term := term + 1
    end do;
    array_const_1[1] := 1;
    array_const_4D0 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_const_4D0[term] := 0.; term := term + 1
    end do;
    array_const_4D0[1] := 4.0;
    array_const_0D0 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms + 1 do
        array_const_0D0[term] := 0.; term := term + 1
    end do;
    array_const_0D0[1] := 0.;
    array_m1 := Array(1 .. max_terms + 2, []);
    term := 1;
    while term <= max_terms do array_m1[term] := 0.; term := term + 1
    end do;
    array_m1[1] := -1.0;
    t_start := 0.5;
    t_end := 5.0;
    array_x1_init[1] := exact_soln_x1(t_start);
    array_x2_init[1] := exact_soln_x2(t_start);
    array_x2_init[2] := exact_soln_x2p(t_start);
    glob_h := 0.00001;
    glob_look_poles := true;
    glob_max_iter := 10;
    glob_h := 0.0002;
    glob_look_poles := true;
    glob_max_iter := 100;
    glob_max_minutes := 15;
    glob_last_good_h := glob_h;
    glob_max_terms := max_terms;
    glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
         + convfloat(3600.0)*convfloat(glob_max_hours);
    glob_abserr := 10.0^glob_log10_abserr;
    glob_relerr := 10.0^glob_log10_relerr;
    chk_data();
    if glob_html_log then
        html_log_file := fopen("html/entry.html", WRITE, TEXT)
    end if;
    omniout_str(ALWAYS, "START of Soultion");
    array_t[1] := t_start;
    array_t[2] := glob_h;
    order_diff := 1;
    term_no := 1;
    while term_no <= order_diff do
        array_x1[term_no] := array_x1_init[term_no]*glob_h^(term_no - 1)/
            factorial_1(term_no - 1);
        term_no := term_no + 1
    end do;
    rows := order_diff;
    r_order := 1;
    while r_order <= rows do
        term_no := 1;
        while term_no <= rows - r_order + 1 do
            it := term_no + r_order - 1;
            array_x1_higher[r_order, term_no] := array_x1_init[it]*
                glob_h^(term_no - 1)/factorial_1(term_no - 1);
            term_no := term_no + 1
        end do;
        r_order := r_order + 1
    end do;
    order_diff := 2;
    term_no := 1;
    while term_no <= order_diff do
        array_x2[term_no] := array_x2_init[term_no]*glob_h^(term_no - 1)/
            factorial_1(term_no - 1);
        term_no := term_no + 1
    end do;
    rows := order_diff;
    r_order := 1;
    while r_order <= rows do
        term_no := 1;
        while term_no <= rows - r_order + 1 do
            it := term_no + r_order - 1;
            array_x2_higher[r_order, term_no] := array_x2_init[it]*
                glob_h^(term_no - 1)/factorial_1(term_no - 1);
            term_no := term_no + 1
        end do;
        r_order := r_order + 1
    end do;
    current_iter := 1;
    glob_clock_start_sec := elapsed_time_seconds();
    start_array_x1();
    if glob_small_float < abs(array_x1_higher[1, 1]) then
        tmp := abs(array_x1_higher[1, 1]);
        log10norm := log10(tmp);
        if log10norm < glob_log10normmin then
            glob_log10normmin := log10norm
        end if
    end if;
    display_alot(current_iter);
    start_array_x2();
    if glob_small_float < abs(array_x2_higher[1, 1]) then
        tmp := abs(array_x2_higher[1, 1]);
        log10norm := log10(tmp);
        if log10norm < glob_log10normmin then
            glob_log10normmin := log10norm
        end if
    end if;
    display_alot(current_iter);
    glob_clock_sec := elapsed_time_seconds();
    glob_current_iter := 0;
    glob_iter := 0;
    omniout_str(DEBUGL, " ");
    glob_reached_optimal_h := true;
    glob_optimal_clock_start_sec := elapsed_time_seconds();
    while glob_current_iter < glob_max_iter and array_t[1] <= t_end and
    convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
    convfloat(glob_max_sec) do
        omniout_str(INFO, " ");
        omniout_str(INFO, "TOP MAIN SOLVE Loop");
        glob_iter := glob_iter + 1;
        glob_clock_sec := elapsed_time_seconds();
        glob_current_iter := glob_current_iter + 1;
        sub_iter := 1;
        while sub_iter <= 3 do atomall(); sub_iter := sub_iter + 1 end do;
        if glob_look_poles then check_for_pole() end if;
        array_t[1] := array_t[1] + glob_h;
        array_t[2] := glob_h;
        order_diff := 1;
        order_diff := 1;
        order_diff := 1;
        ord := 2;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x1_higher_work[2, iii] := array_x1_higher[2, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 1;
        temp_sum := 0.;
        ord := 2;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x1_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x1_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 1;
        ord := 1;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 1;
        temp_sum := 0.;
        ord := 1;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x1_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x1_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 1;
        ord := 1;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x1_higher_work[1, iii] := array_x1_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 1;
        temp_sum := 0.;
        ord := 1;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x1_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x1_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        term_no := glob_max_terms;
        while 1 <= term_no do
            array_x1[term_no] := array_x1_higher_work2[1, term_no];
            ord := 1;
            while ord <= order_diff do
                array_x1_higher[ord, term_no] :=
                    array_x1_higher_work2[ord, term_no];
                ord := ord + 1
            end do;
            term_no := term_no - 1
        end do;
        order_diff := 2;
        order_diff := 2;
        order_diff := 2;
        ord := 3;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[3, iii] := array_x2_higher[3, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 3;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 2;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 2;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 2;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[2, iii] := array_x2_higher[2, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 2;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 1;
        calc_term := 3;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 1;
        calc_term := 3;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 1;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 1;
        calc_term := 2;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        order_diff := 2;
        ord := 1;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            array_x2_higher_work[1, iii] := array_x2_higher[1, iii]/(
                glob_h^(calc_term - 1)*
                factorial_3(iii - calc_term, iii - 1));
            iii := iii - 1
        end do;
        order_diff := 2;
        temp_sum := 0.;
        ord := 1;
        calc_term := 1;
        iii := glob_max_terms;
        while calc_term <= iii do
            temp_sum := temp_sum + array_x2_higher_work[ord, iii];
            iii := iii - 1
        end do;
        array_x2_higher_work2[ord, calc_term] :=
            temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!;
        term_no := glob_max_terms;
        while 1 <= term_no do
            array_x2[term_no] := array_x2_higher_work2[1, term_no];
            ord := 1;
            while ord <= order_diff do
                array_x2_higher[ord, term_no] :=
                    array_x2_higher_work2[ord, term_no];
                ord := ord + 1
            end do;
            term_no := term_no - 1
        end do;
        display_alot(current_iter)
    end do;
    omniout_str(ALWAYS, "Finished!");
    if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
        "Maximum Iterations Reached before Solution Completed!")
    end if;
    if convfloat(glob_max_sec) <=
    elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
        omniout_str(ALWAYS,
        "Maximum Time Reached before Solution Completed!")
