|\^/| Maple 11 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> #BEGIN OUTFILE1
> # Begin Function number 3
> display_poles := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_t ;
> local rad_given;
> if (glob_type_given_pole = 4) then # if number 1
> rad_given := sqrt(expt(array_t[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 2;
> if (array_poles[1,1] <> glob_large_float) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 2;
> if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 2;
> if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 2
> ;
> if (glob_type_given_pole = 4) then # if number 2
> rad_given := sqrt(expt(array_t[1] - array_given_rad_poles[2,1],2.0) + expt(array_given_rad_poles[2,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[2,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 3
> omniout_str(ALWAYS,"NO POLE (given) for Equation 2");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 2");
> fi;# end if 3;
> if (array_poles[2,1] <> glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4, array_poles[2,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2");
> fi;# end if 3;
> if ((array_real_poles[2,1] > 0.0) and (array_real_poles[2,1] <> glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4, array_real_poles[2,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[2,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2");
> fi;# end if 3;
> if ((array_complex_poles[2,1] > 0.0) and (array_complex_poles[2,1] <> glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4, array_complex_poles[2,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[2,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_large_float, array_pole,
glob_type_given_pole, array_given_rad_poles, array_given_ord_poles,
array_complex_poles, array_poles, array_real_poles, array_t;
if glob_type_given_pole = 4 then
rad_given := sqrt(
expt(array_t[1] - array_given_rad_poles[1, 1], 2.0)
+ expt(array_given_rad_poles[1, 2], 2.0));
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ")
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_poles[1, 1], 4, " ");
omniout_str(ALWAYS, "Order of pole (ratio test) \
Not computed")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if 0. < array_real_poles[1, 1] and
array_real_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_real_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_real_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if 0. < array_complex_poles[1, 1] and
array_complex_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_complex_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if;
if glob_type_given_pole = 4 then
rad_given := sqrt(
expt(array_t[1] - array_given_rad_poles[2, 1], 2.0)
+ expt(array_given_rad_poles[2, 2], 2.0));
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 2 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[2, 1], 4, " ")
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 2")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 2")
end if;
if array_poles[2, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 2 ", 4,
array_poles[2, 1], 4, " ");
omniout_str(ALWAYS, "Order of pole (ratio test) \
Not computed")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2")
end if;
if 0. < array_real_poles[2, 1] and
array_real_poles[2, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 2 ", 4,
array_real_poles[2, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_real_poles[2, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 2")
end if;
if 0. < array_complex_poles[2, 1] and
array_complex_poles[2, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 2 ", 4,
array_complex_poles[2, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_complex_poles[2, 2], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 2")
end if
end proc
> # End Function number 3
> # Begin Function number 4
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 3;
> ret;;
> end;
check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
> # End Function number 4
> # Begin Function number 5
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_3D0,
> array_const_1,
> array_const_2D0,
> array_const_4D0,
> #END CONST
> array_x2_init,
> array_x1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_x2,
> array_t,
> array_x1,
> 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_m1,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_x2[1]) < min_size) then # if number 3
> min_size := omniabs(array_x2[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (omniabs(array_x1[1]) < min_size) then # if number 3
> min_size := omniabs(array_x1[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < 1.0) then # if number 3
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_3D0,
array_const_1, array_const_2D0, array_const_4D0, array_x2_init,
array_x1_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_x2,
array_t, array_x1, 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_m1, array_x2_higher,
array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
min_size := glob_large_float;
if omniabs(array_x2[1]) < min_size then
min_size := omniabs(array_x2[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if omniabs(array_x1[1]) < min_size then
min_size := omniabs(array_x1[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 5
> # Begin Function number 6
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_3D0,
> array_const_1,
> array_const_2D0,
> array_const_4D0,
> #END CONST
> array_x2_init,
> array_x1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_x2,
> array_t,
> array_x1,
> 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_m1,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := omniabs(array_x2[no_terms-3] + array_x2[no_terms - 2] * hn_div_ho + array_x2[no_terms - 1] * hn_div_ho_2 + array_x2[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> est_tmp := omniabs(array_x1[no_terms-3] + array_x1[no_terms - 2] * hn_div_ho + array_x1[no_terms - 1] * hn_div_ho_2 + array_x1[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_3D0,
array_const_1, array_const_2D0, array_const_4D0, array_x2_init,
array_x1_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_x2,
array_t, array_x1, 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_m1, array_x2_higher,
array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
max_estimated_step_error := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := omniabs(array_x2[no_terms - 3]
+ array_x2[no_terms - 2]*hn_div_ho
+ array_x2[no_terms - 1]*hn_div_ho_2
+ array_x2[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
est_tmp := omniabs(array_x1[no_terms - 3]
+ array_x1[no_terms - 2]*hn_div_ho
+ array_x1[no_terms - 1]*hn_div_ho_2
+ array_x1[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
> # End Function number 6
> # Begin Function number 7
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_3D0,
> array_const_1,
> array_const_2D0,
> array_const_4D0,
> #END CONST
> array_x2_init,
> array_x1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_x2,
> array_t,
> array_x1,
> 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_m1,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_t[1]) >= glob_check_sign * glob_next_display) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_3D0,
array_const_1, array_const_2D0, array_const_4D0, array_x2_init,
array_x1_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_x2,
array_t, array_x1, 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_m1, array_x2_higher,
array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_t[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 7
> # Begin Function number 8
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_3D0,
> array_const_1,
> array_const_2D0,
> array_const_4D0,
> #END CONST
> array_x2_init,
> array_x1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_x2,
> array_t,
> array_x1,
> 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_m1,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 3
> if (iter >= 0) then # if number 4
> ind_var := array_t[1];
> omniout_float(ALWAYS,"t[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_x2(ind_var);
> omniout_float(ALWAYS,"x2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x2[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 5
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 6
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 5;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> analytic_val_y := exact_soln_x1(ind_var);
> omniout_float(ALWAYS,"x1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_x1[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 5
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 6
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 5;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 5;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_3D0,
array_const_1, array_const_2D0, array_const_4D0, array_x2_init,
array_x1_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_x2,
array_t, array_x1, 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_m1, array_x2_higher,
array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_t[1];
omniout_float(ALWAYS, "t[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_x2(ind_var);
omniout_float(ALWAYS, "x2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x2[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x2[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
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_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
analytic_val_y := exact_soln_x1(ind_var);
omniout_float(ALWAYS, "x1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_x1[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "x1[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
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_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 8
> # Begin Function number 9
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_3D0,
> array_const_1,
> array_const_2D0,
> array_const_4D0,
> #END CONST
> array_x2_init,
> array_x1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_x2,
> array_t,
> array_x1,
> 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_m1,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_x2_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_x2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 4
> glob_normmax := tmp;
> fi;# end if 4
> fi;# end if 3;
> if (omniabs(array_x1_higher[1,1]) > glob_small_float) then # if number 3
> tmp := omniabs(array_x1_higher[1,1]);
> if (tmp < glob_normmax) then # if number 4
> glob_normmax := tmp;
> fi;# end if 4
> fi;# end if 3;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 3
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 4
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 4
> fi;# end if 3;
> if ( not glob_reached_optimal_h) then # if number 3
> 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 3;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_3D0,
array_const_1, array_const_2D0, array_const_4D0, array_x2_init,
array_x1_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_x2,
array_t, array_x1, 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_m1, array_x2_higher,
array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_x2_higher[1, 1]) then
tmp := omniabs(array_x2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < omniabs(array_x1_higher[1, 1]) then
tmp := omniabs(array_x1_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(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");
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;
return hnew
end proc
> # End Function number 9
> # Begin Function number 10
> prog_report := proc(t_start,t_end)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_3D0,
> array_const_1,
> array_const_2D0,
> array_const_4D0,
> #END CONST
> array_x2_init,
> array_x1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_x2,
> array_t,
> array_x1,
> 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_m1,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> 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));
> glob_total_exp_sec := glob_optimal_expect_sec + total_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 3
> 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));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 3;
> 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;
prog_report := proc(t_start, t_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_3D0,
array_const_1, array_const_2D0, array_const_4D0, array_x2_init,
array_x1_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_x2,
array_t, array_x1, 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_m1, array_x2_higher,
array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
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));
glob_total_exp_sec := glob_optimal_expect_sec + total_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));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_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
> # End Function number 10
> # Begin Function number 11
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_3D0,
> array_const_1,
> array_const_2D0,
> array_const_4D0,
> #END CONST
> array_x2_init,
> array_x1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_x2,
> array_t,
> array_x1,
> 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_m1,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad;
> #TOP CHECK FOR POLE
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> #TOP radius ratio test in Henrici1
> found_sing := 1;
> n := glob_max_terms - 2 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_x2_higher[1,n]) = 0.0) or (omniabs(array_x2_higher[1,n+1]) = 0.0)) then # if number 3
> found_sing := 0;
> else
> tmp_rad := omniabs(array_x2_higher[1,n] * glob_h / array_x2_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 4
> if (tmp_rad < rad_c) then # if number 5
> rad_c := tmp_rad;
> fi;# end if 5;
> elif
> (cnt = 0) then # if number 5
> if (tmp_rad < rad_c) then # if number 6
> rad_c := tmp_rad;
> fi;# end if 6;
> elif
> (cnt > 0) then # if number 6
> found_sing := 0;
> fi;# end if 6
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_pole[1]) then # if number 6
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM radius ratio test in Henrici1
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> #TOP radius ratio test in Henrici2
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_x1_higher[1,n]) = 0.0) or (omniabs(array_x1_higher[1,n+1]) = 0.0)) then # if number 5
> found_sing := 0;
> else
> tmp_rad := omniabs(array_x1_higher[1,n] * glob_h / array_x1_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 6
> if (tmp_rad < rad_c) then # if number 7
> rad_c := tmp_rad;
> fi;# end if 7;
> elif
> (cnt = 0) then # if number 7
> if (tmp_rad < rad_c) then # if number 8
> rad_c := tmp_rad;
> fi;# end if 8;
> elif
> (cnt > 0) then # if number 8
> found_sing := 0;
> fi;# end if 8
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_pole[1]) then # if number 8
> array_pole[1] := rad_c;
> array_poles[2,1] := rad_c;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM radius ratio test in Henrici2
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 2 - 1;
> while ((m >= 10) and ((omniabs(array_x2_higher[1,m]) = 0.0) or (omniabs(array_x2_higher[1,m-1]) = 0.0) or (omniabs(array_x2_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 7
> 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)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 8
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[1,1] := rcs;
> array_real_poles[1,2] := ord_no;
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 8
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 7;
> #BOTTOM RADII REAL EQ = 1
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_x1_higher[1,m]) = 0.0) or (omniabs(array_x1_higher[1,m-1]) = 0.0) or (omniabs(array_x1_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 7
> 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)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 8
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[2,1] := rcs;
> array_real_poles[2,2] := ord_no;
> else
> array_real_poles[2,1] := glob_large_float;
> array_real_poles[2,2] := glob_large_float;
> fi;# end if 8
> else
> array_real_poles[2,1] := glob_large_float;
> array_real_poles[2,2] := glob_large_float;
> fi;# end if 7;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 2 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 1
> if (omniabs(array_x2_higher[1,n]) <> 0.0) then # if number 7
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 7;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 7
> rad_c := glob_large_float;
> ord_no := 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 ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 8
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 9
> 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 (omniabs(rcs) <> 0.0) then # if number 10
> if (rcs > 0.0) then # if number 11
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 11
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 10
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 9
> fi;# end if 8;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 7;
> #BOTTOM RADII COMPLEX EQ = 1
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 1
> if (omniabs(array_x1_higher[1,n]) <> 0.0) then # if number 7
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 7;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 7
> rad_c := glob_large_float;
> ord_no := 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 ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 8
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 9
> 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 (omniabs(rcs) <> 0.0) then # if number 10
> if (rcs > 0.0) then # if number 11
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 11
