|\^/| Maple 12 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 1
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 1;
> 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 3
> # Begin Function number 4
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_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_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 1
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> if (min_size < 1.0) then # if number 1
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_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_1,
array_const_0D0, array_const_0D1, array_const_0D2, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y[1]) < min_size then
min_size := omniabs(array_y[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 4
> # Begin Function number 5
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_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_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms;
> max_value3 := 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,"");
> value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (value3 > max_value3) then # if number 1
> max_value3 := value3;
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> fi;# end if 1;
> omniout_float(ALWAYS,"max_value3",32,max_value3,32,"");
> max_value3;
> end;
test_suggested_h := proc()
local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_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_1,
array_const_0D0, array_const_0D1, array_const_0D2, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
max_value3 := 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, "");
value3 := omniabs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_value3 < value3 then
max_value3 := value3;
omniout_float(ALWAYS, "value3", 32, value3, 32, "")
end if;
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, "");
max_value3
end proc
> # End Function number 5
> # Begin Function number 6
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_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_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1
> ret := true;
> else
> ret := false;
> fi;# end if 1;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_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_1,
array_const_0D0, array_const_0D1, array_const_0D2, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 6
> # Begin Function number 7
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_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_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> 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 1
> if (iter >= 0) then # if number 2
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 4
> glob_good_digits := -trunc(log10(relerr)) + 2;
> else
> glob_good_digits := Digits;
> fi;# end if 4;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 3;
> 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 2;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_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_1,
array_const_0D0, array_const_0D1, array_const_0D2, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[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)) + 2
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, " ")
end if
end if
end proc
> # End Function number 7
> # Begin Function number 8
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_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_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 2
> fi;# end if 1;
> if ( not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1;
> 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_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_1,
array_const_0D0, array_const_0D1, array_const_0D2, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_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_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 8
> # Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_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_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> 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(x_end),convfloat(x_start),convfloat(array_x[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(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 1;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_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_1,
array_const_0D0, array_const_0D1, array_const_0D2, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
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(x_end), convfloat(x_start),
convfloat(array_x[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(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[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 9
> # Begin Function number 10
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_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_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > glob_small_float * glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1;
> n := n - 1;
> od;# end do number 2;
> m := n + cnt;
> if (m <= 10) then # if number 1
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> elif
> (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_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) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2;
> #BOTTOM RADII COMPLEX EQ = 1
> found_sing := 0;
> #TOP WHICH RADII EQ = 1
> if (1 <> found_sing and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found_sing := 1;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found_sing := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing ) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 3;
> fi;# end if 2;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if (array_pole[1] > array_poles[1,1]) then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2;
> #BOTTOM WHICH RADIUS EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 2;
> #BOTTOM ADJUST ALL SERIES
> if (reached_interval()) then # if number 2
> display_pole();
> fi;# end if 2
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no,
rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_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_1,
array_const_0D0, array_const_0D1, array_const_0D2, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (
omniabs(array_y_higher[1, m]) < glob_small_float*glob_small_float or
omniabs(array_y_higher[1, m - 1]) < glob_small_float*glob_small_float
or
omniabs(array_y_higher[1, m - 2]) < glob_small_float*glob_small_float)
do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if glob_small_float*glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y_higher[1, n]) 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
elif glob_large_float <= omniabs(array_y_higher[1, m]) or
glob_large_float <= omniabs(array_y_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y_higher[1, m - 5]) or
omniabs(array_y_higher[1, m]) <= glob_small_float or
omniabs(array_y_higher[1, m - 1]) <= glob_small_float or
omniabs(array_y_higher[1, m - 2]) <= glob_small_float or
omniabs(array_y_higher[1, m - 3]) <= glob_small_float or
omniabs(array_y_higher[1, m - 4]) <= glob_small_float or
omniabs(array_y_higher[1, m - 5]) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_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) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) 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_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found_sing := 0;
if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 2;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1")
end if
end if
end if;
if 1 <> found_sing and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and
-1.0*glob_smallish_float < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 1")
end if
end if
end if;
if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
array_type_pole[1] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 1")
end if
end if;
if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1]
and 0. < array_real_pole[1, 1] and
-1.0*glob_smallish_float < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 1")
end if
end if
end if;
if 1 <> found_sing and array_complex_pole[1, 1] <> glob_large_float
and array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found_sing := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1")
end if
end if
end if;
if 1 <> found_sing then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 1")
end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_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_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[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_pole() end if
end proc
> # End Function number 10
> # Begin Function number 11
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_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_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 2
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 3;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 2;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_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_1,
array_const_0D0, array_const_0D1, array_const_0D2, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
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_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 11
> # Begin Function number 12
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_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_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> #emit pre sqrt 1 $eq_no = 1
> array_tmp4[1] := sqrt(array_tmp3[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0;
> #emit pre sqrt ID_FULL iii = 2 $eq_no = 1
> #emit pre sqrt 2 $eq_no = 1
> array_tmp4[2] := 0.0;
> array_tmp4[2] := (array_tmp3[2]-ats(2,array_tmp4,array_tmp4,2)) / array_tmp4[1] / 2.0;
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0.0;
> array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre sqrt ID_FULL iii = 3 $eq_no = 1
> #emit pre sqrt 3 $eq_no = 1
> array_tmp4[3] := 0.0;
> array_tmp4[3] := (array_tmp3[3]-ats(3,array_tmp4,array_tmp4,2)) / array_tmp4[1] / 2.0;
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0.0;
> array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre sqrt ID_FULL iii = 4 $eq_no = 1
> #emit pre sqrt 4 $eq_no = 1
> array_tmp4[4] := 0.0;
> array_tmp4[4] := (array_tmp3[4]-ats(4,array_tmp4,array_tmp4,2)) / array_tmp4[1] / 2.0;
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0.0;
> array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre sqrt ID_FULL iii = 5 $eq_no = 1
> #emit pre sqrt 5 $eq_no = 1
> array_tmp4[5] := 0.0;
> array_tmp4[5] := (array_tmp3[5]-ats(5,array_tmp4,array_tmp4,2)) / array_tmp4[1] / 2.0;
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_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 sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0.0;
> array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0;
> #emit sqrt FULL $eq_no = 1
> array_tmp4[kkk] := 0.0;
> array_tmp4[kkk] := (array_tmp3[kkk] - ats(kkk,array_tmp4,array_tmp4,2)) / array_tmp4[1] / 2.0;
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 2
> 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_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 2
> 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_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_1,
array_const_0D0, array_const_0D1, array_const_0D2, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
array_tmp1[1] := array_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4[1] := sqrt(array_tmp3[1]);
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0);
array_tmp4[2] := 0.;
array_tmp4[2] := (array_tmp3[2] - ats(2, array_tmp4, array_tmp4, 2))/(
array_tmp4[1]*2.0);
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp3[3] := 0.;
array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4[3] := 0.;
array_tmp4[3] := (array_tmp3[3] - ats(3, array_tmp4, array_tmp4, 2))/(
array_tmp4[1]*2.0);
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp3[4] := 0.;
array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4[4] := 0.;
array_tmp4[4] := (array_tmp3[4] - ats(4, array_tmp4, array_tmp4, 2))/(
array_tmp4[1]*2.0);
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp3[5] := 0.;
array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4[5] := 0.;
array_tmp4[5] := (array_tmp3[5] - ats(5, array_tmp4, array_tmp4, 2))/(
array_tmp4[1]*2.0);
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp3[kkk] := 0.;
array_tmp3[kkk] :=
-ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0);
array_tmp4[kkk] := 0.;
array_tmp4[kkk] := (
array_tmp3[kkk] - ats(kkk, array_tmp4, array_tmp4, 2))/(
array_tmp4[1]*2.0);
array_tmp5[kkk] := array_tmp4[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp5[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_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_y_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 12
> #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\n", 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 \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", 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\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", 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, " | \n")
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 Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
> # 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,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_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, 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_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
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 6
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # End Function number 16
> # Begin Function number 17
> 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 17
> # Begin Function number 18
> 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 18
> # Begin Function number 19
> 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 19
> # Begin Function number 20
> 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 20
> # Begin Function number 21
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 21
> # Begin Function number 22
> 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 22
> # Begin Function number 23
