|\^/| 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_a1,
> 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_a1, 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_a1,
> 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_a1, 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_a1,
> 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_a1, 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_a1,
> 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_a1, 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_a1,
> 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_a1, 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_a1,
> 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_a1, 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_a1,
> 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_a1, 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_a1,
> 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_a1, 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_a1,
> 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 arcsin FULL $eq_no = 1
> array_tmp4[1] := arcsin(array_tmp3[1]);
> array_tmp4_a1[1] := cos(array_tmp4[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 arcsin FULL $eq_no = 1
> temp := att(1,array_tmp4_a1,array_tmp4,2);
> array_tmp4[2] := (array_tmp3[2] - temp) / array_tmp4_a1[1];
> temp2 := att(1,array_tmp3,array_tmp4,1);
> array_tmp4_a1[2] := -temp2;
> #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 arcsin FULL $eq_no = 1
> temp := att(2,array_tmp4_a1,array_tmp4,2);
> array_tmp4[3] := (array_tmp3[3] - temp) / array_tmp4_a1[1];
> temp2 := att(2,array_tmp3,array_tmp4,1);
> array_tmp4_a1[3] := -temp2;
> #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 arcsin FULL $eq_no = 1
> temp := att(3,array_tmp4_a1,array_tmp4,2);
> array_tmp4[4] := (array_tmp3[4] - temp) / array_tmp4_a1[1];
> temp2 := att(3,array_tmp3,array_tmp4,1);
> array_tmp4_a1[4] := -temp2;
> #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 arcsin FULL $eq_no = 1
> temp := att(4,array_tmp4_a1,array_tmp4,2);
> array_tmp4[5] := (array_tmp3[5] - temp) / array_tmp4_a1[1];
> temp2 := att(4,array_tmp3,array_tmp4,1);
> array_tmp4_a1[5] := -temp2;
> #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 arcsin $eq_no = 1
> temp := att(kkk-1,array_tmp4_a1,array_tmp4,2);
> array_tmp4[kkk] := (array_tmp3[kkk] - temp) / array_tmp4_a1[1];
> temp2 := att(kkk-1,array_tmp3,array_tmp4,1);
> array_tmp4_a1[kkk] := -temp2;
> #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;
Warning, `temp` is implicitly declared local to procedure `atomall`
Warning, `temp2` is implicitly declared local to procedure `atomall`
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term, temp, temp2;
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_a1, 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] := arcsin(array_tmp3[1]);
array_tmp4_a1[1] := cos(array_tmp4[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);
temp := att(1, array_tmp4_a1, array_tmp4, 2);
array_tmp4[2] := (array_tmp3[2] - temp)/array_tmp4_a1[1];
temp2 := att(1, array_tmp3, array_tmp4, 1);
array_tmp4_a1[2] := -temp2;
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)
;
temp := att(2, array_tmp4_a1, array_tmp4, 2);
array_tmp4[3] := (array_tmp3[3] - temp)/array_tmp4_a1[1];
temp2 := att(2, array_tmp3, array_tmp4, 1);
array_tmp4_a1[3] := -temp2;
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)
;
temp := att(3, array_tmp4_a1, array_tmp4, 2);
array_tmp4[4] := (array_tmp3[4] - temp)/array_tmp4_a1[1];
temp2 := att(3, array_tmp3, array_tmp4, 1);
array_tmp4_a1[4] := -temp2;
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)
;
temp := att(4, array_tmp4_a1, array_tmp4, 2);
array_tmp4[5] := (array_tmp3[5] - temp)/array_tmp4_a1[1];
temp2 := att(4, array_tmp3, array_tmp4, 1);
array_tmp4_a1[5] := -temp2;
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);
temp := att(kkk - 1, array_tmp4_a1, array_tmp4, 2);
array_tmp4[kkk] := (array_tmp3[kkk] - temp)/array_tmp4_a1[1];
temp2 := att(kkk - 1, array_tmp3, array_tmp4, 1);
array_tmp4_a1[kkk] := -temp2;
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(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x +
> 0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(sqrt( 0.1 * x + 0.2)));
> end;
exact_soln_y := proc(x)
return 10.0*(0.1*x + 0.2)*arcsin(sqrt(0.1*x + 0.2))
+ 5.0*sqrt(0.1*x + 0.2)*sqrt(0.8 - 0.1*x)
- 5.0*arcsin(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_a1,
> 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/arcsin_sqrtpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = arcsin(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 := 0.0;");
> 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,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> 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(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x +");
> omniout_str(ALWAYS,"0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(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_a1:= 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_a1[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_a1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4_a1[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 := 0.0;
> x_end := 0.5 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #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 ) = arcsin(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,"2013-01-28T12:06:42-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"arcsin_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = arcsin(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,"arcsin_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"arcsin_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_a1, 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/arcsin_sqrtpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = arcsin(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 := 0.0;");
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, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
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(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.\
1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x +");
omniout_str(ALWAYS, "0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(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_a1 := 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_a1[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_a1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_a1[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.;
x_end := 0.5;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
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 ) = arcsin(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, "2013-01-28T12:06:42-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"arcsin_sqrt");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = arcsin(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, "arcsin_sqrt diffeq.mxt");
logitem_str(html_log_file, "arcsin_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/arcsin_sqrtpostode.ode#################
diff ( y , x , 1 ) = arcsin(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 := 0.0;
x_end := 0.5 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#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(10.0 * (0.1 * x + 0.2) * arcsin(sqrt ( 0.1 * x + 0.2)) + 5.0 * sqrt( 0.1 * x +
0.2) * sqrt( 0.8 - 0.1 * x) - 5.0 * arcsin(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 = 0.5
estimated_steps = 500
step_error = 2.0000000000000000000000000000000e-13
est_needed_step_err = 2.0000000000000000000000000000000e-13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 1.1718309454379427110227424203722e-90
max_value3 = 1.1718309454379427110227424203722e-90
value3 = 1.1718309454379427110227424203722e-90
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (analytic) = 0.6090571729975816513572313056163
y[1] (numeric) = 0.6090571729975816513572313056163
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.001
y[1] (analytic) = 0.6095208831026770820978879838655
y[1] (numeric) = 0.60952088310267708209788798386545
absolute error = 5e-32
relative error = 8.2031643847020135928787867007718e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.8MB, time=0.13
x[1] = 0.002
y[1] (analytic) = 0.6099847181843472541779969702107
y[1] (numeric) = 0.60998471818434725417799697021069
absolute error = 1e-32
relative error = 1.6393853324334984658192728658359e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.003
y[1] (analytic) = 0.6104486782191861298431324520456
y[1] (numeric) = 0.61044867821918612984313245204548
absolute error = 1.2e-31
relative error = 1.9657672181397222901078238641304e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.004
y[1] (analytic) = 0.6109127631838086164442505419117
y[1] (numeric) = 0.6109127631838086164442505419117
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.005
y[1] (analytic) = 0.6113769730548505410074765302546
y[1] (numeric) = 0.61137697305485054100747653025455
absolute error = 5e-32
relative error = 8.1782602557251007235327047029670e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.006
y[1] (analytic) = 0.6118413078089686248489230972898
y[1] (numeric) = 0.6118413078089686248489230972897
absolute error = 1.0e-31
relative error = 1.6344107323858946277117925364759e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.8MB, time=0.27
x[1] = 0.007
y[1] (analytic) = 0.6123057674228404582344384153974
y[1] (numeric) = 0.61230576742284045823443841539743
absolute error = 3e-32
relative error = 4.8995128898210879084248664485216e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.008
y[1] (analytic) = 0.6127703518731644750841833511355
y[1] (numeric) = 0.61277035187316447508418335113545
absolute error = 5e-32
relative error = 8.1596637055229709110119341743027e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.009
y[1] (analytic) = 0.6132350611366599277219372527391
y[1] (numeric) = 0.61323506113665992772193725273911
absolute error = 1e-32
relative error = 1.6306960631808186744711612244906e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (analytic) = 0.6136998951900668616690320848583
y[1] (numeric) = 0.61369989519006686166903208485818
absolute error = 1.2e-31
relative error = 1.9553531121727699994384824642355e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.011
y[1] (analytic) = 0.6141648540101460904828149472665
y[1] (numeric) = 0.61416485401014609048281494726634
absolute error = 1.6e-31
relative error = 2.6051637268933786515637906762677e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=0.42
x[1] = 0.012
y[1] (analytic) = 0.614629937573679170639539288377
y[1] (numeric) = 0.61462993757367917063953928837691
absolute error = 9e-32
relative error = 1.4642957411948582543910877742619e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.013
y[1] (analytic) = 0.6150951458574683764615853976086
y[1] (numeric) = 0.6150951458574683764615853976086
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.014
y[1] (analytic) = 0.6155604788383366750889110329727
y[1] (numeric) = 0.61556047883833667508891103297269
absolute error = 1e-32
relative error = 1.6245357432419371577124896761349e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.015
y[1] (analytic) = 0.6160259364931277014946333117
y[1] (numeric) = 0.61602593649312770149463331169984
absolute error = 1.6e-31
relative error = 2.5972932391586882063779294420356e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.016
y[1] (analytic) = 0.6164915187987057335446432622956
y[1] (numeric) = 0.61649151879870573354464326229554
absolute error = 6e-32
relative error = 9.7324939874137915561132465820690e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.1MB, time=0.57
x[1] = 0.017
y[1] (analytic) = 0.61695722573195566710115470611
y[1] (numeric) = 0.61695722573195566710115470611004
absolute error = 4e-32
relative error = 6.4834316435056181832915716351622e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.018
y[1] (analytic) = 0.6174230572697829911700894053354
y[1] (numeric) = 0.61742305726978299117008940533541
absolute error = 1e-32
relative error = 1.6196350107525220299561710247658e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.019
y[1] (analytic) = 0.6178890133891137630922006823022
y[1] (numeric) = 0.61788901338911376309220068230217
absolute error = 3e-32