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 10
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 9
> fi;# end if 8;
> array_complex_poles[2,1] := rad_c;
> array_complex_poles[2,2] := ord_no;
> fi;# end if 7;
> #BOTTOM RADII COMPLEX EQ = 2
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 7
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> array_x2[term] := array_x2[term]* ratio;
> array_x2_higher[1,term] := array_x2_higher[1,term]* ratio;
> array_t[term] := array_t[term]* ratio;
> array_x1[term] := array_x1[term]* ratio;
> array_x1_higher[1,term] := array_x1_higher[1,term]* ratio;
> array_t[term] := array_t[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 7;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 7
> display_poles();
> fi;# end if 7
> 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_sing, h_new, ratio, term, local_test,
tmp_rad, tmp_ratio, prev_tmp_rad;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_3D0,
array_const_1, array_const_2D0, array_const_4D0, array_x2_init,
array_x1_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_x2,
array_t, array_x1, 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_m1, array_x2_higher,
array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 12;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_x2_higher[1, n]) = 0. or
omniabs(array_x2_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_x2_higher[1, n]*glob_h/array_x2_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[1, 1] := rad_c
end if
end if;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_x1_higher[1, n]) = 0. or
omniabs(array_x1_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_x1_higher[1, n]*glob_h/array_x1_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[2, 1] := rad_c
end if
end if;
n := glob_max_terms;
m := n - 3;
while 10 <= m and (omniabs(array_x2_higher[1, m]) = 0. or
omniabs(array_x2_higher[1, m - 1]) = 0. or
omniabs(array_x2_higher[1, m - 2]) = 0.) 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)*rm0 - convfloat(m - 1)*rm1;
if 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[1, 1] := rcs;
array_real_poles[1, 2] := ord_no
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_x1_higher[1, m]) = 0. or
omniabs(array_x1_higher[1, m - 1]) = 0. or
omniabs(array_x1_higher[1, m - 2]) = 0.) 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)*rm0 - convfloat(m - 1)*rm1;
if 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[2, 1] := rcs;
array_real_poles[2, 2] := ord_no
else
array_real_poles[2, 1] := glob_large_float;
array_real_poles[2, 2] := glob_large_float
end if
else
array_real_poles[2, 1] := glob_large_float;
array_real_poles[2, 2] := glob_large_float
end if;
n := glob_max_terms - 3;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_x2_higher[1, n]) <> 0. then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := 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 omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. 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 omniabs(rcs) <> 0. then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(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_poles[1, 1] := rad_c;
array_complex_poles[1, 2] := ord_no
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_x1_higher[1, n]) <> 0. then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := 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 omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. 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 omniabs(rcs) <> 0. then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(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_poles[2, 1] := rad_c;
array_complex_poles[2, 2] := ord_no
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_x2[term] := array_x2[term]*ratio;
array_x2_higher[1, term] := array_x2_higher[1, term]*ratio;
array_t[term] := array_t[term]*ratio;
array_x1[term] := array_x1[term]*ratio;
array_x1_higher[1, term] := array_x1_higher[1, term]*ratio;
array_t[term] := array_t[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
> # End Function number 11
> # Begin Function number 12
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_3D0,
> array_const_1,
> array_const_2D0,
> array_const_4D0,
> #END CONST
> array_x2_init,
> array_x1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_x2,
> array_t,
> array_x1,
> 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_m1,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 7
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 1;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_x2[iii]) > array_norms[iii]) then # if number 8
> array_norms[iii] := omniabs(array_x2[iii]);
> fi;# end if 8;
> iii := iii + 1;
> od;# end do number 1
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_x1[iii]) > array_norms[iii]) then # if number 8
> array_norms[iii] := omniabs(array_x1[iii]);
> fi;# end if 8;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 7;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_3D0,
array_const_1, array_const_2D0, array_const_4D0, array_x2_init,
array_x1_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_x2,
array_t, array_x1, 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_m1, array_x2_higher,
array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_x2[iii]) then
array_norms[iii] := omniabs(array_x2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_x1[iii]) then
array_norms[iii] := omniabs(array_x1[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 12
> # Begin Function number 13
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_3D0,
> array_const_1,
> array_const_2D0,
> array_const_4D0,
> #END CONST
> array_x2_init,
> array_x1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_x2,
> array_t,
> array_x1,
> 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_m1,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre diff $eq_no = 1 i = 1 order_d = 1
> array_tmp1[1] := array_x2_higher[2,1];
> #emit pre mult CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_3D0[1] * array_tmp1[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> #emit pre mult CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_2D0[1] * array_x2[1];
> #emit pre sub FULL FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp3[1] - array_tmp4[1];
> #emit pre diff $eq_no = 1 i = 1 order_d = 2
> array_tmp6[1] := array_x1_higher[3,1];
> #emit pre sub FULL FULL $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
> #emit pre diff $eq_no = 1 i = 1 order_d = 1
> array_tmp8[1] := array_x1_higher[2,1];
> #emit pre sub FULL FULL $eq_no = 1 i = 1
> array_tmp9[1] := array_tmp7[1] - array_tmp8[1];
> #emit pre add FULL FULL $eq_no = 1 i = 1
> array_tmp10[1] := array_tmp9[1] + array_x1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_x2_set_initial[1,3]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp10[1] * expt(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 * (1.0);
> array_x2_higher[3,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre mult CONST FULL $eq_no = 2 i = 1
> array_tmp12[1] := array_const_4D0[1] * array_x2[1];
> #emit pre diff $eq_no = 2 i = 1 order_d = 1
> array_tmp13[1] := array_x2_higher[2,1];
> #emit pre mult CONST FULL $eq_no = 2 i = 1
> array_tmp14[1] := array_const_2D0[1] * array_tmp13[1];
> #emit pre sub FULL FULL $eq_no = 2 i = 1
> array_tmp15[1] := array_tmp12[1] - array_tmp14[1];
> #emit pre mult CONST FULL $eq_no = 2 i = 1
> array_tmp16[1] := array_const_2D0[1] * array_x1[1];
> #emit pre sub FULL FULL $eq_no = 2 i = 1
> array_tmp17[1] := array_tmp15[1] - array_tmp16[1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_x1_set_initial[2,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_x1[2] := temporary;
> array_x1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_x1_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre diff $eq_no = 1 i = 2 order_d = 1
> array_tmp1[2] := array_x2_higher[2,2];
> #emit pre mult CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_const_3D0[1] * array_tmp1[2];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre mult CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_const_2D0[1] * array_x2[2];
> #emit pre sub FULL FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp3[2] - array_tmp4[2];
> #emit pre diff $eq_no = 1 i = 2 order_d = 2
> array_tmp6[2] := array_x1_higher[3,2];
> #emit pre sub FULL FULL $eq_no = 1 i = 2
> array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
> #emit pre diff $eq_no = 1 i = 2 order_d = 1
> array_tmp8[2] := array_x1_higher[2,2];
> #emit pre sub FULL FULL $eq_no = 1 i = 2
> array_tmp9[2] := array_tmp7[2] - array_tmp8[2];
> #emit pre add FULL FULL $eq_no = 1 i = 2
> array_tmp10[2] := array_tmp9[2] + array_x1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_x2_set_initial[1,4]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp10[2] * expt(glob_h , (2)) * factorial_3(1,3);
> array_x2[4] := temporary;
> array_x2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[2,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x2_higher[3,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre mult CONST FULL $eq_no = 2 i = 2
> array_tmp12[2] := array_const_4D0[1] * array_x2[2];
> #emit pre diff $eq_no = 2 i = 2 order_d = 1
> array_tmp13[2] := array_x2_higher[2,2];
> #emit pre mult CONST FULL $eq_no = 2 i = 2
> array_tmp14[2] := array_const_2D0[1] * array_tmp13[2];
> #emit pre sub FULL FULL $eq_no = 2 i = 2
> array_tmp15[2] := array_tmp12[2] - array_tmp14[2];
> #emit pre mult CONST FULL $eq_no = 2 i = 2
> array_tmp16[2] := array_const_2D0[1] * array_x1[2];
> #emit pre sub FULL FULL $eq_no = 2 i = 2
> array_tmp17[2] := array_tmp15[2] - array_tmp16[2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_x1_set_initial[2,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[2] * expt(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 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre diff $eq_no = 1 i = 3 order_d = 1
> array_tmp1[3] := array_x2_higher[2,3];
> #emit pre mult CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_const_3D0[1] * array_tmp1[3];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre mult CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_const_2D0[1] * array_x2[3];
> #emit pre sub FULL FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp3[3] - array_tmp4[3];
> #emit pre diff $eq_no = 1 i = 3 order_d = 2
> array_tmp6[3] := array_x1_higher[3,3];
> #emit pre sub FULL FULL $eq_no = 1 i = 3
> array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
> #emit pre diff $eq_no = 1 i = 3 order_d = 1
> array_tmp8[3] := array_x1_higher[2,3];
> #emit pre sub FULL FULL $eq_no = 1 i = 3
> array_tmp9[3] := array_tmp7[3] - array_tmp8[3];
> #emit pre add FULL FULL $eq_no = 1 i = 3
> array_tmp10[3] := array_tmp9[3] + array_x1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_x2_set_initial[1,5]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp10[3] * expt(glob_h , (2)) * factorial_3(2,4);
> array_x2[5] := temporary;
> array_x2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_x2_higher[2,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_x2_higher[3,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre mult CONST FULL $eq_no = 2 i = 3
> array_tmp12[3] := array_const_4D0[1] * array_x2[3];
> #emit pre diff $eq_no = 2 i = 3 order_d = 1
> array_tmp13[3] := array_x2_higher[2,3];
> #emit pre mult CONST FULL $eq_no = 2 i = 3
> array_tmp14[3] := array_const_2D0[1] * array_tmp13[3];
> #emit pre sub FULL FULL $eq_no = 2 i = 3
> array_tmp15[3] := array_tmp12[3] - array_tmp14[3];
> #emit pre mult CONST FULL $eq_no = 2 i = 3
> array_tmp16[3] := array_const_2D0[1] * array_x1[3];
> #emit pre sub FULL FULL $eq_no = 2 i = 3
> array_tmp17[3] := array_tmp15[3] - array_tmp16[3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_x1_set_initial[2,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_x1[4] := temporary;
> array_x1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_x1_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre diff $eq_no = 1 i = 4 order_d = 1
> array_tmp1[4] := array_x2_higher[2,4];
> #emit pre mult CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_const_3D0[1] * array_tmp1[4];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre mult CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_const_2D0[1] * array_x2[4];
> #emit pre sub FULL FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp3[4] - array_tmp4[4];
> #emit pre diff $eq_no = 1 i = 4 order_d = 2
> array_tmp6[4] := array_x1_higher[3,4];
> #emit pre sub FULL FULL $eq_no = 1 i = 4
> array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
> #emit pre diff $eq_no = 1 i = 4 order_d = 1
> array_tmp8[4] := array_x1_higher[2,4];
> #emit pre sub FULL FULL $eq_no = 1 i = 4
> array_tmp9[4] := array_tmp7[4] - array_tmp8[4];
> #emit pre add FULL FULL $eq_no = 1 i = 4
> array_tmp10[4] := array_tmp9[4] + array_x1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_x2_set_initial[1,6]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp10[4] * expt(glob_h , (2)) * factorial_3(3,5);
> array_x2[6] := temporary;
> array_x2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_x2_higher[2,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_x2_higher[3,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre mult CONST FULL $eq_no = 2 i = 4
> array_tmp12[4] := array_const_4D0[1] * array_x2[4];
> #emit pre diff $eq_no = 2 i = 4 order_d = 1
> array_tmp13[4] := array_x2_higher[2,4];
> #emit pre mult CONST FULL $eq_no = 2 i = 4
> array_tmp14[4] := array_const_2D0[1] * array_tmp13[4];
> #emit pre sub FULL FULL $eq_no = 2 i = 4
> array_tmp15[4] := array_tmp12[4] - array_tmp14[4];
> #emit pre mult CONST FULL $eq_no = 2 i = 4
> array_tmp16[4] := array_const_2D0[1] * array_x1[4];
> #emit pre sub FULL FULL $eq_no = 2 i = 4
> array_tmp17[4] := array_tmp15[4] - array_tmp16[4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_x1_set_initial[2,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_x1[5] := temporary;
> array_x1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_x1_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre diff $eq_no = 1 i = 5 order_d = 1
> array_tmp1[5] := array_x2_higher[2,5];
> #emit pre mult CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_const_3D0[1] * array_tmp1[5];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre mult CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_const_2D0[1] * array_x2[5];
> #emit pre sub FULL FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp3[5] - array_tmp4[5];
> #emit pre diff $eq_no = 1 i = 5 order_d = 2
> array_tmp6[5] := array_x1_higher[3,5];
> #emit pre sub FULL FULL $eq_no = 1 i = 5
> array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
> #emit pre diff $eq_no = 1 i = 5 order_d = 1
> array_tmp8[5] := array_x1_higher[2,5];
> #emit pre sub FULL FULL $eq_no = 1 i = 5
> array_tmp9[5] := array_tmp7[5] - array_tmp8[5];
> #emit pre add FULL FULL $eq_no = 1 i = 5
> array_tmp10[5] := array_tmp9[5] + array_x1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_x2_set_initial[1,7]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp10[5] * expt(glob_h , (2)) * factorial_3(4,6);
> array_x2[7] := temporary;
> array_x2_higher[1,7] := temporary;
> temporary := temporary / glob_h * (6.0);
> array_x2_higher[2,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_x2_higher[3,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre mult CONST FULL $eq_no = 2 i = 5
> array_tmp12[5] := array_const_4D0[1] * array_x2[5];
> #emit pre diff $eq_no = 2 i = 5 order_d = 1
> array_tmp13[5] := array_x2_higher[2,5];
> #emit pre mult CONST FULL $eq_no = 2 i = 5
> array_tmp14[5] := array_const_2D0[1] * array_tmp13[5];
> #emit pre sub FULL FULL $eq_no = 2 i = 5
> array_tmp15[5] := array_tmp12[5] - array_tmp14[5];
> #emit pre mult CONST FULL $eq_no = 2 i = 5
> array_tmp16[5] := array_const_2D0[1] * array_x1[5];
> #emit pre sub FULL FULL $eq_no = 2 i = 5
> array_tmp17[5] := array_tmp15[5] - array_tmp16[5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_x1_set_initial[2,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp17[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_x1[6] := temporary;
> array_x1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_x1_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit diff $eq_no = 1
> array_tmp1[kkk] := array_x2_higher[2,kkk];
> #emit mult CONST FULL $eq_no = 1 i = 1
> array_tmp2[kkk] := array_const_3D0[1] * array_tmp1[kkk];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit mult CONST FULL $eq_no = 1 i = 1
> array_tmp4[kkk] := array_const_2D0[1] * array_x2[kkk];
> #emit FULL - FULL sub $eq_no = 1
> array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk];
> #emit diff $eq_no = 1
> array_tmp6[kkk] := array_x1_higher[3,kkk];
> #emit FULL - FULL sub $eq_no = 1
> array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
> #emit diff $eq_no = 1
> array_tmp8[kkk] := array_x1_higher[2,kkk];
> #emit FULL - FULL sub $eq_no = 1
> array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk];
> #emit FULL - FULL add $eq_no = 1
> array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_x2_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp10[kkk] * expt(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 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_x2_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> #emit mult CONST FULL $eq_no = 2 i = 1
> array_tmp12[kkk] := array_const_4D0[1] * array_x2[kkk];
> #emit diff $eq_no = 2
> array_tmp13[kkk] := array_x2_higher[2,kkk];
> #emit mult CONST FULL $eq_no = 2 i = 1
> array_tmp14[kkk] := array_const_2D0[1] * array_tmp13[kkk];
> #emit FULL - FULL sub $eq_no = 2
> array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk];
> #emit mult CONST FULL $eq_no = 2 i = 1
> array_tmp16[kkk] := array_const_2D0[1] * array_x1[kkk];
> #emit FULL - FULL sub $eq_no = 2
> array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk];