> 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");
> else
> fprintf(file,"No Pole");
> fi;# end if 8
> 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")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # End Function number 23
> # Begin Function number 24
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 24
> # Begin Function number 25
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # End Function number 25
> # Begin Function number 26
> 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 8
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 8;
> if (glob_max_iter < 2) then # if number 8
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 8;
> if (errflag) then # if number 8
> quit;
> fi;# end if 8
> 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 26
> # Begin Function number 27
> 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 8
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 9
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 9
> fi;# end if 8;
> 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 27
> # Begin Function number 28
> 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 8
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 8;
> 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 28
> # Begin Function number 29
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 29
> # Begin Function number 30
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 8
> if (array_fact_1[nnn] = 0) then # if number 9
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 9;
> else
> ret := factorial_2(nnn);
> fi;# end if 8;
> 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 30
> # Begin Function number 31
> 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 8
> if (array_fact_2[mmm,nnn] = 0) then # if number 9
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 9;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 8;
> 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 31
> # Begin Function number 32
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 33
> # Begin Function number 34
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 34
> # Begin Function number 35
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 35
> # Begin Function number 36
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 36
> # Begin Function number 37
> 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 37
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(0.8 * (x + 2.0) * sqrt(sqrt(0.1 * x + 0.2)));
> end;
exact_soln_y := proc(x) return 0.8*(x + 2.0)*sqrt(sqrt(0.1*x + 0.2)) 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,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> 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_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_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> 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;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_value3 := 0.0;
> glob_ratio_of_radius := 0.01;
> 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_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 := 0.1e-200;
> glob_smallish_float := 0.1e-100;
> 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 := 1;
> 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/sqrt_sqrtpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> 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,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 0.5 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> 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:=0.001;");
> 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_y := proc(x)");
> omniout_str(ALWAYS,"return(0.8 * (x + 2.0) * sqrt(sqrt(0.1 * x + 0.2)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> 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_y_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..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= 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_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_complex_pole := Array(0..(1+ 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 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D0[1] := 0.0;
> array_const_0D1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D1[1] := 0.1;
> array_const_0D2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D2[1] := 0.2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3;
> iiif := iiif + 1;
> od;# end do number 2;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 0.5 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.001;
> 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_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> if (glob_display_interval < glob_h) then # if number 2
> glob_h := glob_display_interval;
> fi;# end if 2;
> if (glob_max_h < glob_h) then # if number 2
> glob_h := glob_max_h;
> fi;# end if 2;
> found_h := -1.0;
> best_h := 0.0;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 3;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 3
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 4
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 4;
> r_order := r_order + 1;
> od;# end do number 3
> ;
> atomall();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> value3 := test_suggested_h();
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2
> best_h := glob_h;
> found_h := 1.0;
> fi;# end if 2;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> glob_h := glob_h * 0.5;
> od;# end do number 2;
> if (found_h > 0.0) then # if number 2
> glob_h := best_h ;
> else
> omniout_str(ALWAYS,"No increment to obtain desired accuracy found");
> fi;# end if 2;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2;
> #BEGIN SOLUTION CODE
> if (found_h > 0.0) then # if number 2
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_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_y_higher[r_order,term_no] := array_y_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
> ;
> 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_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> if (reached_interval()) then # if number 3
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 3;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3;#was right paren 0004C
> if (reached_interval()) then # if number 3
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 3;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_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_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_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 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4;
> term_no := term_no - 1;
> od;# end do number 3;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 2;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 3;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 3;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-01-28T19:38:02-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sqrt_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[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_pole(html_log_file,array_type_pole[1])
> ;
> if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 4
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 4;
> log_revs(html_log_file," 165 | ")
> ;
> logitem_str(html_log_file,"sqrt_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"sqrt_sqrt maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3;
> if (glob_html_log) then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> fi;# end if 2
> #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, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, value3, min_value, est_answer, best_h,
found_h, repeat_it;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, 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_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_1,
array_const_0D0, array_const_0D1, array_const_0D2, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
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;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_value3 := 0.;
glob_ratio_of_radius := 0.01;
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_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 := 0.1*10^(-200);
glob_smallish_float := 0.1*10^(-100);
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 := 1;
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/sqrt_sqrtpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
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, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 0.5 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
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:=0.001;");
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_y := proc(x)");
omniout_str(ALWAYS,
"return(0.8 * (x + 2.0) * sqrt(sqrt(0.1 * x + 0.2)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_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 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := 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_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_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 <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[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_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 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 <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 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_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[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_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_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_0D1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D1[term] := 0.; term := term + 1
end do;
array_const_0D1[1] := 0.1;
array_const_0D2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D2[term] := 0.; term := term + 1
end do;
array_const_0D2[1] := 0.2;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
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;
x_start := 0.1;
x_end := 0.5;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_desired_digits_correct := 10;
glob_display_interval := 0.001;
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_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
found_h := -1.0;
best_h := 0.;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
while opt_iter <= 20 and found_h < 0. do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_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_y_higher[r_order, term_no] := array_y_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;
atomall();
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
value3 := test_suggested_h();
omniout_float(ALWAYS, "value3", 32, value3, 32, "");
if value3 < est_needed_step_err and found_h < 0. then
best_h := glob_h; found_h := 1.0
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1;
glob_h := glob_h*0.5
end do;
if 0. < found_h then glob_h := best_h
else omniout_str(ALWAYS,
"No increment to obtain desired accuracy found")
end if;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
if 0. < found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_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_y_higher[r_order, term_no] := array_y_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_x[1] < glob_check_sign*x_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;
atomall();
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_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_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 ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));")
;
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-01-28T19:38:02-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sqrt_sqrt");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[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_pole(html_log_file, array_type_pole[1]);
if array_type_pole[1] = 1 or array_type_pole[1] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_total_exp_sec));
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 165 | ");
logitem_str(html_log_file, "sqrt_sqrt diffeq.mxt");
logitem_str(html_log_file, "sqrt_sqrt maple results");
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/sqrt_sqrtpostode.ode#################
diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 0.5 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.001;
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_y := proc(x)
return(0.8 * (x + 2.0) * sqrt(sqrt(0.1 * x + 0.2)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
opt_iter = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 0.4
estimated_steps = 400
step_error = 2.5000000000000000000000000000000e-13
est_needed_step_err = 2.5000000000000000000000000000000e-13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 8.4135105462372732904425552992627e-91
max_value3 = 8.4135105462372732904425552992627e-91
value3 = 8.4135105462372732904425552992627e-91
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 1.1372713678556830191114874919567
y[1] (numeric) = 1.1372713678556830191114874919567
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.101
y[1] (analytic) = 1.1379483553881370327381823752768
y[1] (numeric) = 1.1379483553881370327381823752767
absolute error = 1e-31
relative error = 8.7877450260817422782925078054484e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.102
y[1] (analytic) = 1.1386254234807807318966501493581
y[1] (numeric) = 1.138625423480780731896650149358
absolute error = 1e-31
relative error = 8.7825195132478030402489174324988e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.103
y[1] (analytic) = 1.1393025721048682840552323014437
y[1] (numeric) = 1.1393025721048682840552323014436
absolute error = 1e-31
relative error = 8.7772995908584147857677139498219e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.8MB, time=0.31
x[1] = 0.104
y[1] (analytic) = 1.1399798012316777787949962525529
y[1] (numeric) = 1.1399798012316777787949962525528
absolute error = 1e-31
relative error = 8.7720852502786606600717227238068e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.105
y[1] (analytic) = 1.1406571108325111965408527226457
y[1] (numeric) = 1.1406571108325111965408527226456
absolute error = 1e-31
relative error = 8.7668764828910566903865648477940e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.106