    end if;
    glob_clock_sec := elapsed_time_seconds();
    omniout_str(INFO,
        "diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;");
    omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - di\
        ff(x1,t,2) - diff (x1,t,1) + x1;");
    omniout_int(INFO, "Iterations                       ", 32, glob_iter, 4,
        " ");
    prog_report(t_start, t_end);
    if glob_html_log then
        logstart(html_log_file);
        logitem_str(html_log_file, "2012-06-02T02:04:48-05:00");
        logitem_str(html_log_file, "Maple");
        logitem_str(html_log_file,
            "<a href=\"complicated2.ode.txt\">complicated2</a>");
        logitem_str(html_log_file,
            "diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;")
            ;
        logitem_float(html_log_file, t_start);
        logitem_float(html_log_file, t_end);
        logitem_float(html_log_file, array_t[1]);
        logitem_float(html_log_file, glob_h);
        logitem_integer(html_log_file, Digits);
        logitem_integer(html_log_file, glob_max_terms);
        logitem_float(html_log_file, array_1st_rel_error[1]);
        logitem_float(html_log_file, array_last_rel_error[1]);
        logitem_integer(html_log_file, glob_iter);
        logitem_pole(html_log_file, array_type_pole[1]);
        if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
            logitem_float(html_log_file, array_pole[1]);
            logitem_float(html_log_file, array_pole[2]);
            0
        else
            logitem_str(html_log_file, "NA");
            logitem_str(html_log_file, "NA");
            0
        end if;
        logitem_time(html_log_file, convfloat(glob_clock_sec));
        if glob_percent_done < 100.0 then
            logitem_time(html_log_file, convfloat(glob_optimal_expect_sec))
                ;
            0
        else logitem_str(html_log_file, "Done"); 0
        end if;
        log_revs(html_log_file, "<td> 076 </td>");
        logitem_str(html_log_file, "<a href=\"diffeq.complicated2.mxt.txt\
            \">complicated2 diffeq.mxt</a>");
        logitem_str(html_log_file, "<a href=\"results.complicated2.mxt.tx\
            t\">complicated2 maple results</a>");
        logitem_str(html_log_file, "sub iter tot order");
        logend(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - \
            2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;");
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logitem_float(html_log_file, array_1st_rel_error[2]);
        logitem_float(html_log_file, array_last_rel_error[2]);
        logditto(html_log_file);
        logitem_pole(html_log_file, array_type_pole[2]);
        if array_type_pole[2] = 1 or array_type_pole[2] = 2 then
            logitem_float(html_log_file, array_pole[1]);
            logitem_float(html_log_file, array_pole[2]);
            0
        else
            logitem_str(html_log_file, "NA");
            logitem_str(html_log_file, "NA");
            0
        end if;
        logditto(html_log_file);
        if glob_percent_done < 100.0 then logditto(html_log_file); 0
        else logditto(html_log_file); 0
        end if;
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logditto(html_log_file);
        logend(html_log_file)
    end if;
    if glob_html_log then fclose(html_log_file) end if
end proc

>   mainprog();
##############ECHO OF PROBLEM#################
##############temp/complicated2postode.ode#################
diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
!
#BEGIN FIRST INPUT BLOCK
Digits := 32;
max_terms := 30;
#END FIRST INPUT BLOCK
!
#BEGIN SECOND INPUT BLOCK
t_start := 0.5;
t_end := 5.0;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_h := 0.00001 ;
glob_look_poles := true;
glob_max_iter := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE  BLOCK
glob_h := 0.0002 ;
glob_look_poles := true;
glob_max_iter := 100;
glob_max_minutes := 15;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c1 + 6.0 * c3 * exp(-t);
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
c1 + c2 * exp(2.0 * t) + c3 * exp(-t);
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 0.0001;
c2 := 0.0002;
c3 := 0.0003;
2.0 * c2 * exp(2.0 * t) - c3 * exp(-t);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
t[1]                              = 0.5                                          
x1[1] (analytic)                  = 0.0012917551874827401624868391629841         
x1[1] (numeric)                   = 0.0012917551874827401624868391629841         
absolute error                    = 0                                            
relative error                    = 0                                          % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082561556360559907415319735476789        
x2[1] (numeric)                   = 0.00082561556360559907415319735476789        
absolute error                    = 0                                            
relative error                    = 0                                          % 
h                                 = 0.0002                                       
t[1]                              = 0.5                                          
x1[1] (analytic)                  = 0.0012917551874827401624868391629841         
x1[1] (numeric)                   = 0.0012917551874827401624868391629841         
absolute error                    = 0                                            
relative error                    = 0                                          % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082561556360559907415319735476789        
x2[1] (numeric)                   = 0.00082561556360559907415319735476789        
absolute error                    = 0                                            
relative error                    = 0                                          % 
h                                 = 0.0002                                       
 
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5002                                       
x1[1] (analytic)                  = 0.0012915368582788917633066026400632         
x1[1] (numeric)                   = 0.0012912082618714470719389782893821         
absolute error                    = 3.285964074446913676243506811e-07            
relative error                    = 0.025442278734699102782846601681027        % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008257966814495432344339416603249         
x2[1] (numeric)                   = 0.00082579966246014015195362131826852        
absolute error                    = 2.98101059691751967965794362e-09             
relative error                    = 0.00036098602281676298440257604581604      % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5004                                       
x1[1] (analytic)                  = 0.0012913185727365178408202846139762         
x1[1] (numeric)                   = 0.0012906992947447603984997028676901         
absolute error                    = 6.192779917574423205817462861e-07            
relative error                    = 0.047957026626287092814476117297578        % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082597789359022044558440876232671        
x2[1] (numeric)                   = 0.00082606565718303585221911494509763        
absolute error                    = 8.776359281540663470618277092e-08            
relative error                    = 0.010625416672343463443939548995395        % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5006                                       
x1[1] (analytic)                  = 0.0012911003308468869733038234462486         
x1[1] (numeric)                   = 0.001290222605078999043181051201675          
absolute error                    = 8.777257678879301227722445736e-07            
relative error                    = 0.067982769961199909218498750859225        % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082615920006099036141977864461309        
x2[1] (numeric)                   = 0.00082640119879340573961533470880295        
absolute error                    = 2.4199873241537819555606418986e-07           
relative error                    = 0.029292021731103749209002806254569        % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=3.0MB, time=0.21
NO POLE
NO POLE
t[1]                              = 0.5008                                       
x1[1] (analytic)                  = 0.0012908821326012694851428855175656         
x1[1] (numeric)                   = 0.0012897733680819103552231738368234         
absolute error                    = 1.1087645193591299197116807422e-06           
relative error                    = 0.085892002945679281880499594778575        % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082634060089522685551538962782877        
x2[1] (numeric)                   = 0.00082679579953977590483363227840564        
absolute error                    = 4.5519864454904931824265057687e-07           
relative error                    = 0.055086080008159339666829154254598        % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.501                                        
x1[1] (analytic)                  = 0.0012906639779909374464836782020351         
x1[1] (numeric)                   = 0.0012893474861421713484233414002533         
absolute error                    = 1.3164918487660980603368017818e-06           
relative error                    = 0.10200113052007266661140492555809         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082652209612631802672115172787186        
x2[1] (numeric)                   = 0.00082724055237710549620689888674251        
absolute error                    = 7.1845625078746948574715887065e-07           
relative error                    = 0.086925232144993646700864803587998        % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5012                                       
x1[1] (analytic)                  = 0.0012904458670071646728838326718726         
x1[1] (numeric)                   = 0.0012889414792292755017894851154384         
absolute error                    = 1.5043877778891710943475564342e-06           
relative error                    = 0.11657891402900813014156861847808         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082670368578766620467820114309252        
x2[1] (numeric)                   = 0.00082772789272400628224586612424172        
absolute error                    = 1.02420693634007756766498114920e-06          
relative error                    = 0.12389045240124148512504441419958         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5014                                       
x1[1] (analytic)                  = 0.0012902277996412267249633565185424         
x1[1] (numeric)                   = 0.0012885523918122589439967734967094         
absolute error                    = 1.6754078289677809665830218330e-06           
relative error                    = 0.12985364518061548062690778747721         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082688536991268795533779675988916        
x2[1] (numeric)                   = 0.00082825139612771914609102668965443        
absolute error                    = 1.36602621503119075322992976527e-06          
relative error                    = 0.16520140091188594546989034922162         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5016                                       
x1[1] (analytic)                  = 0.001290009775884400908055656176395          
x1[1] (numeric)                   = 0.0012881777138075600658105561724128         
absolute error                    = 1.8320620768408422451000039822e-06           
relative error                    = 0.14201923978326620035441653886691         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082706714853481408648245956670656        
x2[1] (numeric)                   = 0.0008288056064248597676452050750888         
absolute error                    = 1.73845789004568116274550838224e-06          