relative error = 4.8552408846777130646988045810291e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.02
y[1] (analytic) = 0.6183550940668945837778379820439
y[1] (numeric) = 0.61835509406689458377783798204398
absolute error = 8e-32
relative error = 1.2937550085314810994243921347664e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.021
y[1] (analytic) = 0.6188212992800925729852551163342
y[1] (numeric) = 0.6188212992800925729852551163343
absolute error = 1.0e-31
relative error = 1.6159754054415268127495267795049e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.022
y[1] (analytic) = 0.6192876290056953446423651927772
y[1] (numeric) = 0.61928762900569534464236519277707
absolute error = 1.3e-31
relative error = 2.0991861279180250047155951537056e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.2MB, time=0.72
x[1] = 0.023
y[1] (analytic) = 0.6197540832207109822118454970576
y[1] (numeric) = 0.61975408322071098221184549705746
absolute error = 1.4e-31
relative error = 2.2589605101503181335667807210264e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.024
y[1] (analytic) = 0.6202206619021680140994958601316
y[1] (numeric) = 0.62022066190216801409949586013159
absolute error = 1e-32
relative error = 1.6123293876296842653680501617926e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.025
y[1] (analytic) = 0.6206873650271153891057543049593
y[1] (numeric) = 0.62068736502711538910575430495927
absolute error = 3e-32
relative error = 4.8333511668453921281710569318793e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.026
y[1] (analytic) = 0.6211541925726224519202740293642
y[1] (numeric) = 0.62115419257262245192027402936429
absolute error = 9e-32
relative error = 1.4489156006055230746244869500834e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.027
y[1] (analytic) = 0.6216211445157789186594660427454
y[1] (numeric) = 0.62162114451577891865946604274544
absolute error = 4e-32
relative error = 6.4347875475115309735041848610248e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.2MB, time=0.87
x[1] = 0.028
y[1] (analytic) = 0.6220882208336948524469120346621
y[1] (numeric) = 0.62208822083369485244691203466203
absolute error = 7e-32
relative error = 1.1252423314845782813343503428000e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.029
y[1] (analytic) = 0.6225554215035006390365523127825
y[1] (numeric) = 0.62255542150350063903655231278252
absolute error = 2e-32
relative error = 3.2125653892305778726416288451921e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (analytic) = 0.6230227465023469624785539063179
y[1] (numeric) = 0.62302274650234696247855390631784
absolute error = 6e-32
relative error = 9.6304669992934160956861736723055e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.031
y[1] (analytic) = 0.6234901958074047808277641888643
y[1] (numeric) = 0.6234901958074047808277641888644
absolute error = 1.0e-31
relative error = 1.6038744582102435381417814956972e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.032
y[1] (analytic) = 0.6239577693958653018946556315594
y[1] (numeric) = 0.62395776939586530189465563155938
absolute error = 2e-32
relative error = 3.2053451340728719748077647615098e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.033
y[1] (analytic) = 0.6244254672449399590386675536054
y[1] (numeric) = 0.6244254672449399590386675536053
absolute error = 1.0e-31
relative error = 1.6014721571369469391441551323806e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.3MB, time=1.03
x[1] = 0.034
y[1] (analytic) = 0.6248932893318603870038509925553
y[1] (numeric) = 0.62489328933186038700385099255529
absolute error = 1e-32
relative error = 1.6002732259602370412413480865567e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.035
y[1] (analytic) = 0.6253612356338783977967230712678
y[1] (numeric) = 0.6253612356338783977967230712678
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.036
y[1] (analytic) = 0.6258293061282659566062374921429
y[1] (numeric) = 0.62582930612826595660623749214304
absolute error = 1.4e-31
relative error = 2.2370317054360905693089370207238e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.037
y[1] (analytic) = 0.6262975007923151577657780421459
y[1] (numeric) = 0.62629750079231515776577804214588
absolute error = 2e-32
relative error = 3.1933705586719475999844244493334e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.038
y[1] (analytic) = 0.6267658196033382007570822442044
y[1] (numeric) = 0.62676581960333820075708224420431
absolute error = 9e-32
relative error = 1.4359430138828944748408376067800e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.3MB, time=1.18
x[1] = 0.039
y[1] (analytic) = 0.6272342625386673662560025418522
y[1] (numeric) = 0.62723426253866736625600254185213
absolute error = 7e-32
relative error = 1.1160104634061612899629232855888e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (analytic) = 0.6277028295756549922200126544619
y[1] (numeric) = 0.62770282957565499222001265446191
absolute error = 1e-32
relative error = 1.5931105499015011748351245036004e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.041
y[1] (analytic) = 0.6281715206916734500173669900926
y[1] (numeric) = 0.62817152069167345001736699009256
absolute error = 4e-32
relative error = 6.3676875952536650377879377765953e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.042
y[1] (analytic) = 0.6286403358641151205978212518581
y[1] (numeric) = 0.62864033586411512059782125185804
absolute error = 6e-32
relative error = 9.5444082374264650467924422701450e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.043
y[1] (analytic) = 0.6291092750703923707048226218127
y[1] (numeric) = 0.62910927507039237070482262181269
absolute error = 1e-32
relative error = 1.5895489696732064229593416852484e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.044
y[1] (analytic) = 0.6295783382879375291290781536472
y[1] (numeric) = 0.6295783382879375291290781536472
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.3MB, time=1.33
x[1] = 0.045
y[1] (analytic) = 0.6300475254942028630034102520006
y[1] (numeric) = 0.63004752549420286300341025200062
absolute error = 2e-32
relative error = 3.1743637091999057796461969185240e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.046
y[1] (analytic) = 0.6305168366666605541388083619203
y[1] (numeric) = 0.63051683666666055413880836192028
absolute error = 2e-32
relative error = 3.1720009422323373045070722918199e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.047
y[1] (analytic) = 0.6309862717828026754015862369468
y[1] (numeric) = 0.63098627178280267540158623694682
absolute error = 2e-32
relative error = 3.1696410673867046663317150034104e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.048
y[1] (analytic) = 0.6314558308201411671315543984676
y[1] (numeric) = 0.63145583082014116713155439846755
absolute error = 5e-32
relative error = 7.9182101992881273193136205764165e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.049
y[1] (analytic) = 0.631925513756207813601117642372
y[1] (numeric) = 0.63192551375620781360111764237196
absolute error = 4e-32
relative error = 6.3298599485621819606712245469793e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.3MB, time=1.49
x[1] = 0.05
y[1] (analytic) = 0.6323953205685542195152076916603
y[1] (numeric) = 0.63239532056855421951520769166033
absolute error = 3e-32
relative error = 4.7438681192372735522204302786030e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.051
y[1] (analytic) = 0.6328652512347517865519613355036
y[1] (numeric) = 0.6328652512347517865519613355036
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.052
y[1] (analytic) = 0.6333353057323916899440546363321
y[1] (numeric) = 0.63333530573239168994405463633216
absolute error = 6e-32
relative error = 9.4736547065879645214087561222086e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.053
y[1] (analytic) = 0.6338054840390848551006040268464
y[1] (numeric) = 0.6338054840390848551006040268463
absolute error = 1.0e-31
relative error = 1.5777711382792848218372927067981e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.054
y[1] (analytic) = 0.6342757861324619342695453583944
y[1] (numeric) = 0.63427578613246193426954535839438
absolute error = 2e-32
relative error = 3.1532025086360788437263190651000e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.055
y[1] (analytic) = 0.6347462119901732832404022009587
y[1] (numeric) = 0.63474621199017328324040220095872
absolute error = 2e-32
relative error = 3.1508655935562521541057094010402e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.3MB, time=1.64
x[1] = 0.056
y[1] (analytic) = 0.6352167615898889380873549330273
y[1] (numeric) = 0.63521676158988893808735493302736
absolute error = 6e-32
relative error = 9.4455945793724864321870247221227e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.057
y[1] (analytic) = 0.6356874349092985919525223969142
y[1] (numeric) = 0.63568743490929859195252239691412
absolute error = 8e-32
relative error = 1.2584801209955422808916392476381e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.058
y[1] (analytic) = 0.6361582319261115718693681316233
y[1] (numeric) = 0.63615823192611157186936813162315
absolute error = 1.5e-31
relative error = 2.3579039376074941927857426888512e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.059
y[1] (analytic) = 0.6366291526180568156261434311398
y[1] (numeric) = 0.63662915261805681562614343113977
absolute error = 3e-32
relative error = 4.7123195468867231305147031759747e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (analytic) = 0.6371001969628828486692797110698
y[1] (numeric) = 0.63710019696288284866927971106981
absolute error = 1e-32
relative error = 1.5696118205065623601937599878036e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.3MB, time=1.79
x[1] = 0.061
y[1] (analytic) = 0.6375713649383577610466429008477
y[1] (numeric) = 0.63757136493835776104664290084752
absolute error = 1.8e-31
relative error = 2.8232133671405226817135803841750e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.062
y[1] (analytic) = 0.6380426565222691843905628122902
y[1] (numeric) = 0.63804265652226918439056281229002
absolute error = 1.8e-31
relative error = 2.8211279944998094034189469165497e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.063
y[1] (analytic) = 0.6385140716924242689405506680971
y[1] (numeric) = 0.6385140716924242689405506680972
absolute error = 1.0e-31
relative error = 1.5661361970448561793713098146774e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.064
y[1] (analytic) = 0.6389856104266496606056182059822
y[1] (numeric) = 0.6389856104266496606056182059821
absolute error = 1.0e-31
relative error = 1.5649804685465477293615329668156e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.065
y[1] (analytic) = 0.6394572727027914780661120054716
y[1] (numeric) = 0.63945727270279147806611200547154
absolute error = 6e-32
relative error = 9.3829568543959538920819570757282e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.066
y[1] (analytic) = 0.6399290584987152899149769150421
y[1] (numeric) = 0.639929058498715289914976915042
absolute error = 1.0e-31
relative error = 1.5626732162249631332228049931747e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.3MB, time=1.95
x[1] = 0.067
y[1] (analytic) = 0.6404009677923060918383626871547
y[1] (numeric) = 0.64040096779230609183836268715467
absolute error = 3e-32
relative error = 4.6845650629512409262345302233266e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.068
y[1] (analytic) = 0.6408730005614682838354881579287
y[1] (numeric) = 0.64087300056146828383548815792862
absolute error = 8e-32
relative error = 1.2482972434462376929682953646742e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.069
y[1] (analytic) = 0.6413451567841256474776775366449
y[1] (numeric) = 0.64134515678412564747767753664482
absolute error = 8e-32
relative error = 1.2473782510675089923531230357627e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.07
y[1] (analytic) = 0.6418174364382213232064835980089
y[1] (numeric) = 0.64181743643822132320648359800889
absolute error = 1e-32
relative error = 1.5580754638725927485806052089351e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.071
y[1] (analytic) = 0.6422898395017177876708127971197
y[1] (numeric) = 0.64228983950171778767081279711963
absolute error = 7e-32
relative error = 1.0898506514489676400803685269619e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.3MB, time=2.10
x[1] = 0.072
y[1] (analytic) = 0.6427623659525968311029675533963