y[1] (analytic) = 1.1413345008786943773483810753456
y[1] (numeric) = 1.1413345008786943773483810753455
absolute error = 1e-31
relative error = 8.7616732800955083304820187665424e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.107
y[1] (analytic) = 1.1420119713415769897462369875802
y[1] (numeric) = 1.1420119713415769897462369875801
absolute error = 1e-31
relative error = 8.7564756333092671341077793554186e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.108
y[1] (analytic) = 1.1426895221925324996340171324293
y[1] (numeric) = 1.1426895221925324996340171324292
absolute error = 1e-31
relative error = 8.7512835339668875568803369706057e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.109
y[1] (analytic) = 1.1433671534029581392354559053057
y[1] (numeric) = 1.1433671534029581392354559053055
absolute error = 2e-31
relative error = 1.7492193947040367772358865799070e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 1.1440448649442748761068295643318
y[1] (numeric) = 1.1440448649442748761068295643316
absolute error = 2e-31
relative error = 1.7481831886876374597228547905684e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.111
y[1] (analytic) = 1.1447226567879273822004434954263
y[1] (numeric) = 1.1447226567879273822004434954261
absolute error = 2e-31
relative error = 1.7471480870414206089242815374622e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.112
y[1] (analytic) = 1.1454005289053840029830786511756
y[1] (numeric) = 1.1454005289053840029830786511754
absolute error = 2e-31
relative error = 1.7461140880660535519515741940474e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.8MB, time=0.65
x[1] = 0.113
y[1] (analytic) = 1.1460784812681367266092735500495
y[1] (numeric) = 1.1460784812681367266092735500492
absolute error = 3e-31
relative error = 2.6176217850984320706764784977597e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.114
y[1] (analytic) = 1.1467565138477011531493185589201
y[1] (numeric) = 1.1467565138477011531493185589198
absolute error = 3e-31
relative error = 2.6160740870214276949198238341360e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.115
y[1] (analytic) = 1.147434626615616463871839517175
y[1] (numeric) = 1.1474346266156164638718395171748
absolute error = 2e-31
relative error = 1.7430186902229399842622741560147e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.116
y[1] (analytic) = 1.1481128195434453905808480949712
y[1] (numeric) = 1.148112819543445390580848094971
absolute error = 2e-31
relative error = 1.7419890850058735049376788461171e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.117
y[1] (analytic) = 1.1487910926027741850071366113705
y[1] (numeric) = 1.1487910926027741850071366113703
absolute error = 2e-31
relative error = 1.7409605740140905522177393675705e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.118
y[1] (analytic) = 1.1494694457652125882538953702266
y[1] (numeric) = 1.1494694457652125882538953702264
absolute error = 2e-31
relative error = 1.7399331555686382308653317487888e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.119
y[1] (analytic) = 1.1501478790023938002964309027649
y[1] (numeric) = 1.1501478790023938002964309027647
absolute error = 2e-31
relative error = 1.7389068279939308607112445994080e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 1.150826392285974449535863835812
y[1] (numeric) = 1.1508263922859744495358638358118
absolute error = 2e-31
relative error = 1.7378815896177416385238359388435e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.121
y[1] (analytic) = 1.1515049855876345624066854335994
y[1] (numeric) = 1.1515049855876345624066854335992
absolute error = 2e-31
relative error = 1.7368574387711943244474037464540e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=3.9MB, time=1.00
x[1] = 0.122
y[1] (analytic) = 1.1521836588790775330380521889825
y[1] (numeric) = 1.1521836588790775330380521889824
absolute error = 1e-31
relative error = 8.6791718689437747646266700269721e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.123
y[1] (analytic) = 1.1528624121320300929686981667934
y[1] (numeric) = 1.1528624121320300929686981667933
absolute error = 1e-31
relative error = 8.6740619650411178401220808503540e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.124
y[1] (analytic) = 1.1535412453182422809153451278806
y[1] (numeric) = 1.1535412453182422809153451278804
absolute error = 2e-31
relative error = 1.7337914947707259830770407246176e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.125
y[1] (analytic) = 1.1542201584094874125944907871906
y[1] (numeric) = 1.1542201584094874125944907871905
absolute error = 1e-31
relative error = 8.6638583871035278227915841191867e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.126
y[1] (analytic) = 1.1548991513775620505974558830157
y[1] (numeric) = 1.1548991513775620505974558830156
absolute error = 1e-31
relative error = 8.6587646965295752005773496269984e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.127
y[1] (analytic) = 1.1555782241942859743185710572699
y[1] (numeric) = 1.1555782241942859743185710572699
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.128
y[1] (analytic) = 1.156257376831502149936384868377
y[1] (numeric) = 1.156257376831502149936384868377
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.129
y[1] (analytic) = 1.1569366092610767004477745790449
y[1] (numeric) = 1.1569366092610767004477745790449
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 1.1576159214548988757548416808844
y[1] (numeric) = 1.1576159214548988757548416808843
absolute error = 1e-31
relative error = 8.6384437313473867282260833355837e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.131
y[1] (analytic) = 1.1582953133848810228044744364931
y[1] (numeric) = 1.1582953133848810228044744364931
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
memory used=15.2MB, alloc=4.0MB, time=1.35
TOP MAIN SOLVE Loop
x[1] = 0.132
y[1] (analytic) = 1.1589747850229585557804600372856
y[1] (numeric) = 1.1589747850229585557804600372856
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.133
y[1] (analytic) = 1.1596543363410899263480292919964
y[1] (numeric) = 1.1596543363410899263480292919964
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.134
y[1] (analytic) = 1.1603339673112565939507170764376
y[1] (numeric) = 1.1603339673112565939507170764376
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.135
y[1] (analytic) = 1.1610136779054629961594220897376
y[1] (numeric) = 1.1610136779054629961594220897376
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.136
y[1] (analytic) = 1.1616934680957365190735497759466
y[1] (numeric) = 1.1616934680957365190735497759466
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.137
y[1] (analytic) = 1.1623733378541274677741225825563
y[1] (numeric) = 1.1623733378541274677741225825562
absolute error = 1e-31
relative error = 8.6030879015696712557973159547285e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.138
y[1] (analytic) = 1.1630532871527090368287420391593
y[1] (numeric) = 1.1630532871527090368287420391592
absolute error = 1e-31
relative error = 8.5980583267007256171678630405016e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.139
y[1] (analytic) = 1.163733315963577280848287450166
y[1] (numeric) = 1.1637333159635772808482874501659
absolute error = 1e-31
relative error = 8.5930340420991966045736928213812e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 1.164413424258851085095236305207
y[1] (numeric) = 1.1644134242588510850952363052069
absolute error = 1e-31
relative error = 8.5880150397312690103024371237498e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.1MB, time=1.71
x[1] = 0.141
y[1] (analytic) = 1.1650936120106721361434918195869
y[1] (numeric) = 1.1650936120106721361434918195868
absolute error = 1e-31
relative error = 8.5830013115790742499436682767902e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.142
y[1] (analytic) = 1.1657738791912048925896033249146
y[1] (numeric) = 1.1657738791912048925896033249144
absolute error = 2e-31
relative error = 1.7155985699281302559619409568178e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.143
y[1] (analytic) = 1.1664542257726365558152655368274
y[1] (numeric) = 1.1664542257726365558152655368272
absolute error = 2e-31
relative error = 1.7145979291859815256666044297918e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.144
y[1] (analytic) = 1.1671346517271770408009830325533
y[1] (numeric) = 1.1671346517271770408009830325532
absolute error = 1e-31
relative error = 8.5679916924765805410548760445488e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.145
y[1] (analytic) = 1.1678151570270589469907865759154
y[1] (numeric) = 1.1678151570270589469907865759153
absolute error = 1e-31
relative error = 8.5629989813261982388212272134392e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.146
y[1] (analytic) = 1.168495741644537529207888231287
y[1] (numeric) = 1.1684957416445375292078882312869
absolute error = 1e-31
relative error = 8.5580115045400412888035332866001e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.147
y[1] (analytic) = 1.1691764055518906686211625109537
y[1] (numeric) = 1.1691764055518906686211625109536
absolute error = 1e-31
relative error = 8.5530292541951040879634421588999e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.148
y[1] (analytic) = 1.1698571487214188437623411023315
y[1] (numeric) = 1.1698571487214188437623411023315
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.149
y[1] (analytic) = 1.1705379711254451015938090225373
y[1] (numeric) = 1.1705379711254451015938090225372
absolute error = 1e-31
relative error = 8.5430804012152053554745212267391e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 1.1712188727363150286268903479054
y[1] (numeric) = 1.1712188727363150286268903479053
absolute error = 1e-31
relative error = 8.5381137828124566845169473309408e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
memory used=22.8MB, alloc=4.1MB, time=2.06
TOP MAIN SOLVE Loop
x[1] = 0.151
y[1] (analytic) = 1.1718998535263967220905119652055
y[1] (numeric) = 1.1718998535263967220905119652054
absolute error = 1e-31
relative error = 8.5331523593152772321045077484615e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.152
y[1] (analytic) = 1.1725809134680807611501340895319
y[1] (numeric) = 1.1725809134680807611501340895318
absolute error = 1e-31
relative error = 8.5281961228786567051730065970526e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.153
y[1] (analytic) = 1.1732620525337801781768365911193
y[1] (numeric) = 1.1732620525337801781768365911193
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.154
y[1] (analytic) = 1.1739432706959304300664504696929
y[1] (numeric) = 1.1739432706959304300664504696928
absolute error = 1e-31
relative error = 8.5182991798844388692720476398411e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.155
y[1] (analytic) = 1.1746245679269893696086241103793
y[1] (numeric) = 1.1746245679269893696086241103792
absolute error = 1e-31
relative error = 8.5133584577140954774797948128212e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.156
y[1] (analytic) = 1.1753059441994372169057142497069
y[1] (numeric) = 1.1753059441994372169057142497068
absolute error = 1e-31
relative error = 8.5084228913787436935540190724381e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.157
y[1] (analytic) = 1.1759873994857765308413918737946
y[1] (numeric) = 1.1759873994857765308413918737945
absolute error = 1e-31
relative error = 8.5034924731104222710948719073512e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.158
y[1] (analytic) = 1.1766689337585321805988535634873
y[1] (numeric) = 1.1766689337585321805988535634872
absolute error = 1e-31
relative error = 8.4985671951564674253977963004130e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.159
y[1] (analytic) = 1.1773505469902513172285290929364
y[1] (numeric) = 1.1773505469902513172285290929363
absolute error = 1e-31
relative error = 8.4936470497794756370560720280396e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.1MB, time=2.43
x[1] = 0.16
y[1] (analytic) = 1.1780322391535033452651763789517
y[1] (numeric) = 1.1780322391535033452651763789517
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.161
y[1] (analytic) = 1.1787140102208798943942551683725
y[1] (numeric) = 1.1787140102208798943942551683725
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.162
y[1] (analytic) = 1.1793958601649947911674711397168
y[1] (numeric) = 1.1793958601649947911674711397168
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.163
y[1] (analytic) = 1.1800777889584840307673823834842
y[1] (numeric) = 1.1800777889584840307673823834842
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.164
y[1] (analytic) = 1.1807597965740057488209605126949
y[1] (numeric) = 1.180759796574005748820960512695
absolute error = 1e-31
relative error = 8.4691230418033937586174318744938e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.165
y[1] (analytic) = 1.1814418829842401932619989415693
y[1] (numeric) = 1.1814418829842401932619989415694
absolute error = 1e-31
relative error = 8.4642335302526215626148491224170e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.166
y[1] (analytic) = 1.1821240481618896962422611556721
y[1] (numeric) = 1.1821240481618896962422611556722
absolute error = 1e-31
relative error = 8.4593490975411732290483049456261e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.167
y[1] (analytic) = 1.1828062920796786460912620813829
y[1] (numeric) = 1.182806292079678646091262081383
absolute error = 1e-31
relative error = 8.4544697360524011297800864148847e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.168
y[1] (analytic) = 1.1834886147103534593245759462016
y[1] (numeric) = 1.1834886147103534593245759462017
absolute error = 1e-31
relative error = 8.4495954381845879343562673649608e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.169
y[1] (analytic) = 1.1841710160266825527005643041608
y[1] (numeric) = 1.184171016026682552700564304161
absolute error = 2e-31
relative error = 1.6889452392701820947497385613197e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.1MB, time=2.78
x[1] = 0.17
y[1] (analytic) = 1.1848534960014563153254181825059
y[1] (numeric) = 1.184853496001456315325418182506
absolute error = 1e-31
relative error = 8.4398620029794037081700491484886e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.171
y[1] (analytic) = 1.1855360546074870808064085868064
y[1] (numeric) = 1.1855360546074870808064085868065
absolute error = 1e-31