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_x1_set_initial[2,kkk + order_d]) then # if number 2
> temporary := array_tmp17[kkk] * expt(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 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_x1_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_3D0,
array_const_1, array_const_2D0, array_const_4D0, array_x2_init,
array_x1_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_x2,
array_t, array_x1, 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_m1, array_x2_higher,
array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
array_tmp1[1] := array_x2_higher[2, 1];
array_tmp2[1] := array_const_3D0[1]*array_tmp1[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
array_tmp4[1] := array_const_2D0[1]*array_x2[1];
array_tmp5[1] := array_tmp3[1] - array_tmp4[1];
array_tmp6[1] := array_x1_higher[3, 1];
array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
array_tmp8[1] := array_x1_higher[2, 1];
array_tmp9[1] := array_tmp7[1] - array_tmp8[1];
array_tmp10[1] := array_tmp9[1] + array_x1[1];
if not array_x2_set_initial[1, 3] then
if 1 <= glob_max_terms then
temporary := array_tmp10[1]*expt(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*1.0/glob_h;
array_x2_higher[3, 1] := temporary
end if
end if;
kkk := 2;
array_tmp12[1] := array_const_4D0[1]*array_x2[1];
array_tmp13[1] := array_x2_higher[2, 1];
array_tmp14[1] := array_const_2D0[1]*array_tmp13[1];
array_tmp15[1] := array_tmp12[1] - array_tmp14[1];
array_tmp16[1] := array_const_2D0[1]*array_x1[1];
array_tmp17[1] := array_tmp15[1] - array_tmp16[1];
if not array_x1_set_initial[2, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp17[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_x1[2] := temporary;
array_x1_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_x1_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_x2_higher[2, 2];
array_tmp2[2] := array_const_3D0[1]*array_tmp1[2];
array_tmp3[2] := array_tmp2[2];
array_tmp4[2] := array_const_2D0[1]*array_x2[2];
array_tmp5[2] := array_tmp3[2] - array_tmp4[2];
array_tmp6[2] := array_x1_higher[3, 2];
array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
array_tmp8[2] := array_x1_higher[2, 2];
array_tmp9[2] := array_tmp7[2] - array_tmp8[2];
array_tmp10[2] := array_tmp9[2] + array_x1[2];
if not array_x2_set_initial[1, 4] then
if 2 <= glob_max_terms then
temporary := array_tmp10[2]*expt(glob_h, 2)*factorial_3(1, 3);
array_x2[4] := temporary;
array_x2_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[2, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x2_higher[3, 2] := temporary
end if
end if;
kkk := 3;
array_tmp12[2] := array_const_4D0[1]*array_x2[2];
array_tmp13[2] := array_x2_higher[2, 2];
array_tmp14[2] := array_const_2D0[1]*array_tmp13[2];
array_tmp15[2] := array_tmp12[2] - array_tmp14[2];
array_tmp16[2] := array_const_2D0[1]*array_x1[2];
array_tmp17[2] := array_tmp15[2] - array_tmp16[2];
if not array_x1_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp17[2]*expt(glob_h, 1)*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
end if;
kkk := 3;
array_tmp1[3] := array_x2_higher[2, 3];
array_tmp2[3] := array_const_3D0[1]*array_tmp1[3];
array_tmp3[3] := array_tmp2[3];
array_tmp4[3] := array_const_2D0[1]*array_x2[3];
array_tmp5[3] := array_tmp3[3] - array_tmp4[3];
array_tmp6[3] := array_x1_higher[3, 3];
array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
array_tmp8[3] := array_x1_higher[2, 3];
array_tmp9[3] := array_tmp7[3] - array_tmp8[3];
array_tmp10[3] := array_tmp9[3] + array_x1[3];
if not array_x2_set_initial[1, 5] then
if 3 <= glob_max_terms then
temporary := array_tmp10[3]*expt(glob_h, 2)*factorial_3(2, 4);
array_x2[5] := temporary;
array_x2_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_x2_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x2_higher[3, 3] := temporary
end if
end if;
kkk := 4;
array_tmp12[3] := array_const_4D0[1]*array_x2[3];
array_tmp13[3] := array_x2_higher[2, 3];
array_tmp14[3] := array_const_2D0[1]*array_tmp13[3];
array_tmp15[3] := array_tmp12[3] - array_tmp14[3];
array_tmp16[3] := array_const_2D0[1]*array_x1[3];
array_tmp17[3] := array_tmp15[3] - array_tmp16[3];
if not array_x1_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp17[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_x1[4] := temporary;
array_x1_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x1_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_x2_higher[2, 4];
array_tmp2[4] := array_const_3D0[1]*array_tmp1[4];
array_tmp3[4] := array_tmp2[4];
array_tmp4[4] := array_const_2D0[1]*array_x2[4];
array_tmp5[4] := array_tmp3[4] - array_tmp4[4];
array_tmp6[4] := array_x1_higher[3, 4];
array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
array_tmp8[4] := array_x1_higher[2, 4];
array_tmp9[4] := array_tmp7[4] - array_tmp8[4];
array_tmp10[4] := array_tmp9[4] + array_x1[4];
if not array_x2_set_initial[1, 6] then
if 4 <= glob_max_terms then
temporary := array_tmp10[4]*expt(glob_h, 2)*factorial_3(3, 5);
array_x2[6] := temporary;
array_x2_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_x2_higher[2, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_x2_higher[3, 4] := temporary
end if
end if;
kkk := 5;
array_tmp12[4] := array_const_4D0[1]*array_x2[4];
array_tmp13[4] := array_x2_higher[2, 4];
array_tmp14[4] := array_const_2D0[1]*array_tmp13[4];
array_tmp15[4] := array_tmp12[4] - array_tmp14[4];
array_tmp16[4] := array_const_2D0[1]*array_x1[4];
array_tmp17[4] := array_tmp15[4] - array_tmp16[4];
if not array_x1_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp17[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_x1[5] := temporary;
array_x1_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_x1_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_x2_higher[2, 5];
array_tmp2[5] := array_const_3D0[1]*array_tmp1[5];
array_tmp3[5] := array_tmp2[5];
array_tmp4[5] := array_const_2D0[1]*array_x2[5];
array_tmp5[5] := array_tmp3[5] - array_tmp4[5];
array_tmp6[5] := array_x1_higher[3, 5];
array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
array_tmp8[5] := array_x1_higher[2, 5];
array_tmp9[5] := array_tmp7[5] - array_tmp8[5];
array_tmp10[5] := array_tmp9[5] + array_x1[5];
if not array_x2_set_initial[1, 7] then
if 5 <= glob_max_terms then
temporary := array_tmp10[5]*expt(glob_h, 2)*factorial_3(4, 6);
array_x2[7] := temporary;
array_x2_higher[1, 7] := temporary;
temporary := temporary*6.0/glob_h;
array_x2_higher[2, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_x2_higher[3, 5] := temporary
end if
end if;
kkk := 6;
array_tmp12[5] := array_const_4D0[1]*array_x2[5];
array_tmp13[5] := array_x2_higher[2, 5];
array_tmp14[5] := array_const_2D0[1]*array_tmp13[5];
array_tmp15[5] := array_tmp12[5] - array_tmp14[5];
array_tmp16[5] := array_const_2D0[1]*array_x1[5];
array_tmp17[5] := array_tmp15[5] - array_tmp16[5];
if not array_x1_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp17[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_x1[6] := temporary;
array_x1_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_x1_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_x2_higher[2, kkk];
array_tmp2[kkk] := array_const_3D0[1]*array_tmp1[kkk];
array_tmp3[kkk] := array_tmp2[kkk];
array_tmp4[kkk] := array_const_2D0[1]*array_x2[kkk];
array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk];
array_tmp6[kkk] := array_x1_higher[3, kkk];
array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
array_tmp8[kkk] := array_x1_higher[2, kkk];
array_tmp9[kkk] := array_tmp7[kkk] - array_tmp8[kkk];
array_tmp10[kkk] := array_tmp9[kkk] + array_x1[kkk];
order_d := 2;
if kkk + order_d < glob_max_terms then
if not array_x2_set_initial[1, kkk + order_d] then
temporary := array_tmp10[kkk]*expt(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 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_x2_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
array_tmp12[kkk] := array_const_4D0[1]*array_x2[kkk];
array_tmp13[kkk] := array_x2_higher[2, kkk];
array_tmp14[kkk] := array_const_2D0[1]*array_tmp13[kkk];
array_tmp15[kkk] := array_tmp12[kkk] - array_tmp14[kkk];
array_tmp16[kkk] := array_const_2D0[1]*array_x1[kkk];
array_tmp17[kkk] := array_tmp15[kkk] - array_tmp16[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_x1_set_initial[2, kkk + order_d] then
temporary := array_tmp17[kkk]*expt(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 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_x1_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 13
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s
", str)
end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> 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
", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> 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
", prelabel, value, postlabel)
else printf("%-30s = %-32d %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> 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
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_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,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> 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 if 0;
> 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
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> 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 2
> 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 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " |
")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> 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 5
> 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 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\
nutes %d Seconds
", years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\
Seconds
", days_int, hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\
s
", hours_int, minutes_int, sec_int)
elif 0 < minutes_int then printf(" = %d Minutes %d Seconds
", minutes_int, sec_int)
else printf(" = %d Seconds
", sec_int)
end if
else printf(" Unknown
")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> 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 + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_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 + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_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 6
> 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 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_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 + arr_aa[iii_att]*arr_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
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,m,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_int(ALWAYS,"m",4, m ,4," ");
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, m, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_int(ALWAYS, "m", 4, m, 4, " ");
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 16
> # Begin Function number 17
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> elif
> (pole = 4) then # if number 9
> fprintf(file,"Yes");
> else
> fprintf(file,"No");
> fi;# end if 9
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
elif pole = 4 then fprintf(file, "Yes")
else fprintf(file, "No")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file)
fprintf(file, "
")
end proc
> # End Function number 24
> # Begin Function number 25
> 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 9
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 9;
> if (glob_max_iter < 2) then # if number 9
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 9;
> if (errflag) then # if number 9
> quit;
> fi;# end if 9
> 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
> # End Function number 25
> # Begin Function number 26
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 9
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 10
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 10
> fi;# end if 9;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 26
> # Begin Function number 27
> 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 (sub2 > glob_small_float) then # if number 9
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 9;
> rrr;
> 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 < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 9
> if (array_fact_1[nnn] = 0) then # if number 10
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 10;
> else
> ret := factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 29
> # Begin Function number 30
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9
> if (array_fact_2[mmm,nnn] = 0) then # if number 10
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 10;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_x1 := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> return(2.0 * c1 + 6.0 * c3 * exp(-t));
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return 2.0*c1 + 6.0*c3*exp(-t)
end proc
> exact_soln_x1p := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> return( - 6.0 * c3 * exp(-t));
> end;
exact_soln_x1p := proc(t)
local c1, c2, c3;
c1 := 1.0; c2 := 0.0002; c3 := 0.0003; return -6.0*c3*exp(-t)
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t));
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return c1 + c2*exp(2.0*t) + c3*exp(-t)
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := 1.0;
> c2 := 0.0002;
> c3 := 0.0003;
> return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t));
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return 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
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> t_start,t_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_3D0,
> array_const_1,
> array_const_2D0,
> array_const_4D0,
> #END CONST
> array_x2_init,
> array_x1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_x2,
> array_t,
> array_x1,
> 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_m1,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_estimated_step_error := 0.0;
> glob_ratio_of_radius := 0.1;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_sec_in_minute := 60;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_disp_incr := 0.1;
> glob_h := 0.1;
> glob_max_h := 0.1;
> glob_min_h := 0.000001;
> glob_type_given_pole := 0;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_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/mtest6_rev_sm_hpostode.ode#################");
> omniout_str(ALWAYS,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1;");
> omniout_str(ALWAYS,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=64;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"## problem from Boyce DePrima -");
> omniout_str(ALWAYS,"## _Elementary Differential Equations and Boundary Value Problems_");
> omniout_str(ALWAYS,"## page 269");
> omniout_str(ALWAYS,"##");
> omniout_str(ALWAYS,"t_start := 0.5;");
> omniout_str(ALWAYS,"t_end := 0.8;");
> omniout_str(ALWAYS,"array_x1_init[0 + 1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"## I think following line should be omitted");
> omniout_str(ALWAYS,"## diff(x1,1,exact_soln_x1p(t_start));");
> omniout_str(ALWAYS,"array_x2_init[0 + 1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1 + 1] := exact_soln_x2p(t_start);");
> omniout_str(ALWAYS,"glob_max_h := 0.0001 ;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 100;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> 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 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"return(2.0 * c1 + 6.0 * c3 * exp(-t));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x1p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"return( - 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 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"return(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 := 1.0;");
> omniout_str(ALWAYS,"c2 := 0.0002;");
> omniout_str(ALWAYS,"c3 := 0.0003;");
> omniout_str(ALWAYS,"return( 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 := 0.0;
> glob_smallish_float := 0.0;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=64;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_x2_init:= Array(0..(max_terms + 1),[]);
> array_x1_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(4 + 1),[]);
> array_real_pole:= Array(0..(4 + 1),[]);
> array_complex_pole:= Array(0..(4 + 1),[]);
> array_1st_rel_error:= Array(0..(3 + 1),[]);
> array_last_rel_error:= Array(0..(3 + 1),[]);
> array_type_pole:= Array(0..(3 + 1),[]);
> array_type_real_pole:= Array(0..(3 + 1),[]);
> array_type_complex_pole:= Array(0..(3 + 1),[]);
> array_x2:= Array(0..(max_terms + 1),[]);
> array_t:= Array(0..(max_terms + 1),[]);
> array_x1:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_tmp6:= Array(0..(max_terms + 1),[]);
> array_tmp7:= Array(0..(max_terms + 1),[]);
> array_tmp8:= Array(0..(max_terms + 1),[]);
> array_tmp9:= Array(0..(max_terms + 1),[]);
> array_tmp10:= Array(0..(max_terms + 1),[]);
> array_tmp11:= Array(0..(max_terms + 1),[]);
> array_tmp12:= Array(0..(max_terms + 1),[]);
> array_tmp13:= Array(0..(max_terms + 1),[]);
> array_tmp14:= Array(0..(max_terms + 1),[]);
> array_tmp15:= Array(0..(max_terms + 1),[]);
> array_tmp16:= Array(0..(max_terms + 1),[]);