y[1] (numeric) = 0.64276236595259683110296755339624
absolute error = 6e-32
relative error = 9.3347095564747093698237981278891e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.073
y[1] (analytic) = 0.643235015768859534733521175312
y[1] (numeric) = 0.64323501576885953473352117531195
absolute error = 5e-32
relative error = 7.7732086677891662976354725219823e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.074
y[1] (analytic) = 0.6437077889285262482449411226685
y[1] (numeric) = 0.64370778892852624824494112266846
absolute error = 4e-32
relative error = 6.2139996886757228148973380853199e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.075
y[1] (analytic) = 0.6441806854096365672638765273268
y[1] (numeric) = 0.64418068540963656726387652732674
absolute error = 6e-32
relative error = 9.3141569374818816946877272022654e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.076
y[1] (analytic) = 0.6446537051902493108920261167875
y[1] (numeric) = 0.64465370519024931089202611678747
absolute error = 3e-32
relative error = 4.6536613003948284831078318783337e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.077
y[1] (analytic) = 0.6451268482484424992755029077918
y[1] (numeric) = 0.64512684824844249927550290779172
absolute error = 8e-32
relative error = 1.2400662012006588411379054445679e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.3MB, time=2.25
x[1] = 0.078
y[1] (analytic) = 0.6456001145623133312126122591918
y[1] (numeric) = 0.64560011456231333121261225919171
absolute error = 9e-32
relative error = 1.3940517972338928211751843643381e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.079
y[1] (analytic) = 0.6460735041099781617999600947252
y[1] (numeric) = 0.64607350410997816179996009472517
absolute error = 3e-32
relative error = 4.6434345022905065752388098162810e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (analytic) = 0.6465470168695724801168083270176
y[1] (numeric) = 0.64654701686957248011680832701747
absolute error = 1.3e-31
relative error = 2.0106813055828361759538783202293e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.081
y[1] (analytic) = 0.647020652819250886947594734136
y[1] (numeric) = 0.64702065281925088694759473413591
absolute error = 9e-32
relative error = 1.3909911470034951358571696390334e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.082
y[1] (analytic) = 0.6474944119371870725425347593326
y[1] (numeric) = 0.64749441193718707254253475933259
absolute error = 1e-32
relative error = 1.5444148730306095975758043623074e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.3MB, time=2.41
x[1] = 0.083
y[1] (analytic) = 0.6479682942015737944162229232389
y[1] (numeric) = 0.6479682942015737944162229232389
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.084
y[1] (analytic) = 0.6484422995906228551841517557181
y[1] (numeric) = 0.64844229959062285518415175571818
absolute error = 8e-32
relative error = 1.2337258079941101139796928757729e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.085
y[1] (analytic) = 0.6489164280825650804370663718461
y[1] (numeric) = 0.64891642808256508043706637184598
absolute error = 1.2e-31
relative error = 1.8492365858971867985105668721379e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.086
y[1] (analytic) = 0.649390679655650296653073033072
y[1] (numeric) = 0.64939067965565029665307303307206
absolute error = 6e-32
relative error = 9.2394304198846757766555272546497e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.087
y[1] (analytic) = 0.6498650542881473091474202505273
y[1] (numeric) = 0.64986505428814730914742025052725
absolute error = 5e-32
relative error = 7.6939050145986492346571940814242e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.088
y[1] (analytic) = 0.6503395519583438800598712026741
y[1] (numeric) = 0.65033955195834388005987120267406
absolute error = 4e-32
relative error = 6.1506331391885134978746727334811e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.3MB, time=2.56
x[1] = 0.089
y[1] (analytic) = 0.6508141726445467063795864540647
y[1] (numeric) = 0.6508141726445467063795864540647
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (analytic) = 0.6512889163250813980074361758667
y[1] (numeric) = 0.65128891632508139800743617586664
absolute error = 6e-32
relative error = 9.2125013179330495353017431156290e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.091
y[1] (analytic) = 0.6517637829782924558556612820461
y[1] (numeric) = 0.65176378297829245585566128204605
absolute error = 5e-32
relative error = 7.6714910072972392049801919078231e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.092
y[1] (analytic) = 0.6522387725825432499848031076663
y[1] (numeric) = 0.65223877258254324998480310766619
absolute error = 1.1e-31
relative error = 1.6864989421658322163264216445438e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.093
y[1] (analytic) = 0.6527138851162159977778214676633
y[1] (numeric) = 0.65271388511621599777782146766322
absolute error = 8e-32
relative error = 1.2256518793951497506565691812849e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.3MB, time=2.71
x[1] = 0.094
y[1] (analytic) = 0.6531891205577117421513211457083
y[1] (numeric) = 0.6531891205577117421513211457083
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.095
y[1] (analytic) = 0.6536644788854503298038070733548
y[1] (numeric) = 0.65366447888545032980380707335481
absolute error = 1e-32
relative error = 1.5298368387786332586324899712303e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.096
y[1] (analytic) = 0.6541399600778703895008886696053
y[1] (numeric) = 0.65413996007787038950088866960523
absolute error = 7e-32
relative error = 1.0701073817851921496626057060768e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.097
y[1] (analytic) = 0.6546155641134293103973540203162
y[1] (numeric) = 0.65461556411342931039735402031615
absolute error = 5e-32
relative error = 7.6380707610759143221424629256862e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.098
y[1] (analytic) = 0.6550912909706032203960347854942
y[1] (numeric) = 0.65509129097060322039603478549407
absolute error = 1.3e-31
relative error = 1.9844562397919843857531583479756e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.099
y[1] (analytic) = 0.655567140627886964543382930522
y[1] (numeric) = 0.65556714062788696454338293052205
absolute error = 5e-32
relative error = 7.6269838589089688909792982155491e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.4MB, time=2.87
x[1] = 0.1
y[1] (analytic) = 0.6560431130637940834616805846994
y[1] (numeric) = 0.65604311306379408346168058469938
absolute error = 2e-32
relative error = 3.0485801316620461567761785830013e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.101
y[1] (analytic) = 0.6565192082568567918178045371763
y[1] (numeric) = 0.65651920825685679181780453717623
absolute error = 7e-32
relative error = 1.0662292758479836721905415609440e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.102
y[1] (analytic) = 0.6569954261856259568284670864246
y[1] (numeric) = 0.65699542618562595682846708642464
absolute error = 4e-32
relative error = 6.0883224457484264441861052590640e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.103
y[1] (analytic) = 0.6574717668286710768018551648088
y[1] (numeric) = 0.65747176682867107680185516480874
absolute error = 6e-32
relative error = 9.1258671515905944480370937759837e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.104
y[1] (analytic) = 0.6579482301645802597155898646028
y[1] (numeric) = 0.65794823016458025971558986460275
absolute error = 5e-32
relative error = 7.5993820953805008656445107532005e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.4MB, time=3.02
x[1] = 0.105
y[1] (analytic) = 0.6584248161719602018309286959577
y[1] (numeric) = 0.65842481617196020183092869595767
absolute error = 3e-32
relative error = 4.5563288720522538256726440602833e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.106
y[1] (analytic) = 0.6589015248294361663431331108386
y[1] (numeric) = 0.65890152482943616634313311083869
absolute error = 9e-32
relative error = 1.3659097241169305215594653257296e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.107
y[1] (analytic) = 0.6593783561156519620679240298475
y[1] (numeric) = 0.65937835611565196206792402984747
absolute error = 3e-32
relative error = 4.5497398757107727334552915196441e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.108
y[1] (analytic) = 0.6598553100092699221639483111091
y[1] (numeric) = 0.65985531000926992216394831110912
absolute error = 2e-32
relative error = 3.0309675009994284461911481373755e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.109
y[1] (analytic) = 0.6603323864889708828911793020446
y[1] (numeric) = 0.6603323864889708828911793020445
absolute error = 1.0e-31
relative error = 1.5143888448619994680789061859245e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 0.6608095855334541624051748158676
y[1] (numeric) = 0.66080958553345416240517481586755
absolute error = 5e-32
relative error = 7.5664761974716692066732939179987e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.4MB, time=3.17
x[1] = 0.111
y[1] (analytic) = 0.661286907121437539587116075046
y[1] (numeric) = 0.66128690712143753958711607504594
absolute error = 6e-32
relative error = 9.0732175934313043631985411909562e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.112
y[1] (analytic) = 0.6617643512316572329095513637445
y[1] (numeric) = 0.66176435123165723290955136374442
absolute error = 8e-32
relative error = 1.2088895367528674795939881700343e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.113
y[1] (analytic) = 0.6622419178428678793377683304356
y[1] (numeric) = 0.66224191784286787933776833043558
absolute error = 2e-32
relative error = 3.0200444069059155843880577279614e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.114
y[1] (analytic) = 0.6627196069338425132667190804147
y[1] (numeric) = 0.66271960693384251326671908041469
absolute error = 1e-32
relative error = 1.5089337776297710569697103286977e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.115
y[1] (analytic) = 0.6631974184833725454934223958961
y[1] (numeric) = 0.66319741848337254549342239589593
absolute error = 1.7e-31
relative error = 2.5633392902638715675787653092608e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.4MB, time=3.33
x[1] = 0.116
y[1] (analytic) = 0.663675352470267742224767618699
y[1] (numeric) = 0.66367535247026774222476761869896
absolute error = 4e-32
relative error = 6.0270431696937209991443630606705e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.117
y[1] (analytic) = 0.6641534088733562041206449272595
y[1] (numeric) = 0.66415340887335620412064492725946
absolute error = 4e-32
relative error = 6.0227049150970152016627455374861e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.118
y[1] (analytic) = 0.6646315876714843453723269358173
y[1] (numeric) = 0.66463158767148434537232693581719
absolute error = 1.1e-31
relative error = 1.6550522430837436680479513120522e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.119
y[1] (analytic) = 0.6651098888435168728160267391523
y[1] (numeric) = 0.66510988884351687281602673915234
absolute error = 4e-32
relative error = 6.0140437950112877964813068093466e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 0.665588312368336765081557721158
y[1] (numeric) = 0.66558831236833676508155772115794
absolute error = 6e-32
relative error = 9.0145813688501162562981840562195e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.121
y[1] (analytic) = 0.6660668582248452517760206398544
y[1] (numeric) = 0.66606685822484525177602063985426
absolute error = 1.4e-31
relative error = 2.1018910980365874424819182558834e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.4MB, time=3.48
x[1] = 0.122
y[1] (analytic) = 0.6665455263919617927024436951737
y[1] (numeric) = 0.66654552639196179270244369517368
absolute error = 2e-32
relative error = 3.0005452303101962647377347741537e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.123
y[1] (analytic) = 0.6670243168486240571133014789723
y[1] (numeric) = 0.66702431684862405711330147897226
absolute error = 4e-32
relative error = 5.9967828742707871351555935421854e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.124
y[1] (analytic) = 0.6675032295737879029988388992606
y[1] (numeric) = 0.66750322957378790299883889926049
absolute error = 1.1e-31
relative error = 1.6479321016954009297889502358256e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.125