relative error = 8.4350028505129247986144907942547e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.172
y[1] (analytic) = 1.186218691817609099453239881802
y[1] (numeric) = 1.1862186918176090994532398818021
absolute error = 1e-31
relative error = 8.4301487314091172817776136392571e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.173
y[1] (analytic) = 1.1869014076046785105274008445452
y[1] (numeric) = 1.1869014076046785105274008445453
absolute error = 1e-31
relative error = 8.4252996381403753480108803334011e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.174
y[1] (analytic) = 1.1875842019415733145394084648024
y[1] (numeric) = 1.1875842019415733145394084648025
absolute error = 1e-31
relative error = 8.4204555631938082219669109254873e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.175
y[1] (analytic) = 1.188267074801193345593839845205
y[1] (numeric) = 1.188267074801193345593839845205
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.176
y[1] (analytic) = 1.1889500261564602437820478303121
y[1] (numeric) = 1.1889500261564602437820478303122
absolute error = 1e-31
relative error = 8.4107824382889974631343645688272e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.177
y[1] (analytic) = 1.1896330559803174276224562695611
y[1] (numeric) = 1.1896330559803174276224562695612
absolute error = 1e-31
relative error = 8.4059533733782283077999598360029e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.178
y[1] (analytic) = 1.1903161642457300665483310940344
y[1] (numeric) = 1.1903161642457300665483310940345
absolute error = 1e-31
relative error = 8.4011292968845123897649051480075e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.1MB, time=3.15
x[1] = 0.179
y[1] (analytic) = 1.1909993509256850534429236610809
y[1] (numeric) = 1.190999350925685053442923661081
absolute error = 1e-31
relative error = 8.3963102013680033851599454356908e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 1.1916826159931909772218830940816
y[1] (numeric) = 1.1916826159931909772218830940817
absolute error = 1e-31
relative error = 8.3914960794033584257195677508535e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.181
y[1] (analytic) = 1.19236595942127809546283461706
y[1] (numeric) = 1.1923659594212780954628346170601
absolute error = 1e-31
relative error = 8.3866869235797031887517035609200e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.182
y[1] (analytic) = 1.1930493811829983070820211554049
y[1] (numeric) = 1.193049381182998307082021155405
absolute error = 1e-31
relative error = 8.3818827265005970870960579232523e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.183
y[1] (analytic) = 1.193732881251425125057905744697
y[1] (numeric) = 1.1937328812514251250579057446971
absolute error = 1e-31
relative error = 8.3770834807839985587390105634742e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.184
y[1] (analytic) = 1.1944164595996536492016325595221
y[1] (numeric) = 1.1944164595996536492016325595221
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.185
y[1] (analytic) = 1.1951001162008005389742446432057
y[1] (numeric) = 1.1951001162008005389742446432057
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.186
y[1] (analytic) = 1.1957838510280039863505566876305
y[1] (numeric) = 1.1957838510280039863505566876306
absolute error = 1e-31
relative error = 8.3627153782040920309227207476675e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.187
y[1] (analytic) = 1.1964676640544236887295814796907
y[1] (numeric) = 1.1964676640544236887295814796907
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.188
y[1] (analytic) = 1.1971515552532408218914088975071
y[1] (numeric) = 1.1971515552532408218914088975072
absolute error = 1e-31
relative error = 8.3531612652707439166224494851863e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.1MB, time=3.51
x[1] = 0.189
y[1] (analytic) = 1.1978355245976580130004366052779
y[1] (numeric) = 1.197835524597658013000436605278
absolute error = 1e-31
relative error = 8.3483915735083148864997529778832e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 1.198519572060899313654851860562
y[1] (numeric) = 1.1985195720608993136548518605621
absolute error = 1e-31
relative error = 8.3436267818343803029643356027310e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.191
y[1] (analytic) = 1.1992036976162101729822641119094
y[1] (numeric) = 1.1992036976162101729822641119095
absolute error = 1e-31
relative error = 8.3388668829808530815113847808570e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.192
y[1] (analytic) = 1.1998879012368574107813883280455
y[1] (numeric) = 1.1998879012368574107813883280456
absolute error = 1e-31
relative error = 8.3341118696937371996902118725977e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.193
y[1] (analytic) = 1.2005721828961291907096792623069
y[1] (numeric) = 1.200572182896129190709679262307
absolute error = 1e-31
relative error = 8.3293617347330939652951765188355e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.194
y[1] (analytic) = 1.201256542567334993516817117702
y[1] (numeric) = 1.2012565425673349935168171177021
absolute error = 1e-31
relative error = 8.3246164708730083806422032339102e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.195
y[1] (analytic) = 1.2019409802238055903239453388463
y[1] (numeric) = 1.2019409802238055903239453388464
absolute error = 1e-31
relative error = 8.3198760709015556026135413433460e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.196
y[1] (analytic) = 1.2026254958388930159485615170905
y[1] (numeric) = 1.2026254958388930159485615170906
absolute error = 1e-31
relative error = 8.3151405276207674981546115178262e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.197
y[1] (analytic) = 1.2033100893859705422749626544348
y[1] (numeric) = 1.2033100893859705422749626544349
absolute error = 1e-31
relative error = 8.3104098338465992949079692939664e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.1MB, time=3.86
x[1] = 0.198
y[1] (analytic) = 1.2039947608384326516701462902951
y[1] (numeric) = 1.2039947608384326516701462902952
absolute error = 1e-31
relative error = 8.3056839824088963266705981159508e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.199
y[1] (analytic) = 1.2046795101696950104450692528708
y[1] (numeric) = 1.2046795101696950104450692528709
absolute error = 1e-31
relative error = 8.3009629661513608733619216032221e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 1.2053643373531944423611660537526
y[1] (numeric) = 1.2053643373531944423611660537527
absolute error = 1e-31
relative error = 8.2962467779315190951910969713868e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.201
y[1] (analytic) = 1.2060492423623889021820292005117
y[1] (numeric) = 1.2060492423623889021820292005118
absolute error = 1e-31
relative error = 8.2915354106206880607133188293019e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.202
y[1] (analytic) = 1.2067342251707574492701539573293
y[1] (numeric) = 1.2067342251707574492701539573294
absolute error = 1e-31
relative error = 8.2868288571039428684660249679102e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.203
y[1] (analytic) = 1.2074192857518002212286503382576
y[1] (numeric) = 1.2074192857518002212286503382577
absolute error = 1e-31
relative error = 8.2821271102800838618770532686036e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.204
y[1] (analytic) = 1.2081044240790384075878253714596
y[1] (numeric) = 1.2081044240790384075878253714597
absolute error = 1e-31
relative error = 8.2774301630616039371379515133794e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.205
y[1] (analytic) = 1.2087896401260142235365389257509
y[1] (numeric) = 1.208789640126014223536538925751
absolute error = 1e-31
relative error = 8.2727380083746559437367896984340e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.206
y[1] (analytic) = 1.2094749338662908836982366429694
y[1] (numeric) = 1.2094749338662908836982366429695
absolute error = 1e-31
relative error = 8.2680506391590201773459674595544e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.207
y[1] (analytic) = 1.2101603052734525759515637711297
y[1] (numeric) = 1.2101603052734525759515637711299
absolute error = 2e-31
relative error = 1.6526736096736143929523294868134e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.1MB, time=4.22
x[1] = 0.208
y[1] (analytic) = 1.2108457543211044352954639439812
y[1] (numeric) = 1.2108457543211044352954639439814
absolute error = 2e-31
relative error = 1.6517380457937498681185157664867e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.209
y[1] (analytic) = 1.2115312809828725177586672024823
y[1] (numeric) = 1.2115312809828725177586672024825
absolute error = 2e-31
relative error = 1.6508034347883041630794408389963e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 1.2122168852324037743534718028387
y[1] (numeric) = 1.212216885232403774353471802839
absolute error = 3e-31
relative error = 2.4748046628841059704907198863005e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.211
y[1] (analytic) = 1.2129025670433660250737246041205
y[1] (numeric) = 1.2129025670433660250737246041207
absolute error = 2e-31
relative error = 1.6489370657985359460943302734412e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.212
y[1] (analytic) = 1.2135883263894479329369050760871
y[1] (numeric) = 1.2135883263894479329369050760873
absolute error = 2e-31
relative error = 1.6480053050198735518249839284040e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.213
y[1] (analytic) = 1.2142741632443589780702182147076
y[1] (numeric) = 1.2142741632443589780702182147078
absolute error = 2e-31
relative error = 1.6470744915269374470293767386110e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.214
y[1] (analytic) = 1.2149600775818294318406018989639
y[1] (numeric) = 1.2149600775818294318406018989641
absolute error = 2e-31
relative error = 1.6461446239292557501309401838096e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.215
y[1] (analytic) = 1.2156460693756103310285544678818
y[1] (numeric) = 1.215646069375610331028554467882
absolute error = 2e-31
relative error = 1.6452157008390243772461693511693e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.216
y[1] (analytic) = 1.216332138599473452045688541338
y[1] (numeric) = 1.2163321385994734520456885413381
absolute error = 1e-31
relative error = 8.2214386043555036108610315101826e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.1MB, time=4.58
x[1] = 0.217
y[1] (analytic) = 1.2170182852272112851959173520527
y[1] (numeric) = 1.2170182852272112851959173520528
absolute error = 1e-31
relative error = 8.2168034132149867709516151661266e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.218
y[1] (analytic) = 1.2177045092326370089801800992967
y[1] (numeric) = 1.2177045092326370089801800992968
absolute error = 1e-31
relative error = 8.2121729238743786681353614884423e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.219
y[1] (analytic) = 1.2183908105895844644446130772175
y[1] (numeric) = 1.2183908105895844644446130772176
absolute error = 1e-31
relative error = 8.2075471294476997255754551822598e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 1.2190771892719081295720735723323
y[1] (numeric) = 1.2190771892719081295720735723324
absolute error = 1e-31
relative error = 8.2029260230621522424787837937666e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.221
y[1] (analytic) = 1.2197636452534830937169237656406
y[1] (numeric) = 1.2197636452534830937169237656407
absolute error = 1e-31
relative error = 8.1983095978580892365305594728316e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.222
y[1] (analytic) = 1.2204501785082050320829821149841
y[1] (numeric) = 1.2204501785082050320829821149842
absolute error = 1e-31
relative error = 8.1936978469889833739634246863157e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.223
y[1] (analytic) = 1.2211367890099901802445499327237
y[1] (numeric) = 1.2211367890099901802445499327238
absolute error = 1e-31
relative error = 8.1890907636213959869752504908989e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.224
y[1] (analytic) = 1.2218234767327753087104211125236
y[1] (numeric) = 1.2218234767327753087104211125237
absolute error = 1e-31
relative error = 8.1844883409349461782108960670311e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.225
y[1] (analytic) = 1.2225102416505176975307831970228
y[1] (numeric) = 1.2225102416505176975307831970229
absolute error = 1e-31
relative error = 8.1798905721222800120242539015435e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.226
y[1] (analytic) = 1.223197083737195110946918215446
y[1] (numeric) = 1.223197083737195110946918215446
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.2MB, time=4.94
x[1] = 0.227
y[1] (analytic) = 1.2238840029668057720836119567557
y[1] (numeric) = 1.2238840029668057720836119567558
absolute error = 1e-31
relative error = 8.1707089689538334261191658889956e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.228
y[1] (analytic) = 1.2245709993133683376841805797846
y[1] (numeric) = 1.2245709993133683376841805797847
absolute error = 1e-31
relative error = 8.1661251210482038742909151935291e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.229
y[1] (analytic) = 1.2252580727509218728880236969013
y[1] (numeric) = 1.2252580727509218728880236969014
absolute error = 1e-31
relative error = 8.1615458999165986862994989582388e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 1.2259452232535258260506133021762
y[1] (numeric) = 1.2259452232535258260506133021763
absolute error = 1e-31
relative error = 8.1569712988163396215594564309159e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.231
y[1] (analytic) = 1.226632450795260003605828148707
y[1] (numeric) = 1.226632450795260003605828148707
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.232
y[1] (analytic) = 1.2273197553502245449705434127573
y[1] (numeric) = 1.2273197553502245449705434127573
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.233
y[1] (analytic) = 1.228007136892539897491385714647
y[1] (numeric) = 1.228007136892539897491385714647
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.234
y[1] (analytic) = 1.2286945953963467914335637979161
y[1] (numeric) = 1.2286945953963467914335637979161
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.235
y[1] (analytic) = 1.2293821308358062150116853991695
y[1] (numeric) = 1.2293821308358062150116853991695
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.2MB, time=5.30
x[1] = 0.236
y[1] (analytic) = 1.2300697431850993894624710711956