relative error                    = 0.2101954953869750421116203459023          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.3MB, time=0.46
NO POLE
NO POLE
t[1]                              = 0.5018                                       
x1[1] (analytic)                  = 0.0012897917957279662718586291348401         
x1[1] (numeric)                   = 0.0012878153134415530491686728715136         
absolute error                    = 1.9764822864132226899562633265e-06           
relative error                    = 0.15324041391484306672920401838244         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082724902168748965324935586679766        
x2[1] (numeric)                   = 0.00082938588980163611375144738424647        
absolute error                    = 2.13686811414646050209151744881e-06          
relative error                    = 0.25831014097635360146110850108992         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.502                                        
x1[1] (analytic)                  = 0.0012895738591632036100858259251            
x1[1] (numeric)                   = 0.0012874633802319854090614562967487         
absolute error                    = 2.1104789312182010243696283513e-06           
relative error                    = 0.1636570806876992348001860489537          % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008274309894041739636559251804687         
x2[1] (numeric)                   = 0.00082998831084999053704448838473328        
absolute error                    = 2.55732144581657338856320426458e-06          
relative error                    = 0.30906764172055954392630620744039         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5022                                       
x1[1] (analytic)                  = 0.0012893559661813954601176818675888         
x1[1] (numeric)                   = 0.0012871203765632066149180127233284         
absolute error                    = 2.2355896181888451996691442604e-06           
relative error                    = 0.17338808496848628109200693605887         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008276130517183405841277537278848         
x2[1] (numeric)                   = 0.00083060952730445872402226716831399        
absolute error                    = 2.99647558611813989451344042919e-06          
relative error                    = 0.36206238892640406355706562555309         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5024                                       
x1[1] (analytic)                  = 0.0012891381167738261026528185659675         
x1[1] (numeric)                   = 0.0012867849965599386316309592136305         
absolute error                    = 2.3531202138874710218593523370e-06           
relative error                    = 0.1825343757406186550195891558038          % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082779520866347734502869438387111        
x2[1] (numeric)                   = 0.00083124670064420313381041312071037        
absolute error                    = 3.45149198072578878171873683926e-06          
relative error                    = 0.4169499828705725130594699353077          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5026                                       
x1[1] (analytic)                  = 0.001288920310931781561359415133927          
x1[1] (numeric)                   = 0.0012864561311595581139247542780511         
absolute error                    = 2.4641797722234474346608558759e-06           
relative error                    = 0.19118170078661043040262837991741         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082797746027308634619323399650282        
x2[1] (numeric)                   = 0.00083189742016903480962903440737714        
absolute error                    = 3.91995989594846343580041087432e-06          
relative error                    = 0.47343799608452733855855314386003         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=11.4MB, alloc=4.3MB, time=0.71
t[1]                              = 0.5028                                       
x1[1] (analytic)                  = 0.0012887025486465496025266491407532         
x1[1] (numeric)                   = 0.0012861328384486556494389390542836         
absolute error                    = 2.5697101978939530877100864696e-06           
relative error                    = 0.19940289561720603183523866136131         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082815980658068396246110896163522        
x2[1] (numeric)                   = 0.00083255963851863506015183090214562        
absolute error                    = 4.39983193795109769072194051040e-06          
relative error                    = 0.53127813049961649440971130454916         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.503                                        
x1[1] (analytic)                  = 0.0012884848299094197347162072617323         
x1[1] (numeric)                   = 0.0012858143184704445210952406469852         
absolute error                    = 2.6705114389752136209666147471e-06           
relative error                    = 0.20725982774379657405541030276805         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008283422476198008492141699458837         
x2[1] (numeric)                   = 0.00083323161691026728945373480144587        
absolute error                    = 4.88936929046644023956485556217e-06          
relative error                    = 0.59025955811330319432696946647497         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5032                                       
x1[1] (analytic)                  = 0.0012882671547116832084138656194575         
x1[1] (numeric)                   = 0.0012854998918291762073528876146982         
absolute error                    = 2.7672628825070010609780047593e-06           
relative error                    = 0.2148050481909802384185824230488          % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082852478342398194791549665092172        
x2[1] (numeric)                   = 0.00083391187863021609224147191618073        
absolute error                    = 5.38709520623414432597526525901e-06          
relative error                    = 0.6502032665783758276457106309965          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5034                                       
x1[1] (analytic)                  = 0.0012880495230446330156811398020981         
x1[1] (numeric)                   = 0.0012851889815192808716149512180003         
absolute error                    = 2.8605415253521440661885840978e-06           
relative error                    = 0.22208319433173080249937925007846         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082870741402678649165076351232339        
x2[1] (numeric)                   = 0.00083459916953495859433095396265964        
absolute error                    = 5.89175550817210268019045033625e-06          
relative error                    = 0.71095725806812465341567885723921         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5036                                       
x1[1] (analytic)                  = 0.0012878319348995638898070045446997         
x1[1] (numeric)                   = 0.001284881097493204928964252723747          
absolute error                    = 2.9508374063589608427518209527e-06           
relative error                    = 0.22913218148990010043823236557433         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082889013946178801067185722653652        
x2[1] (numeric)                   = 0.0008352924245055669298902344323985         
absolute error                    = 6.40228504377891921837720586198e-06          
relative error                    = 0.77239247265458219962325331798544         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5038                                       
x1[1] (analytic)                  = 0.0012876143902677723049596830595824         
x1[1] (numeric)                   = 0.0012845758235551715075980164240496         
absolute error                    = 3.0385667126007973616666355328e-06           
relative error                    = 0.23598421511652234559976506844964         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008290729597625743379427469999303         
x2[1] (numeric)                   = 0.00083599073895807572958382261720254        
absolute error                    = 6.91777919550139164107561727224e-06          
relative error                    = 0.83439932686774270953097033969047         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.4MB, time=0.97
NO POLE
NO POLE
t[1]                              = 0.504                                        
x1[1] (analytic)                  = 0.0012873968891405564758385060019091         
x1[1] (numeric)                   = 0.001284272806230302609395341437726          
absolute error                    = 3.1240829102538664431645641831e-06           
relative error                    = 0.24266665055711368517266495397951         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082925587496274761468760841422102        
x2[1] (numeric)                   = 0.000836693344647783710080852986653          
absolute error                    = 7.43746968503609539324457243198e-06          
relative error                    = 0.89688477460231516180546826574603         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5042                                       
x1[1] (analytic)                  = 0.0012871794315092163573258400564985         
x1[1] (numeric)                   = 0.0012839717453113780706101189432598         
absolute error                    = 3.2076861978382867157211132387e-06           
relative error                    = 0.2492027233590330488644558539607          % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082943888509592429594120180293885        
x2[1] (numeric)                   = 0.00083739958912031113056407872717169        
absolute error                    = 7.96070402438683462287692423284e-06          
relative error                    = 0.95976981154749963145190448249774         % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5044                                       
x1[1] (analytic)                  = 0.00128696201736505364413908613196           
x1[1] (numeric)                   = 0.0012836723858303792768551293612507         
absolute error                    = 3.2896315346743672839567707093e-06           
relative error                    = 0.25561216961240323411376257794102         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082962199019573515610150603395714        
x2[1] (numeric)                   = 0.00083810891825977705582390438840943        
absolute error                    = 8.48692806404189972239835445229e-06          
relative error                    = 1.0229873562102125359311685270037          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5046                                       
x1[1] (analytic)                  = 0.0012867446466993717704827471482299         
x1[1] (numeric)                   = 0.001283374511240075240001900050656          
absolute error                    = 3.3701354592965304808470975739e-06           
relative error                    = 0.26191175288284771441807327863938         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082980519029582529448460859346626        
x2[1] (numeric)                   = 0.00083882086146730106282281487607864        
absolute error                    = 9.01567117147576833820628261238e-06          
relative error                    = 1.0864804507021321890501790389405          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5048                                       
x1[1] (analytic)                  = 0.0012865273195034759097005654035915         
x1[1] (numeric)                   = 0.0012830779376232744422926180291822         
absolute error                    = 3.4493818802014674079473744093e-06           