y[1] (analytic) = 0.6679822645464273564101263625918
y[1] (numeric) = 0.66798226454642735641012636259178
absolute error = 2e-32
relative error = 2.9940914694165390497802346751214e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.126
y[1] (analytic) = 0.6684614217455345908167726899054
y[1] (numeric) = 0.66846142174553459081677268990542
absolute error = 2e-32
relative error = 2.9919452865020332939775366248130e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.127
y[1] (analytic) = 0.6689407011501199064992224318933
y[1] (numeric) = 0.66894070115011990649922243189329
absolute error = 1e-32
relative error = 1.4949008159926355404670977482856e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
memory used=91.5MB, alloc=4.4MB, time=3.64
TOP MAIN SOLVE Loop
x[1] = 0.128
y[1] (analytic) = 0.6694201027392117099755644401484
y[1] (numeric) = 0.66942010273921170997556444014838
absolute error = 2e-32
relative error = 2.9876605017031388336013399063594e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.129
y[1] (analytic) = 0.6698996264918564934627787399603
y[1] (numeric) = 0.66989962649185649346277873996024
absolute error = 6e-32
relative error = 8.9565656745039816067450437942941e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 0.6703792723871188143723489396501
y[1] (numeric) = 0.67037927238711881437234893965009
absolute error = 1e-32
relative error = 1.4916928986171541617707934915930e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.131
y[1] (analytic) = 0.6708590404040812748401675997883
y[1] (numeric) = 0.67085904040408127484016759978817
absolute error = 1.3e-31
relative error = 1.9378139395974535468500408627796e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.132
y[1] (analytic) = 0.6713389305218445012906621735106
y[1] (numeric) = 0.67133893052184450129066217351048
absolute error = 1.2e-31
relative error = 1.7874726839797853055503388545061e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.4MB, time=3.80
x[1] = 0.133
y[1] (analytic) = 0.6718189427195271240350693164531
y[1] (numeric) = 0.671818942719527124035069316453
absolute error = 1.0e-31
relative error = 1.4884962843589881235862661113392e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.134
y[1] (analytic) = 0.672299076976265756903785551551
y[1] (numeric) = 0.67229907697626575690378555155086
absolute error = 1.4e-31
relative error = 2.0824065478367811937833537835391e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.135
y[1] (analytic) = 0.6727793332712149769127224601103
y[1] (numeric) = 0.6727793332712149769127224601101
absolute error = 2.0e-31
relative error = 2.9727429204394832346396502840342e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.136
y[1] (analytic) = 0.6732597115835473039635947561522
y[1] (numeric) = 0.67325971158354730396359475615218
absolute error = 2e-32
relative error = 2.9706218352140510557974773211427e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.137
y[1] (analytic) = 0.6737402118924531805780697860585
y[1] (numeric) = 0.67374021189245318057806978605837
absolute error = 1.3e-31
relative error = 1.9295271041466566092976211009857e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.138
y[1] (analytic) = 0.6742208341771409516657071800052
y[1] (numeric) = 0.67422083417714095166570718000503
absolute error = 1.7e-31
relative error = 2.5214290538422484551179272512152e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.4MB, time=3.95
x[1] = 0.139
y[1] (analytic) = 0.6747015784168368443256175655827
y[1] (numeric) = 0.67470157841683684432561756558268
absolute error = 2e-32
relative error = 2.9642734862024905391480450671527e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 0.6751824445907849476817694373346
y[1] (numeric) = 0.67518244459078494768176943733446
absolute error = 1.4e-31
relative error = 2.0735136276366204805811912000800e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.141
y[1] (analytic) = 0.6756634326782471927518734587348
y[1] (numeric) = 0.67566343267824719275187345873467
absolute error = 1.3e-31
relative error = 1.9240348628117390191115182901036e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.142
y[1] (analytic) = 0.6761445426585033323497736553574
y[1] (numeric) = 0.67614454265850333234977365535735
absolute error = 5e-32
relative error = 7.3948685296500617628840718182296e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.143
y[1] (analytic) = 0.6766257745108509210212751396609
y[1] (numeric) = 0.6766257745108509210212751396608
absolute error = 1.0e-31
relative error = 1.4779218257284450919086321054780e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=103.0MB, alloc=4.4MB, time=4.10
x[1] = 0.144
y[1] (analytic) = 0.677107128214605295013338188938
y[1] (numeric) = 0.67710712821460529501333818893786
absolute error = 1.4e-31
relative error = 2.0676196449024501720063654877639e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.145
y[1] (analytic) = 0.6775886037490995522765686785562
y[1] (numeric) = 0.67758860374909955227656867855609
absolute error = 1.1e-31
relative error = 1.6234039266801375721484580794231e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.146
y[1] (analytic) = 0.6780702010936845325009350526384
y[1] (numeric) = 0.67807020109368453250093505263836
absolute error = 4e-32
relative error = 5.8990942140625733180930287324903e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.147
y[1] (analytic) = 0.6785519202277287971846421938149
y[1] (numeric) = 0.67855192022772879718464219381481
absolute error = 9e-32
relative error = 1.3263539210057072963970632483184e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.148
y[1] (analytic) = 0.6790337611306186097360927326137
y[1] (numeric) = 0.67903376113061860973609273261357
absolute error = 1.3e-31
relative error = 1.9144850733716797055628132570268e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.149
y[1] (analytic) = 0.679515723781757915608866515452
y[1] (numeric) = 0.67951572378175791560886651545186
absolute error = 1.4e-31
relative error = 2.0602908085900925532057233508706e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.4MB, time=4.26
x[1] = 0.15
y[1] (analytic) = 0.6799978081605683224696491280433
y[1] (numeric) = 0.6799978081605683224696491280432
absolute error = 1.0e-31
relative error = 1.4705929754465757820455995020002e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.151
y[1] (analytic) = 0.6804800142464890803990405483521
y[1] (numeric) = 0.680480014246489080399040548352
absolute error = 1.0e-31
relative error = 1.4695508744769273361062685272543e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.152
y[1] (analytic) = 0.6809623420189770621251751800064
y[1] (numeric) = 0.68096234201897706212517518000626
absolute error = 1.4e-31
relative error = 2.0559139817470035555128698180933e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.153
y[1] (analytic) = 0.6814447914575067432900846933234
y[1] (numeric) = 0.68144479145750674329008469332334
absolute error = 6e-32
relative error = 8.8048218655643588638662325157754e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.154
y[1] (analytic) = 0.6819273625415701827487352768161
y[1] (numeric) = 0.68192736254157018274873527681605
absolute error = 5e-32
relative error = 7.3321592220098087077393489713252e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.4MB, time=4.41
x[1] = 0.155
y[1] (analytic) = 0.682410055250677002900671077227
y[1] (numeric) = 0.68241005525067700290067107722689
absolute error = 1.1e-31
relative error = 1.6119340439611857785217589926657e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.156
y[1] (analytic) = 0.6828928695643543700541957807906
y[1] (numeric) = 0.68289286956435437005419578079056
absolute error = 4e-32
relative error = 5.8574341280672114508793931306699e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.157
y[1] (analytic) = 0.6833758054621469748230244625494
y[1] (numeric) = 0.68337580546214697482302446254938
absolute error = 2e-32
relative error = 2.9266473644724058881998319183281e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.158
y[1] (analytic) = 0.6838588629236170125553380041459
y[1] (numeric) = 0.68385886292361701255533800414583
absolute error = 7e-32
relative error = 1.0236030238862106506351128203046e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.159
y[1] (analytic) = 0.6843420419283441637951725535923
y[1] (numeric) = 0.68434204192834416379517255359218
absolute error = 1.2e-31
relative error = 1.7535091028729302605949447299728e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 0.6848253424559255747760766730715
y[1] (numeric) = 0.68482534245592557477607667307149
absolute error = 1e-32
relative error = 1.4602263351028932408652737240844e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.4MB, time=4.57
x[1] = 0.161
y[1] (analytic) = 0.6853087644859758379469689928586
y[1] (numeric) = 0.68530876448597583794696899285844
absolute error = 1.6e-31
relative error = 2.3347140484918494109869767894935e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.162
y[1] (analytic) = 0.6857923079981269725301293609648
y[1] (numeric) = 0.68579230799812697253012936096471
absolute error = 9e-32
relative error = 1.3123506774626262924911529366328e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.163
y[1] (analytic) = 0.6862759729720284051112566491137
y[1] (numeric) = 0.68627597297202840511125664911357
absolute error = 1.3e-31
relative error = 1.8942816755920232102236661384080e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.164
y[1] (analytic) = 0.6867597593873469502615265461338
y[1] (numeric) = 0.6867597593873469502615265461337
absolute error = 1.0e-31
relative error = 1.4561132715348555608011965726562e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.165
y[1] (analytic) = 0.6872436672237667911915828398352
y[1] (numeric) = 0.68724366722376679119158283983508
absolute error = 1.2e-31
relative error = 1.7461055768583452919394895600924e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.4MB, time=4.72
x[1] = 0.166
y[1] (analytic) = 0.6877276964609894604373958578915
y[1] (numeric) = 0.68772769646098946043739585789148
absolute error = 2e-32
relative error = 2.9081277521494259504907582764615e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.167
y[1] (analytic) = 0.6882118470787338205779219072069
y[1] (numeric) = 0.68821184707873382057792190720678
absolute error = 1.2e-31
relative error = 1.7436491468341663710452112206287e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.168
y[1] (analytic) = 0.6886961190567360449844977196877
y[1] (numeric) = 0.68869611905673604498449771968762
absolute error = 8e-32
relative error = 1.1616153741300443394522361983133e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.169
y[1] (analytic) = 0.6891805123747495986019040802846
y[1] (numeric) = 0.68918051237474959860190408028443
absolute error = 1.7e-31
relative error = 2.4666977221137762217594905336857e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 0.6896650270125452187610329805987
y[1] (numeric) = 0.68966502701254521876103298059859
absolute error = 1.1e-31
relative error = 1.5949772091023990143448995864653e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.171
y[1] (analytic) = 0.6901496629499108960230928082872
y[1] (numeric) = 0.69014966294991089602309280828714
absolute error = 6e-32
relative error = 8.6937664713971800819915243456635e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.4MB, time=4.87
x[1] = 0.172
y[1] (analytic) = 0.6906344201666518550552862489296
y[1] (numeric) = 0.69063442016665185505528624892961
absolute error = 1e-32
relative error = 1.4479440508607975807342216467565e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.173
y[1] (analytic) = 0.6911192986425905355378957429561
y[1] (numeric) = 0.69111929864259053553789574295599
absolute error = 1.1e-31
relative error = 1.5916210155909137979505025957910e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.174
y[1] (analytic) = 0.6916042983575665731027115056725
y[1] (numeric) = 0.69160429835756657310271150567243
absolute error = 7e-32
relative error = 1.0121394584480918919053356086786e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.175
y[1] (analytic) = 0.6920894192914367803027372833639
y[1] (numeric) = 0.69208941929143678030273728336367
absolute error = 2.3e-31
relative error = 3.3232699935721411354168337025967e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.176
y[1] (analytic) = 0.6925746614240751276131091828998
y[1] (numeric) = 0.69257466142407512761310918289984
absolute error = 4e-32