y[1] (numeric) = 1.2300697431850993894624710711956
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.237
y[1] (analytic) = 1.2307574324184277441592759514452
y[1] (numeric) = 1.2307574324184277441592759514452
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.238
y[1] (analytic) = 1.2314451985100128917683306967536
y[1] (numeric) = 1.2314451985100128917683306967537
absolute error = 1e-31
relative error = 8.1205400062459132742455207113913e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.239
y[1] (analytic) = 1.2321330414340966034466130333025
y[1] (numeric) = 1.2321330414340966034466130333026
absolute error = 1e-31
relative error = 8.1160066841165645397825111271839e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 1.2328209611649407840812615982348
y[1] (numeric) = 1.2328209611649407840812615982349
absolute error = 1e-31
relative error = 8.1114779152932381659867770917633e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.241
y[1] (analytic) = 1.2335089576768274475704439760761
y[1] (numeric) = 1.2335089576768274475704439760762
absolute error = 1e-31
relative error = 8.1069536931728913455129517331991e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.242
y[1] (analytic) = 1.2341970309440586921455910591666
y[1] (numeric) = 1.2341970309440586921455910591667
absolute error = 1e-31
relative error = 8.1024340111649974917081246924421e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.243
y[1] (analytic) = 1.2348851809409566757349100866823
y[1] (numeric) = 1.2348851809409566757349100866824
absolute error = 1e-31
relative error = 8.0979188626915169445881328106856e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.244
y[1] (analytic) = 1.2355734076418635913680889415159
y[1] (numeric) = 1.235573407641863591368088941516
absolute error = 1e-31
relative error = 8.0934082411868677583991647740256e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.245
y[1] (analytic) = 1.2362617110211416426221045083093
y[1] (numeric) = 1.2362617110211416426221045083094
absolute error = 1e-31
relative error = 8.0889021400978965705012228896295e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.2MB, time=5.66
x[1] = 0.246
y[1] (analytic) = 1.2369500910531730191080481192722
y[1] (numeric) = 1.2369500910531730191080481192722
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.247
y[1] (analytic) = 1.2376385477123598719988813370951
y[1] (numeric) = 1.2376385477123598719988813370952
absolute error = 1e-31
relative error = 8.0799034730163434350423159735309e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.248
y[1] (analytic) = 1.2383270809731242895980355462716
y[1] (numeric) = 1.2383270809731242895980355462717
absolute error = 1e-31
relative error = 8.0754108939793366309845383458246e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.249
y[1] (analytic) = 1.2390156908099082729487690454794
y[1] (numeric) = 1.2390156908099082729487690454795
absolute error = 1e-31
relative error = 8.0709228092691004150577266458651e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 1.2397043771971737114841955543462
y[1] (numeric) = 1.2397043771971737114841955543463
absolute error = 1e-31
relative error = 8.0664392123941902013874928160453e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.251
y[1] (analytic) = 1.2403931401094023587178982679372
y[1] (numeric) = 1.2403931401094023587178982679373
absolute error = 1e-31
relative error = 8.0619600968754168936408772543494e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.252
y[1] (analytic) = 1.2410819795210958079750438116511
y[1] (numeric) = 1.2410819795210958079750438116513
absolute error = 2e-31
relative error = 1.6114970912491636631733608925018e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.253
y[1] (analytic) = 1.2417708954067754681639106679091
y[1] (numeric) = 1.2417708954067754681639106679093
absolute error = 2e-31
relative error = 1.6106030568101261445170490387817e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.254
y[1] (analytic) = 1.2424598877409825395877468640566
y[1] (numeric) = 1.2424598877409825395877468640567
absolute error = 1e-31
relative error = 8.0485495738472603878701954644021e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.2MB, time=6.02
x[1] = 0.255
y[1] (analytic) = 1.2431489564982779897968719282862
y[1] (numeric) = 1.2431489564982779897968719282864
absolute error = 2e-31
relative error = 1.6088176638410510546345030521061e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.256
y[1] (analytic) = 1.2438381016532425294809383371257
y[1] (numeric) = 1.2438381016532425294809383371259
absolute error = 2e-31
relative error = 1.6079263027412553547259196855741e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.257
y[1] (analytic) = 1.2445273231804765884012678941185
y[1] (numeric) = 1.2445273231804765884012678941187
absolute error = 2e-31
relative error = 1.6070358301888143085219540129611e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.258
y[1] (analytic) = 1.245216621054600291363178694769
y[1] (numeric) = 1.2452166210546002913631786947692
absolute error = 2e-31
relative error = 1.6061462449048886788480457602080e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.259
y[1] (analytic) = 1.2459059952502534342282185476181
y[1] (numeric) = 1.2459059952502534342282185476184
absolute error = 3e-31
relative error = 2.4078863184195675851004805869116e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 1.2465954457420954599662209354707
y[1] (numeric) = 1.246595445742095459966220935471
absolute error = 3e-31
relative error = 2.4065545965588754094419285311587e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.261
y[1] (analytic) = 1.2472849725048054347470998143103
y[1] (numeric) = 1.2472849725048054347470998143106
absolute error = 3e-31
relative error = 2.4052241998677987375939382059262e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.262
y[1] (analytic) = 1.2479745755130820240722997603158
y[1] (numeric) = 1.2479745755130820240722997603161
absolute error = 3e-31
relative error = 2.4038951264424634795683749221340e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.263
y[1] (analytic) = 1.2486642547416434689458181876344
y[1] (numeric) = 1.2486642547416434689458181876347
absolute error = 3e-31
relative error = 2.4025673743825708957044139444436e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.264
y[1] (analytic) = 1.2493540101652275620847165711768
y[1] (numeric) = 1.249354010165227562084716571177
absolute error = 2e-31
relative error = 1.6008272945275928708201235042958e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.2MB, time=6.38
x[1] = 0.265
y[1] (analytic) = 1.2500438417585916241690378196762
y[1] (numeric) = 1.2500438417585916241690378196765
absolute error = 3e-31
relative error = 2.3999158267757458236996407496590e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.266
y[1] (analytic) = 1.2507337494965124801310471546051
y[1] (numeric) = 1.2507337494965124801310471546053
absolute error = 2e-31
relative error = 1.5990613516306787388209728521002e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.267
y[1] (analytic) = 1.251423733353786435483714060262
y[1] (numeric) = 1.2514237333537864354837140602622
absolute error = 2e-31
relative error = 1.5981796946107507636513808912603e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.268
y[1] (analytic) = 1.2521137933052292526883530794448
y[1] (numeric) = 1.252113793305229252688353079445
absolute error = 2e-31
relative error = 1.5972989122023493648301002349248e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.269
y[1] (analytic) = 1.2528039293256761275613414375964
y[1] (numeric) = 1.2528039293256761275613414375966
absolute error = 2e-31
relative error = 1.5964190031527945831401211487583e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 1.2534941413899816657198316861694
y[1] (numeric) = 1.2534941413899816657198316861696
absolute error = 2e-31
relative error = 1.5955399662117516560886558801739e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.271
y[1] (analytic) = 1.2541844294730198590663777631917
y[1] (numeric) = 1.2541844294730198590663777631919
absolute error = 2e-31
relative error = 1.5946618001312255966808781066607e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.272
y[1] (analytic) = 1.2548747935496840623123930756359
y[1] (numeric) = 1.2548747935496840623123930756361
absolute error = 2e-31
relative error = 1.5937845036655557871059859295899e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.273
y[1] (analytic) = 1.255565233594886969540359414205
y[1] (numeric) = 1.2555652335948869695403594142052
absolute error = 2e-31
relative error = 1.5929080755714105872880264263223e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.2MB, time=6.73
x[1] = 0.274
y[1] (analytic) = 1.2562557495835605908047057165415
y[1] (numeric) = 1.2562557495835605908047057165417
absolute error = 2e-31
relative error = 1.5920325146077819582540923173320e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.275
y[1] (analytic) = 1.2569463414906562287712758996526
y[1] (numeric) = 1.2569463414906562287712758996528
absolute error = 2e-31
relative error = 1.5911578195359801002726731474413e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.276
y[1] (analytic) = 1.257637009291144455395305186524
y[1] (numeric) = 1.2576370092911444553953051865242
absolute error = 2e-31
relative error = 1.5902839891196281057151145242847e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.277
y[1] (analytic) = 1.2583277529600150886378245554674
y[1] (numeric) = 1.2583277529600150886378245554677
absolute error = 3e-31
relative error = 2.3841165331869849398899641089013e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.278
y[1] (analytic) = 1.2590185724722771692204131437156
y[1] (numeric) = 1.2590185724722771692204131437159
absolute error = 3e-31
relative error = 2.3828083759789478350903727795236e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.279
y[1] (analytic) = 1.2597094678029589374182186391469
y[1] (numeric) = 1.2597094678029589374182186391472
absolute error = 3e-31
relative error = 2.3815015102111255927403390926115e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 1.2604004389271078098911658957906
y[1] (numeric) = 1.2604004389271078098911658957909
absolute error = 3e-31
relative error = 2.3801959340427504361734978142455e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.281
y[1] (analytic) = 1.2610914858197903565532742099348
y[1] (numeric) = 1.2610914858197903565532742099351
absolute error = 3e-31
relative error = 2.3788916456364841521565435156001e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.282
y[1] (analytic) = 1.2617826084560922774800038942346
y[1] (numeric) = 1.2617826084560922774800038942349
absolute error = 3e-31
relative error = 2.3775886431584102012216738463880e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.283
y[1] (analytic) = 1.2624738068111183798535529872006
y[1] (numeric) = 1.2624738068111183798535529872009
absolute error = 3e-31
relative error = 2.3762869247780258495968081376295e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.2MB, time=7.10
x[1] = 0.284
y[1] (analytic) = 1.2631650808599925549460251348393
y[1] (numeric) = 1.2631650808599925549460251348396
absolute error = 3e-31
relative error = 2.3749864886682343226650282265537e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.285
y[1] (analytic) = 1.263856430577857755140389880019
y[1] (numeric) = 1.2638564305778577551403898800193
absolute error = 3e-31
relative error = 2.3736873330053369798849358941047e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.286
y[1] (analytic) = 1.264547855939875970989156793349
y[1] (numeric) = 1.2645478559398759709891567933493
absolute error = 3e-31
relative error = 2.3723894559690255111038678017885e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.287
y[1] (analytic) = 1.2652393569212282083106850769888
y[1] (numeric) = 1.2652393569212282083106850769891
absolute error = 3e-31
relative error = 2.3710928557423741541961543139277e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.288
y[1] (analytic) = 1.265930933497114465323050469851
y[1] (numeric) = 1.2659309334971144653230504698513
absolute error = 3e-31
relative error = 2.3697975305118319339588530982650e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.289
y[1] (analytic) = 1.266622585642753709815391479126
y[1] (numeric) = 1.2666225856427537098153914791263
absolute error = 3e-31
relative error = 2.3685034784672149221976319167204e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 1.2673143133333838563566571589405
y[1] (numeric) = 1.2673143133333838563566571589407
absolute error = 2e-31
relative error = 1.5781404652011323459571450355827e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.291
y[1] (analytic) = 1.268006116544261743541678852271
y[1] (numeric) = 1.2680061165442617435416788522712
absolute error = 2e-31
relative error = 1.5772794578078731697860462552164e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.292
y[1] (analytic) = 1.2686979952506631112744885069661
y[1] (numeric) = 1.2686979952506631112744885069663
absolute error = 2e-31
relative error = 1.5764192955982797424474511088894e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.2MB, time=7.45
x[1] = 0.293
y[1] (analytic) = 1.2693899494278825780888063708884
y[1] (numeric) = 1.2693899494278825780888063708886
absolute error = 2e-31
relative error = 1.5755599773744902520474121666536e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.294
y[1] (analytic) = 1.2700819790512336185056210647754
y[1] (numeric) = 1.2700819790512336185056210647756
absolute error = 2e-31
relative error = 1.5747015019408619953258413784847e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.295
y[1] (analytic) = 1.2707740840960485404277852244368
y[1] (numeric) = 1.270774084096048540427785224437
absolute error = 2e-31
relative error = 1.5738438681039663015408129114651e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.296
y[1] (analytic) = 1.2714662645376784625715500963538
y[1] (numeric) = 1.271466264537678462571550096354
absolute error = 2e-31
relative error = 1.5729870746725834701699370075461e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.297
y[1] (analytic) = 1.2721585203514932919349626626315
y[1] (numeric) = 1.2721585203514932919349626626316
absolute error = 1e-31
relative error = 7.8606556022884886119259827104198e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.298
y[1] (analytic) = 1.2728508515128817013030490625742
y[1] (numeric) = 1.2728508515128817013030490625743
absolute error = 1e-31