> array_tmp17:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_x2_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x2_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x2_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x1_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x1_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x1_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_x1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(3+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x1_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x2_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x2_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x2_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x1_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x1_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x1_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_x2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_t := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp7 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp8 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp9 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp10 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp11 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp12 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp13 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp14 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp15 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp16 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp17 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_2[1] := 2;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D0[1] := 0.0;
> array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_3D0[1] := 3.0;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1[1] := 1;
> array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_2D0[1] := 2.0;
> array_const_4D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_4D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_4D0[1] := 4.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> ## problem from Boyce DePrima -
> ## _Elementary Differential Equations and Boundary Value Problems_
> ## page 269
> ##
> t_start := 0.5;
> t_end := 0.8;
> array_x1_init[0 + 1] := exact_soln_x1(t_start);
> ## I think following line should be omitted
> ## diff(x1,1,exact_soln_x1p(t_start));
> array_x2_init[0 + 1] := exact_soln_x2(t_start);
> array_x2_init[1 + 1] := exact_soln_x2p(t_start);
> glob_max_h := 0.0001 ;
> glob_look_poles := true;
> glob_max_iter := 100;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #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);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_x2_set_initial[1,1] := true;
> array_x2_set_initial[1,2] := true;
> array_x2_set_initial[1,3] := false;
> array_x2_set_initial[1,4] := false;
> array_x2_set_initial[1,5] := false;
> array_x2_set_initial[1,6] := false;
> array_x2_set_initial[1,7] := false;
> array_x2_set_initial[1,8] := false;
> array_x2_set_initial[1,9] := false;
> array_x2_set_initial[1,10] := false;
> array_x2_set_initial[1,11] := false;
> array_x2_set_initial[1,12] := false;
> array_x2_set_initial[1,13] := false;
> array_x2_set_initial[1,14] := false;
> array_x2_set_initial[1,15] := false;
> array_x2_set_initial[1,16] := false;
> array_x2_set_initial[1,17] := false;
> array_x2_set_initial[1,18] := false;
> array_x2_set_initial[1,19] := false;
> array_x2_set_initial[1,20] := false;
> array_x2_set_initial[1,21] := false;
> array_x2_set_initial[1,22] := false;
> array_x2_set_initial[1,23] := false;
> array_x2_set_initial[1,24] := false;
> array_x2_set_initial[1,25] := false;
> array_x2_set_initial[1,26] := false;
> array_x2_set_initial[1,27] := false;
> array_x2_set_initial[1,28] := false;
> array_x2_set_initial[1,29] := false;
> array_x2_set_initial[1,30] := false;
> array_x1_set_initial[2,1] := true;
> array_x1_set_initial[2,2] := false;
> array_x1_set_initial[2,3] := false;
> array_x1_set_initial[2,4] := false;
> array_x1_set_initial[2,5] := false;
> array_x1_set_initial[2,6] := false;
> array_x1_set_initial[2,7] := false;
> array_x1_set_initial[2,8] := false;
> array_x1_set_initial[2,9] := false;
> array_x1_set_initial[2,10] := false;
> array_x1_set_initial[2,11] := false;
> array_x1_set_initial[2,12] := false;
> array_x1_set_initial[2,13] := false;
> array_x1_set_initial[2,14] := false;
> array_x1_set_initial[2,15] := false;
> array_x1_set_initial[2,16] := false;
> array_x1_set_initial[2,17] := false;
> array_x1_set_initial[2,18] := false;
> array_x1_set_initial[2,19] := false;
> array_x1_set_initial[2,20] := false;
> array_x1_set_initial[2,21] := false;
> array_x1_set_initial[2,22] := false;
> array_x1_set_initial[2,23] := false;
> array_x1_set_initial[2,24] := false;
> array_x1_set_initial[2,25] := false;
> array_x1_set_initial[2,26] := false;
> array_x1_set_initial[2,27] := false;
> array_x1_set_initial[2,28] := false;
> array_x1_set_initial[2,29] := false;
> array_x1_set_initial[2,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(t_start,t_end);
> glob_h := check_sign(t_start,t_end);
> found_h := false;
> glob_h := glob_min_h;
> if (glob_max_h < glob_h) then # if number 7
> glob_h := glob_max_h;
> fi;# end if 7;
> if (glob_display_interval < glob_h) then # if number 7
> glob_h := glob_display_interval;
> fi;# end if 7;
> best_h := glob_h;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(t_start,t_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := 0.0;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_t[1] := t_start;
> array_t[2] := glob_h;
> glob_next_display := t_start;
> 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] * expt(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]* expt(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_x1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x1[term_no] := array_x1_init[term_no] * expt(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]* expt(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
> ;
> if (glob_subiter_method = 1 ) then # if number 7
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 8
> subiter := 1;
> while (subiter <= 3) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 3 + glob_max_terms) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 8;
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 8
> found_h := true;
> glob_h := glob_max_h;
> best_h := glob_h;
> elif
> ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 9
> glob_h := glob_h/2.0;
> best_h := glob_h;
> found_h := true;
> else
> glob_h := glob_h*2.0;
> best_h := glob_h;
> fi;# end if 9;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 9
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 9;
> if (opt_iter > 100) then # if number 9
> glob_h := glob_max_h;
> found_h := false;
> fi;# end if 9;
> if (glob_display_interval < glob_h) then # if number 9
> glob_h := glob_display_interval;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_t[1] := t_start;
> array_t[2] := glob_h;
> glob_next_display := t_start;
> order_diff := 2;
> #Start Series array_x2
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_x2[term_no] := array_x2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> array_x2_higher[r_order,term_no] := array_x2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> order_diff := 2;
> #Start Series array_x1
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_x1[term_no] := array_x1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> array_x1_higher[r_order,term_no] := array_x1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> 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 ((glob_check_sign * array_t[1]) < (glob_check_sign * t_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> if (glob_subiter_method = 1 ) then # if number 10
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 11
> subiter := 1;
> while (subiter <= 3) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 3 + glob_max_terms) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 11;
> display_alot(current_iter);
> if (glob_look_poles) then # if number 11
> #left paren 0004C
> check_for_pole();
> fi;# end if 11;#was right paren 0004C
> if (reached_interval()) then # if number 11
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 11;
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> #Jump Series array_x2;
> order_diff := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x2
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_x2_higher_work[3,iii] := array_x2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_x2_higher_work[2,iii] := array_x2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_x2_higher_work[1,iii] := array_x2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(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 2
> array_x2[term_no] := array_x2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_x2_higher[ord,term_no] := array_x2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_x1;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x1
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_x1_higher_work[2,iii] := array_x1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> array_x1_higher_work[1,iii] := array_x1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(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 2
> array_x1[term_no] := array_x1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_x1_higher[ord,term_no] := array_x1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 11
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 11;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 11
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 11;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1;");
> omniout_str(INFO,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if (glob_html_log) then # if number 11
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-05-26T03:26:08-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest6_rev_sm_h")
> ;
> logitem_str(html_log_file,"diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1;")
> ;
> logitem_float(html_log_file,t_start)
> ;
> logitem_float(html_log_file,t_end)
> ;
> logitem_float(html_log_file,array_t[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> 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_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 12
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 12;
> log_revs(html_log_file," 189 | ")
> ;
> logitem_str(html_log_file,"mtest6_rev_sm_h diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest6_rev_sm_h maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[2])
> ;
> 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)
> ;
> logditto(html_log_file)
> ;
> if (glob_percent_done < 100.0) then # if number 12
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 12;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 11;
> if (glob_html_log) then # if number 11
> fclose(html_log_file);
> fi;# end if 11
> ;
> ;;
> fi;# end if 10
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, t_start, t_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_3D0,
array_const_1, array_const_2D0, array_const_4D0, array_x2_init,
array_x1_init, array_norms, array_fact_1, array_pole, array_real_pole,
array_complex_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_type_real_pole, array_type_complex_pole, array_x2,
array_t, array_x1, 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_m1, array_x2_higher,
array_x2_higher_work, array_x2_higher_work2, array_x2_set_initial,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_estimated_step_error := 0.;
glob_ratio_of_radius := 0.1;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_disp_incr := 0.1;
glob_h := 0.1;
glob_max_h := 0.1;
glob_min_h := 0.1*10^(-5);
glob_type_given_pole := 0;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
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/mtest6_rev_sm_hpostode.ode#################");
omniout_str(ALWAYS, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - \
diff(x1,t,2) - diff (x1,t,1)+x1;");
omniout_str(ALWAYS,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=64;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "## problem from Boyce DePrima -");
omniout_str(ALWAYS, "## _Elementary Differential Equations and Bounda\
ry Value Problems_");
omniout_str(ALWAYS, "## page 269");
omniout_str(ALWAYS, "##");
omniout_str(ALWAYS, "t_start := 0.5;");
omniout_str(ALWAYS, "t_end := 0.8;");
omniout_str(ALWAYS, "array_x1_init[0 + 1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "## I think following line should be omitted");
omniout_str(ALWAYS, "## diff(x1,1,exact_soln_x1p(t_start));");
omniout_str(ALWAYS, "array_x2_init[0 + 1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[1 + 1] := exact_soln_x2p(t_start);")
;
omniout_str(ALWAYS, "glob_max_h := 0.0001 ;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 100;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
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 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "return(2.0 * c1 + 6.0 * c3 * exp(-t));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x1p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "return( - 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 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS, "return(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 := 1.0;");
omniout_str(ALWAYS, "c2 := 0.0002;");
omniout_str(ALWAYS, "c3 := 0.0003;");
omniout_str(ALWAYS,
"return( 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.;
glob_smallish_float := 0.;
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 64;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_x2_init := Array(0 .. max_terms + 1, []);
array_x1_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. 5, []);
array_real_pole := Array(0 .. 5, []);
array_complex_pole := Array(0 .. 5, []);
array_1st_rel_error := Array(0 .. 4, []);
array_last_rel_error := Array(0 .. 4, []);
array_type_pole := Array(0 .. 4, []);
array_type_real_pole := Array(0 .. 4, []);
array_type_complex_pole := Array(0 .. 4, []);
array_x2 := Array(0 .. max_terms + 1, []);
array_t := Array(0 .. max_terms + 1, []);
array_x1 := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_tmp6 := Array(0 .. max_terms + 1, []);
array_tmp7 := Array(0 .. max_terms + 1, []);
array_tmp8 := Array(0 .. max_terms + 1, []);
array_tmp9 := Array(0 .. max_terms + 1, []);
array_tmp10 := Array(0 .. max_terms + 1, []);
array_tmp11 := Array(0 .. max_terms + 1, []);
array_tmp12 := Array(0 .. max_terms + 1, []);
array_tmp13 := Array(0 .. max_terms + 1, []);
array_tmp14 := Array(0 .. max_terms + 1, []);
array_tmp15 := Array(0 .. max_terms + 1, []);
array_tmp16 := Array(0 .. max_terms + 1, []);
array_tmp17 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_x2_higher := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x2_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x2_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x1_higher := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x1_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x1_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []);
array_x1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 4, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 4, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 4, 0 .. 4, []);
array_real_poles := Array(0 .. 4, 0 .. 4, []);
array_complex_poles := Array(0 .. 4, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
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_x1_init[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_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 3 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do
array_type_complex_pole[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_t[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_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp10[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp11[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp12[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp13[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp14[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp15[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp16[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp17[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x2_set_initial[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_x1_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x1_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_x1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 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 <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_complex_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[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_t := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_t[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_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[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_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[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_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[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_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[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_tmp8 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp8[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_tmp10 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp10[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_tmp12 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp12[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_tmp14 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp14[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_tmp16 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp16[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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2[term] := 0.; term := term + 1
end do;
array_const_2[1] := 2;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_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_4D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_4D0[term] := 0.; term := term + 1
end do;
array_const_4D0[1] := 4.0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
t_start := 0.5;
t_end := 0.8;
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_max_h := 0.0001;
glob_look_poles := true;
glob_max_iter := 100;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