relative error = 5.7755505980758551648556669579736e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.4MB, time=5.03
x[1] = 0.177
y[1] (analytic) = 0.6930600247353727244631630762324
y[1] (numeric) = 0.69306002473537272446316307623235
absolute error = 5e-32
relative error = 7.2143823356557353631320164616672e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.178
y[1] (analytic) = 0.6935455092052378002995862446305
y[1] (numeric) = 0.69354550920523780029958624463039
absolute error = 1.1e-31
relative error = 1.5860530929838116103173373437163e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.179
y[1] (analytic) = 0.694031114813595685680589090488
y[1] (numeric) = 0.69403111481359568568058909048803
absolute error = 3e-32
relative error = 4.3225727722679208895560207242954e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 0.6945168415403887934010329070236
y[1] (numeric) = 0.69451684154038879340103290702344
absolute error = 1.6e-31
relative error = 2.3037598288492388132059561641577e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.181
y[1] (analytic) = 0.6950026893655765996484498581985
y[1] (numeric) = 0.69500268936557659964844985819847
absolute error = 3e-32
relative error = 4.3165300593851049382194145733871e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.182
y[1] (analytic) = 0.69548865826913562518989148271
y[1] (numeric) = 0.69548865826913562518989148270995
absolute error = 5e-32
relative error = 7.1891898459473265719340409813740e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.4MB, time=5.18
x[1] = 0.183
y[1] (analytic) = 0.6959747482310594165895421969455
y[1] (numeric) = 0.69597474823105941658954219694546
absolute error = 4e-32
relative error = 5.7473349574344386095320189392936e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.184
y[1] (analytic) = 0.6964609592313585274570344323578
y[1] (numeric) = 0.69646095923135852745703443235773
absolute error = 7e-32
relative error = 1.0050814632489196464612863967068e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.185
y[1] (analytic) = 0.6969472912500604997264022027948
y[1] (numeric) = 0.69694729125006049972640220279478
absolute error = 2e-32
relative error = 2.8696574692366686008096930728494e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.186
y[1] (analytic) = 0.6974337442672098449656100569291
y[1] (numeric) = 0.69743374426720984496561005692892
absolute error = 1.8e-31
relative error = 2.5808903208307636710757832781687e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.187
y[1] (analytic) = 0.6979203182628680257165945300589
y[1] (numeric) = 0.6979203182628680257165945300588
absolute error = 1.0e-31
relative error = 1.4328283241402283508852387512258e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.188
y[1] (analytic) = 0.6984070132171134368657553682163
y[1] (numeric) = 0.69840701321711343686575536821613
absolute error = 1.7e-31
relative error = 2.4341107231572456377718836077625e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
memory used=133.5MB, alloc=4.4MB, time=5.34
TOP MAIN SOLVE Loop
x[1] = 0.189
y[1] (analytic) = 0.6988938291100413870448339556942
y[1] (numeric) = 0.69889382911004138704483395569424
absolute error = 4e-32
relative error = 5.7233299728708819823762047444248e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 0.6993807659217640800621165348311
y[1] (numeric) = 0.69938076592176408006211653483092
absolute error = 1.8e-31
relative error = 2.5737053229189837393778057116017e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.191
y[1] (analytic) = 0.6998678236324105963638999641248
y[1] (numeric) = 0.69986782363241059636389996412467
absolute error = 1.3e-31
relative error = 1.8574935953660800999739812199881e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.192
y[1] (analytic) = 0.7003550022221268745261579175431
y[1] (numeric) = 0.70035500222212687452615791754294
absolute error = 1.6e-31
relative error = 2.2845556823659821402904328837684e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.193
y[1] (analytic) = 0.7008423016710756927763455841952
y[1] (numeric) = 0.70084230167107569277634558419514
absolute error = 6e-32
relative error = 8.5611270690905909247674059683368e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.4MB, time=5.49
x[1] = 0.194
y[1] (analytic) = 0.7013297219594366505452810833935
y[1] (numeric) = 0.70132972195943665054528108339338
absolute error = 1.2e-31
relative error = 1.7110354265998230828417288758602e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.195
y[1] (analytic) = 0.7018172630674061500490419655119
y[1] (numeric) = 0.70181726306740615004904196551192
absolute error = 2e-32
relative error = 2.8497446632456370393211715902026e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.196
y[1] (analytic) = 0.7023049249751973779008153239836
y[1] (numeric) = 0.70230492497519737790081532398353
absolute error = 7e-32
relative error = 9.9671805665426769048875678003106e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.197
y[1] (analytic) = 0.7027927076630402867526401982392
y[1] (numeric) = 0.7027927076630402867526401982391
absolute error = 1.0e-31
relative error = 1.4228946730612039603232466409710e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.198
y[1] (analytic) = 0.7032806111111815769669811014075
y[1] (numeric) = 0.70328061111118157696698110140753
absolute error = 3e-32
relative error = 4.2657226043243359569136803217350e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.199
y[1] (analytic) = 0.7037686352998846783180716601475
y[1] (numeric) = 0.70376863529988467831807166014745
absolute error = 5e-32
relative error = 7.1046076071142855537522038492403e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=5.65
x[1] = 0.2
y[1] (analytic) = 0.7042567802094297317229675070826
y[1] (numeric) = 0.70425678020942973172296750708252
absolute error = 8e-32
relative error = 1.1359493049709772645838593580654e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.201
y[1] (analytic) = 0.7047450458201135710022477189595
y[1] (numeric) = 0.70474504582011357100224771895944
absolute error = 6e-32
relative error = 8.5137171741559176280548734326552e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.202
y[1] (analytic) = 0.7052334321122497046703042458437
y[1] (numeric) = 0.70523343211224970467030424584366
absolute error = 4e-32
relative error = 5.6718808523010194579148327014279e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.203
y[1] (analytic) = 0.7057219390661682977551589284141
y[1] (numeric) = 0.70572193906616829775515892841404
absolute error = 6e-32
relative error = 8.5019320894846683036289140567505e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.204
y[1] (analytic) = 0.7062105666622161536477478517158
y[1] (numeric) = 0.70621056666221615364774785171567
absolute error = 1.3e-31
relative error = 1.8408107459284110855937632507824e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.4MB, time=5.80
x[1] = 0.205
y[1] (analytic) = 0.706699314880756695980612934581
y[1] (numeric) = 0.70669931488075669598061293458102
absolute error = 2e-32
relative error = 2.8300579297115428194593207592860e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.206
y[1] (analytic) = 0.707188183702169950535940804336
y[1] (numeric) = 0.70718818370216995053594080433593
absolute error = 7e-32
relative error = 9.8983554325732734359375793585828e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.207
y[1] (analytic) = 0.7076771731068525271828891563688
y[1] (numeric) = 0.70767717310685252718288915636882
absolute error = 2e-32
relative error = 2.8261473960218001952476841993834e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.208
y[1] (analytic) = 0.708166283075217601844140947662
y[1] (numeric) = 0.70816628307521760184414094766197
absolute error = 3e-32
relative error = 4.2362931866403983904331624868430e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.209
y[1] (analytic) = 0.7086555135876948984916269224629
y[1] (numeric) = 0.70865551358769489849162692246278
absolute error = 1.2e-31
relative error = 1.6933474403166441576135082340716e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 0.7091448646247306711713571169135
y[1] (numeric) = 0.7091448646247306711713571169134
absolute error = 1.0e-31
relative error = 1.4101491104066384379877121972699e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.4MB, time=5.96
x[1] = 0.211
y[1] (analytic) = 0.7096343361667876860573021376597
y[1] (numeric) = 0.70963433616678768605730213765957
absolute error = 1.3e-31
relative error = 1.8319293948235006700930470118215e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.212
y[1] (analytic) = 0.710123928194345203534265157226
y[1] (numeric) = 0.71012392819434520353426515722575
absolute error = 2.5e-31
relative error = 3.5205122665797642675782058115708e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.213
y[1] (analytic) = 0.7106136406878989603096857162753
y[1] (numeric) = 0.71061364068789896030968571627529
absolute error = 1e-32
relative error = 1.4072344558879630862175737381478e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.214
y[1] (analytic) = 0.7111034736279611515543165697729
y[1] (numeric) = 0.71110347362796115155431656977279
absolute error = 1.1e-31
relative error = 1.5468916139418322891236557009788e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.215
y[1] (analytic) = 0.7115934269950604130717149605324
y[1] (numeric) = 0.71159342699506041307171496053228
absolute error = 1.2e-31
relative error = 1.6863562175769365322268150147027e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.4MB, time=6.12
x[1] = 0.216
y[1] (analytic) = 0.7120835007697418034964898496711
y[1] (numeric) = 0.71208350076974180349648984967106
absolute error = 4e-32
relative error = 5.6173187493827829672158528602641e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.217
y[1] (analytic) = 0.7125736949325667865212467790967
y[1] (numeric) = 0.71257369493256678652124677909661
absolute error = 9e-32
relative error = 1.2630272579528353017788817684217e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.218
y[1] (analytic) = 0.7130640094641132131521721863338
y[1] (numeric) = 0.71306400946411321315217218633378
absolute error = 2e-32
relative error = 2.8047972881187115396406522690743e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.219
y[1] (analytic) = 0.7135544443449753039931991367536
y[1] (numeric) = 0.7135544443449753039931991367536
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 0.7140449995557636315586965825946
y[1] (numeric) = 0.7140449995557636315586965825945
absolute error = 1.0e-31
relative error = 1.4004719599214903508593961172008e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.221
y[1] (analytic) = 0.7145356750771051026146244020733
y[1] (numeric) = 0.71453567507710510261462440207328
absolute error = 2e-32
relative error = 2.7990204964702164624589626272560e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.4MB, time=6.27
x[1] = 0.222
y[1] (analytic) = 0.7150264708896429405480966153678
y[1] (numeric) = 0.71502647088964294054809661536773
absolute error = 7e-32
relative error = 9.7898473482954154376207644802094e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.223
y[1] (analytic) = 0.7155173869740366677652953173176
y[1] (numeric) = 0.7155173869740366677652953173176
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.224
y[1] (analytic) = 0.7160084233109620881176780093363
y[1] (numeric) = 0.71600842331096208811767800933616
absolute error = 1.4e-31
relative error = 1.9552842598221511755903958163412e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.225
y[1] (analytic) = 0.7164995798811112693564211552532
y[1] (numeric) = 0.71649957988111126935642115525313
absolute error = 7e-32
relative error = 9.7697196154134655093868724987916e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.226
y[1] (analytic) = 0.716990856665192525615042927622
y[1] (numeric) = 0.71699085666519252561504292762193
absolute error = 7e-32
relative error = 9.7630254764444421668885463740285e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.4MB, time=6.43
x[1] = 0.227
y[1] (analytic) = 0.7174822536439303999201482524222
y[1] (numeric) = 0.71748225364393039992014825242215
absolute error = 5e-32
relative error = 6.9688134788088886006518028462698e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.228
y[1] (analytic) = 0.7179737707980656467302394010729
y[1] (numeric) = 0.71797377079806564673023940107277
absolute error = 1.3e-31
relative error = 1.8106511029713265938731535351185e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.229