relative error = 7.8563800213624608312889725605424e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.299
y[1] (analytic) = 1.2735432579972511067897082689142
y[1] (numeric) = 1.2735432579972511067897082689143
absolute error = 1e-31
relative error = 7.8521086246617188782485830110266e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 1.2742357397800276454162401669183
y[1] (numeric) = 1.2742357397800276454162401669184
absolute error = 1e-31
relative error = 7.8478414062740919137443413389558e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.301
y[1] (analytic) = 1.2749282968366561527264323742409
y[1] (numeric) = 1.274928296836656152726432374241
absolute error = 1e-31
relative error = 7.8435783602983284210240022160570e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.302
y[1] (analytic) = 1.275620929142600140438130328472
y[1] (numeric) = 1.2756209291426001404381303284721
absolute error = 1e-31
relative error = 7.8393194808440713041109601414549e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.2MB, time=7.82
x[1] = 0.303
y[1] (analytic) = 1.2763136366733417741312153578603
y[1] (numeric) = 1.2763136366733417741312153578603
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.304
y[1] (analytic) = 1.2770064194043818509719156386655
y[1] (numeric) = 1.2770064194043818509719156386655
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.305
y[1] (analytic) = 1.2776992773112397774733751300222
y[1] (numeric) = 1.2776992773112397774733751300222
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.306
y[1] (analytic) = 1.2783922103694535472924057640721
y[1] (numeric) = 1.2783922103694535472924057640721
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.307
y[1] (analytic) = 1.279085218554579719062348355452
y[1] (numeric) = 1.279085218554579719062348355452
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.308
y[1] (analytic) = 1.2797783018421933942619678800099
y[1] (numeric) = 1.2797783018421933942619678800099
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.309
y[1] (analytic) = 1.2804714602078881951203089578621
y[1] (numeric) = 1.2804714602078881951203089578621
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 1.2811646936272762425574375606039
y[1] (numeric) = 1.281164693627276242557437560604
absolute error = 1e-31
relative error = 7.8053977367169448183082794045992e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.311
y[1] (analytic) = 1.2818580020759881341609951466463
y[1] (numeric) = 1.2818580020759881341609951466464
absolute error = 1e-31
relative error = 7.8011760926755155400248654199778e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.312
y[1] (analytic) = 1.2825513855296729221984916122726
y[1] (numeric) = 1.2825513855296729221984916122727
absolute error = 1e-31
relative error = 7.7969585568457845273271131598811e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
memory used=87.7MB, alloc=4.2MB, time=8.17
TOP MAIN SOLVE Loop
x[1] = 0.313
y[1] (analytic) = 1.2832448439639980916652636290957
y[1] (numeric) = 1.2832448439639980916652636290959
absolute error = 2e-31
relative error = 1.5585490246911217974253731268210e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.314
y[1] (analytic) = 1.2839383773546495383680251211478
y[1] (numeric) = 1.283938377354649538368025121148
absolute error = 2e-31
relative error = 1.5577071573486893878659401099838e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.315
y[1] (analytic) = 1.2846319856773315470439368168513
y[1] (numeric) = 1.2846319856773315470439368168515
absolute error = 2e-31
relative error = 1.5568661081916666354825855626058e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.316
y[1] (analytic) = 1.2853256689077667695151219926121
y[1] (numeric) = 1.2853256689077667695151219926123
absolute error = 2e-31
relative error = 1.5560258760719710587746616686071e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.317
y[1] (analytic) = 1.2860194270216962028785557057307
y[1] (numeric) = 1.2860194270216962028785557057309
absolute error = 2e-31
relative error = 1.5551864598436259540683049612417e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.318
y[1] (analytic) = 1.2867132599948791677312549947625
y[1] (numeric) = 1.2867132599948791677312549947627
absolute error = 2e-31
relative error = 1.5543478583627556264322314436680e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.319
y[1] (analytic) = 1.2874071678030932864306977053628
y[1] (numeric) = 1.287407167803093286430697705363
absolute error = 2e-31
relative error = 1.5535100704875806334461271678463e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 1.288101150422134461390397779036
y[1] (numeric) = 1.2881011504221344613903977790363
absolute error = 3e-31
relative error = 2.3290096426176195626722081142284e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.321
y[1] (analytic) = 1.2887952078278168534105650210692
y[1] (numeric) = 1.2887952078278168534105650210695
absolute error = 3e-31
relative error = 2.3277553964964775448321664885314e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.2MB, time=8.54
x[1] = 0.322
y[1] (analytic) = 1.2894893399959728600437775422702
y[1] (numeric) = 1.2894893399959728600437775422705
absolute error = 3e-31
relative error = 2.3265023656646662551200417433525e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.323
y[1] (analytic) = 1.2901835469024530939955952469539
y[1] (numeric) = 1.2901835469024530939955952469542
absolute error = 3e-31
relative error = 2.3252505484220230849708810374681e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.324
y[1] (analytic) = 1.2908778285231263615600429169253
y[1] (numeric) = 1.2908778285231263615600429169256
absolute error = 3e-31
relative error = 2.3239999430714944199314749205046e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.325
y[1] (analytic) = 1.2915721848338796410898916179975
y[1] (numeric) = 1.2915721848338796410898916179978
absolute error = 3e-31
relative error = 2.3227505479191286197286577089917e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.326
y[1] (analytic) = 1.2922666158106180615016673318623
y[1] (numeric) = 1.2922666158106180615016673318626
absolute error = 3e-31
relative error = 2.3215023612740690171992648654824e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.327
y[1] (analytic) = 1.2929611214292648808153158918937
y[1] (numeric) = 1.292961121429264880815315891894
absolute error = 3e-31
relative error = 2.3202553814485469360229851703227e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.328
y[1] (analytic) = 1.2936557016657614647284534767233
y[1] (numeric) = 1.2936557016657614647284534767236
absolute error = 3e-31
relative error = 2.3190096067578747271995537068278e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.329
y[1] (analytic) = 1.294350356496067265225132090172
y[1] (numeric) = 1.2943503564960672652251320901723
absolute error = 3e-31
relative error = 2.3177650355204388242119390848293e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 1.295045085896159799219049630365
y[1] (numeric) = 1.2950450858961597992190496303653
absolute error = 3e-31
relative error = 2.3165216660576928168173849084140e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.331
y[1] (analytic) = 1.295739889842034627231134324592
y[1] (numeric) = 1.2957398898420346272311343245923
absolute error = 3e-31
relative error = 2.3152794966941505434083712548184e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
memory used=95.3MB, alloc=4.2MB, time=8.91
TOP MAIN SOLVE Loop
x[1] = 0.332
y[1] (analytic) = 1.2964347683097053321014334797088
y[1] (numeric) = 1.2964347683097053321014334797091
absolute error = 3e-31
relative error = 2.3140385257573792018857668764575e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.333
y[1] (analytic) = 1.297129721275203497735236670608
y[1] (numeric) = 1.2971297212752034977352366706083
absolute error = 3e-31
relative error = 2.3127987515779924789866469705590e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.334
y[1] (analytic) = 1.297824748714578687883363661518
y[1] (numeric) = 1.2978247487145786878833636615183
absolute error = 3e-31
relative error = 2.3115601724896436980094546843924e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.335
y[1] (analytic) = 1.2985198506038984249565475266234
y[1] (numeric) = 1.2985198506038984249565475266236
absolute error = 2e-31
relative error = 1.5402151912193459899195913614630e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.336
y[1] (analytic) = 1.2992150269192481688738436077372
y[1] (numeric) = 1.2992150269192481688738436077374
absolute error = 2e-31
relative error = 1.5393910619572203016647251307446e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.337
y[1] (analytic) = 1.2999102776367312959449951174991
y[1] (numeric) = 1.2999102776367312959449951174993
absolute error = 2e-31
relative error = 1.5385677261018729355426198809247e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.338
y[1] (analytic) = 1.3006056027324690777866863668207
y[1] (numeric) = 1.3006056027324690777866863668208
absolute error = 1e-31
relative error = 7.6887259127523318335912419962561e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.339
y[1] (analytic) = 1.3013010021826006602726147650581
y[1] (numeric) = 1.3013010021826006602726147650582
absolute error = 1e-31
relative error = 7.6846171510108341823002468663105e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 1.3019964759632830425173129106615
y[1] (numeric) = 1.3019964759632830425173129106616
absolute error = 1e-31
relative error = 7.6805123397906992837554720390223e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.2MB, time=9.27
x[1] = 0.341
y[1] (analytic) = 1.3026920240506910558936522588267
y[1] (numeric) = 1.3026920240506910558936522588268
absolute error = 1e-31
relative error = 7.6764114736077286345069977386231e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.342
y[1] (analytic) = 1.3033876464210173430839600209711
y[1] (numeric) = 1.3033876464210173430839600209712
absolute error = 1e-31
relative error = 7.6723145469876753106211600510395e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.343
y[1] (analytic) = 1.3040833430504723371646811186614
y[1] (numeric) = 1.3040833430504723371646811186615
absolute error = 1e-31
relative error = 7.6682215544662216701969681557478e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.344
y[1] (analytic) = 1.3047791139152842407245171819456
y[1] (numeric) = 1.3047791139152842407245171819457
absolute error = 1e-31
relative error = 7.6641324905889571153329640709543e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.345
y[1] (analytic) = 1.3054749589916990050159747488845
y[1] (numeric) = 1.3054749589916990050159747488846
absolute error = 1e-31
relative error = 7.6600473499113559133607327071080e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.346
y[1] (analytic) = 1.3061708782559803091402549894398
y[1] (numeric) = 1.3061708782559803091402549894399
absolute error = 1e-31
relative error = 7.6559661269987550771619163173833e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.347
y[1] (analytic) = 1.3068668716844095392654174427593
y[1] (numeric) = 1.3068668716844095392654174427595
absolute error = 2e-31
relative error = 1.5303777632852664608772462360720e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.348
y[1] (analytic) = 1.3075629392532857678777504223066
y[1] (numeric) = 1.3075629392532857678777504223068
absolute error = 2e-31
relative error = 1.5295630825558167950777251121594e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.349
y[1] (analytic) = 1.3082590809389257330662809082126
y[1] (numeric) = 1.3082590809389257330662809082128
absolute error = 2e-31
relative error = 1.5287491821303606419408713360434e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = 1.3089552967176638178403569106841
y[1] (numeric) = 1.3089552967176638178403569106842
absolute error = 1e-31
relative error = 7.6396803046490579808814006009853e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
memory used=103.0MB, alloc=4.2MB, time=9.63
TOP MAIN SOLVE Loop
x[1] = 0.351
y[1] (analytic) = 1.3096515865658520294802354522885
y[1] (numeric) = 1.3096515865658520294802354522886
absolute error = 1e-31
relative error = 7.6356185893851692894902425966730e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.352
y[1] (analytic) = 1.310347950459859978920609480448
y[1] (numeric) = 1.3103479504598599789206094804481
absolute error = 1e-31
relative error = 7.6315607594841893941317267585840e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.353
y[1] (analytic) = 1.3110443883760748601670071845194
y[1] (numeric) = 1.3110443883760748601670071845195
absolute error = 1e-31
relative error = 7.6275068095798801002642722843537e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.354
y[1] (analytic) = 1.3117409002909014297449973544145
y[1] (numeric) = 1.3117409002909014297449973544146
absolute error = 1e-31
relative error = 7.6234567343156911066723901201737e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.355
y[1] (analytic) = 1.312437486180761986182134579825
y[1] (numeric) = 1.3124374861807619861821345798251
absolute error = 1e-31
relative error = 7.6194105283447384093990573943209e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.356
y[1] (analytic) = 1.3131341460220963495225782507613
y[1] (numeric) = 1.3131341460220963495225782507614
absolute error = 1e-31
relative error = 7.6153681863297827629651283969124e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.357
y[1] (analytic) = 1.3138308797913618408743194812988
y[1] (numeric) = 1.3138308797913618408743194812989
absolute error = 1e-31
relative error = 7.6113297029432081986995797398232e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.358
y[1] (analytic) = 1.3145276874650332619889502391439
y[1] (numeric) = 1.314527687465033261988950239144
absolute error = 1e-31
relative error = 7.6072950728670006000050037821232e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.359
y[1] (analytic) = 1.3152245690196028748739091238953
y[1] (numeric) = 1.3152245690196028748739091238954
absolute error = 1e-31
relative error = 7.6032642907927263343833784407045e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.2MB, time=9.99
x[1] = 0.36
y[1] (analytic) = 1.3159215244315803814371383966764
y[1] (numeric) = 1.3159215244315803814371383966765
absolute error = 1e-31
relative error = 7.5992373514215109420477531335459e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.361
y[1] (analytic) = 1.316618553677492903164087023161
y[1] (numeric) = 1.3166185536774929031640870231611
absolute error = 1e-31