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);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_x2_set_initial[1, 1] := true;
array_x2_set_initial[1, 2] := true;
array_x2_set_initial[1, 3] := false;
array_x2_set_initial[1, 4] := false;
array_x2_set_initial[1, 5] := false;
array_x2_set_initial[1, 6] := false;
array_x2_set_initial[1, 7] := false;
array_x2_set_initial[1, 8] := false;
array_x2_set_initial[1, 9] := false;
array_x2_set_initial[1, 10] := false;
array_x2_set_initial[1, 11] := false;
array_x2_set_initial[1, 12] := false;
array_x2_set_initial[1, 13] := false;
array_x2_set_initial[1, 14] := false;
array_x2_set_initial[1, 15] := false;
array_x2_set_initial[1, 16] := false;
array_x2_set_initial[1, 17] := false;
array_x2_set_initial[1, 18] := false;
array_x2_set_initial[1, 19] := false;
array_x2_set_initial[1, 20] := false;
array_x2_set_initial[1, 21] := false;
array_x2_set_initial[1, 22] := false;
array_x2_set_initial[1, 23] := false;
array_x2_set_initial[1, 24] := false;
array_x2_set_initial[1, 25] := false;
array_x2_set_initial[1, 26] := false;
array_x2_set_initial[1, 27] := false;
array_x2_set_initial[1, 28] := false;
array_x2_set_initial[1, 29] := false;
array_x2_set_initial[1, 30] := false;
array_x1_set_initial[2, 1] := true;
array_x1_set_initial[2, 2] := false;
array_x1_set_initial[2, 3] := false;
array_x1_set_initial[2, 4] := false;
array_x1_set_initial[2, 5] := false;
array_x1_set_initial[2, 6] := false;
array_x1_set_initial[2, 7] := false;
array_x1_set_initial[2, 8] := false;
array_x1_set_initial[2, 9] := false;
array_x1_set_initial[2, 10] := false;
array_x1_set_initial[2, 11] := false;
array_x1_set_initial[2, 12] := false;
array_x1_set_initial[2, 13] := false;
array_x1_set_initial[2, 14] := false;
array_x1_set_initial[2, 15] := false;
array_x1_set_initial[2, 16] := false;
array_x1_set_initial[2, 17] := false;
array_x1_set_initial[2, 18] := false;
array_x1_set_initial[2, 19] := false;
array_x1_set_initial[2, 20] := false;
array_x1_set_initial[2, 21] := false;
array_x1_set_initial[2, 22] := false;
array_x1_set_initial[2, 23] := false;
array_x1_set_initial[2, 24] := false;
array_x1_set_initial[2, 25] := false;
array_x1_set_initial[2, 26] := false;
array_x1_set_initial[2, 27] := false;
array_x1_set_initial[2, 28] := false;
array_x1_set_initial[2, 29] := false;
array_x1_set_initial[2, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(t_start, t_end);
glob_h := check_sign(t_start, t_end);
found_h := false;
glob_h := glob_min_h;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
best_h := glob_h;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(t_start, t_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err,
16, "");
estimated_step_error := 0.;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_t[1] := t_start;
array_t[2] := glob_h;
glob_next_display := t_start;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x2[term_no] := array_x2_init[term_no]*
expt(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]*
expt(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_x1[term_no] := array_x1_init[term_no]*
expt(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]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 3 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 3 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if est_needed_step_err < estimated_step_error and opt_iter = 1 or
glob_max_h <= glob_h then
found_h := true; glob_h := glob_max_h; best_h := glob_h
elif est_needed_step_err < estimated_step_error and not found_h
then glob_h := glob_h/2.0; best_h := glob_h; found_h := true
else glob_h := glob_h*2.0; best_h := glob_h
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_t[1] := t_start;
array_t[2] := glob_h;
glob_next_display := t_start;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x2[term_no] := array_x2_init[term_no]*
expt(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]*
expt(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_x1[term_no] := array_x1_init[term_no]*
expt(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]*
expt(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();
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
glob_check_sign*array_t[1] < glob_check_sign*t_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 3 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 3 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 3;
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]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
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*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
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]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
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*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
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]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
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*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
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]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
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*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
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]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
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*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
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]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
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*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_x2[term_no] := array_x2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x2_higher[ord, term_no] :=
array_x2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 2;
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]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
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*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 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]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
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*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 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]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
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*
expt(glob_h, calc_term - 1)/factorial_1(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
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 \
- diff(x1,t,2) - diff (x1,t,1)+x1;");
omniout_str(INFO,
"diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;")
;
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-05-26T03:26:08-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest6_rev_sm_h");
logitem_str(html_log_file, "diff (x2,t,2) = 3.0 * diff(x2,t,1\
) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1;");
logitem_float(html_log_file, t_start);
logitem_float(html_log_file, t_end);
logitem_float(html_log_file, array_t[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
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_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_total_exp_sec));
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 189 | ");
logitem_str(html_log_file, "mtest6_rev_sm_h diffeq.mxt");
logitem_str(html_log_file, "mtest6_rev_sm_h maple results");
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff (x1,t,1) = 4.0 * x2 - 2.0 *\
diff (x2,t ,1) - 2.0 * x1;");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_good_digits(html_log_file, array_last_rel_error[2]);
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);
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 if
end proc
> # End Function number 13
> main();
##############ECHO OF PROBLEM#################
##############temp/mtest6_rev_sm_hpostode.ode#################
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
!
#BEGIN FIRST INPUT BLOCK
Digits:=64;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
## problem from Boyce DePrima -
## _Elementary Differential Equations and Boundary Value Problems_
## page 269
##
t_start := 0.5;
t_end := 0.8;
array_x1_init[0 + 1] := exact_soln_x1(t_start);
## I think following line should be omitted
## diff(x1,1,exact_soln_x1p(t_start));
array_x2_init[0 + 1] := exact_soln_x2(t_start);
array_x2_init[1 + 1] := exact_soln_x2p(t_start);
glob_max_h := 0.0001 ;
glob_look_poles := true;
glob_max_iter := 100;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x1 := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return(2.0 * c1 + 6.0 * c3 * exp(-t));
end;
exact_soln_x1p := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return( - 6.0 * c3 * exp(-t));
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return(c1 + c2 * exp(2.0 * t) + c3 * exp(-t));
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := 1.0;
c2 := 0.0002;
c3 := 0.0003;
return( 2.0 * c2 * exp(2.0 * t) - c3 * exp(-t));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 0.3
estimated_steps = 300000
step_error = 3.3333333333333333333333333333333e-16
est_needed_step_err = 3.3333333333333333333333333333333e-16
opt_iter = 1
bytes used=4000004, alloc=3210676, time=0.14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.1158013774365979338391678604982e-178
estimated_step_error = 2.1158013774365979338391678604982e-178
best_h = 2.0e-06
opt_iter = 2
bytes used=8000868, alloc=4848776, time=0.28
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.4198903214825858626085046185924e-170
estimated_step_error = 1.4198903214825858626085046185924e-170
best_h = 4.00e-06
opt_iter = 3
bytes used=12001832, alloc=4848776, time=0.44
bytes used=16002624, alloc=4914300, time=0.59
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 9.5287233537605262951698596080266e-163
estimated_step_error = 9.5287233537605262951698596080266e-163
best_h = 8.000e-06
opt_iter = 4
bytes used=20003552, alloc=4914300, time=0.74
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.3946189437624795102738106461558e-155
estimated_step_error = 6.3946189437624795102738106461558e-155
best_h = 1.60000e-05
opt_iter = 5
bytes used=24004212, alloc=4914300, time=0.89
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.2913574018014516751056109669648e-147
estimated_step_error = 4.2913574018014516751056109669648e-147
best_h = 3.200000e-05
opt_iter = 6
bytes used=28004940, alloc=4914300, time=1.04
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.8798829091270685721220365466171e-139
estimated_step_error = 2.8798829091270685721220365466171e-139
best_h = 6.4000000e-05
opt_iter = 7
bytes used=32005800, alloc=4914300, time=1.19
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.9326589954065832399494506349008e-131
estimated_step_error = 1.9326589954065832399494506349008e-131
best_h = 0.000128
opt_iter = 8
bytes used=36006696, alloc=4914300, time=1.35
bytes used=40007516, alloc=4914300, time=1.50
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.2969885711609859332831343834859e-123
estimated_step_error = 1.2969885711609859332831343834859e-123
best_h = 0.0001
START of Soultion
TOP MAIN SOLVE Loop
bytes used=44008908, alloc=4914300, time=1.65
t[1] = 0.5
x2[1] (analytic) = 1.0007256155636055990741531973548
x2[1] (numeric) = 1.0007256155636055990741531973548
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.0001
x1[1] (analytic) = 2.001091755187482740162486839163
x1[1] (numeric) = 2.001091755187482740162486839163
absolute error = 0
relative error = 0 %
Correct digits = 64
h = 0.0001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.573e+04
Order of pole (six term test) = 1.303e+07
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
Radius of convergence (six term test) for eq 2 = 4.800e+27
Order of pole (six term test) = 1.274e+54
bytes used=48009568, alloc=4914300, time=1.81
bytes used=52010908, alloc=4979824, time=1.96
bytes used=56011584, alloc=4979824, time=2.11
bytes used=60012676, alloc=4979824, time=2.27
bytes used=64013588, alloc=4979824, time=2.42
bytes used=68014880, alloc=4979824, time=2.57
bytes used=72015544, alloc=4979824, time=2.73
bytes used=76016304, alloc=4979824, time=2.88
bytes used=80017316, alloc=4979824, time=3.04
bytes used=84018092, alloc=4979824, time=3.19
bytes used=88018952, alloc=4979824, time=3.35
bytes used=92019636, alloc=4979824, time=3.51
bytes used=96020384, alloc=4979824, time=3.66
bytes used=100021664, alloc=4979824, time=3.82
bytes used=104022604, alloc=4979824, time=3.97
bytes used=108023512, alloc=4979824, time=4.12
bytes used=112024336, alloc=5045348, time=4.28
bytes used=116025132, alloc=5045348, time=4.43
bytes used=120026000, alloc=5045348, time=4.59
bytes used=124026780, alloc=5045348, time=4.74
bytes used=128027884, alloc=5045348, time=4.90
bytes used=132028900, alloc=5045348, time=5.05
bytes used=136029684, alloc=5045348, time=5.21
bytes used=140030504, alloc=5045348, time=5.36
bytes used=144031256, alloc=5045348, time=5.52
bytes used=148031912, alloc=5045348, time=5.67
bytes used=152032652, alloc=5045348, time=5.82
bytes used=156033400, alloc=5045348, time=5.98
bytes used=160034264, alloc=5045348, time=6.14
bytes used=164034976, alloc=5045348, time=6.29
bytes used=168035684, alloc=5045348, time=6.45
bytes used=172036352, alloc=5045348, time=6.60
bytes used=176037024, alloc=5045348, time=6.75
bytes used=180037732, alloc=5045348, time=6.91
bytes used=184038736, alloc=5045348, time=7.06
bytes used=188039548, alloc=5045348, time=7.22
bytes used=192040640, alloc=5045348, time=7.37
bytes used=196041304, alloc=5045348, time=7.53
bytes used=200042060, alloc=5045348, time=7.68
bytes used=204043100, alloc=5045348, time=7.83
bytes used=208043916, alloc=5045348, time=7.99
bytes used=212045104, alloc=5045348, time=8.14
bytes used=216045860, alloc=5045348, time=8.29
bytes used=220046720, alloc=5045348, time=8.45
bytes used=224047568, alloc=5045348, time=8.61
bytes used=228048316, alloc=5045348, time=8.76
bytes used=232049008, alloc=5045348, time=8.91
bytes used=236049692, alloc=5045348, time=9.07
bytes used=240050508, alloc=5045348, time=9.22
bytes used=244051216, alloc=5045348, time=9.38
bytes used=248051904, alloc=5045348, time=9.54
bytes used=252052636, alloc=5045348, time=9.69
bytes used=256053320, alloc=5045348, time=9.85
bytes used=260054200, alloc=5045348, time=10.00
bytes used=264055088, alloc=5045348, time=10.15
bytes used=268055808, alloc=5045348, time=10.31
bytes used=272056520, alloc=5045348, time=10.46
bytes used=276057448, alloc=5045348, time=10.62
bytes used=280058440, alloc=5045348, time=10.77
bytes used=284059264, alloc=5045348, time=10.93
bytes used=288060008, alloc=5045348, time=11.08
bytes used=292061004, alloc=5045348, time=11.24
bytes used=296061900, alloc=5045348, time=11.39
bytes used=300062588, alloc=5045348, time=11.55
bytes used=304063336, alloc=5045348, time=11.70
bytes used=308064036, alloc=5045348, time=11.86
bytes used=312064780, alloc=5045348, time=12.01
bytes used=316065588, alloc=5045348, time=12.17
bytes used=320066300, alloc=5045348, time=12.32
bytes used=324067172, alloc=5045348, time=12.48
bytes used=328067956, alloc=5045348, time=12.63
bytes used=332068644, alloc=5045348, time=12.79
bytes used=336069532, alloc=5045348, time=12.94
bytes used=340070500, alloc=5045348, time=13.10
bytes used=344071200, alloc=5045348, time=13.26
bytes used=348071884, alloc=5045348, time=13.41
bytes used=352072708, alloc=5110872, time=13.57
bytes used=356073400, alloc=5110872, time=13.72
bytes used=360074300, alloc=5110872, time=13.88
bytes used=364075312, alloc=5110872, time=14.03
bytes used=368076360, alloc=5110872, time=14.19
bytes used=372077160, alloc=5110872, time=14.34
bytes used=376077900, alloc=5110872, time=14.50
bytes used=380078804, alloc=5110872, time=14.65
bytes used=384079524, alloc=5110872, time=14.81
bytes used=388080296, alloc=5110872, time=14.96
bytes used=392081000, alloc=5110872, time=15.12
bytes used=396081684, alloc=5110872, time=15.27
bytes used=400082476, alloc=5110872, time=15.43
bytes used=404083308, alloc=5110872, time=15.59
bytes used=408084132, alloc=5110872, time=15.74
bytes used=412085184, alloc=5110872, time=15.90
bytes used=416086064, alloc=5110872, time=16.05
bytes used=420086908, alloc=5110872, time=16.20
bytes used=424087668, alloc=5110872, time=16.36
bytes used=428088344, alloc=5110872, time=16.51
bytes used=432089116, alloc=5110872, time=16.67
bytes used=436090112, alloc=5110872, time=16.82
bytes used=440090952, alloc=5110872, time=16.98
bytes used=444091780, alloc=5110872, time=17.13
bytes used=448092772, alloc=5110872, time=17.29
bytes used=452093548, alloc=5110872, time=17.44
bytes used=456094296, alloc=5110872, time=17.60
bytes used=460095172, alloc=5110872, time=17.76
bytes used=464095900, alloc=5110872, time=17.91
bytes used=468097108, alloc=5110872, time=18.06
bytes used=472097896, alloc=5110872, time=18.22
bytes used=476098820, alloc=5110872, time=18.37
bytes used=480099564, alloc=5110872, time=18.53
bytes used=484100824, alloc=5110872, time=18.68
bytes used=488101952, alloc=5110872, time=18.84
bytes used=492102676, alloc=5110872, time=19.00
bytes used=496103504, alloc=5110872, time=19.15
bytes used=500104284, alloc=5110872, time=19.30
bytes used=504105024, alloc=5110872, time=19.46
bytes used=508105696, alloc=5110872, time=19.61
bytes used=512106596, alloc=5110872, time=19.77
TOP MAIN SOLVE Loop
bytes used=516107440, alloc=5110872, time=19.92
t[1] = 0.51
x2[1] (analytic) = 1.0007347876264365393661995311595
x2[1] (numeric) = 1.0007348429461450453830298675891
absolute error = 5.5319708506016830336429565547572e-08
relative error = 5.5279090114599951870891924380675e-06 %
Correct digits = 8
h = 0.0001
x1[1] (analytic) = 2.0010808920418620786970381472244
x1[1] (numeric) = 2.0010807828654335314007942343835
absolute error = 1.0917642854729624391284082515233e-07
relative error = 5.4558728226071283748098831279477e-06 %