y[1] (analytic) = 0.7184654081083552145025355192442
y[1] (numeric) = 0.71846540810835521450253551924421
absolute error = 1e-32
relative error = 1.3918554584734929969524430429514e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 0.7189571655555722282877446221203
y[1] (numeric) = 0.71895716555557222828774462212016
absolute error = 1.4e-31
relative error = 1.9472648261571379450200363636562e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.231
y[1] (analytic) = 0.7194490431205059723527317255132
y[1] (numeric) = 0.71944904312050597235273172551307
absolute error = 1.3e-31
relative error = 1.8069382570326848684889084282987e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.232
y[1] (analytic) = 0.7199410407839618728310269215833
y[1] (numeric) = 0.71994104078396187283102692158327
absolute error = 3e-32
relative error = 4.1670078937758912695042074413665e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.4MB, time=6.58
x[1] = 0.233
y[1] (analytic) = 0.720433158526761480401117346851
y[1] (numeric) = 0.72043315852676148040111734685101
absolute error = 1e-32
relative error = 1.3880538231262624828458815617824e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.234
y[1] (analytic) = 0.7209253963297424529924671287255
y[1] (numeric) = 0.72092539632974245299246712872539
absolute error = 1.1e-31
relative error = 1.5258166872746337024881589536330e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.235
y[1] (analytic) = 0.7214177541737585385192095349051
y[1] (numeric) = 0.72141775417375853851920953490501
absolute error = 9e-32
relative error = 1.2475434584095759194852748581171e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.236
y[1] (analytic) = 0.7219102320396795576414556877343
y[1] (numeric) = 0.72191023203967955764145568773431
absolute error = 1e-32
relative error = 1.3852137781377717472837310822134e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.237
y[1] (analytic) = 0.7224028299083913865541643429273
y[1] (numeric) = 0.72240282990839138655416434292722
absolute error = 8e-32
relative error = 1.1074153739146464679726163367853e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.238
y[1] (analytic) = 0.7228955477607959398035173689986
y[1] (numeric) = 0.72289554776079593980351736899859
absolute error = 1e-32
relative error = 1.3833257143408180561163497145094e-30 %
Correct digits = 31
h = 0.001
memory used=167.8MB, alloc=4.4MB, time=6.74
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.239
y[1] (analytic) = 0.723388385577811153130745700274
y[1] (numeric) = 0.72338838557781115313074570027399
absolute error = 1e-32
relative error = 1.3823832673249841165728739666768e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 0.7238813433403709663433506724822
y[1] (numeric) = 0.72388134334037096634335067248219
absolute error = 1e-32
relative error = 1.3814418746938160749962799796264e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.241
y[1] (analytic) = 0.7243744210294253062136657856727
y[1] (numeric) = 0.72437442102942530621366578567254
absolute error = 1.6e-31
relative error = 2.2088024556778286782936844502926e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.242
y[1] (analytic) = 0.7248676186259400694047040745436
y[1] (numeric) = 0.72486761862594006940470407454353
absolute error = 7e-32
relative error = 9.6569357219587328619780952926201e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.243
y[1] (analytic) = 0.7253609361108971054232364012199
y[1] (numeric) = 0.72536093611089710542323640121978
absolute error = 1.2e-31
relative error = 1.6543488079657732020961963920195e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.4MB, time=6.90
x[1] = 0.244
y[1] (analytic) = 0.7258543734652941996000461200743
y[1] (numeric) = 0.72585437346529419960004612007421
absolute error = 9e-32
relative error = 1.2399181335827996512807510092850e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.245
y[1] (analytic) = 0.7263479306701450560973056983617
y[1] (numeric) = 0.7263479306701450560973056983616
absolute error = 1.0e-31
relative error = 1.3767506697201950382213613610672e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.246
y[1] (analytic) = 0.7268416077064792809430210102102
y[1] (numeric) = 0.72684160770647928094302101021003
absolute error = 1.7e-31
relative error = 2.3388864671139074878331832770606e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.247
y[1] (analytic) = 0.7273354045553423650924891549096
y[1] (numeric) = 0.72733540455534236509248915490957
absolute error = 3e-32
relative error = 4.1246445329222694484993633503239e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.248
y[1] (analytic) = 0.7278293211977956675167157834441
y[1] (numeric) = 0.72782932119779566751671578344408
absolute error = 2e-32
relative error = 2.7478969886903991339128934343614e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.249
y[1] (analytic) = 0.7283233576149163983177380498334
y[1] (numeric) = 0.72832335761491639831773804983339
absolute error = 1e-32
relative error = 1.3730165173814542766353052076948e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.4MB, time=7.05
x[1] = 0.25
y[1] (analytic) = 0.7288175137877976018707994360911
y[1] (numeric) = 0.72881751378779760187079943609093
absolute error = 1.7e-31
relative error = 2.3325454833882761842087504543316e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.251
y[1] (analytic) = 0.7293117896975481399933228314572
y[1] (numeric) = 0.72931178969754813999332283145712
absolute error = 8e-32
relative error = 1.0969245407807912547884636793271e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.252
y[1] (analytic) = 0.729806185325292675140628378043
y[1] (numeric) = 0.72980618532529267514062837804294
absolute error = 6e-32
relative error = 8.2213608498339206810930137489737e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.253
y[1] (analytic) = 0.7303007006521716536283427261124
y[1] (numeric) = 0.73030070065217165362834272611228
absolute error = 1.2e-31
relative error = 1.6431587686118586887572375919203e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.254
y[1] (analytic) = 0.7307953356593412888814464729472
y[1] (numeric) = 0.73079533565934128888144647294718
absolute error = 2e-32
relative error = 2.7367443419648422608361269922999e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.4MB, time=7.21
x[1] = 0.255
y[1] (analytic) = 0.7312900903279735447099066895784
y[1] (numeric) = 0.7312900903279735447099066895783
absolute error = 1.0e-31
relative error = 1.3674463981202230671657483515545e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.256
y[1] (analytic) = 0.7317849646392561186108415696249
y[1] (numeric) = 0.73178496463925611861084156962491
absolute error = 1e-32
relative error = 1.3665216536567737837336899077912e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.257
y[1] (analytic) = 0.732279958574392425097164364076
y[1] (numeric) = 0.73227995857439242509716436407591
absolute error = 9e-32
relative error = 1.2290381423958755960549161948423e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.258
y[1] (analytic) = 0.732775072114601579052653895057
y[1] (numeric) = 0.73277507211460157905265389505695
absolute error = 5e-32
relative error = 6.8233762177134081206568641633587e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.259
y[1] (analytic) = 0.7332703052411183791133990704699
y[1] (numeric) = 0.73327030524111837911339907046978
absolute error = 1.2e-31
relative error = 1.6365042896499248503830870081907e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 0.7337656579351932910755649498601
y[1] (numeric) = 0.73376565793519329107556494986003
absolute error = 7e-32
relative error = 9.5398304953353990547478719028386e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.4MB, time=7.36
x[1] = 0.261
y[1] (analytic) = 0.7342611301780924313294280399698
y[1] (numeric) = 0.73426113017809243132942803996975
absolute error = 5e-32
relative error = 6.8095665077453681149323332909251e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.262
y[1] (analytic) = 0.7347567219510975503196286261624
y[1] (numeric) = 0.73475672195109755031962862616239
absolute error = 1e-32
relative error = 1.3609946940595066438078772097262e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.263
y[1] (analytic) = 0.735252433235506016031588073272
y[1] (numeric) = 0.73525243323550601603158807327185
absolute error = 1.5e-31
relative error = 2.0401156557880312239125771150687e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.264
y[1] (analytic) = 0.7357482640126307975040391564251
y[1] (numeric) = 0.73574826401263079750403915642503
absolute error = 7e-32
relative error = 9.5141237056045966151897433375251e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.265
y[1] (analytic) = 0.73624421426380044836761760902
y[1] (numeric) = 0.73624421426380044836761760901988
absolute error = 1.2e-31
relative error = 1.6298939628339588442765386346291e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.4MB, time=7.52
x[1] = 0.266
y[1] (analytic) = 0.7367402839703590904094632013101
y[1] (numeric) = 0.73674028397035909040946320130997
absolute error = 1.3e-31
relative error = 1.7645295476367656594590830955858e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.267
y[1] (analytic) = 0.7372364731136663971637787889528
y[1] (numeric) = 0.73723647311366639716377878895272
absolute error = 8e-32
relative error = 1.0851335075993409020466204584576e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.268
y[1] (analytic) = 0.7377327816750975775282958964235
y[1] (numeric) = 0.73773278167509757752829589642334
absolute error = 1.6e-31
relative error = 2.1688069714985915305488112444828e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.269
y[1] (analytic) = 0.7382292096360433594065955253814
y[1] (numeric) = 0.73822920963604335940659552538132
absolute error = 8e-32
relative error = 1.0836742702099398733939543951317e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 0.7387257569779099733762330029017
y[1] (numeric) = 0.73872575697790997337623300290162
absolute error = 8e-32
relative error = 1.0829458597365819246420012600351e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.271
y[1] (analytic) = 0.7392224236821191363826158089509
y[1] (numeric) = 0.73922242368211913638261580895088
absolute error = 2e-32
relative error = 2.7055456327174961108653811626293e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.4MB, time=7.67
x[1] = 0.272
y[1] (analytic) = 0.7397192097301080354585834465999
y[1] (numeric) = 0.73971920973010803545858344659988
absolute error = 2e-32
relative error = 2.7037286225535695220458598143850e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.273
y[1] (analytic) = 0.7402161151033293114696385422192
y[1] (numeric) = 0.74021611510332931146963854221915
absolute error = 5e-32
relative error = 6.7547840393910267896337563698941e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.274
y[1] (analytic) = 0.7407131397832510428847784863063
y[1] (numeric) = 0.74071313978325104288477848630625
absolute error = 5e-32
relative error = 6.7502515230972005949519861857454e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.275
y[1] (analytic) = 0.7412102837513567295728770486412
y[1] (numeric) = 0.74121028375135672957287704864119
absolute error = 1e-32
relative error = 1.3491447999599743483076047010818e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.276
y[1] (analytic) = 0.7417075469891452766245655241632
y[1] (numeric) = 0.74170754698914527662456552416306
absolute error = 1.4e-31
relative error = 1.8875364093072773945821685975827e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.4MB, time=7.83
x[1] = 0.277
y[1] (analytic) = 0.7422049294781309781995630883063
y[1] (numeric) = 0.7422049294781309781995630883062
absolute error = 1.0e-31
relative error = 1.3473367802921132948642571676804e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.278
y[1] (analytic) = 0.7427024311998435013994061625305
y[1] (numeric) = 0.74270243119984350139940616253032
absolute error = 1.8e-31
relative error = 2.4235816719922153489513064280383e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.279
y[1] (analytic) = 0.7432000521358278701655267124262
y[1] (numeric) = 0.74320005213582787016552671242616
absolute error = 4e-32
relative error = 5.3821309464453005939676176279375e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 0.7436977922676444492026295220786
y[1] (numeric) = 0.74369779226764444920262952207851
absolute error = 9e-32
relative error = 1.2101689817523419370818670191552e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.281