relative error = 7.5952142494640178809460998346796e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.362
y[1] (analytic) = 1.317315656733884960826994650903
y[1] (numeric) = 1.3173156567338849608269946509031
absolute error = 1e-31
relative error = 7.5911949796404273280241850658349e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.363
y[1] (analytic) = 1.318012833577318454226391600318
y[1] (numeric) = 1.3180128335773184542263916003181
absolute error = 1e-31
relative error = 7.5871795366804150365549231202430e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.364
y[1] (analytic) = 1.3187100841843726419647501066459
y[1] (numeric) = 1.318710084184372641964750106646
absolute error = 1e-31
relative error = 7.5831679153231312493622729195295e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.365
y[1] (analytic) = 1.319407408531644121252222207756
y[1] (numeric) = 1.3194074085316441212522222077561
absolute error = 1e-31
relative error = 7.5791601103171796677683406552238e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.366
y[1] (analytic) = 1.3201048065957468077443998297385
y[1] (numeric) = 1.3201048065957468077443998297386
absolute error = 1e-31
relative error = 7.5751561164205964760929477723802e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.367
y[1] (analytic) = 1.3208022783533119154120327788604
y[1] (numeric) = 1.3208022783533119154120327788604
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.368
y[1] (analytic) = 1.3214998237809879364426405046496
y[1] (numeric) = 1.3214998237809879364426405046496
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.369
y[1] (analytic) = 1.3221974428554406211739536546161
y[1] (numeric) = 1.3221974428554406211739536546161
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
memory used=110.6MB, alloc=4.3MB, time=10.35
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 1.3228951355533529580591215964133
y[1] (numeric) = 1.3228951355533529580591215964132
absolute error = 1e-31
relative error = 7.5591781474176382178853346158170e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.371
y[1] (analytic) = 1.3235929018514251536636222381021
y[1] (numeric) = 1.3235929018514251536636222381021
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.372
y[1] (analytic) = 1.3242907417263746126938106315943
y[1] (numeric) = 1.3242907417263746126938106315943
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.373
y[1] (analytic) = 1.3249886551549359180570429983252
y[1] (numeric) = 1.3249886551549359180570429983251
absolute error = 1e-31
relative error = 7.5472344318530503225396464440830e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.374
y[1] (analytic) = 1.3256866421138608109533129697468
y[1] (numeric) = 1.3256866421138608109533129697467
absolute error = 1e-31
relative error = 7.5432607392457366369066826129869e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.375
y[1] (analytic) = 1.3263847025799181709983369883317
y[1] (numeric) = 1.3263847025799181709983369883316
absolute error = 1e-31
relative error = 7.5392908109911450579030022538775e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.376
y[1] (analytic) = 1.3270828365298939963780259674428
y[1] (numeric) = 1.3270828365298939963780259674427
absolute error = 1e-31
relative error = 7.5353246419404950479491647174456e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.377
y[1] (analytic) = 1.327781043940591384034280460659
y[1] (numeric) = 1.3277810439405913840342804606588
absolute error = 2e-31
relative error = 1.5062724453908422880361363300955e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.378
y[1] (analytic) = 1.3284793247888305098820467429434
y[1] (numeric) = 1.3284793247888305098820467429432
absolute error = 2e-31
relative error = 1.5054807121803808232947427765942e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.3MB, time=10.71
x[1] = 0.379
y[1] (analytic) = 1.3291776790514486090575713574133
y[1] (numeric) = 1.3291776790514486090575713574131
absolute error = 2e-31
relative error = 1.5046897277324695477713846619003e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 1.3298761067052999561977918324065
y[1] (numeric) = 1.3298761067052999561977918324063
absolute error = 2e-31
relative error = 1.5038994910246923068293724836611e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.381
y[1] (analytic) = 1.3305746077272558457508014240532
y[1] (numeric) = 1.3305746077272558457508014240529
absolute error = 3e-31
relative error = 2.2546650015546867394934542649281e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.382
y[1] (analytic) = 1.3312731820942045723173258896451
y[1] (numeric) = 1.3312731820942045723173258896448
absolute error = 3e-31
relative error = 2.2534818851234935361201469619097e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.383
y[1] (analytic) = 1.3319718297830514110231504467548
y[1] (numeric) = 1.3319718297830514110231504467545
absolute error = 3e-31
relative error = 2.2522998857180284977642851394775e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.384
y[1] (analytic) = 1.3326705507707185979224352222904
y[1] (numeric) = 1.3326705507707185979224352222901
absolute error = 3e-31
relative error = 2.2511190018155805417656628303732e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.385
y[1] (analytic) = 1.3333693450341453104318576444875
y[1] (numeric) = 1.3333693450341453104318576444872
absolute error = 3e-31
relative error = 2.2499392318961518696637581312300e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.386
y[1] (analytic) = 1.3340682125502876477955203792281
y[1] (numeric) = 1.3340682125502876477955203792277
absolute error = 4e-31
relative error = 2.9983474325899359965008644685204e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.387
y[1] (analytic) = 1.3347671532961186115805635600503
y[1] (numeric) = 1.33476715329611861158056356005
absolute error = 3e-31
relative error = 2.2475830279398918010041862666266e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.388
y[1] (analytic) = 1.335466167248628086203420208766
y[1] (numeric) = 1.3354661672486280862034202087657
absolute error = 3e-31
relative error = 2.2464065908765775782289862808670e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.3MB, time=11.07
x[1] = 0.389
y[1] (analytic) = 1.3361652543848228194866538907371
y[1] (numeric) = 1.3361652543848228194866538907368
absolute error = 3e-31
relative error = 2.2452312617433051252329331549874e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 1.3368644146817264032463177955853
y[1] (numeric) = 1.336864414681726403246317795585
absolute error = 3e-31
relative error = 2.2440570390335538291170891835458e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.391
y[1] (analytic) = 1.3375636481163792539097745804138
y[1] (numeric) = 1.3375636481163792539097745804134
absolute error = 4e-31
relative error = 2.9905118949913077010093843876469e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.392
y[1] (analytic) = 1.338262954665838593163916458512
y[1] (numeric) = 1.3382629546658385931639164585116
absolute error = 4e-31
relative error = 2.9889492091625531640718233046960e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.393
y[1] (analytic) = 1.3389623343071784286337251619986
y[1] (numeric) = 1.3389623343071784286337251619982
absolute error = 4e-31
relative error = 2.9873879925604679860441965274615e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.394
y[1] (analytic) = 1.3396617870174895345911115519247
y[1] (numeric) = 1.3396617870174895345911115519243
absolute error = 4e-31
relative error = 2.9858282431905921443272460107864e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.395
y[1] (analytic) = 1.3403613127738794326939747940252
y[1] (numeric) = 1.3403613127738794326939747940249
absolute error = 3e-31
relative error = 2.2382024692965034959219774446706e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.396
y[1] (analytic) = 1.3410609115534723727554211625573
y[1] (numeric) = 1.3410609115534723727554211625569
absolute error = 4e-31
relative error = 2.9827131381873158497859594163366e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.397
y[1] (analytic) = 1.3417605833334093135430826785133
y[1] (numeric) = 1.341760583333409313543082678513
absolute error = 3e-31
relative error = 2.2358683339369946848478486368254e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.3MB, time=11.43
x[1] = 0.398
y[1] (analytic) = 1.3424603280908479036084759319405
y[1] (numeric) = 1.3424603280908479036084759319402
absolute error = 3e-31
relative error = 2.2347029087007641730153028294198e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.399
y[1] (analytic) = 1.3431601458029624621463415811339
y[1] (numeric) = 1.3431601458029624621463415811336
absolute error = 3e-31
relative error = 2.2335385764491637483447997126112e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 1.3438600364469439598839051641098
y[1] (numeric) = 1.3438600364469439598839051641096
absolute error = 2e-31
relative error = 1.4882502238014581093444081138903e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.401
y[1] (analytic) = 1.34456
y[1] (numeric) = 1.3445599999999999999999999999998
absolute error = 2e-31
relative error = 1.4874754566549651930743142738145e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.402
y[1] (analytic) = 1.3452600364393547990739930998413
y[1] (numeric) = 1.3452600364393547990739930998411
absolute error = 2e-31
relative error = 1.4867014152101152571794220921651e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.403
y[1] (analytic) = 1.3459601457422491680644551476744
y[1] (numeric) = 1.3459601457422491680644551476742
absolute error = 2e-31
relative error = 1.4859280984854652624915321202184e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.404
y[1] (analytic) = 1.3466603278859404933175157539028
y[1] (numeric) = 1.3466603278859404933175157539027
absolute error = 1e-31
relative error = 7.4257775275065357992199448401484e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.405
y[1] (analytic) = 1.3473605828477027176048453235069
y[1] (numeric) = 1.3473605828477027176048453235068
absolute error = 1e-31
relative error = 7.4219181763983205143419773321750e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.406
y[1] (analytic) = 1.3480609106048263211912050219563
y[1] (numeric) = 1.3480609106048263211912050219562
absolute error = 1e-31
relative error = 7.4180624342214333531436462875130e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.407
y[1] (analytic) = 1.34876131113461830293150646152
y[1] (numeric) = 1.3487613111346183029315064615199
absolute error = 1e-31
relative error = 7.4142102961032455003161631140308e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.3MB, time=11.79
x[1] = 0.408
y[1] (analytic) = 1.3494617844144021613973228701345
y[1] (numeric) = 1.3494617844144021613973228701345
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.409
y[1] (analytic) = 1.350162330421517876032793644064
y[1] (numeric) = 1.350162330421517876032793644064
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 1.3508629491333218883398643242667
y[1] (numeric) = 1.3508629491333218883398643242667
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.411
y[1] (analytic) = 1.3515636405271870830928041746783
y[1] (numeric) = 1.3515636405271870830928041746782
absolute error = 1e-31
relative error = 7.3988376870655001798352825658508e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.412
y[1] (analytic) = 1.3522644045805027695819436785256
y[1] (numeric) = 1.3522644045805027695819436785255
absolute error = 1e-31
relative error = 7.3950034964517042698416163139299e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.413
y[1] (analytic) = 1.3529652412706746628865744063092
y[1] (numeric) = 1.3529652412706746628865744063091
absolute error = 1e-31
relative error = 7.3911728808407700786912038447339e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.414
y[1] (analytic) = 1.3536661505751248651769538462248
y[1] (numeric) = 1.3536661505751248651769538462247
absolute error = 1e-31
relative error = 7.3873458354198734469267875292212e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.415
y[1] (analytic) = 1.3543671324712918470453579245486
y[1] (numeric) = 1.3543671324712918470453579245485
absolute error = 1e-31
relative error = 7.3835223553846595499262840611748e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.416
y[1] (analytic) = 1.3550681869366304288661240798815
y[1] (numeric) = 1.3550681869366304288661240798815
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.3MB, time=12.15
x[1] = 0.417
y[1] (analytic) = 1.355769313948611762184627891135
y[1] (numeric) = 1.355769313948611762184627891135
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.418
y[1] (analytic) = 1.3564705134847233111351363947518
y[1] (numeric) = 1.3564705134847233111351363947518
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.419
y[1] (analytic) = 1.3571717855224688338874813618851
y[1] (numeric) = 1.3571717855224688338874813618851
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 1.3578731300393683641224959411132
y[1] (numeric) = 1.3578731300393683641224959411131
absolute error = 1e-31
relative error = 7.3644582684319508740285957366140e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.421
y[1] (analytic) = 1.3585745470129581925361582067434
y[1] (numeric) = 1.3585745470129581925361582067434
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.422
y[1] (analytic) = 1.3592760364207908483723852868626
y[1] (numeric) = 1.3592760364207908483723852868626
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.423
y[1] (analytic) = 1.3599775982404350809844218790175
y[1] (numeric) = 1.3599775982404350809844218790175
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.424
y[1] (analytic) = 1.3606792324494758414247670947673
y[1] (numeric) = 1.3606792324494758414247670947673
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.425
y[1] (analytic) = 1.3613809390255142640635837073331
y[1] (numeric) = 1.3613809390255142640635837073331
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.426
y[1] (analytic) = 1.3620827179461676482355340091838
y[1] (numeric) = 1.3620827179461676482355340091838
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.3MB, time=12.51
x[1] = 0.427
y[1] (analytic) = 1.3627845691890694399149866186437
y[1] (numeric) = 1.3627845691890694399149866186437
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.428
y[1] (analytic) = 1.3634864927318692134195387064848
y[1] (numeric) = 1.3634864927318692134195387064848
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.429
y[1] (analytic) = 1.3641884885522326531417982449768