Correct digits = 8
h = 0.0001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.581e+04
Order of pole (six term test) = 1.316e+07
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
Radius of convergence (six term test) for eq 2 = 4.435e+27
Order of pole (six term test) = -1.340e+54
bytes used=520108252, alloc=5110872, time=20.08
bytes used=524109192, alloc=5110872, time=20.23
bytes used=528110072, alloc=5110872, time=20.39
bytes used=532110776, alloc=5110872, time=20.55
bytes used=536111576, alloc=5110872, time=20.70
bytes used=540112280, alloc=5110872, time=20.86
bytes used=544113168, alloc=5110872, time=21.01
bytes used=548113912, alloc=5110872, time=21.17
bytes used=552115028, alloc=5110872, time=21.32
bytes used=556115740, alloc=5110872, time=21.47
bytes used=560116556, alloc=5110872, time=21.63
bytes used=564117748, alloc=5110872, time=21.79
bytes used=568118568, alloc=5110872, time=21.94
bytes used=572119600, alloc=5110872, time=22.10
bytes used=576120508, alloc=5110872, time=22.25
bytes used=580121280, alloc=5110872, time=22.40
bytes used=584122088, alloc=5110872, time=22.56
bytes used=588122916, alloc=5110872, time=22.71
bytes used=592123632, alloc=5110872, time=22.87
bytes used=596124428, alloc=5110872, time=23.02
bytes used=600125372, alloc=5110872, time=23.18
bytes used=604126144, alloc=5110872, time=23.33
bytes used=608127108, alloc=5110872, time=23.49
bytes used=612127812, alloc=5110872, time=23.65
bytes used=616128508, alloc=5110872, time=23.80
bytes used=620129804, alloc=5110872, time=23.96
bytes used=624130672, alloc=5110872, time=24.11
bytes used=628131336, alloc=5110872, time=24.27
bytes used=632132120, alloc=5110872, time=24.42
bytes used=636132976, alloc=5110872, time=24.58
bytes used=640134004, alloc=5110872, time=24.73
bytes used=644135020, alloc=5110872, time=24.89
bytes used=648135676, alloc=5110872, time=25.05
bytes used=652136560, alloc=5110872, time=25.20
bytes used=656137344, alloc=5110872, time=25.36
bytes used=660138372, alloc=5110872, time=25.51
bytes used=664139224, alloc=5110872, time=25.67
bytes used=668139880, alloc=5110872, time=25.83
bytes used=672140564, alloc=5110872, time=25.98
bytes used=676141256, alloc=5110872, time=26.14
bytes used=680142020, alloc=5110872, time=26.29
bytes used=684142844, alloc=5110872, time=26.44
bytes used=688144092, alloc=5110872, time=26.60
bytes used=692145092, alloc=5110872, time=26.75
bytes used=696146396, alloc=5110872, time=26.91
bytes used=700147120, alloc=5110872, time=27.07
bytes used=704148088, alloc=5110872, time=27.23
bytes used=708148856, alloc=5110872, time=27.38
bytes used=712150044, alloc=5110872, time=27.54
bytes used=716151276, alloc=5110872, time=27.70
bytes used=720152060, alloc=5110872, time=27.85
bytes used=724152720, alloc=5110872, time=28.00
bytes used=728153376, alloc=5110872, time=28.16
bytes used=732154180, alloc=5110872, time=28.31
bytes used=736154856, alloc=5110872, time=28.47
bytes used=740155524, alloc=5110872, time=28.62
bytes used=744156452, alloc=5110872, time=28.78
bytes used=748157264, alloc=5110872, time=28.94
bytes used=752158268, alloc=5110872, time=29.09
bytes used=756159024, alloc=5110872, time=29.24
bytes used=760159884, alloc=5110872, time=29.40
bytes used=764160552, alloc=5110872, time=29.56
bytes used=768161272, alloc=5110872, time=29.71
bytes used=772162072, alloc=5110872, time=29.87
bytes used=776162872, alloc=5110872, time=30.03
bytes used=780163556, alloc=5110872, time=30.18
bytes used=784164348, alloc=5110872, time=30.33
bytes used=788165396, alloc=5110872, time=30.49
bytes used=792166056, alloc=5110872, time=30.64
bytes used=796167012, alloc=5110872, time=30.80
bytes used=800167764, alloc=5110872, time=30.95
bytes used=804168556, alloc=5110872, time=31.11
bytes used=808169332, alloc=5110872, time=31.27
bytes used=812170280, alloc=5110872, time=31.42
bytes used=816171060, alloc=5110872, time=31.58
bytes used=820171924, alloc=5110872, time=31.74
bytes used=824172928, alloc=5110872, time=31.89
bytes used=828173648, alloc=5110872, time=32.04
bytes used=832174456, alloc=5110872, time=32.20
bytes used=836175120, alloc=5110872, time=32.35
bytes used=840175784, alloc=5110872, time=32.51
bytes used=844176784, alloc=5110872, time=32.66
bytes used=848177680, alloc=5110872, time=32.82
bytes used=852178400, alloc=5110872, time=32.98
bytes used=856179080, alloc=5110872, time=33.14
bytes used=860180012, alloc=5110872, time=33.30
bytes used=864180680, alloc=5110872, time=33.45
bytes used=868181560, alloc=5110872, time=33.60
bytes used=872182576, alloc=5110872, time=33.76
bytes used=876183336, alloc=5110872, time=33.92
bytes used=880184216, alloc=5110872, time=34.07
bytes used=884184900, alloc=5110872, time=34.23
bytes used=888185576, alloc=5110872, time=34.38
bytes used=892186580, alloc=5110872, time=34.54
bytes used=896187332, alloc=5110872, time=34.69
bytes used=900187988, alloc=5110872, time=34.85
bytes used=904188676, alloc=5110872, time=35.01
bytes used=908189392, alloc=5110872, time=35.16
bytes used=912190288, alloc=5110872, time=35.32
bytes used=916191012, alloc=5110872, time=35.47
bytes used=920191868, alloc=5110872, time=35.63
bytes used=924192620, alloc=5110872, time=35.78
bytes used=928193424, alloc=5110872, time=35.94
bytes used=932194268, alloc=5110872, time=36.10
bytes used=936195004, alloc=5110872, time=36.25
bytes used=940196052, alloc=5110872, time=36.40
bytes used=944196796, alloc=5110872, time=36.56
bytes used=948197664, alloc=5110872, time=36.72
bytes used=952198452, alloc=5110872, time=36.87
bytes used=956199168, alloc=5110872, time=37.02
bytes used=960200408, alloc=5110872, time=37.18
bytes used=964201172, alloc=5110872, time=37.33
bytes used=968201864, alloc=5110872, time=37.49
bytes used=972202584, alloc=5110872, time=37.64
bytes used=976203324, alloc=5110872, time=37.80
bytes used=980204056, alloc=5110872, time=37.96
bytes used=984204780, alloc=5110872, time=38.11
TOP MAIN SOLVE Loop
bytes used=988205620, alloc=5110872, time=38.27
t[1] = 0.52
x2[1] (analytic) = 1.000744199567261370205597366143
x2[1] (numeric) = 1.0007444238070847829267772204405
absolute error = 2.2423982341272117985429747798384e-07
relative error = 2.2407306833223340431872172083163e-05 %
Correct digits = 7
h = 0.0001
x1[1] (analytic) = 2.0010701369863463498101608136496
x1[1] (numeric) = 2.0010697002697144267897951467495
absolute error = 4.3671663192302036566690008078862e-07
relative error = 2.1824154178859756745016717156998e-05 %
Correct digits = 7
h = 0.0001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.589e+04
Order of pole (six term test) = 1.329e+07
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
Radius of convergence (six term test) for eq 2 = 6.209e+27
Order of pole (six term test) = -7.376e+53
bytes used=992206408, alloc=5110872, time=38.42
bytes used=996207396, alloc=5110872, time=38.57
bytes used=1000208104, alloc=5110872, time=38.73
bytes used=1004208804, alloc=5110872, time=38.88
bytes used=1008209644, alloc=5110872, time=39.05
bytes used=1012210408, alloc=5110872, time=39.20
bytes used=1016211716, alloc=5110872, time=39.36
bytes used=1020212564, alloc=5110872, time=39.51
bytes used=1024213348, alloc=5110872, time=39.67
bytes used=1028214244, alloc=5110872, time=39.82
bytes used=1032215708, alloc=5110872, time=39.98
bytes used=1036216656, alloc=5110872, time=40.14
bytes used=1040217516, alloc=5110872, time=40.29
bytes used=1044218236, alloc=5110872, time=40.45
bytes used=1048219068, alloc=5110872, time=40.60
bytes used=1052219800, alloc=5110872, time=40.76
bytes used=1056220504, alloc=5110872, time=40.91
bytes used=1060221488, alloc=5110872, time=41.07
bytes used=1064222208, alloc=5110872, time=41.22
bytes used=1068222952, alloc=5110872, time=41.38
bytes used=1072223820, alloc=5110872, time=41.53
bytes used=1076224552, alloc=5110872, time=41.69
bytes used=1080225292, alloc=5110872, time=41.84
bytes used=1084226136, alloc=5110872, time=42.00
bytes used=1088226884, alloc=5110872, time=42.15
bytes used=1092227560, alloc=5110872, time=42.31
bytes used=1096228280, alloc=5110872, time=42.46
bytes used=1100229508, alloc=5110872, time=42.62
bytes used=1104230420, alloc=5110872, time=42.78
bytes used=1108231396, alloc=5110872, time=42.93
bytes used=1112232208, alloc=5110872, time=43.09
bytes used=1116232876, alloc=5110872, time=43.24
bytes used=1120233748, alloc=5110872, time=43.40
bytes used=1124234916, alloc=5110872, time=43.55
bytes used=1128235956, alloc=5110872, time=43.71
bytes used=1132236792, alloc=5110872, time=43.86
bytes used=1136237504, alloc=5110872, time=44.02
bytes used=1140238264, alloc=5110872, time=44.18
bytes used=1144238924, alloc=5110872, time=44.33
bytes used=1148239832, alloc=5110872, time=44.48
bytes used=1152240588, alloc=5110872, time=44.64
bytes used=1156241480, alloc=5110872, time=44.80
bytes used=1160242244, alloc=5110872, time=44.96
bytes used=1164242960, alloc=5110872, time=45.12
bytes used=1168243752, alloc=5110872, time=45.27
bytes used=1172244644, alloc=5110872, time=45.43
bytes used=1176245296, alloc=5110872, time=45.59
bytes used=1180246072, alloc=5110872, time=45.74
bytes used=1184246844, alloc=5110872, time=45.90
bytes used=1188247584, alloc=5110872, time=46.05
bytes used=1192248476, alloc=5110872, time=46.21
bytes used=1196249200, alloc=5110872, time=46.36
bytes used=1200250204, alloc=5110872, time=46.52
bytes used=1204251124, alloc=5110872, time=46.68
bytes used=1208251936, alloc=5110872, time=46.83
bytes used=1212253020, alloc=5110872, time=46.99
bytes used=1216253760, alloc=5110872, time=47.14
bytes used=1220254620, alloc=5110872, time=47.30
bytes used=1224255416, alloc=5110872, time=47.45
bytes used=1228256652, alloc=5110872, time=47.61
bytes used=1232257400, alloc=5110872, time=47.76
bytes used=1236258468, alloc=5110872, time=47.91
bytes used=1240259168, alloc=5110872, time=48.07
bytes used=1244260064, alloc=5110872, time=48.22
bytes used=1248260760, alloc=5110872, time=48.38
bytes used=1252261480, alloc=5110872, time=48.53
bytes used=1256262204, alloc=5110872, time=48.69
bytes used=1260262892, alloc=5110872, time=48.84
bytes used=1264263744, alloc=5110872, time=49.00
bytes used=1268264572, alloc=5110872, time=49.15
bytes used=1272265232, alloc=5110872, time=49.31
bytes used=1276266364, alloc=5110872, time=49.46
bytes used=1280267236, alloc=5110872, time=49.62
bytes used=1284267948, alloc=5110872, time=49.77
bytes used=1288268784, alloc=5110872, time=49.93
bytes used=1292269612, alloc=5110872, time=50.09
bytes used=1296270408, alloc=5110872, time=50.24
bytes used=1300271320, alloc=5110872, time=50.40
bytes used=1304271976, alloc=5110872, time=50.55
bytes used=1308272808, alloc=5110872, time=50.71
bytes used=1312273712, alloc=5110872, time=50.86
bytes used=1316274380, alloc=5110872, time=51.02
bytes used=1320275160, alloc=5110872, time=51.18
bytes used=1324275980, alloc=5110872, time=51.33
bytes used=1328277368, alloc=5110872, time=51.49
bytes used=1332278168, alloc=5110872, time=51.65
bytes used=1336278944, alloc=5110872, time=51.80
bytes used=1340279704, alloc=5110872, time=51.95
bytes used=1344280428, alloc=5110872, time=52.11
bytes used=1348281120, alloc=5110872, time=52.27
bytes used=1352282116, alloc=5110872, time=52.42
bytes used=1356282892, alloc=5110872, time=52.57
bytes used=1360283708, alloc=5110872, time=52.73
bytes used=1364284408, alloc=5110872, time=52.88
bytes used=1368285164, alloc=5110872, time=53.04
bytes used=1372286056, alloc=5110872, time=53.19
bytes used=1376286796, alloc=5110872, time=53.35
bytes used=1380287516, alloc=5110872, time=53.50
bytes used=1384288280, alloc=5110872, time=53.66
bytes used=1388288956, alloc=5110872, time=53.81
bytes used=1392289736, alloc=5110872, time=53.97
bytes used=1396290500, alloc=5110872, time=54.12
bytes used=1400291168, alloc=5110872, time=54.28
bytes used=1404291920, alloc=5110872, time=54.43
bytes used=1408292604, alloc=5110872, time=54.59
bytes used=1412293800, alloc=5110872, time=54.75
bytes used=1416294516, alloc=5110872, time=54.90
bytes used=1420295260, alloc=5110872, time=55.06
bytes used=1424296048, alloc=5110872, time=55.21
bytes used=1428296988, alloc=5110872, time=55.37
bytes used=1432297816, alloc=5110872, time=55.52
bytes used=1436298528, alloc=5110872, time=55.68
bytes used=1440299380, alloc=5110872, time=55.84
bytes used=1444300192, alloc=5110872, time=55.99
bytes used=1448300840, alloc=5110872, time=56.15
bytes used=1452301616, alloc=5110872, time=56.30
bytes used=1456302436, alloc=5110872, time=56.46
TOP MAIN SOLVE Loop
bytes used=1460303164, alloc=5110872, time=56.61
t[1] = 0.53
x2[1] (analytic) = 1.0007538556887570982080529143471
x2[1] (numeric) = 1.0007543669662728092922294867088
absolute error = 5.1127751571108417657236166266000e-07
relative error = 5.1089237658665169546403960391323e-05 %
Correct digits = 7
h = 0.0001
x1[1] (analytic) = 2.0010594889454210393528278357407
x1[1] (numeric) = 2.0010585062920566188918108460945
absolute error = 9.8265336442046101698964624539146e-07
relative error = 4.9106654242364851477123150024894e-05 %
Correct digits = 7
h = 0.0001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.597e+04
Order of pole (six term test) = 1.342e+07
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
Radius of convergence (six term test) for eq 2 = 4.468e+27
Order of pole (six term test) = -1.023e+54
bytes used=1464303896, alloc=5110872, time=56.77
bytes used=1468304676, alloc=5110872, time=56.93
bytes used=1472305412, alloc=5110872, time=57.09
bytes used=1476306112, alloc=5110872, time=57.24
bytes used=1480307128, alloc=5110872, time=57.40
bytes used=1484307892, alloc=5110872, time=57.56
bytes used=1488308776, alloc=5110872, time=57.71
bytes used=1492309468, alloc=5110872, time=57.87
bytes used=1496310236, alloc=5110872, time=58.02
bytes used=1500310952, alloc=5110872, time=58.18
bytes used=1504311652, alloc=5110872, time=58.34
bytes used=1508312376, alloc=5110872, time=58.49
bytes used=1512313108, alloc=5110872, time=58.64
bytes used=1516314060, alloc=5110872, time=58.80
bytes used=1520314848, alloc=5110872, time=58.95
bytes used=1524315620, alloc=5110872, time=59.11
bytes used=1528316484, alloc=5110872, time=59.26
bytes used=1532317228, alloc=5110872, time=59.42
bytes used=1536318112, alloc=5110872, time=59.57
bytes used=1540318772, alloc=5110872, time=59.73
bytes used=1544319676, alloc=5110872, time=59.88
bytes used=1548320624, alloc=5110872, time=60.04
bytes used=1552321396, alloc=5110872, time=60.19
bytes used=1556322124, alloc=5110872, time=60.35
bytes used=1560323064, alloc=5110872, time=60.51
bytes used=1564323908, alloc=5110872, time=60.66
bytes used=1568325016, alloc=5110872, time=60.81
bytes used=1572325672, alloc=5110872, time=60.97
bytes used=1576326492, alloc=5110872, time=61.13
bytes used=1580327480, alloc=5110872, time=61.28
bytes used=1584328320, alloc=5110872, time=61.44
bytes used=1588329108, alloc=5110872, time=61.59
bytes used=1592330012, alloc=5110872, time=61.75
bytes used=1596330868, alloc=5110872, time=61.90
bytes used=1600331688, alloc=5110872, time=62.06
bytes used=1604332476, alloc=5110872, time=62.21
bytes used=1608333152, alloc=5110872, time=62.37
bytes used=1612334024, alloc=5110872, time=62.52
bytes used=1616334716, alloc=5110872, time=62.68
bytes used=1620335836, alloc=5110872, time=62.83
bytes used=1624336736, alloc=5110872, time=62.99
bytes used=1628337412, alloc=5110872, time=63.14
bytes used=1632338072, alloc=5110872, time=63.30
bytes used=1636338792, alloc=5110872, time=63.45
bytes used=1640339688, alloc=5110872, time=63.61
bytes used=1644340504, alloc=5110872, time=63.76
bytes used=1648341244, alloc=5110872, time=63.92
bytes used=1652341952, alloc=5110872, time=64.08
bytes used=1656342712, alloc=5110872, time=64.23
bytes used=1660343452, alloc=5110872, time=64.39
bytes used=1664344348, alloc=5110872, time=64.54
bytes used=1668345108, alloc=5110872, time=64.69
bytes used=1672345960, alloc=5110872, time=64.85
bytes used=1676346640, alloc=5110872, time=65.00
bytes used=1680347316, alloc=5110872, time=65.16
bytes used=1684348188, alloc=5110872, time=65.32
bytes used=1688348936, alloc=5110872, time=65.47
bytes used=1692350020, alloc=5110872, time=65.63
bytes used=1696350740, alloc=5110872, time=65.78
bytes used=1700351624, alloc=5110872, time=65.94
bytes used=1704352300, alloc=5110872, time=66.09
bytes used=1708353004, alloc=5110872, time=66.25
bytes used=1712353796, alloc=5110872, time=66.40
bytes used=1716354636, alloc=5110872, time=66.56
bytes used=1720355420, alloc=5110872, time=66.72
bytes used=1724356316, alloc=5110872, time=66.87
bytes used=1728357036, alloc=5110872, time=67.03
bytes used=1732357940, alloc=5110872, time=67.18
bytes used=1736358656, alloc=5110872, time=67.34
bytes used=1740359364, alloc=5110872, time=67.49
bytes used=1744360244, alloc=5110872, time=67.65
bytes used=1748360980, alloc=5110872, time=67.80
bytes used=1752361816, alloc=5110872, time=67.96
bytes used=1756362708, alloc=5110872, time=68.11
bytes used=1760363644, alloc=5110872, time=68.27
bytes used=1764364412, alloc=5110872, time=68.42
bytes used=1768365204, alloc=5110872, time=68.58
bytes used=1772365988, alloc=5110872, time=68.74
bytes used=1776366776, alloc=5110872, time=68.89
bytes used=1780367556, alloc=5110872, time=69.05
bytes used=1784368372, alloc=5110872, time=69.20
bytes used=1788369068, alloc=5110872, time=69.36
bytes used=1792369756, alloc=5110872, time=69.51
bytes used=1796370780, alloc=5110872, time=69.67
bytes used=1800371484, alloc=5110872, time=69.82
bytes used=1804372220, alloc=5110872, time=69.98
bytes used=1808373068, alloc=5110872, time=70.13
bytes used=1812373764, alloc=5110872, time=70.29
bytes used=1816375356, alloc=5110872, time=70.45
bytes used=1820376252, alloc=5110872, time=70.60
bytes used=1824377248, alloc=5110872, time=70.76
bytes used=1828378068, alloc=5110872, time=70.91
bytes used=1832378888, alloc=5110872, time=71.07
bytes used=1836379724, alloc=5110872, time=71.22
bytes used=1840380612, alloc=5110872, time=71.38