y[1] (analytic) = 0.7441956515768689279273186093222
y[1] (numeric) = 0.74419565157686892792731860932209
absolute error = 1.1e-31
relative error = 1.4781059223729951912842740354335e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.282
y[1] (analytic) = 0.7446936300450923044419230671348
y[1] (numeric) = 0.74469363004509230444192306713475
absolute error = 5e-32
relative error = 6.7141704967950948900738384673685e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.4MB, time=7.98
x[1] = 0.283
y[1] (analytic) = 0.7451917276539208695334727366772
y[1] (numeric) = 0.74519172765392086953347273667711
absolute error = 9e-32
relative error = 1.2077428755596366525969036177751e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.284
y[1] (analytic) = 0.7456899443849761906977742374102
y[1] (numeric) = 0.74568994438497619069777423741005
absolute error = 1.5e-31
relative error = 2.0115599134666583718249276583501e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.285
y[1] (analytic) = 0.7461882802198950961885379993017
y[1] (numeric) = 0.74618828021989509618853799930178
absolute error = 8e-32
relative error = 1.0721154716665438181804002081949e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.286
y[1] (analytic) = 0.7466867351403296590915070613761
y[1] (numeric) = 0.74668673514032965909150706137603
absolute error = 7e-32
relative error = 9.3747480309589868430523923662237e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.287
y[1] (analytic) = 0.7471853091279471814235385197536
y[1] (numeric) = 0.74718530912794718142353851975357
absolute error = 3e-32
relative error = 4.0150682345472658860407204042790e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.288
memory used=202.1MB, alloc=4.4MB, time=8.14
y[1] (analytic) = 0.7476840021644301782565886269014
y[1] (numeric) = 0.74768400216443017825658862690121
absolute error = 1.9e-31
relative error = 2.5411804913570335276800499236918e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.289
y[1] (analytic) = 0.7481828142314763618665526620276
y[1] (numeric) = 0.74818281423147636186655266202751
absolute error = 9e-32
relative error = 1.2029145589563805648394220611761e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 0.7486817453107986259069108104533
y[1] (numeric) = 0.74868174531079862590691081045327
absolute error = 3e-32
relative error = 4.0070430710910635593967761519648e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.291
y[1] (analytic) = 0.7491807953841250296071314073389
y[1] (numeric) = 0.74918079538412502960713140733879
absolute error = 1.1e-31
relative error = 1.4682704185389597206738953767557e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.292
y[1] (analytic) = 0.7496799644331987819957830183699
y[1] (numeric) = 0.74967996443319878199578301836984
absolute error = 6e-32
relative error = 8.0034151700137077380175110820180e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.293
y[1] (analytic) = 0.7501792524397782261483069468916
y[1] (numeric) = 0.75017925243977822614830694689153
absolute error = 7e-32
relative error = 9.3311031693214357255897207227141e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=206.0MB, alloc=4.4MB, time=8.29
x[1] = 0.294
y[1] (analytic) = 0.7506786593856368234594018735347
y[1] (numeric) = 0.75067865938563682345940187353472
absolute error = 2e-32
relative error = 2.6642558370272849892294965712244e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.295
y[1] (analytic) = 0.7511781852525631379399724506047
y[1] (numeric) = 0.75117818525256313793997245060459
absolute error = 1.1e-31
relative error = 1.4643662736693492487785766810255e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.296
y[1] (analytic) = 0.7516778300223608205385937893963
y[1] (numeric) = 0.75167783002236082053859378939617
absolute error = 1.3e-31
relative error = 1.7294643370835185578515430814630e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.297
y[1] (analytic) = 0.7521775936768485934874438941689
y[1] (numeric) = 0.75217759367684859348744389416875
absolute error = 1.5e-31
relative error = 1.9942098948568677152117528095956e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.298
y[1] (analytic) = 0.7526774761978602346726562117504
y[1] (numeric) = 0.75267747619786023467265621175034
absolute error = 6e-32
relative error = 7.9715418485868824632340927454747e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.299
y[1] (analytic) = 0.7531774775672445620290445806569
y[1] (numeric) = 0.75317747756724456202904458065676
absolute error = 1.4e-31
relative error = 1.8587916416751938392266951719292e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
memory used=209.8MB, alloc=4.4MB, time=8.45
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 0.753677597766865417959152978198
y[1] (numeric) = 0.75367759776686541795915297819773
absolute error = 2.7e-31
relative error = 3.5824336665970389842357498227129e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.301
y[1] (analytic) = 0.7541778367786016537765825783062
y[1] (numeric) = 0.75417783677860165377658257830617
absolute error = 3e-32
relative error = 3.9778416358855259753857084220923e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.302
y[1] (analytic) = 0.7546781945843471141735487467675
y[1] (numeric) = 0.75467819458434711417354874676747
absolute error = 3e-32
relative error = 3.9752042943977003823677535459428e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.303
y[1] (analytic) = 0.7551786711660106217126207141443
y[1] (numeric) = 0.75517867116601062171262071414415
absolute error = 1.5e-31
relative error = 1.9862849114686603840122093378180e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.304
y[1] (analytic) = 0.7556792665055159613425967799888
y[1] (numeric) = 0.75567926650551596134259677998875
absolute error = 5e-32
relative error = 6.6165636952320740831603464097832e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.4MB, time=8.60
x[1] = 0.305
y[1] (analytic) = 0.7561799805848018649384680149155
y[1] (numeric) = 0.75617998058480186493846801491539
absolute error = 1.1e-31
relative error = 1.4546801399705138203424690369756e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.306
y[1] (analytic) = 0.7566808133858219958654235397591
y[1] (numeric) = 0.75668081338582199586542353975906
absolute error = 4e-32
relative error = 5.2862447801493950240939746731639e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.307
y[1] (analytic) = 0.7571817648905449335668505733925
y[1] (numeric) = 0.75718176489054493356685057339237
absolute error = 1.3e-31
relative error = 1.7168929050845837881273276985162e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.308
y[1] (analytic) = 0.7576828350809541581762825527935
y[1] (numeric) = 0.75768283508095415817628255279342
absolute error = 8e-32
relative error = 1.0558507636173709679876417302412e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.309
y[1] (analytic) = 0.7581840239390480351532487406665
y[1] (numeric) = 0.75818402393904803515324874066646
absolute error = 4e-32
relative error = 5.2757640278655728883654467903594e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 0.7586853314468397999429788473102
y[1] (numeric) = 0.75868533144683979994297884731009
absolute error = 1.1e-31
relative error = 1.4498764565571091741722185410824e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.4MB, time=8.76
x[1] = 0.311
y[1] (analytic) = 0.7591867575863575426599163045076
y[1] (numeric) = 0.75918675758635754265991630450747
absolute error = 1.3e-31
relative error = 1.7123586350913463030485262453182e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.312
y[1] (analytic) = 0.7596883023396441927949939399795
y[1] (numeric) = 0.75968830233964419279499393997943
absolute error = 7e-32
relative error = 9.2143053650316899208054801614316e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.313
y[1] (analytic) = 0.7601899656887575039466259113965
y[1] (numeric) = 0.76018996568875750394662591139643
absolute error = 7e-32
relative error = 9.2082246753385729800235849194084e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.314
y[1] (analytic) = 0.7606917476157700385753698690896
y[1] (numeric) = 0.76069174761577003857536986908957
absolute error = 3e-32
relative error = 3.9437788163245830063397348789496e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.315
y[1] (analytic) = 0.7611936481027691527822134264352
y[1] (numeric) = 0.76119364810276915278221342643515
absolute error = 5e-32
relative error = 6.5686307452278521685374526714991e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.4MB, time=8.91
x[1] = 0.316
y[1] (analytic) = 0.7616956671318569811104391264134
y[1] (numeric) = 0.76169566713185698111043912641334
absolute error = 6e-32
relative error = 7.8771617837775375286105864901104e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.317
y[1] (analytic) = 0.7621978046851504213710222020593
y[1] (numeric) = 0.76219780468515042137102220205923
absolute error = 7e-32
relative error = 9.1839676747580877021021294197006e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.318
y[1] (analytic) = 0.7627000607447811194915155374362
y[1] (numeric) = 0.76270006074478111949151553743613
absolute error = 7e-32
relative error = 9.1779198144608230475063888665043e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.319
y[1] (analytic) = 0.7632024352928954543883763443664
y[1] (numeric) = 0.76320243529289545438837634436644
absolute error = 4e-32
relative error = 5.2410734230229669252573140878543e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 0.7637049283116545228626891784563
y[1] (numeric) = 0.76370492831165452286268917845631
absolute error = 1e-32
relative error = 1.3094062417676550890195046943506e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.321
y[1] (analytic) = 0.7642075397832341245192400259476
y[1] (numeric) = 0.76420753978323412451924002594749
absolute error = 1.1e-31
relative error = 1.4393995645633288396751419989332e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.4MB, time=9.07
x[1] = 0.322
y[1] (analytic) = 0.764710269689824746708896300624
y[1] (numeric) = 0.76471026968982474670889630062398
absolute error = 2e-32
relative error = 2.6153696102593508144098147174843e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.323
y[1] (analytic) = 0.7652131180136315494942476973938
y[1] (numeric) = 0.76521311801363154949424769739379
absolute error = 1e-32
relative error = 1.3068254796726915805349506783211e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.324
y[1] (analytic) = 0.7657160847368743506384629562579
y[1] (numeric) = 0.7657160847368743506384629562578
absolute error = 1.0e-31
relative error = 1.3059670809235167577977565195323e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.325
y[1] (analytic) = 0.7662191698417876106173176971697
y[1] (numeric) = 0.76621916984178761061731769716959
absolute error = 1.1e-31
relative error = 1.4356205682339335889328046034331e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.326
y[1] (analytic) = 0.7667223733106204176543485927833
y[1] (numeric) = 0.76672237331062041765434859278322
absolute error = 8e-32
relative error = 1.0434024463714167583401684134158e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.4MB, time=9.22
x[1] = 0.327
y[1] (analytic) = 0.7672256951256364727790892522811
y[1] (numeric) = 0.76722569512563647277908925228106
absolute error = 4e-32
relative error = 5.2135897238751668458849232746269e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.328
y[1] (analytic) = 0.7677291352691140749083432953719
y[1] (numeric) = 0.76772913526911407490834329537187
absolute error = 3e-32
relative error = 3.9076281753308766359505864482267e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.329
y[1] (analytic) = 0.7682326937233461059504502011517
y[1] (numeric) = 0.76823269372334610595045020115162
absolute error = 8e-32
relative error = 1.0413511512022343728228255550064e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 0.7687363704706400159324996218269
y[1] (numeric) = 0.7687363704706400159324996218267
absolute error = 2.0e-31
relative error = 2.6016721425259858348973778874948e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.331
y[1] (analytic) = 0.7692401654933178081504499563123
y[1] (numeric) = 0.76924016549331780815044995631219
absolute error = 1.1e-31
relative error = 1.4299825325612894268767612579465e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.332
y[1] (analytic) = 0.7697440787737160243421070834381
y[1] (numeric) = 0.76974407877371602434210708343792