y[1] (numeric) = 1.3641884885522326531417982449768
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 1.3648905566278415353093710130139
y[1] (numeric) = 1.3648905566278415353093710130138
absolute error = 1e-31
relative error = 7.3265947598805566776644902186824e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.431
y[1] (analytic) = 1.3655926969363937097729972217184
y[1] (numeric) = 1.3655926969363937097729972217184
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.432
y[1] (analytic) = 1.3662949094556030818227827553402
y[1] (numeric) = 1.3662949094556030818227827553402
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.433
y[1] (analytic) = 1.366997194163199594032470152324
y[1] (numeric) = 1.366997194163199594032470152324
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.434
y[1] (analytic) = 1.3676995510369292081316945811159
y[1] (numeric) = 1.3676995510369292081316945811158
absolute error = 1e-31
relative error = 7.3115473295421081460182505979664e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.435
y[1] (analytic) = 1.3684019800545538869061701946116
y[1] (numeric) = 1.3684019800545538869061701946116
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.436
y[1] (analytic) = 1.3691044811938515761257523761302
y[1] (numeric) = 1.3691044811938515761257523761302
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.3MB, time=12.87
x[1] = 0.437
y[1] (analytic) = 1.3698070544326161865003215184119
y[1] (numeric) = 1.3698070544326161865003215184119
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.438
y[1] (analytic) = 1.3705096997486575756634341054058
y[1] (numeric) = 1.3705096997486575756634341054058
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.439
y[1] (analytic) = 1.3712124171198015301836869945193
y[1] (numeric) = 1.3712124171198015301836869945193
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 1.3719152065238897476037409245554
y[1] (numeric) = 1.3719152065238897476037409245554
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.441
y[1] (analytic) = 1.3726180679387798185069494017657
y[1] (numeric) = 1.3726180679387798185069494017657
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.442
y[1] (analytic) = 1.3733210013423452086115392432959
y[1] (numeric) = 1.3733210013423452086115392432959
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.443
y[1] (analytic) = 1.3740240067124752408922891837997
y[1] (numeric) = 1.3740240067124752408922891837997
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.444
y[1] (analytic) = 1.3747270840270750777296530771457
y[1] (numeric) = 1.3747270840270750777296530771457
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.445
y[1] (analytic) = 1.3754302332640657030862743509443
y[1] (numeric) = 1.3754302332640657030862743509442
absolute error = 1e-31
relative error = 7.2704523705784522209262292246604e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.3MB, time=13.23
x[1] = 0.446
y[1] (analytic) = 1.3761334544013839047108384970719
y[1] (numeric) = 1.3761334544013839047108384970718
absolute error = 1e-31
relative error = 7.2667370799076938190324769408461e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.447
y[1] (analytic) = 1.3768367474169822563692105064816
y[1] (numeric) = 1.3768367474169822563692105064815
absolute error = 1e-31
relative error = 7.2630252052471166081170907799967e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.448
y[1] (analytic) = 1.3775401122888291001028042813472
y[1] (numeric) = 1.3775401122888291001028042813471
absolute error = 1e-31
relative error = 7.2593167420618079816967732809906e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.449
y[1] (analytic) = 1.3782435489949085285141311820078
y[1] (numeric) = 1.3782435489949085285141311820077
absolute error = 1e-31
relative error = 7.2556116858247248288124678689506e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 1.3789470575132203670794749902563
y[1] (numeric) = 1.3789470575132203670794749902562
absolute error = 1e-31
relative error = 7.2519100320166766716853538846947e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.451
y[1] (analytic) = 1.3796506378217801564886406942458
y[1] (numeric) = 1.3796506378217801564886406942456
absolute error = 2e-31
relative error = 1.4496423552252617692738561909133e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.452
y[1] (analytic) = 1.3803542898986191350117246236822
y[1] (numeric) = 1.380354289898619135011724623682
absolute error = 2e-31
relative error = 1.4489033827300171452545037207342e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.453
y[1] (analytic) = 1.3810580137217842208928535870252
y[1] (numeric) = 1.3810580137217842208928535870251
absolute error = 1e-31
relative error = 7.2408254400922739884221245411439e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.454
y[1] (analytic) = 1.381761809269337994770840785131
y[1] (numeric) = 1.3817618092693379947708407851309
absolute error = 1e-31
relative error = 7.2371373509649259223446609603019e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.455
y[1] (analytic) = 1.3824656765193586821267063981491
y[1] (numeric) = 1.382465676519358682126706398149
absolute error = 1e-31
relative error = 7.2334526417878627814374125060106e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.3MB, time=13.59
x[1] = 0.456
y[1] (analytic) = 1.3831696154499401357580108645258
y[1] (numeric) = 1.3831696154499401357580108645257
absolute error = 1e-31
relative error = 7.2297713080886581767046822731401e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.457
y[1] (analytic) = 1.3838736260391918182799489926703
y[1] (numeric) = 1.3838736260391918182799489926703
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.458
y[1] (analytic) = 1.3845777082652387846531531672111
y[1] (numeric) = 1.3845777082652387846531531672111
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.459
y[1] (analytic) = 1.3852818621062216647381540328061
y[1] (numeric) = 1.385281862106221664738154032806
absolute error = 1e-31
relative error = 7.2187475152498695038899931076433e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 1.3859860875402966458764471591757
y[1] (numeric) = 1.3859860875402966458764471591757
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.461
y[1] (analytic) = 1.3866903845456354554981143114027
y[1] (numeric) = 1.3866903845456354554981143114027
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.462
y[1] (analytic) = 1.3873947531004253437559480695824
y[1] (numeric) = 1.3873947531004253437559480695823
absolute error = 1e-31
relative error = 7.2077539414452137781164542234389e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.463
y[1] (analytic) = 1.3880991931828690661860286616249
y[1] (numeric) = 1.3880991931828690661860286616249
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.464
y[1] (analytic) = 1.3888037047711848663947019923967
y[1] (numeric) = 1.3888037047711848663947019923966
absolute error = 1e-31
relative error = 7.2004416215519600818263660809596e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.3MB, time=13.95
x[1] = 0.465
y[1] (analytic) = 1.389508287843606458771907971444
y[1] (numeric) = 1.3895082878436064587719079714439
absolute error = 1e-31
relative error = 7.1967904671652678523904932680740e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.466
y[1] (analytic) = 1.3902129423783830112308083602804
y[1] (numeric) = 1.3902129423783830112308083602803
absolute error = 1e-31
relative error = 7.1931426439549266015735281978826e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.467
y[1] (analytic) = 1.3909176683537791279736634786215
y[1] (numeric) = 1.3909176683537791279736634786215
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.468
y[1] (analytic) = 1.3916224657480748322839072270408
y[1] (numeric) = 1.3916224657480748322839072270407
absolute error = 1e-31
relative error = 7.1858569735179154712190135617093e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.469
y[1] (analytic) = 1.3923273345395655493443700012748
y[1] (numeric) = 1.3923273345395655493443700012747
absolute error = 1e-31
relative error = 7.1822191175374295972374269746653e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 1.3930322747065620890815991908521
y[1] (numeric) = 1.393032274706562089081599190852
absolute error = 1e-31
relative error = 7.1785845752256306201557783074584e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.471
y[1] (analytic) = 1.3937372862273906290362270718319
y[1] (numeric) = 1.3937372862273906290362270718318
absolute error = 1e-31
relative error = 7.1749533422244131927500222411538e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.472
y[1] (analytic) = 1.3944423690803926972593360202417
y[1] (numeric) = 1.3944423690803926972593360202416
absolute error = 1e-31
relative error = 7.1713254141831642861028058580696e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.473
y[1] (analytic) = 1.3951475232439251552347710892789
y[1] (numeric) = 1.3951475232439251552347710892788
absolute error = 1e-31
relative error = 7.1677007867587472847582740535941e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.474
y[1] (analytic) = 1.3958527486963601808273501095053
y[1] (numeric) = 1.3958527486963601808273501095052
absolute error = 1e-31
relative error = 7.1640794556154861220548287742098e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.3MB, time=14.32
x[1] = 0.475
y[1] (analytic) = 1.3965580454160852512569215871056
y[1] (numeric) = 1.3965580454160852512569215871056
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.476
y[1] (analytic) = 1.3972634133815031260982207908118
y[1] (numeric) = 1.3972634133815031260982207908118
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.477
y[1] (analytic) = 1.3979688525710318303064745333054
y[1] (numeric) = 1.3979688525710318303064745333054
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.478
y[1] (analytic) = 1.3986743629631046372687052678137
y[1] (numeric) = 1.3986743629631046372687052678136
absolute error = 1e-31
relative error = 7.1496270074007126716967718816258e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.479
y[1] (analytic) = 1.3993799445361700518806852351971
y[1] (numeric) = 1.399379944536170051880685235197
absolute error = 1e-31
relative error = 7.1460220928881034211218212970223e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 1.4000855972686917936494915111048
y[1] (numeric) = 1.4000855972686917936494915111047
absolute error = 1e-31
relative error = 7.1424204487983817453794981529973e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.481
y[1] (analytic) = 1.4007913211391487798216129167341
y[1] (numeric) = 1.400791321139148779821612916734
absolute error = 1e-31
relative error = 7.1388220708476545590176089829043e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.482
y[1] (analytic) = 1.401497116126035108536559870386
y[1] (numeric) = 1.401497116126035108536559870386
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.483
y[1] (analytic) = 1.4022029822078600420059283703526
y[1] (numeric) = 1.4022029822078600420059283703526
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.484
y[1] (analytic) = 1.4029089193631479897178694127062
y[1] (numeric) = 1.4029089193631479897178694127062
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
memory used=156.4MB, alloc=4.3MB, time=14.67
TOP MAIN SOLVE Loop
x[1] = 0.485
y[1] (analytic) = 1.4036149275704384916669152602927
y[1] (numeric) = 1.4036149275704384916669152602926
absolute error = 1e-31
relative error = 7.1244611350132308305121732918885e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.486
y[1] (analytic) = 1.40432100680828620160911409165
y[1] (numeric) = 1.4043210068082862016091140916499
absolute error = 1e-31
relative error = 7.1208790237552650706207838950575e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.487
y[1] (analytic) = 1.4050271570552608703424246706942
y[1] (numeric) = 1.4050271570552608703424246706941
absolute error = 1e-31
relative error = 7.1173001530864301999055036918454e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.488
y[1] (analytic) = 1.4057333782899473290123227898256
y[1] (numeric) = 1.4057333782899473290123227898255
absolute error = 1e-31
relative error = 7.1137245187738542667314040744104e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.489
y[1] (analytic) = 1.406439670490945472442571350618
y[1] (numeric) = 1.4064396704909454724425713506179
absolute error = 1e-31
relative error = 7.1101521165918926405007081540131e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 1.4071460336368702424911060574628
y[1] (numeric) = 1.4071460336368702424911060574628
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.491
y[1] (analytic) = 1.4078524677063516114309888104441
y[1] (numeric) = 1.407852467706351611430988810444
absolute error = 1e-31
relative error = 7.1030169917532790045204195510243e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.492
y[1] (analytic) = 1.4085589726780345653563809943253
y[1] (numeric) = 1.4085589726780345653563809943252
absolute error = 1e-31
relative error = 7.0994542606813373917378464076023e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.493
y[1] (analytic) = 1.4092655485305790876134889708371
y[1] (numeric) = 1.4092655485305790876134889708371
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.3MB, time=15.03
x[1] = 0.494
y[1] (analytic) = 1.4099721952426601422564341914594
y[1] (numeric) = 1.4099721952426601422564341914594
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.495
y[1] (analytic) = 1.4106789127929676575280004576013
y[1] (numeric) = 1.4106789127929676575280004576013
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.496
y[1] (analytic) = 1.4113857011602065093652109644962
y[1] (numeric) = 1.4113857011602065093652109644962
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.497
y[1] (analytic) = 1.4120925603230965049296878742438
y[1] (numeric) = 1.4120925603230965049296878742438
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.498
y[1] (analytic) = 1.4127994902603723661627472722537
y[1] (numeric) = 1.4127994902603723661627472722537
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.499
y[1] (analytic) = 1.4135064909507837133651824698724
y[1] (numeric) = 1.4135064909507837133651824698724
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
Finished!
diff ( y , x , 1 ) = sqrt(sqrt(0.1 * x + 0.2));
Iterations = 400
Total Elapsed Time = 15 Seconds
Elapsed Time(since restart) = 15 Seconds
Time to Timeout = 2 Minutes 44 Seconds
Percent Done = 100.2 %
> quit
memory used=162.4MB, alloc=4.3MB, time=15.22