bytes used=1844381496, alloc=5110872, time=71.53
bytes used=1848382824, alloc=5110872, time=71.68
bytes used=1852383548, alloc=5110872, time=71.84
bytes used=1856384640, alloc=5110872, time=71.99
bytes used=1860385436, alloc=5110872, time=72.15
bytes used=1864386240, alloc=5110872, time=72.30
bytes used=1868386936, alloc=5110872, time=72.46
bytes used=1872388148, alloc=5110872, time=72.62
bytes used=1876389292, alloc=5110872, time=72.77
bytes used=1880389984, alloc=5110872, time=72.92
bytes used=1884390692, alloc=5110872, time=73.08
bytes used=1888391668, alloc=5110872, time=73.24
bytes used=1892392568, alloc=5110872, time=73.39
bytes used=1896393296, alloc=5110872, time=73.54
bytes used=1900394076, alloc=5110872, time=73.70
bytes used=1904395080, alloc=5110872, time=73.85
bytes used=1908395744, alloc=5110872, time=74.01
bytes used=1912396476, alloc=5110872, time=74.17
bytes used=1916397144, alloc=5110872, time=74.32
bytes used=1920397904, alloc=5110872, time=74.47
bytes used=1924398724, alloc=5110872, time=74.63
bytes used=1928399400, alloc=5110872, time=74.79
TOP MAIN SOLVE Loop
bytes used=1932400084, alloc=5110872, time=74.94
t[1] = 0.54
x2[1] (analytic) = 1.0007637603859253016627203164665
x2[1] (numeric) = 1.0007646814386052129465369345331
absolute error = 9.2105267991128381661806666202041e-07
relative error = 9.2034975322857170654153176435346e-05 %
Correct digits = 7
h = 0.0001
x1[1] (analytic) = 2.0010489468542731813969777772086
x1[1] (numeric) = 2.0010471998130530135802422561648
absolute error = 1.7470412201678167355210437628634e-06
relative error = 8.7306271189129757302527869511055e-05 %
Correct digits = 7
h = 0.0001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.605e+04
Order of pole (six term test) = 1.356e+07
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
Radius of convergence (six term test) for eq 2 = 5.080e+27
Order of pole (six term test) = -2.778e+52
bytes used=1936400912, alloc=5110872, time=75.10
bytes used=1940401700, alloc=5110872, time=75.25
bytes used=1944402392, alloc=5110872, time=75.41
bytes used=1948403192, alloc=5110872, time=75.57
bytes used=1952403872, alloc=5110872, time=75.72
bytes used=1956404644, alloc=5110872, time=75.88
bytes used=1960405392, alloc=5110872, time=76.03
bytes used=1964406112, alloc=5110872, time=76.19
bytes used=1968406780, alloc=5110872, time=76.35
bytes used=1972407440, alloc=5110872, time=76.50
bytes used=1976408308, alloc=5110872, time=76.65
bytes used=1980409008, alloc=5110872, time=76.81
bytes used=1984409724, alloc=5110872, time=76.97
bytes used=1988410632, alloc=5110872, time=77.12
bytes used=1992411420, alloc=5110872, time=77.28
bytes used=1996412356, alloc=5110872, time=77.43
bytes used=2000413608, alloc=5110872, time=77.59
bytes used=2004414416, alloc=5110872, time=77.74
bytes used=2008415220, alloc=5110872, time=77.90
bytes used=2012416080, alloc=5110872, time=78.06
bytes used=2016417096, alloc=5110872, time=78.21
bytes used=2020417804, alloc=5110872, time=78.37
bytes used=2024418580, alloc=5110872, time=78.52
bytes used=2028419260, alloc=5110872, time=78.68
bytes used=2032420280, alloc=5110872, time=78.83
bytes used=2036420988, alloc=5110872, time=78.99
bytes used=2040421720, alloc=5110872, time=79.14
bytes used=2044422456, alloc=5110872, time=79.29
bytes used=2048423396, alloc=5110872, time=79.45
bytes used=2052424332, alloc=5110872, time=79.60
bytes used=2056425068, alloc=5110872, time=79.76
bytes used=2060425876, alloc=5110872, time=79.91
bytes used=2064426744, alloc=5110872, time=80.07
bytes used=2068427736, alloc=5110872, time=80.23
bytes used=2072428716, alloc=5110872, time=80.38
bytes used=2076429440, alloc=5110872, time=80.54
bytes used=2080430168, alloc=5110872, time=80.69
bytes used=2084431060, alloc=5110872, time=80.85
bytes used=2088431740, alloc=5110872, time=81.01
bytes used=2092432584, alloc=5110872, time=81.16
bytes used=2096433292, alloc=5110872, time=81.32
bytes used=2100434176, alloc=5110872, time=81.47
bytes used=2104435456, alloc=5110872, time=81.63
bytes used=2108436184, alloc=5110872, time=81.78
bytes used=2112436844, alloc=5110872, time=81.94
bytes used=2116437552, alloc=5110872, time=82.09
bytes used=2120438268, alloc=5110872, time=82.25
bytes used=2124439048, alloc=5110872, time=82.40
bytes used=2128440036, alloc=5110872, time=82.56
bytes used=2132440720, alloc=5110872, time=82.71
bytes used=2136441788, alloc=5110872, time=82.87
bytes used=2140442544, alloc=5110872, time=83.02
bytes used=2144443496, alloc=5110872, time=83.18
bytes used=2148444324, alloc=5110872, time=83.33
bytes used=2152444980, alloc=5110872, time=83.49
bytes used=2156445688, alloc=5110872, time=83.64
bytes used=2160446396, alloc=5110872, time=83.80
bytes used=2164447292, alloc=5110872, time=83.95
bytes used=2168448308, alloc=5110872, time=84.11
bytes used=2172449256, alloc=5110872, time=84.27
bytes used=2176450796, alloc=5110872, time=84.42
bytes used=2180451516, alloc=5110872, time=84.58
bytes used=2184452196, alloc=5110872, time=84.73
bytes used=2188452932, alloc=5110872, time=84.88
bytes used=2192453980, alloc=5110872, time=85.04
bytes used=2196454984, alloc=5110872, time=85.19
bytes used=2200455932, alloc=5110872, time=85.35
bytes used=2204456728, alloc=5110872, time=85.50
bytes used=2208457540, alloc=5110872, time=85.66
bytes used=2212458344, alloc=5110872, time=85.81
bytes used=2216459024, alloc=5110872, time=85.97
bytes used=2220459740, alloc=5110872, time=86.12
bytes used=2224460568, alloc=5110872, time=86.28
bytes used=2228461332, alloc=5110872, time=86.44
bytes used=2232462120, alloc=5110872, time=86.59
bytes used=2236463264, alloc=5110872, time=86.74
bytes used=2240464104, alloc=5110872, time=86.90
bytes used=2244464784, alloc=5110872, time=87.05
bytes used=2248465744, alloc=5110872, time=87.21
bytes used=2252466400, alloc=5110872, time=87.36
bytes used=2256467216, alloc=5110872, time=87.52
bytes used=2260468116, alloc=5110872, time=87.67
bytes used=2264468892, alloc=5110872, time=87.83
bytes used=2268469732, alloc=5110872, time=87.98
bytes used=2272470584, alloc=5110872, time=88.14
bytes used=2276471332, alloc=5110872, time=88.29
bytes used=2280472076, alloc=5110872, time=88.45
bytes used=2284472944, alloc=5110872, time=88.61
bytes used=2288473756, alloc=5110872, time=88.76
bytes used=2292474464, alloc=5110872, time=88.91
bytes used=2296475388, alloc=5110872, time=89.07
bytes used=2300476168, alloc=5110872, time=89.22
bytes used=2304476932, alloc=5110872, time=89.38
bytes used=2308477656, alloc=5110872, time=89.53
bytes used=2312478484, alloc=5110872, time=89.69
bytes used=2316479340, alloc=5110872, time=89.84
bytes used=2320480052, alloc=5110872, time=90.00
bytes used=2324480988, alloc=5110872, time=90.15
bytes used=2328481776, alloc=5110872, time=90.31
bytes used=2332482484, alloc=5110872, time=90.47
bytes used=2336483212, alloc=5110872, time=90.62
bytes used=2340483996, alloc=5110872, time=90.78
bytes used=2344484732, alloc=5110872, time=90.93
bytes used=2348485536, alloc=5110872, time=91.09
bytes used=2352486332, alloc=5110872, time=91.24
bytes used=2356487252, alloc=5110872, time=91.40
bytes used=2360488268, alloc=5110872, time=91.55
bytes used=2364489072, alloc=5110872, time=91.71
bytes used=2368490292, alloc=5110872, time=91.86
bytes used=2372490988, alloc=5110872, time=92.02
bytes used=2376491668, alloc=5110872, time=92.17
bytes used=2380492484, alloc=5110872, time=92.33
bytes used=2384493320, alloc=5110872, time=92.49
bytes used=2388494228, alloc=5110872, time=92.64
bytes used=2392495252, alloc=5110872, time=92.80
bytes used=2396496004, alloc=5110872, time=92.95
bytes used=2400496900, alloc=5110872, time=93.11
TOP MAIN SOLVE Loop
bytes used=2404497664, alloc=5110872, time=93.27
bytes used=2408498740, alloc=5110872, time=93.43
t[1] = 0.55
x2[1] (analytic) = 1.0007739181479034326310074925802
x2[1] (numeric) = 1.0007753764381360060543037329804
absolute error = 1.4582902325734232962404002540424e-06
relative error = 0.00014571625080639880938589051826771 %
Correct digits = 6
h = 0.0001
x1[1] (analytic) = 2.0010385096586848760515748659368
x1[1] (numeric) = 2.001035779702046288397314940137
absolute error = 2.7299566385876542599257997805830e-06
relative error = 0.00013642699155516503354307852901987 %
Correct digits = 6
h = 0.0001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.613e+04
Order of pole (six term test) = 1.369e+07
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
Radius of convergence (six term test) for eq 2 = 4.594e+27
Order of pole (six term test) = 1.677e+54
bytes used=2412499644, alloc=5110872, time=93.58
bytes used=2416500320, alloc=5110872, time=93.74
bytes used=2420501128, alloc=5110872, time=93.89
bytes used=2424501900, alloc=5110872, time=94.05
bytes used=2428502632, alloc=5110872, time=94.20
bytes used=2432503420, alloc=5110872, time=94.36
bytes used=2436504148, alloc=5110872, time=94.51
bytes used=2440504884, alloc=5110872, time=94.67
bytes used=2444505776, alloc=5110872, time=94.82
bytes used=2448506588, alloc=5110872, time=94.98
bytes used=2452507252, alloc=5110872, time=95.13
bytes used=2456508012, alloc=5110872, time=95.28
bytes used=2460508796, alloc=5110872, time=95.44
bytes used=2464509424, alloc=5110872, time=95.59
bytes used=2468510220, alloc=5110872, time=95.75
bytes used=2472511148, alloc=5110872, time=95.91
bytes used=2476511872, alloc=5110872, time=96.06
bytes used=2480513028, alloc=5110872, time=96.22
bytes used=2484514364, alloc=5110872, time=96.37
bytes used=2488515500, alloc=5110872, time=96.53
bytes used=2492516264, alloc=5110872, time=96.68
bytes used=2496517152, alloc=5110872, time=96.84
bytes used=2500517916, alloc=5110872, time=96.99
bytes used=2504518856, alloc=5110872, time=97.15
bytes used=2508519724, alloc=5110872, time=97.30
bytes used=2512520392, alloc=5110872, time=97.46
bytes used=2516521184, alloc=5110872, time=97.61
bytes used=2520522136, alloc=5110872, time=97.77
bytes used=2524522824, alloc=5110872, time=97.92
bytes used=2528523500, alloc=5110872, time=98.08
bytes used=2532524696, alloc=5110872, time=98.23
bytes used=2536525472, alloc=5110872, time=98.39
bytes used=2540526852, alloc=5110872, time=98.55
bytes used=2544527752, alloc=5110872, time=98.70
bytes used=2548528488, alloc=5110872, time=98.86
bytes used=2552529212, alloc=5110872, time=99.01
bytes used=2556529940, alloc=5110872, time=99.17
bytes used=2560530640, alloc=5110872, time=99.32
bytes used=2564531316, alloc=5110872, time=99.48
bytes used=2568531980, alloc=5110872, time=99.63
bytes used=2572532676, alloc=5110872, time=99.79
bytes used=2576533448, alloc=5110872, time=99.95
bytes used=2580534128, alloc=5110872, time=100.10
bytes used=2584534804, alloc=5110872, time=100.26
bytes used=2588535484, alloc=5110872, time=100.41
bytes used=2592536180, alloc=5110872, time=100.57
bytes used=2596536904, alloc=5110872, time=100.72
bytes used=2600537596, alloc=5110872, time=100.88
bytes used=2604538260, alloc=5110872, time=101.03
bytes used=2608539188, alloc=5110872, time=101.18
bytes used=2612539944, alloc=5110872, time=101.34
bytes used=2616540664, alloc=5110872, time=101.49
bytes used=2620541448, alloc=5110872, time=101.65
bytes used=2624542308, alloc=5110872, time=101.80
bytes used=2628543168, alloc=5110872, time=101.96
bytes used=2632543976, alloc=5110872, time=102.11
bytes used=2636544736, alloc=5110872, time=102.27
bytes used=2640545444, alloc=5110872, time=102.42
bytes used=2644547032, alloc=5110872, time=102.58
bytes used=2648547736, alloc=5110872, time=102.73
bytes used=2652548572, alloc=5110872, time=102.89
bytes used=2656549500, alloc=5110872, time=103.05
bytes used=2660550716, alloc=5110872, time=103.20
bytes used=2664551552, alloc=5110872, time=103.36
bytes used=2668552284, alloc=5110872, time=103.52
bytes used=2672553036, alloc=5110872, time=103.67
bytes used=2676554248, alloc=5110872, time=103.83
bytes used=2680555288, alloc=5110872, time=103.98
bytes used=2684556008, alloc=5110872, time=104.14
bytes used=2688556692, alloc=5110872, time=104.30
bytes used=2692557404, alloc=5110872, time=104.46
bytes used=2696558228, alloc=5110872, time=104.61
bytes used=2700558916, alloc=5110872, time=104.77
bytes used=2704559832, alloc=5110872, time=104.92
bytes used=2708560520, alloc=5110872, time=105.08
bytes used=2712561268, alloc=5110872, time=105.23
bytes used=2716562368, alloc=5110872, time=105.38
bytes used=2720563068, alloc=5110872, time=105.54
bytes used=2724564020, alloc=5110872, time=105.70
bytes used=2728564944, alloc=5110872, time=105.85
bytes used=2732565656, alloc=5110872, time=106.00
bytes used=2736566368, alloc=5110872, time=106.16
bytes used=2740567288, alloc=5110872, time=106.32
bytes used=2744568000, alloc=5110872, time=106.47
bytes used=2748568688, alloc=5110872, time=106.63
bytes used=2752569512, alloc=5110872, time=106.78
bytes used=2756570300, alloc=5110872, time=106.94
bytes used=2760571032, alloc=5110872, time=107.10
bytes used=2764571692, alloc=5110872, time=107.25
bytes used=2768572580, alloc=5110872, time=107.41
bytes used=2772573548, alloc=5110872, time=107.57
bytes used=2776574252, alloc=5110872, time=107.72
bytes used=2780575092, alloc=5110872, time=107.88
bytes used=2784575932, alloc=5110872, time=108.03
bytes used=2788576676, alloc=5110872, time=108.19
bytes used=2792577556, alloc=5110872, time=108.34
bytes used=2796578344, alloc=5110872, time=108.50
bytes used=2800579012, alloc=5110872, time=108.65
bytes used=2804579712, alloc=5110872, time=108.81
bytes used=2808580496, alloc=5110872, time=108.96
bytes used=2812581256, alloc=5110872, time=109.12
bytes used=2816582268, alloc=5110872, time=109.28
bytes used=2820583132, alloc=5110872, time=109.43
bytes used=2824583876, alloc=5110872, time=109.58
bytes used=2828584612, alloc=5110872, time=109.74
bytes used=2832585388, alloc=5110872, time=109.89
bytes used=2836586076, alloc=5110872, time=110.05
bytes used=2840587424, alloc=5110872, time=110.21
bytes used=2844588100, alloc=5110872, time=110.36
bytes used=2848588764, alloc=5110872, time=110.52
bytes used=2852589420, alloc=5110872, time=110.68
bytes used=2856590092, alloc=5110872, time=110.83
bytes used=2860591040, alloc=5110872, time=110.99
bytes used=2864592020, alloc=5110872, time=111.14
bytes used=2868592704, alloc=5110872, time=111.30
bytes used=2872593704, alloc=5110872, time=111.45
bytes used=2876594428, alloc=5110872, time=111.61
TOP MAIN SOLVE Loop
bytes used=2880595168, alloc=5110872, time=111.76
t[1] = 0.56
x2[1] (analytic) = 1.0007843335598132448746773988584
x2[1] (numeric) = 1.0007864613822716859333729492599
absolute error = 2.1278224584410586955504014534794e-06
relative error = 0.00021261548438436726140398743334008 %
Correct digits = 6
h = 0.0001
x1[1] (analytic) = 2.0010281763149278667941020454403
x1[1] (numeric) = 2.001024244817015825879615747072
absolute error = 3.9314979120409144862983683441894e-06
relative error = 0.00019647389070158517615518525991681 %
Correct digits = 6
h = 0.0001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.621e+04
Order of pole (six term test) = 1.383e+07
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
Radius of convergence (six term test) for eq 2 = 5.694e+27
Order of pole (six term test) = 4.276e+53
bytes used=2884595964, alloc=5110872, time=111.92
bytes used=2888596744, alloc=5110872, time=112.07
bytes used=2892597464, alloc=5110872, time=112.23
bytes used=2896598224, alloc=5110872, time=112.38
bytes used=2900598900, alloc=5110872, time=112.54
bytes used=2904599884, alloc=5110872, time=112.69
bytes used=2908600756, alloc=5110872, time=112.85
bytes used=2912601636, alloc=5110872, time=113.00
bytes used=2916602804, alloc=5110872, time=113.16
bytes used=2920603576, alloc=5110872, time=113.31
bytes used=2924604400, alloc=5110872, time=113.47
bytes used=2928605084, alloc=5110872, time=113.62
bytes used=2932605772, alloc=5110872, time=113.78
bytes used=2936606792, alloc=5110872, time=113.93
bytes used=2940608012, alloc=5110872, time=114.09
bytes used=2944608776, alloc=5110872, time=114.24
bytes used=2948609492, alloc=5110872, time=114.40
bytes used=2952610264, alloc=5110872, time=114.55
bytes used=2956610964, alloc=5110872, time=114.71
bytes used=2960612052, alloc=5110872, time=114.87
bytes used=2964612740, alloc=5110872, time=115.02
bytes used=2968613468, alloc=5110872, time=115.18
bytes used=2972614152, alloc=5110872, time=115.33
bytes used=2976614928, alloc=5110872, time=115.49
bytes used=2980615676, alloc=5110872, time=115.65
bytes used=2984616356, alloc=5110872, time=115.80
bytes used=2988617052, alloc=5110872, time=115.96
bytes used=2992617848, alloc=5110872, time=116.11
bytes used=2996618648, alloc=5110872, time=116.27
bytes used=3000619320, alloc=5110872, time=116.42
bytes used=3004620084, alloc=5110872, time=116.58
bytes used=3008620800, alloc=5110872, time=116.73
bytes used=3012621808, alloc=5110872, time=116.89
bytes used=3016622492, alloc=5110872, time=117.04
bytes used=3020623248, alloc=5110872, time=117.20
bytes used=3024623920, alloc=5110872, time=117.35
bytes used=3028624780, alloc=5110872, time=117.51
bytes used=3032625644, alloc=5110872, time=117.67
bytes used=3036626496, alloc=5110872, time=117.82
bytes used=3040627180, alloc=5110872, time=117.98
bytes used=3044627920, alloc=5110872, time=118.13
bytes used=3048628600, alloc=5110872, time=118.29
bytes used=3052629396, alloc=5110872, time=118.44
bytes used=3056630092, alloc=5110872, time=118.60
bytes used=3060630780, alloc=5110872, time=118.75
bytes used=3064631568, alloc=5110872, time=118.91
bytes used=3068632328, alloc=5110872, time=119.06
bytes used=3072633012, alloc=5110872, time=119.22
bytes used=3076633916, alloc=5110872, time=119.37
bytes used=3080634720, alloc=5110872, time=119.52
bytes used=3084635408, alloc=5110872, time=119.68
bytes used=3088636100, alloc=5110872, time=119.84
bytes used=3092636972, alloc=5110872, time=119.99
bytes used=3096637904, alloc=5110872, time=120.15
bytes used=3100638736, alloc=5110872, time=120.31
bytes used=3104639444, alloc=5110872, time=120.46