relative error                    = 0.26811571180103089508564006796855         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00082998848542985414088185286713247        
x2[1] (numeric)                   = 0.00083953501907338904280161470888951        
absolute error                    = 9.54653364353490191976184175704e-06          
relative error                    = 1.1502007330367621233142642823482          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.505                                        
x1[1] (analytic)                  = 0.0012863100357686729739277295072664         
x1[1] (numeric)                   = 0.0012827825087748535040894571884186         
absolute error                    = 3.5275269938194698382723188478e-06           
relative error                    = 0.27423614025614678061504635476608         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083017187563149546111924351454314        
x2[1] (numeric)                   = 0.00084025105164751391586217916033071        
absolute error                    = 1.007917601601845474293564578757e-05         
relative error                    = 1.2141071399644107746887631800346          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.4MB, time=1.22
NO POLE
NO POLE
t[1]                              = 0.5052                                       
x1[1] (analytic)                  = 0.0012860927954862716137431508636619         
x1[1] (numeric)                   = 0.0012824880920250184665285930605002         
absolute error                    = 3.6047034612531472145578031617e-06           
relative error                    = 0.28028331034155346763350831647243         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008303553609344373626191108333988         
x2[1] (numeric)                   = 0.00084096867091894759314627387953084        
absolute error                    = 1.061330998451023052716304613204e-05         
relative error                    = 1.2781648055558503323446087070389          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5054                                       
x1[1] (analytic)                  = 0.0012858755986475822178218096943695         
x1[1] (numeric)                   = 0.0012821945746920807158539115331685         
absolute error                    = 3.6810239555015019678981612010e-06           
relative error                    = 0.28626594667268074260217948496212         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083053894137238229996403501027281        
x2[1] (numeric)                   = 0.00084168763206599771693517028547577        
absolute error                    = 1.114869069361541697113527520296e-05         
relative error                    = 1.3423441259952632421267758446851          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5056                                       
x1[1] (analytic)                  = 0.001285658445243916912587170584005          
x1[1] (numeric)                   = 0.001281901861069867617719702475404          
absolute error                    = 3.7565841740492948674681086010e-06           
relative error                    = 0.29219145939935785051042844319647         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008307226169790470804630311551197         
x2[1] (numeric)                   = 0.00084240772716740433020173666376193        
absolute error                    = 1.168511018835724973870550864223e-05         
relative error                    = 1.4066199655007078840936156780014          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5058                                       
x1[1] (analytic)                  = 0.0012854413352665895618636675359888         
x1[1] (numeric)                   = 0.0012816098698691881554261493406806         
absolute error                    = 3.8314653974014064375181953082e-06           
relative error                    = 0.29806614213217231069857424492852         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083090638778816286971999601707344        
x2[1] (numeric)                   = 0.00084312877964073668195360451948294        
absolute error                    = 1.222239185257381223360850240950e-05         
relative error                    = 1.4709709820752846287286429122789          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.506                                        
x1[1] (analytic)                  = 0.0012852242687069157665292585243653         
x1[1] (numeric)                   = 0.0012813185320449187734130521219745         
absolute error                    = 3.9057366619969931162064023908e-06           
relative error                    = 0.30389534006594941168139374174905         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083109025383347519720441727943742        
x2[1] (numeric)                   = 0.00084385063951903031548692923908198        
absolute error                    = 1.276038568555511828251195964456e-05         
relative error                    = 1.5353790550059687291225689930516          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.4MB, time=1.48
NO POLE
NO POLE
t[1]                              = 0.5062                                       
x1[1] (analytic)                  = 0.001285007245556212864168049527763          
x1[1] (numeric)                   = 0.0012810277889505890641985424338174         
absolute error                    = 3.9794566056237999695070939456e-06           
relative error                    = 0.30968359278793793790655126457188         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083127421514874396182434633212867        
x2[1] (numeric)                   = 0.0008445731794393255499777153787798         
absolute error                    = 1.329896429058158815336904665113e-05         
relative error                    = 1.5998287987558882017882257777208          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5064                                       
x1[1] (analytic)                  = 0.0012847902658057999287229880316013         
x1[1] (numeric)                   = 0.0012807375907711067903266393541769         
absolute error                    = 4.0526750346931383963486774244e-06           
relative error                    = 0.31543475558256703950794807035065         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083145827176774343750163542019918        
x2[1] (numeric)                   = 0.00084529629123581015990077119838573        
absolute error                    = 1.383801946806672239913577818655e-05         
relative error                    = 1.6643071502128473593001466321718          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5066                                       
x1[1] (analytic)                  = 0.0012845733294469977701486259846507         
x1[1] (numeric)                   = 0.0012804478951917013083311007888339         
absolute error                    = 4.1254342552964618175251958168e-06           
relative error                    = 0.32115210247066550147063583059519         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083164242372426227874944006741881        
x2[1] (numeric)                   = 0.00084601988304644080228060892908036        
absolute error                    = 1.437745932217852353116886166155e-05         
relative error                    = 1.7288030182242705764769123532502          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5068                                       
x1[1] (analytic)                  = 0.0012843564364711289340639521960578         
x1[1] (numeric)                   = 0.0012801586662674827504430007587956         
absolute error                    = 4.1977702036461836209514372622e-06           
relative error                    = 0.3268384137334873982145349049214          % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083182667105210352625198767426466        
x2[1] (numeric)                   = 0.00084674387685565209504104106039001        
absolute error                    = 1.491720580354856878905338612535e-05         
relative error                    = 1.7933069860192295532700138588808          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.507                                        
x1[1] (analytic)                  = 0.001284139586869517701405294158948          
x1[1] (numeric)                   = 0.0012798698734633803211833314465424         
absolute error                    = 4.2697134061373802219627124056e-06           
relative error                    = 0.33249605025775353743343772304167         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083201101378508461244661319002326        
x2[1] (numeric)                   = 0.00084746820640742657249670290176028        
absolute error                    = 1.545719262234196005008971173702e-05         
relative error                    = 1.8578110585366219546888559217916          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5072                                       
x1[1] (analytic)                  = 0.0012839227806334900880792892867217         
x1[1] (numeric)                   = 0.0012795814908387803080532834157117         
absolute error                    = 4.3412897947097800260058710100e-06           
relative error                    = 0.33812701668614205055080933686813         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083219545195703736710806275907346        
x2[1] (numeric)                   = 0.00084819281543290502962135475694248        
absolute error                    = 1.599736347586766251329199786902e-05         
relative error                    = 1.9223084478829303713626445013821          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.4MB, time=1.74
NO POLE
NO POLE
t[1]                              = 0.5074                                       
x1[1] (analytic)                  = 0.0012837060177543738446159255481629         
x1[1] (numeric)                   = 0.0012792934963550547838100565422093         
absolute error                    = 4.4125213993190608058690059536e-06           
relative error                    = 0.343733015058854308147664340943           % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083237998560180802293506624177892        
x2[1] (numeric)                   = 0.00084891765614512998506061886776453        
absolute error                    = 1.653767054332196212555262598561e-05         
relative error                    = 1.9867933911656081084619451522635          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5076                                       
x1[1] (analytic)                  = 0.0012834892982234984558216514874832         
x1[1] (numeric)                   = 0.0012790058712874590158444468338121         
absolute error                    = 4.4834269360394399772046536711e-06           
relative error                    = 0.34931549037806821278722042246229         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083256461475325722113917951078113        
x2[1] (numeric)                   = 0.00084964268796066017780637479121969        
absolute error                    = 1.707807320740295666719528043856e-05         
relative error                    = 2.051260995816438229237126399538           % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5078                                       
x1[1] (analytic)                  = 0.001283272622032195140432555615423          
x1[1] (numeric)                   = 0.0012787185997256672165227368867395         
absolute error                    = 4.5540223065279239098187286835e-06           
relative error                    = 0.35487566931149499655755308382855         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083274933944526001703589742384568        
x2[1] (numeric)                   = 0.00085036787641386228097035924216083        
absolute error                    = 1.761853696860226393446181831515e-05         
relative error                    = 2.1157071082564817387155338196863          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.508                                        
x1[1] (analytic)                  = 0.0012830559891717968507676151575396         
x1[1] (numeric)                   = 0.001278431668149587136268714209746          
absolute error                    = 4.6243210222097144989009477936e-06           
relative error                    = 0.36041459306812320084209487556965         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083293415971170588563803837477598        
x2[1] (numeric)                   = 0.00085109319223483968014865112692701        
absolute error                    = 1.815903252313379451061275215103e-05         
relative error                    = 2.1801282023802428518023834759022          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5082                                       
x1[1] (analytic)                  = 0.0012828393996336382723820141458102         
x1[1] (numeric)                   = 0.0012781450650691075338029441291456         
absolute error                    = 4.6943345645307385790700166646e-06           
relative error                    = 0.36593314532367633643031794194414         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008331190755864987272514013242712         
x2[1] (numeric)                   = 0.00085181861056633507189346314258043        
absolute error                    = 1.869953497983634464206181830923e-05         
relative error                    = 2.2445212848682231736709292767571          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.4MB, time=1.99
NO POLE
NO POLE
t[1]                              = 0.5084                                       
x1[1] (analytic)                  = 0.0012826228534090558237205308396847         
x1[1] (numeric)                   = 0.0012778587807181426126055475610742         
absolute error                    = 4.7640726909132111149832786105e-06           
relative error                    = 0.37143207594117665211909574518185         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083330408710355687307269621296731        
x2[1] (numeric)                   = 0.0008525441102986608618371987435931         
absolute error                    = 1.924002319510398876450253062579e-05         
relative error                    = 2.3088838147883679926108551618976          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5086                                       
x1[1] (analytic)                  = 0.0012824063504893876557709944627208         
x1[1] (numeric)                   = 0.0012775728067947898292803472104336         
absolute error                    = 4.8335436945978264906472522872e-06           
relative error                    = 0.37691202111976953219002203319161         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083348919429681309078974865926187        
x2[1] (numeric)                   = 0.00085326967350486830907820678376372        
absolute error                    = 1.978047920805521828845812450185e-05         
relative error                    = 2.3732136353301311722094153031242          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5088                                       
x1[1] (analytic)                  = 0.0012821898908659736517178112409428         
x1[1] (numeric)                   = 0.0012772871362406509041384751577715         
absolute error                    = 4.9027546253227475793360831713e-06           
relative error                    = 0.3823735205096254222201772300255          % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083367439720021459018397984488692        
x2[1] (numeric)                   = 0.00085399528496104751500928445032806        
absolute error                    = 2.032088776083292482530460544114e-05         
relative error                    = 2.4375089158402781486351706166793          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.509                                        
x1[1] (analytic)                  = 0.001281973474530155426595559729063          
x1[1] (numeric)                   = 0.0012770017630534133882072049137488         
absolute error                    = 4.9717114767420383883548153142e-06           
relative error                    = 0.38781703174975407870815814249238         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083385969584772302873516249155556        
x2[1] (numeric)                   = 0.0008547209317389274053705022973307         
absolute error                    = 2.086123589120437663533980577514e-05         
relative error                    = 2.5017681026058361417743549786649          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5092                                       
x1[1] (analytic)                  = 0.0012817571014732763269426554107106         
x1[1] (numeric)                   = 0.001276716682127679782814199367395          
absolute error                    = 5.0404193455965441284560433156e-06           
relative error                    = 0.39324294281677776113460289216039         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083404509027331451722845383237174        
x2[1] (numeric)                   = 0.0008554466028598787097050721078087         
absolute error                    = 2.140151258656419247661827543696e-05         
relative error                    = 2.56598987706419680883071560754            % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5094                                       
x1[1] (analytic)                  = 0.0012815407716866814304550845588136         
x1[1] (numeric)                   = 0.0012764318891197867637358554322912         
absolute error                    = 5.1088825668946667192291265224e-06           
relative error                    = 0.39865158251427962800945015139885         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083423058051097962536370648205495        
x2[1] (numeric)                   = 0.0008561722890010653286909917196719         
absolute error                    = 2.194170849008570332728523761695e-05         
relative error                    = 2.6301731203195709477180020251502          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.4MB, time=2.26
NO POLE
NO POLE
t[1]                              = 0.5096                                       
x1[1] (analytic)                  = 0.0012813244851617175456402073422847         
x1[1] (numeric)                   = 0.0012761473803329987409791514241358         
absolute error                    = 5.1771048287188046610559181489e-06           
relative error                    = 0.40404322938271142669788005765748         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008344161665947233873670581103952         
x2[1] (numeric)                   = 0.00085689798224588432699681847308135        
absolute error                    = 2.248181565116093962976036268615e-05         
relative error                    = 2.6943168830141297857712159542203          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5098                                       
x1[1] (analytic)                  = 0.0012811082418897332114706301651619         
x1[1] (numeric)                   = 0.0012758631526200049510011179432601         
absolute error                    = 5.2450892697282604695122219018e-06           
relative error                    = 0.40941811926768578866781220541559         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083460184855856530760480082371625        
x2[1] (numeric)                   = 0.000857623675872019406260527068649          
absolute error                    = 2.302182731345409865572624493275e-05         
relative error                    = 2.7584203597457789823008852340117          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.51                                         
x1[1] (analytic)                  = 0.0012808920418620786970381472243591         
x1[1] (numeric)                   = 0.0012755792033001121071151349282705         
absolute error                    = 5.3128385619665899230122960886e-06           
relative error                    = 0.41477645174866774678915518053278         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083478762643653936619953115948893        
x2[1] (numeric)                   = 0.00085834936417143878524349723295373        
absolute error                    = 2.356173773489941904396607346480e-05         
relative error                    = 2.8224828673464513265031938828705          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5102                                       
x1[1] (analytic)                  = 0.0012806758850701060012077512721846         
x1[1] (numeric)                   = 0.0012752955300889177055784338655913         
absolute error                    = 5.3803549811882956293174065933e-06           
relative error                    = 0.42011839559966161319765324973033         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083497350026269402464858159959997        
x2[1] (numeric)                   = 0.00085907504229752285224782789135388        
absolute error                    = 2.410154203482882759924629175391e-05         
relative error                    = 2.8865038264383425972129775395695          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5104                                       
x1[1] (analytic)                  = 0.0012804597715051688522717135697878         
x1[1] (numeric)                   = 0.0012750121310385829131485477249538         
absolute error                    = 5.4476404665859391231658448340e-06           
relative error                    = 0.42544409342765115885390691360888         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083515947007109223144473450814446        
x2[1] (numeric)                   = 0.00085980070613523261271963776049309        
absolute error                    = 2.464123606414038127490325234863e-05         
relative error                    = 2.9504827457734290257812736676144          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=38.1MB, alloc=4.4MB, time=2.53
t[1]                              = 0.5106                                       
x1[1] (analytic)                  = 0.0012802437011586227076037330176972         
x1[1] (numeric)                   = 0.0012747290044871074758625849183566         
absolute error                    = 5.5146966715152317411480993406e-06           
relative error                    = 0.43075366561260344085466096156148         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083534553589581142769921939997556        
x2[1] (numeric)                   = 0.00086052635219084624224041493350228        
absolute error                    = 2.518081629503481454119553352672e-05         
relative error                    = 3.0144192089362520850469594355193          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5108                                       
x1[1] (analytic)                  = 0.0012800276740218247533131544496155         
x1[1] (numeric)                   = 0.0012744461490152498717663392070629         
absolute error                    = 5.5815250065748815468152425526e-06           
relative error                    = 0.43604721365420380107393905039247         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083553169777094355276699444660709        
x2[1] (numeric)                   = 0.00086125197749831445607338939053408        
absolute error                    = 2.572027972737090330639494392699e-05         
relative error                    = 3.0783128630533389273307423592832          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.511                                        
x1[1] (analytic)                  = 0.0012798116900861339038992560756415         
x1[1] (numeric)                   = 0.0012741635634099404226806862112011         
absolute error                    = 5.6481266761934812185698644404e-06           