bytes used=3108640128, alloc=5110872, time=120.61
bytes used=3112640860, alloc=5110872, time=120.77
bytes used=3116641528, alloc=5110872, time=120.92
bytes used=3120642276, alloc=5110872, time=121.07
bytes used=3124643164, alloc=5110872, time=121.23
bytes used=3128644072, alloc=5110872, time=121.39
bytes used=3132644748, alloc=5110872, time=121.54
bytes used=3136645672, alloc=5110872, time=121.70
bytes used=3140646648, alloc=5110872, time=121.85
bytes used=3144647860, alloc=5110872, time=122.01
bytes used=3148648596, alloc=5110872, time=122.16
bytes used=3152649340, alloc=5110872, time=122.32
bytes used=3156650124, alloc=5110872, time=122.47
bytes used=3160650968, alloc=5110872, time=122.63
bytes used=3164651680, alloc=5110872, time=122.79
bytes used=3168652712, alloc=5110872, time=122.94
bytes used=3172653372, alloc=5110872, time=123.10
bytes used=3176654220, alloc=5110872, time=123.25
bytes used=3180654936, alloc=5110872, time=123.41
bytes used=3184655620, alloc=5110872, time=123.56
bytes used=3188656312, alloc=5110872, time=123.72
bytes used=3192657256, alloc=5110872, time=123.88
bytes used=3196658048, alloc=5110872, time=124.03
bytes used=3200658764, alloc=5110872, time=124.19
bytes used=3204659712, alloc=5110872, time=124.35
bytes used=3208660556, alloc=5110872, time=124.50
bytes used=3212661440, alloc=5110872, time=124.66
bytes used=3216662136, alloc=5110872, time=124.81
bytes used=3220662812, alloc=5110872, time=124.97
bytes used=3224663468, alloc=5110872, time=125.12
bytes used=3228664324, alloc=5110872, time=125.27
bytes used=3232665012, alloc=5110872, time=125.43
bytes used=3236665872, alloc=5110872, time=125.58
bytes used=3240666652, alloc=5110872, time=125.74
bytes used=3244667328, alloc=5110872, time=125.89
bytes used=3248668252, alloc=5110872, time=126.05
bytes used=3252669072, alloc=5110872, time=126.20
bytes used=3256670016, alloc=5110872, time=126.36
bytes used=3260670808, alloc=5110872, time=126.51
bytes used=3264671504, alloc=5110872, time=126.67
bytes used=3268672428, alloc=5110872, time=126.83
bytes used=3272673132, alloc=5110872, time=126.98
bytes used=3276673920, alloc=5110872, time=127.13
bytes used=3280675260, alloc=5110872, time=127.29
bytes used=3284675916, alloc=5110872, time=127.44
bytes used=3288676824, alloc=5110872, time=127.59
bytes used=3292677552, alloc=5110872, time=127.75
bytes used=3296678424, alloc=5110872, time=127.90
bytes used=3300679096, alloc=5110872, time=128.06
bytes used=3304680576, alloc=5110872, time=128.22
bytes used=3308681476, alloc=5110872, time=128.37
bytes used=3312682392, alloc=5110872, time=128.53
bytes used=3316683324, alloc=5110872, time=128.68
bytes used=3320684188, alloc=5110872, time=128.84
bytes used=3324685708, alloc=5110872, time=128.99
bytes used=3328686652, alloc=5110872, time=129.15
bytes used=3332687368, alloc=5110872, time=129.30
bytes used=3336688636, alloc=5110872, time=129.46
bytes used=3340689624, alloc=5110872, time=129.61
bytes used=3344690928, alloc=5110872, time=129.77
bytes used=3348691796, alloc=5110872, time=129.92
TOP MAIN SOLVE Loop
bytes used=3352692576, alloc=5110872, time=130.08
t[1] = 0.57
x2[1] (analytic) = 1.0007950113046470922804150240495
x2[1] (numeric) = 1.0007979458960522539118927636819
absolute error = 2.9345914051616314777396324331495e-06
relative error = 0.00029322602251344825362472727174762 %
Correct digits = 6
h = 0.0001
x1[1] (analytic) = 2.0010179457896591667751322768074
x1[1] (numeric) = 2.0010125940044635105446594504287
absolute error = 5.3517851956562304728263787465749e-06
relative error = 0.00026745313338728015696063131242026 %
Correct digits = 6
h = 0.0001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.629e+04
Order of pole (six term test) = 1.397e+07
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
Radius of convergence (six term test) for eq 2 = 3.898e+27
Order of pole (six term test) = -2.603e+54
bytes used=3356693260, alloc=5110872, time=130.23
bytes used=3360693984, alloc=5110872, time=130.39
bytes used=3364694776, alloc=5110872, time=130.54
bytes used=3368695548, alloc=5110872, time=130.69
bytes used=3372696348, alloc=5110872, time=130.85
bytes used=3376697020, alloc=5110872, time=131.00
bytes used=3380698152, alloc=5110872, time=131.16
bytes used=3384698908, alloc=5110872, time=131.31
bytes used=3388700032, alloc=5110872, time=131.47
bytes used=3392700884, alloc=5110872, time=131.62
bytes used=3396701676, alloc=5110872, time=131.78
bytes used=3400702404, alloc=5110872, time=131.93
bytes used=3404703092, alloc=5110872, time=132.08
bytes used=3408704264, alloc=5110872, time=132.24
bytes used=3412705028, alloc=5110872, time=132.40
bytes used=3416705760, alloc=5110872, time=132.55
bytes used=3420706424, alloc=5110872, time=132.71
bytes used=3424707320, alloc=5110872, time=132.87
bytes used=3428707988, alloc=5110872, time=133.02
bytes used=3432708752, alloc=5110872, time=133.17
bytes used=3436709540, alloc=5110872, time=133.33
bytes used=3440710308, alloc=5110872, time=133.48
bytes used=3444711248, alloc=5110872, time=133.64
bytes used=3448712312, alloc=5110872, time=133.79
bytes used=3452712968, alloc=5110872, time=133.95
bytes used=3456714376, alloc=5110872, time=134.11
bytes used=3460715424, alloc=5110872, time=134.27
bytes used=3464716088, alloc=5110872, time=134.42
bytes used=3468717408, alloc=5110872, time=134.58
bytes used=3472718296, alloc=5110872, time=134.73
bytes used=3476719252, alloc=5110872, time=134.88
bytes used=3480720088, alloc=5110872, time=135.04
bytes used=3484720924, alloc=5110872, time=135.19
bytes used=3488722244, alloc=5110872, time=135.34
bytes used=3492722984, alloc=5110872, time=135.50
bytes used=3496723764, alloc=5110872, time=135.65
bytes used=3500724884, alloc=5110872, time=135.81
bytes used=3504725608, alloc=5110872, time=135.96
bytes used=3508726560, alloc=5110872, time=136.12
bytes used=3512727288, alloc=5110872, time=136.28
bytes used=3516728032, alloc=5110872, time=136.43
bytes used=3520728820, alloc=5110872, time=136.58
bytes used=3524729976, alloc=5110872, time=136.74
bytes used=3528730808, alloc=5110872, time=136.89
bytes used=3532731616, alloc=5110872, time=137.05
bytes used=3536732320, alloc=5110872, time=137.20
bytes used=3540733072, alloc=5110872, time=137.36
bytes used=3544733812, alloc=5110872, time=137.51
bytes used=3548734640, alloc=5110872, time=137.66
bytes used=3552735680, alloc=5110872, time=137.82
bytes used=3556736584, alloc=5110872, time=137.97
bytes used=3560737304, alloc=5110872, time=138.13
bytes used=3564737984, alloc=5110872, time=138.28
bytes used=3568738848, alloc=5110872, time=138.44
bytes used=3572739564, alloc=5110872, time=138.59
bytes used=3576740344, alloc=5110872, time=138.75
bytes used=3580741032, alloc=5110872, time=138.90
bytes used=3584741696, alloc=5110872, time=139.06
bytes used=3588742380, alloc=5110872, time=139.21
bytes used=3592743172, alloc=5110872, time=139.37
bytes used=3596743864, alloc=5110872, time=139.52
bytes used=3600744616, alloc=5110872, time=139.68
bytes used=3604745396, alloc=5110872, time=139.84
bytes used=3608746124, alloc=5110872, time=139.99
bytes used=3612746856, alloc=5110872, time=140.15
bytes used=3616747988, alloc=5110872, time=140.30
bytes used=3620748728, alloc=5110872, time=140.46
bytes used=3624749564, alloc=5110872, time=140.61
bytes used=3628750332, alloc=5110872, time=140.77
bytes used=3632751036, alloc=5110872, time=140.92
bytes used=3636751788, alloc=5110872, time=141.08
bytes used=3640752684, alloc=5110872, time=141.23
bytes used=3644753388, alloc=5110872, time=141.39
bytes used=3648754060, alloc=5110872, time=141.54
bytes used=3652754976, alloc=5110872, time=141.70
bytes used=3656755844, alloc=5110872, time=141.85
bytes used=3660756600, alloc=5110872, time=142.01
bytes used=3664757704, alloc=5110872, time=142.16
bytes used=3668758692, alloc=5110872, time=142.32
bytes used=3672759460, alloc=5110872, time=142.48
bytes used=3676760296, alloc=5110872, time=142.63
bytes used=3680761004, alloc=5110872, time=142.79
bytes used=3684761796, alloc=5110872, time=142.94
bytes used=3688762464, alloc=5110872, time=143.10
bytes used=3692763268, alloc=5110872, time=143.25
bytes used=3696763928, alloc=5110872, time=143.40
bytes used=3700764588, alloc=5110872, time=143.56
bytes used=3704766440, alloc=5110872, time=143.72
bytes used=3708767268, alloc=5110872, time=143.87
bytes used=3712768156, alloc=5110872, time=144.03
bytes used=3716768876, alloc=5110872, time=144.18
bytes used=3720769692, alloc=5110872, time=144.34
bytes used=3724770720, alloc=5110872, time=144.49
bytes used=3728771856, alloc=5110872, time=144.65
bytes used=3732772700, alloc=5110872, time=144.80
bytes used=3736773484, alloc=5110872, time=144.96
bytes used=3740774168, alloc=5110872, time=145.11
bytes used=3744774932, alloc=5110872, time=145.27
bytes used=3748775804, alloc=5110872, time=145.42
bytes used=3752776672, alloc=5110872, time=145.58
bytes used=3756777836, alloc=5110872, time=145.74
bytes used=3760778764, alloc=5110872, time=145.89
bytes used=3764779560, alloc=5110872, time=146.05
bytes used=3768780260, alloc=5110872, time=146.20
bytes used=3772781492, alloc=5110872, time=146.36
bytes used=3776782168, alloc=5110872, time=146.51
bytes used=3780782984, alloc=5110872, time=146.67
bytes used=3784783728, alloc=5110872, time=146.83
bytes used=3788784472, alloc=5110872, time=146.98
bytes used=3792785136, alloc=5110872, time=147.14
bytes used=3796785984, alloc=5110872, time=147.30
bytes used=3800786860, alloc=5110872, time=147.45
bytes used=3804787592, alloc=5110872, time=147.60
bytes used=3808788260, alloc=5110872, time=147.76
bytes used=3812789000, alloc=5110872, time=147.92
bytes used=3816789716, alloc=5110872, time=148.07
bytes used=3820790940, alloc=5110872, time=148.22
TOP MAIN SOLVE Loop
bytes used=3824791864, alloc=5110872, time=148.38
t[1] = 0.58
x2[1] (analytic) = 1.0008059561651928575442831532282
x2[1] (numeric) = 1.0008098398165204554447851228428
absolute error = 3.8836513275979005019696146127510e-06
relative error = 0.0003880523795520722987602762480083 %
Correct digits = 6
h = 0.0001
x1[1] (analytic) = 2.0010078170598177236585215698858
x1[1] (numeric) = 2.0010008260992983781180888658058
absolute error = 6.9909605193455404327040800148479e-06
relative error = 0.00034937197444924094819204359349945 %
Correct digits = 6
h = 0.0001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.637e+04
Order of pole (six term test) = 1.411e+07
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=3828793068, alloc=5110872, time=148.53
bytes used=3832793888, alloc=5110872, time=148.69
bytes used=3836794640, alloc=5110872, time=148.85
bytes used=3840795316, alloc=5110872, time=149.00
bytes used=3844796024, alloc=5110872, time=149.16
bytes used=3848796728, alloc=5110872, time=149.31
bytes used=3852797516, alloc=5110872, time=149.47
bytes used=3856798300, alloc=5110872, time=149.62
bytes used=3860799112, alloc=5110872, time=149.78
bytes used=3864799828, alloc=5110872, time=149.93
bytes used=3868800796, alloc=5110872, time=150.09
bytes used=3872801560, alloc=5110872, time=150.24
bytes used=3876802324, alloc=5110872, time=150.40
bytes used=3880803200, alloc=5110872, time=150.55
bytes used=3884803928, alloc=5110872, time=150.71
bytes used=3888804972, alloc=5110872, time=150.87
bytes used=3892806176, alloc=5110872, time=151.02
bytes used=3896806936, alloc=5110872, time=151.18
bytes used=3900808252, alloc=5110872, time=151.33
bytes used=3904809036, alloc=5110872, time=151.49
bytes used=3908809828, alloc=5110872, time=151.64
bytes used=3912810524, alloc=5110872, time=151.79
bytes used=3916811200, alloc=5110872, time=151.95
bytes used=3920812288, alloc=5110872, time=152.11
bytes used=3924813260, alloc=5110872, time=152.26
bytes used=3928814072, alloc=5110872, time=152.42
bytes used=3932814836, alloc=5110872, time=152.57
bytes used=3936815568, alloc=5110872, time=152.73
bytes used=3940816868, alloc=5110872, time=152.89
bytes used=3944817644, alloc=5110872, time=153.04
bytes used=3948818372, alloc=5110872, time=153.20
bytes used=3952819092, alloc=5110872, time=153.35
bytes used=3956819964, alloc=5110872, time=153.50
bytes used=3960821336, alloc=5110872, time=153.66
bytes used=3964822372, alloc=5110872, time=153.82
bytes used=3968823336, alloc=5110872, time=153.97
bytes used=3972824084, alloc=5110872, time=154.13
bytes used=3976824908, alloc=5110872, time=154.28
bytes used=3980825688, alloc=5110872, time=154.44
bytes used=3984826476, alloc=5110872, time=154.59
bytes used=3988827220, alloc=5110872, time=154.75
bytes used=3992828220, alloc=5110872, time=154.90
bytes used=3996828960, alloc=5110872, time=155.06
bytes used=4000830092, alloc=5110872, time=155.21
bytes used=4004831128, alloc=5110872, time=155.37
bytes used=4008831952, alloc=5110872, time=155.53
bytes used=4012832916, alloc=5110872, time=155.68
bytes used=4016833640, alloc=5110872, time=155.84
bytes used=4020834464, alloc=5110872, time=155.99
bytes used=4024835300, alloc=5110872, time=156.15
bytes used=4028836032, alloc=5110872, time=156.30
bytes used=4032836776, alloc=5110872, time=156.46
bytes used=4036837520, alloc=5110872, time=156.61
bytes used=4040838800, alloc=5110872, time=156.77
bytes used=4044839508, alloc=5110872, time=156.93
bytes used=4048840280, alloc=5110872, time=157.08
bytes used=4052841000, alloc=5110872, time=157.23
bytes used=4056842268, alloc=5110872, time=157.39
bytes used=4060842960, alloc=5110872, time=157.54
bytes used=4064843724, alloc=5110872, time=157.70
bytes used=4068844492, alloc=5110872, time=157.86
bytes used=4072845248, alloc=5110872, time=158.01
bytes used=4076845908, alloc=5110872, time=158.16
bytes used=4080846624, alloc=5110872, time=158.38
bytes used=4084847292, alloc=5110872, time=158.75
bytes used=4088848032, alloc=5110872, time=159.12
bytes used=4092849376, alloc=5110872, time=159.49
bytes used=4096850360, alloc=5110872, time=159.86
bytes used=4100851136, alloc=5110872, time=160.23
bytes used=4104851916, alloc=5110872, time=160.60
bytes used=4108852560, alloc=5110872, time=160.97
bytes used=4112853308, alloc=5110872, time=161.33
bytes used=4116853968, alloc=5110872, time=161.70
bytes used=4120854668, alloc=5110872, time=162.07
bytes used=4124855784, alloc=5110872, time=162.44
bytes used=4128856536, alloc=5110872, time=162.81
bytes used=4132857364, alloc=5110872, time=163.17
bytes used=4136858432, alloc=5110872, time=163.54
bytes used=4140859184, alloc=5110872, time=163.91
bytes used=4144859964, alloc=5110872, time=164.28
bytes used=4148860764, alloc=5110872, time=164.65
bytes used=4152861556, alloc=5110872, time=165.02
bytes used=4156862324, alloc=5110872, time=165.38
bytes used=4160863028, alloc=5110872, time=165.75
bytes used=4164863768, alloc=5110872, time=166.12
bytes used=4168864616, alloc=5110872, time=166.49
bytes used=4172865464, alloc=5110872, time=166.86
bytes used=4176866480, alloc=5110872, time=167.22
bytes used=4180867220, alloc=5110872, time=167.59
bytes used=4184868048, alloc=5110872, time=167.96
bytes used=4188868772, alloc=5110872, time=168.33
bytes used=4192869700, alloc=5110872, time=168.70
bytes used=4196870396, alloc=5110872, time=169.07
bytes used=4200871624, alloc=5110872, time=169.44
bytes used=4204872868, alloc=5110872, time=169.82
bytes used=4208873660, alloc=5110872, time=170.19
bytes used=4212875120, alloc=5110872, time=170.56
bytes used=4216876280, alloc=5110872, time=170.93
bytes used=4220877252, alloc=5110872, time=171.30
bytes used=4224878000, alloc=5110872, time=171.67
bytes used=4228878728, alloc=5110872, time=172.04
bytes used=4232879528, alloc=5110872, time=172.41
bytes used=4236880364, alloc=5110872, time=172.77
bytes used=4240881420, alloc=5110872, time=173.14
bytes used=4244882284, alloc=5110872, time=173.51
bytes used=4248882960, alloc=5110872, time=173.88
bytes used=4252883652, alloc=5110872, time=174.25
bytes used=4256884360, alloc=5110872, time=174.62
bytes used=4260885104, alloc=5110872, time=174.99
bytes used=4264885844, alloc=5110872, time=175.36
bytes used=4268886516, alloc=5110872, time=175.74
bytes used=4272887248, alloc=5110872, time=176.11
bytes used=4276888144, alloc=5110872, time=176.48
bytes used=4280889064, alloc=5110872, time=176.85
bytes used=4284889764, alloc=5110872, time=177.22
bytes used=4288890572, alloc=5110872, time=177.58
bytes used=4292891800, alloc=5110872, time=177.95
TOP MAIN SOLVE Loop
bytes used=4296892852, alloc=5110872, time=178.32
bytes used=4300893576, alloc=5110872, time=178.69
t[1] = 0.59
x2[1] (analytic) = 1.0008171730259982862801800140618
x2[1] (numeric) = 1.0008221531971810411539313473588
absolute error = 4.9801711827548737513332970283374e-06
relative error = 0.00049761048441017344064260472066758 %
Correct digits = 6
h = 0.0001
x1[1] (analytic) = 2.000997789112522112663621650095
x1[1] (numeric) = 2.0009889399247201054663350419579
absolute error = 8.8491878020071972866081370839074e-06
relative error = 0.00044223875959063245578125737433036 %
Correct digits = 6
h = 0.0001
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.646e+04
Order of pole (six term test) = 1.425e+07
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
bytes used=4304894284, alloc=5110872, time=179.06
bytes used=4308895292, alloc=5110872, time=179.43
bytes used=4312896008, alloc=5110872, time=179.80
bytes used=4316896828, alloc=5110872, time=180.17
bytes used=4320897800, alloc=5110872, time=180.54
bytes used=4324898580, alloc=5110872, time=180.91
Finished!
Maximum Time Reached before Solution Completed!
diff (x2,t,2) = 3.0 * diff(x2,t,1) - 2.0 * x2 - diff(x1,t,2) - diff (x1,t,1)+x1;
diff (x1,t,1) = 4.0 * x2 - 2.0 * diff (x2,t ,1) - 2.0 * x1;
Iterations = 906
Total Elapsed Time = 3 Minutes 0 Seconds
Elapsed Time(since restart) = 2 Minutes 59 Seconds
Expected Time Remaining = 6 Minutes 57 Seconds
Optimized Time Remaining = 6 Minutes 54 Seconds
Expected Total Time = 9 Minutes 54 Seconds
Time to Timeout Unknown
Percent Done = 30.23 %
> quit
bytes used=4325110996, alloc=5110872, time=180.92