relative error                    = 0.44132482301465389174800087169251         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083571795573059504987431312643056        
x2[1] (numeric)                   = 0.00086197757953972992083164085980836        
absolute error                    = 2.625962380913487095732773337780e-05         
relative error                    = 3.1421634092064446109337798923801          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5112                                       
x1[1] (analytic)                  = 0.0012795957493429108019056060610889         
x1[1] (numeric)                   = 0.0012738812466332087515319108811716         
absolute error                    = 5.7145027097020503736951799173e-06           
relative error                    = 0.44658656553341338121480795601297         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083590430980888687174857692657073        
x2[1] (numeric)                   = 0.00086270315617778345138777615261058        
absolute error                    = 2.679884636889657963919922603985e-05         
relative error                    = 3.2059705942924986632467966944623          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5114                                       
x1[1] (analytic)                  = 0.0012793798517835178175744882270767         
x1[1] (numeric)                   = 0.0012735991977957944675945906408409         
absolute error                    = 5.7806539877233499798975862358e-06           
relative error                    = 0.45183250147834021384961437362149         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083609076003995448625047500406982        
x2[1] (numeric)                   = 0.0008634287055984003545614187393118         
absolute error                    = 2.733794555844586831094373524198e-05         
relative error                    = 3.2697342041119390923462366970995          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5116                                       
x1[1] (analytic)                  = 0.0012791639973993190485013968590695         
x1[1] (numeric)                   = 0.0012733174161347352273680348208104         
absolute error                    = 5.8465812645838211333620382591e-06           
relative error                    = 0.45706268128797896298107807029898         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083627730645794788200841171445351        
x2[1] (numeric)                   = 0.00086415422626202257619177814636738        
absolute error                    = 2.787691980407469418336643191387e-05         
relative error                    = 3.3334540575000622974362326935277          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.4MB, time=2.79
NO POLE
NO POLE
t[1]                              = 0.5118                                       
x1[1] (analytic)                  = 0.0012789481861816803192896006095455         
x1[1] (numeric)                   = 0.0012730359009943327042852273880033         
absolute error                    = 5.9122851873476150043732215422e-06           
relative error                    = 0.46227714705150286734189829038691         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083646394909703157405522291609771        
x2[1] (numeric)                   = 0.00086487971686223356318328472717437        
absolute error                    = 2.841576776520198912806181107666e-05         
relative error                    = 3.3971300013439910265702940867315          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.512                                        
x1[1] (analytic)                  = 0.0012787324181219691812047754809758         
x1[1] (numeric)                   = 0.0012727546518099873515989773037288         
absolute error                    = 5.9777663119818296057981772470e-06           
relative error                    = 0.4674759337658125311604196111757          % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083665068799138460946718195917937        
x2[1] (numeric)                   = 0.00086560517629061915253151760429359        
absolute error                    = 2.895448829923454306433564511422e-05         
relative error                    = 3.460761906351614835220076373195           % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5122                                       
x1[1] (analytic)                  = 0.0012785166932115549118297068753011         
x1[1] (numeric)                   = 0.0012724736680944695762849769864205         
absolute error                    = 6.0430251170853355447298888806e-06           
relative error                    = 0.47265907040334608013467509226164         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083683752317520057300529626835942        
x2[1] (numeric)                   = 0.00086633060360692459844540692375485        
absolute error                    = 2.949308043172402544011065539543e-05         
relative error                    = 3.52434966345902544274657389896            % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5124                                       
x1[1] (analytic)                  = 0.0012783010114418085147190606960915         
x1[1] (numeric)                   = 0.0012721929494262601100868847711932         
absolute error                    = 6.1080620155484046321759248983e-06           
relative error                    = 0.47782658081910302991430346569276         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083702445468268759275889542871143        
x2[1] (numeric)                   = 0.00086705599801370950796525242572829        
absolute error                    = 3.003154333102191520635699701686e-05         
relative error                    = 3.5878931807800938656600838156702          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5126                                       
x1[1] (analytic)                  = 0.0012780853728041027190542234895835         
x1[1] (numeric)                   = 0.0012719124954396477100033070360427         
absolute error                    = 6.1728773644550090509164535408e-06           
relative error                    = 0.4829784845210923769523799714515          % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083721148254806834579151168477479        
x2[1] (numeric)                   = 0.00086778135883482276398835175357476        
absolute error                    = 3.056987628675441819684006879997e-05         
relative error                    = 3.6513923810163765020898653386214          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=45.7MB, alloc=4.4MB, time=3.05
t[1]                              = 0.5128                                       
x1[1] (analytic)                  = 0.0012778697772898119792982116107845         
x1[1] (numeric)                   = 0.0012716323058163193249611411474195         
absolute error                    = 6.2374714734926543370704633650e-06           
relative error                    = 0.48811479732476990741882876846013         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008373986068055800637890537629762         
x2[1] (numeric)                   = 0.00086850668549712169032575596819964        
absolute error                    = 3.110807869154162653670220522344e-05         
relative error                    = 3.714847199257883419411217747635           % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.513                                        
x1[1] (analytic)                  = 0.0012776542248903124748506494008434         
x1[1] (numeric)                   = 0.0012713523802782177853928980423931         
absolute error                    = 6.3018446120946894577513584503e-06           
relative error                    = 0.49323553190893313140803042217512         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083758582748947453871027492802935        
x2[1] (numeric)                   = 0.00086923197751494648928572522257979        
absolute error                    = 3.164615002547195057545029455044e-05         
relative error                    = 3.7782575811157250764939349519208          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5132                                       
x1[1] (analytic)                  = 0.0012774387155969821097028163618863         
x1[1] (numeric)                   = 0.0012710727185814759757030900358497         
absolute error                    = 6.3659970155061339997263260366e-06           
relative error                    = 0.49834069828791193208665219817301         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083777314463401812843953618428816        
x2[1] (numeric)                   = 0.00086995723447693467936307882816669        
absolute error                    = 3.218408984291655092354264387853e-05         
relative error                    = 3.8416234811365547457495129602923          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5134                                       
x1[1] (analytic)                  = 0.0012772232494012005120927633155174         
x1[1] (numeric)                   = 0.0012707933205112652430035040451253         
absolute error                    = 6.4299288899352690892592703921e-06           
relative error                    = 0.50343030421265876367772939137166         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083796055827349176244186553339435        
x2[1] (numeric)                   = 0.00087068245603482285013311245274643        
absolute error                    = 3.272189776133108769124691935208e-05         
relative error                    = 3.9049448614562817128759263386503          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5136                                       
x1[1] (analytic)                  = 0.0012770078262943490341604975311922         
x1[1] (numeric)                   = 0.0012705141858774202491750200393412         
absolute error                    = 6.4936404169287849854774918510e-06           
relative error                    = 0.50850435551144440099660693548629         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083814806844219094742031419992721        
x2[1] (numeric)                   = 0.0008714076418939362075270700647979         
absolute error                    = 3.325957345174526010675586487069e-05         
relative error                    = 3.9682216906569476238536766991694          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5138                                       
x1[1] (analytic)                  = 0.0012767924462678107516032368106682         
x1[1] (numeric)                   = 0.0012702353145107232413531587041724         
absolute error                    = 6.5571317570875102500781064958e-06           
relative error                    = 0.51356285637925317929502983232248         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083833567517442577297561073712817        
x2[1] (numeric)                   = 0.00087213279180511152710384300901078        
absolute error                    = 3.379711663068575412823227188261e-05         
relative error                    = 4.0314539427961072307169113292463          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.4MB, time=3.32
NO POLE
NO POLE
t[1]                              = 0.514                                        
x1[1] (analytic)                  = 0.0012765771093129704633307325147448         
x1[1] (numeric)                   = 0.0012699567062597483538321422935765         
absolute error                    = 6.6204030532221094985902211683e-06           
relative error                    = 0.51860580962360233684490549184812         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008385233785045209172681139251402         
x2[1] (numeric)                   = 0.00087285790555783747323754372438703        
absolute error                    = 3.433452705331655596942979924683e-05         
relative error                    = 4.0946415965826813987181535785169          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5142                                       
x1[1] (analytic)                  = 0.0012763618154212146911206615185049         
x1[1] (numeric)                   = 0.0012696783609881815339103580806491         
absolute error                    = 6.6834544330331572103034378558e-06           
relative error                    = 0.52363321687334693362361251124579         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083871117846681565268206537456791        
x2[1] (numeric)                   = 0.00087358298297442880382618180149778        
absolute error                    = 3.487180450761315114411642692987e-05         
relative error                    = 4.1577846346771786633602643978428          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5144                                       
x1[1] (analytic)                  = 0.0012761465645839316792740870812734         
x1[1] (numeric)                   = 0.0012694002785725444060259997989746         
absolute error                    = 6.7462860113872732480872822988e-06           
relative error                    = 0.52864507875604382086533560850362         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083889907509566385149214274853093        
x2[1] (numeric)                   = 0.00087430802390507863414164232679199        
absolute error                    = 3.540894880941478264949957826106e-05         
relative error                    = 4.2208830430975172267884231218099          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5146                                       
x1[1] (analytic)                  = 0.0012759313567925113942709886175111         
x1[1] (numeric)                   = 0.0012691224589002611929343601975251         
absolute error                    = 6.8088978922502013366284199860e-06           
relative error                    = 0.53364139504860890622406924583538         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083908706842543399153231451674996        
x2[1] (numeric)                   = 0.00087503302822365641946562923943431        
absolute error                    = 3.594595979822242793331472268435e-05         
relative error                    = 4.2839368107145115201286647855099          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5148                                       
x1[1] (analytic)                  = 0.0012757161920383455244258603548666         
x1[1] (numeric)                   = 0.0012688449018680169886502113697379         
absolute error                    = 6.8712901703285357756489851287e-06           
relative error                    = 0.53862216480528909692481783458772         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083927515849050916186699715557149        
x2[1] (numeric)                   = 0.00087575799582413926238630897324409        
absolute error                    = 3.648283733363010051931181767260e-05         
relative error                    = 4.3469459288234922922653872833657          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.515                                        
x1[1] (analytic)                  = 0.0012755010703128274795433788656077         
x1[1] (numeric)                   = 0.0012685676073803634708556866995444         
absolute error                    = 6.9334629324640086876921660633e-06           
relative error                    = 0.54358738646636478066566505999342         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083946334532528706846451570820467        
x2[1] (numeric)                   = 0.00087648292661758109058098612817999        
absolute error                    = 3.701958129229402211647041997532e-05         
relative error                    = 4.4099103907805711140833947194844          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.4MB, time=3.58
NO POLE
NO POLE
t[1]                              = 0.5152                                       
x1[1] (analytic)                  = 0.0012752859916073523905741394576611         
x1[1] (numeric)                   = 0.0012682905753485347588999418393705         
absolute error                    = 6.9954162588176316741976182906e-06           
relative error                    = 0.54853705795048435841794633448501         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083965162896418003987286861981033        
x2[1] (numeric)                   = 0.00087720782052953863768524614028379        
absolute error                    = 3.755619156535859781237752047346e-05         
relative error                    = 4.4728301916937939750720749871914          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5154                                       
x1[1] (analytic)                  = 0.0012750709559133171092704614114891         
x1[1] (numeric)                   = 0.0012680138056894417444190048963316         
absolute error                    = 7.0571502238753648514565151575e-06           
relative error                    = 0.55347117673309544561562075818871         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00083984000944161503289779776245017        
x2[1] (numeric)                   = 0.0008779326774978853782611311720576         
absolute error                    = 3.809266805627034536333340960743e-05         
relative error                    = 4.5357053281609007967883656272254          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5156                                       
x1[1] (analytic)                  = 0.0012748559632221202078422620490348         
x1[1] (numeric)                   = 0.0012677372983248179953285884642424         
absolute error                    = 7.1186648973022125136735847924e-06           
relative error                    = 0.55838973991306624674812895392827         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008400284867920336382831645652709         
x2[1] (numeric)                   = 0.00087865749747095494473996765853266        
absolute error                    = 3.862901067892130645680309326176e-05         
relative error                    = 4.5985357980466576781993073523397          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5158                                       
x1[1] (analytic)                  = 0.0012746410135251619786129996209726         
x1[1] (numeric)                   = 0.0012674610531804943881751686601181         
absolute error                    = 7.1799603446675904378309608545e-06           
relative error                    = 0.56329274426927537727384975094983         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084021706104989208639363316566634        
x2[1] (numeric)                   = 0.00087938228040596436708620751333261        
absolute error                    = 3.916521935607228069257434766627e-05         
relative error                    = 4.6613216002937900463164584450847          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.516                                        
x1[1] (analytic)                  = 0.0012744261068138444336756849984992         
x1[1] (numeric)                   = 0.0012671850701857830670125588085922         
absolute error                    = 7.2410366280613666631261899070e-06           
relative error                    = 0.56818018630868064182646742049822         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084040573224966125289966149752755        
x2[1] (numeric)                   = 0.00088010702626767496053072098862274        
absolute error                    = 3.970129401801370763105949109519e-05         
relative error                    = 4.7240627347624460776149912609457          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.4MB, time=3.86
NO POLE
NO POLE
t[1]                              = 0.5162                                       
x1[1] (analytic)                  = 0.0012742112430795713045489621559082         
x1[1] (numeric)                   = 0.0012669093492729542511995658352817         
absolute error                    = 7.3018938066170533493963206265e-06           
relative error                    = 0.57305206230714983164481386266568         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084059450042582666446480123305994        
x2[1] (numeric)                   = 0.00088083173502725504325095435091289        
absolute error                    = 4.023723460142837878615311785295e-05         
relative error                    = 4.7867592020938849516520502597138          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5164                                       
x1[1] (analytic)                  = 0.0012739964223137480418332574301895         
x1[1] (numeric)                   = 0.0012666338903767918980053720357443         
absolute error                    = 7.3625319369561438278853944452e-06           
relative error                    = 0.57790836834414340597065789497342         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084078336561288850443530749501307        
x2[1] (numeric)                   = 0.00088155640666131406435349462199687        
absolute error                    = 4.077304104842555991818712698380e-05         
relative error                    = 4.8494110035947342207863644676902          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5166                                       
x1[1] (analytic)                  = 0.0012737816445077818148669975439001         
x1[1] (numeric)                   = 0.0012663586934342163350905997909953         
absolute error                    = 7.4229510735654797763977529048e-06           
relative error                    = 0.58274910033217481493318922539766         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084097232784536161853205925653825        
x2[1] (numeric)                   = 0.0008822810411510823073385062631674         
absolute error                    = 4.130871330572068880644700662915e-05         
relative error                    = 4.9120181411387122546695187374394          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5168                                       
x1[1] (analytic)                  = 0.0012735669096530815113828963775561         
x1[1] (numeric)                   = 0.0012660837583839637692192497026148         
absolute error                    = 7.4831512691177421636466749413e-06           
relative error                    = 0.58757425404183482478135594847771         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008411613871577755205447913462566         
x2[1] (numeric)                   = 0.00088300563848171422802851709828461        
absolute error                    = 4.184425132393870748372575202801e-05         
relative error                    = 4.9745806170831801412922525190903          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.517                                        
x1[1] (analytic)                  = 0.0012733522177410577371643104777951         
x1[1] (numeric)                   = 0.0012658090851663140988625894514962         
absolute error                    = 7.5431325747436383017210262989e-06           
relative error                    = 0.59238382512304779942412289510458         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.0008413505435846743980286389764889         
x2[1] (numeric)                   = 0.00088373019864169679287623915533899        
absolute error                    = 4.237965505702239484760017885009e-05         
relative error                    = 5.0370984341982851610688691885701          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5172                                       
x1[1] (analytic)                  = 0.0012731375687631228157016632875658         
x1[1] (numeric)                   = 0.0012655346737228597503719790192133         
absolute error                    = 7.6028950402630653296842683525e-06           
relative error                    = 0.59717780912312731454629064292867         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084153979716061711800299571296767        
x2[1] (numeric)                   = 0.00088445472162234699208020184970749        
absolute error                    = 4.291492446172987407720613673982e-05         
relative error                    = 5.0995715956067956640965749127149          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.4MB, time=4.11
NO POLE
NO POLE
t[1]                              = 0.5174                                       
x1[1] (analytic)                  = 0.0012729229627106907878489380845994         
x1[1] (numeric)                   = 0.0012652605239963093546819456984721         
absolute error                    = 7.6624387143814331669923861273e-06           
relative error                    = 0.60195620150211304743762471633979         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084172914792017723265268580471965        
x2[1] (numeric)                   = 0.00088517920741738508715412075837311        
absolute error                    = 4.345005949720785450143495365346e-05         
relative error                    = 5.1620001047330139309259256470164          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5176                                       
x1[1] (analytic)                  = 0.0012727083995751774114802396144245         
x1[1] (numeric)                   = 0.0012649866359303210134073540454643         
absolute error                    = 7.7217636448563980728855689602e-06           
relative error                    = 0.60671899764579831670205000956996         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084191859589794298503145179317699        
x2[1] (numeric)                   = 0.00088590365602257217831509448045901        
absolute error                    = 4.398506012462919328364268728202e-05         
relative error                    = 5.2243839652593970746646748854915          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5178                                       
x1[1] (analytic)                  = 0.0012724938793480001611464244041865         
x1[1] (numeric)                   = 0.001264713009469360694645460575345          
absolute error                    = 7.7808698786394665009638288415e-06           
relative error                    = 0.61146619287679600417132320725454         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084210814112851731476775831994364        
x2[1] (numeric)                   = 0.00088662806743540239746015562623378        
absolute error                    = 4.451992630688508269239730629014e-05         
relative error                    = 5.2867231810897227771671882663432          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.518                                        
x1[1] (analytic)                  = 0.0012722794020205782277317997435378         
x1[1] (numeric)                   = 0.0012644396445585819709543517329455         
absolute error                    = 7.8397574619962567774480105923e-06           
relative error                    = 0.61619778246393823127337570448005         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084229778364651786377291305301299        
x2[1] (numeric)                   = 0.00088735244165484149360718697340955        
absolute error                    = 4.505465800832362983427392039656e-05         
relative error                    = 5.349017756317812189147623233904           % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5182                                       
x1[1] (analytic)                  = 0.0012720649675843325181108913188656         
x1[1] (numeric)                   = 0.0012641665411437238828324603589815         
absolute error                    = 7.8984264406086352784309598841e-06           
relative error                    = 0.62091376163026068619023609249595         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084248752348657698195150565160216        
x2[1] (numeric)                   = 0.00088807677868110481856592491807739        
absolute error                    = 4.558925519452783661441926647523e-05         
relative error                    = 5.4112676952009713712749642882304          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
memory used=64.8MB, alloc=4.4MB, time=4.38
t[1]                              = 0.5184                                       
x1[1] (analytic)                  = 0.0012718505760306856548052794871294         
x1[1] (numeric)                   = 0.0012638936991710241958385258403996         
absolute error                    = 7.9568768596614589667536467298e-06           
relative error                    = 0.62561412555978471922092390560808         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084267736068334173291416569013793        
x2[1] (numeric)                   = 0.00088880107851546877446860150506765        
absolute error                    = 4.612371783212704155443581492972e-05         
relative error                    = 5.4734730021374392081734376463653          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5186                                       
x1[1] (analytic)                  = 0.0012716362273510619756405041755803         
x1[1] (numeric)                   = 0.0012636211185871457312351627306443         
absolute error                    = 8.0151087639162444053414449360e-06           
relative error                    = 0.63029886940327823343574302541413         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084286729527147389969264046229865        
x2[1] (numeric)                   = 0.00088952534116011067981611144470841        
absolute error                    = 4.665804588863678012347098240976e-05         
relative error                    = 5.5356336816472371840224197424572          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5188                                       
x1[1] (analytic)                  = 0.0012714219215368875334030383936394         
x1[1] (numeric)                   = 0.0012633487993391137997253136456282         
absolute error                    = 8.0731221977737336777247480112e-06           
relative error                    = 0.63496798828314913940613540529249         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084305732728564999045719358638684        
x2[1] (numeric)                   = 0.00089024956661797277082428874642769        
absolute error                    = 4.719223933232278036709516004085e-05         
relative error                    = 5.5977497383559076491679587633598          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.519                                        
x1[1] (analytic)                  = 0.0012712076585795900954973303432135         
x1[1] (numeric)                   = 0.0012630767413742630648325687293862         
absolute error                    = 8.1309172053270306647616138273e-06           
relative error                    = 0.63962147729760198893255938351281         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084324745676056124423632533367627        
x2[1] (numeric)                   = 0.00089097375489264670041760038146337        
absolute error                    = 4.772629813208545618127504778710e-05         
relative error                    = 5.6598211769807046789453423929413          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5192                                       
x1[1] (analytic)                  = 0.0012709934384705991436029141137296         
x1[1] (numeric)                   = 0.0012628049446401924146972006668803         
absolute error                    = 8.1884938304067289057134468493e-06           
relative error                    = 0.64425933152416873524242770359574         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084343768373091363663881560174858        
x2[1] (numeric)                   = 0.00089169790598827544548160180518892        
absolute error                    = 4.826022225736180884278620344034e-05         
relative error                    = 5.721848002318867406602693564685           % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5194                                       
x1[1] (analytic)                  = 0.0012707792612013458733315889481744         
x1[1] (numeric)                   = 0.0012625334090847266352661082512217         
absolute error                    = 8.2458521166192380654806969527e-06           
relative error                    = 0.64888154602270786112189782881026         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084362800823142788557809045520348        
x2[1] (numeric)                   = 0.0008924220199094699986156294702335         
absolute error                    = 4.879401167804211303753901503002e-05         
relative error                    = 5.7838302192376615660833609143982          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.4MB, time=4.65
NO POLE
NO POLE
t[1]                              = 0.5196                                       
x1[1] (analytic)                  = 0.001270565126763263193884667066423          
x1[1] (numeric)                   = 0.0012622621346558838597762006387131         
absolute error                    = 8.3029921073793341084664277099e-06           
relative error                    = 0.65348811583795192595778384289001         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084381843029683945699891315649824        
x2[1] (numeric)                   = 0.00089314609666123861607794351249023        
absolute error                    = 4.932766636439915907903035599199e-05         
relative error                    = 5.8457678326659224055022948061555          % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.5198                                       
x1[1] (analytic)                  = 0.0012703510351477857277102900321493         
x1[1] (numeric)                   = 0.0012619911213018479239330581703356         
absolute error                    = 8.3599138459378037772318618137e-06           
relative error                    = 0.65807903600167152892254935000275         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084400894996189857060640061004145        
x2[1] (numeric)                   = 0.00089387013624892672946426017077526        
absolute error                    = 4.986118628702815885785956073381e-05         
relative error                    = 5.907660847586872400407150681482           % 
h                                 = 0.0002                                       
 
TOP MAIN SOLVE Loop
NO POLE
NO POLE
t[1]                              = 0.52                                         
x1[1] (analytic)                  = 0.00127013698634634981016081364961           
x1[1] (numeric)                   = 0.0012617203689709448874025485803488         
absolute error                    = 8.4166173754049227582650692612e-06           
relative error                    = 0.66265430153451344679429847633838         % 
h                                 = 0.0002                                       
x2[1] (analytic)                  = 0.00084419956726137020559736614303792        
x2[1] (numeric)                   = 0.00089459413867816591389049463884138        
absolute error                    = 5.039457141679570829312849580346e-05         
relative error                    = 5.9695092690320213873677185514294          % 
h                                 = 0.0002                                       
Finished!
Maximum Iterations Reached before Solution Completed!
diff (x1,t,1) = 4.0 * x2 -  2.0 * diff (x2,t ,1) - 2.0 * x1;
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1) + x1;
Iterations                        = 100                                 
Total Elapsed Time               = 4 Seconds
Elapsed Time(since restart)      = 4 Seconds
Expected Time Remaining          = 17 Minutes 28 Seconds
Optimized Time Remaining         = 17 Minutes 25 Seconds
Time to Timeout                  = 14 Minutes 55 Seconds
Percent Done                     = 0.4489                                     % 
> quit
memory used=70.6MB, alloc=4.4MB, time=4.77