absolute error = 1.8e-31
relative error = 2.3384395536599527374056523556492e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.4MB, time=9.38
x[1] = 0.333
y[1] (analytic) = 0.7702481102941857298829192589228
y[1] (numeric) = 0.77024811029418572988291925892266
absolute error = 1.4e-31
relative error = 1.8175961502395496301956442598980e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.334
y[1] (analytic) = 0.7707522600370924990045442844134
y[1] (numeric) = 0.77075226003709249900454428441343
absolute error = 3e-32
relative error = 3.8923012692244649649757823331210e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.335
y[1] (analytic) = 0.7712565279848164000361451607332
y[1] (numeric) = 0.77125652798481640003614516073313
absolute error = 7e-32
relative error = 9.0760982189544693806329248370827e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.336
y[1] (analytic) = 0.7717609141197519806683705410363
y[1] (numeric) = 0.7717609141197519806683705410363
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.337
y[1] (analytic) = 0.7722654184243082532399764028416
y[1] (numeric) = 0.77226541842430825323997640284151
absolute error = 9e-32
relative error = 1.1654024361680146190204474726726e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.338
y[1] (analytic) = 0.7727700408809086800470454608894
y[1] (numeric) = 0.77277004088090868004704546088944
absolute error = 4e-32
relative error = 5.1761841018581083903714386026413e-30 %
Correct digits = 31
h = 0.001
memory used=236.5MB, alloc=4.4MB, time=9.54
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.339
y[1] (analytic) = 0.7732747814719911586747609454703
y[1] (numeric) = 0.77327478147199115867476094547023
absolute error = 7e-32
relative error = 9.0524095285700811414561842611130e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 0.773779640180008007351691473272
y[1] (numeric) = 0.77377964018000800735169147327197
absolute error = 3e-32
relative error = 3.8770728049940624568715528926735e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.341
y[1] (analytic) = 0.7742846169874259503265438399263
y[1] (numeric) = 0.77428461698742595032654383992631
absolute error = 1e-32
relative error = 1.2915147454314458769146076005976e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.342
y[1] (analytic) = 0.774789711876726103267340665267
y[1] (numeric) = 0.77478971187672610326734066526694
absolute error = 6e-32
relative error = 7.7440367470375466036753797775635e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.343
y[1] (analytic) = 0.7752949248304039586829799238739
y[1] (numeric) = 0.77529492483040395868297992387382
absolute error = 8e-32
relative error = 1.0318653900320581684724428874012e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.4MB, time=9.69
x[1] = 0.344
y[1] (analytic) = 0.7758002558309693713671334947511
y[1] (numeric) = 0.775800255830969371367133494751
absolute error = 1.0e-31
relative error = 1.2889915831864317631888953650428e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.345
y[1] (analytic) = 0.7763057048609465438644419649799
y[1] (numeric) = 0.77630570486094654386444196497976
absolute error = 1.4e-31
relative error = 1.8034132574753792982786806698130e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.346
y[1] (analytic) = 0.7768112719028740119589630229027
y[1] (numeric) = 0.77681127190287401195896302290255
absolute error = 1.5e-31
relative error = 1.9309709504158012030464909542729e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.347
y[1] (analytic) = 0.7773169569393046301848308768273
y[1] (numeric) = 0.77731695693930463018483087682733
absolute error = 3e-32
relative error = 3.8594295071247873230308481008573e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.348
y[1] (analytic) = 0.7778227599528055573590842353981
y[1] (numeric) = 0.77782275995280555735908423539805
absolute error = 5e-32
relative error = 6.4281996586257970904237483095887e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.349
y[1] (analytic) = 0.7783286809259582421366204856551
y[1] (numeric) = 0.77832868092595824213662048565511
absolute error = 1e-32
relative error = 1.2848042536609660995537761570455e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.4MB, time=9.85
x[1] = 0.35
y[1] (analytic) = 0.7788347198413584085872338044118
y[1] (numeric) = 0.77883471984135840858723380441161
absolute error = 1.9e-31
relative error = 2.4395419870174930351573398074596e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.351
y[1] (analytic) = 0.7793408766816160417946950378968
y[1] (numeric) = 0.77934087668161604179469503789682
absolute error = 2e-32
relative error = 2.5662711399354195088122894992675e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.352
y[1] (analytic) = 0.7798471514293553734778312836697
y[1] (numeric) = 0.77984715142935537347783128366957
absolute error = 1.3e-31
relative error = 1.6669933301894789587189791992589e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.353
y[1] (analytic) = 0.7803535440672148676335632075812
y[1] (numeric) = 0.78035354406721486763356320758118
absolute error = 2e-32
relative error = 2.5629408813548391700609572162663e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.354
y[1] (analytic) = 0.7808600545778472062018582270715
y[1] (numeric) = 0.7808600545778472062018582270714
absolute error = 1.0e-31
relative error = 1.2806392056264491830135151212750e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.4MB, time=10.00
x[1] = 0.355
y[1] (analytic) = 0.7813666829439192747525577903125
y[1] (numeric) = 0.78136668294391927475255779031249
absolute error = 1e-32
relative error = 1.2798088552129533385523697632866e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.356
y[1] (analytic) = 0.7818734291481121481940370786768
y[1] (numeric) = 0.78187342914811214819403707867677
absolute error = 3e-32
relative error = 3.8369381643633049537848735085219e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.357
y[1] (analytic) = 0.7823802931731210765036555576927
y[1] (numeric) = 0.7823802931731210765036555576926
absolute error = 1.0e-31
relative error = 1.2781508030375774777396173028365e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.358
y[1] (analytic) = 0.7828872750016554704799568990739
y[1] (numeric) = 0.78288727500165547047995689907388
absolute error = 2e-32
relative error = 2.5546461973031441322553499121503e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.359
y[1] (analytic) = 0.7833943746164388875165768935592
y[1] (numeric) = 0.78339437461643888751657689355916
absolute error = 4e-32
relative error = 5.1059850946191148273382535782322e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 0.78390159200020901739781807118
y[1] (numeric) = 0.78390159200020901739781807117988
absolute error = 1.2e-31
relative error = 1.5308043920896642792497313157981e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.4MB, time=10.16
x[1] = 0.361
y[1] (analytic) = 0.7844089271357176681158498421933
y[1] (numeric) = 0.78440892713571766811584984219324
absolute error = 6e-32
relative error = 7.6490715396484592116167972234369e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.362
y[1] (analytic) = 0.7849163800057307517094930682652
y[1] (numeric) = 0.78491638000573075170949306826518
absolute error = 2e-32
relative error = 2.5480421239080241939180244166674e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.363
y[1] (analytic) = 0.7854239505930282701245480695735
y[1] (numeric) = 0.78542395059302827012454806957338
absolute error = 1.2e-31
relative error = 1.5278372897770042472116686796084e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.364
y[1] (analytic) = 0.7859316388804043010956251693202
y[1] (numeric) = 0.78593163888040430109562516932005
absolute error = 1.5e-31
relative error = 1.9085629408390007808460670591108e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.365
y[1] (analytic) = 0.7864394448506669840494369727006
y[1] (numeric) = 0.78643944485066698404943697270053
absolute error = 7e-32
relative error = 8.9008760252726065405531867641879e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.4MB, time=10.31
x[1] = 0.366
y[1] (analytic) = 0.7869473684866385060295116726672
y[1] (numeric) = 0.78694736848663850602951167266701
absolute error = 1.9e-31
relative error = 2.4143927231802667802086487665351e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.367
y[1] (analytic) = 0.7874554097711550876422867698579
y[1] (numeric) = 0.78745540977115508764228676985782
absolute error = 8e-32
relative error = 1.0159305404130635606178028155158e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.368
y[1] (analytic) = 0.787963568687066969024542688833
y[1] (numeric) = 0.78796356868706696902454268883294
absolute error = 6e-32
relative error = 7.6145652393516291866923404563031e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.369
y[1] (analytic) = 0.7884718452172383958321358672659
y[1] (numeric) = 0.78847184521723839583213586726582
absolute error = 8e-32
relative error = 1.0146208832346897395534918105286e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 0.7889802393445476052499909889917
y[1] (numeric) = 0.78898023934454760524999098899181
absolute error = 1.1e-31
relative error = 1.3942047533583792217161171603526e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.371
y[1] (analytic) = 0.7894887510518868120233121258048
y[1] (numeric) = 0.78948875105188681202331212580473
absolute error = 7e-32
relative error = 8.8664974525266487468617193095641e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.4MB, time=10.47
x[1] = 0.372
y[1] (analytic) = 0.7899973803221621945099726466266
y[1] (numeric) = 0.78999738032216219450997264662655
absolute error = 5e-32
relative error = 6.3291349117651402938526964588223e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.373
y[1] (analytic) = 0.7905061271382938807540438461515
y[1] (numeric) = 0.79050612713829388075404384615142
absolute error = 8e-32
relative error = 1.0120098662562867501140028722877e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.374
y[1] (analytic) = 0.7910149914832159345804223382854
y[1] (numeric) = 0.79101499148321593458042233828532
absolute error = 8e-32
relative error = 1.0113588346788933302333226067457e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.375
y[1] (analytic) = 0.7915239733398763417105163526672
y[1] (numeric) = 0.79152397333987634171051635266704
absolute error = 1.6e-31
relative error = 2.0214169802699939091728753716687e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.376
y[1] (analytic) = 0.7920330726912369958989511652662
y[1] (numeric) = 0.79203307269123699589895116526612
absolute error = 8e-32
relative error = 1.0100588316112764134119600503429e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.4MB, time=10.62
x[1] = 0.377
y[1] (analytic) = 0.7925422895202736850912539865094
y[1] (numeric) = 0.79254228952027368509125398650926
absolute error = 1.4e-31
relative error = 1.7664672516685776162808260520670e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.378
y[1] (analytic) = 0.7930516238099760776024787225898
y[1] (numeric) = 0.79305162380997607760247872258971
absolute error = 9e-32
relative error = 1.1348567646532553267664353941505e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.379
y[1] (analytic) = 0.7935610755433477083167311175649
y[1] (numeric) = 0.79356107554334770831673111756474
absolute error = 1.6e-31
relative error = 2.0162279241134492111886376426115e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 0.7940706447034059649075548755455
y[1] (numeric) = 0.79407064470340596490755487554535
absolute error = 1.5e-31
relative error = 1.8890006953477877758919485169377e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.381
y[1] (analytic) = 0.7945803312731820740791394537311
y[1] (numeric) = 0.79458033127318207407913945373107
absolute error = 3e-32
relative error = 3.7755779773619638934867322763072e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.382
y[1] (analytic) = 0.7950901352357210878283103082411
y[1] (numeric) = 0.79509013523572108782831030824108
absolute error = 2e-32
relative error = 2.5154380759699127701636246492403e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.4MB, time=10.77
x[1] = 0.383
y[1] (analytic) = 0.7956000565740818697272624656426
y[1] (numeric) = 0.79560005657408186972726246564254
absolute error = 6e-32
relative error = 7.5414775934487546625394948167360e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.384
y[1] (analytic) = 0.7961100952713370812269983837782
y[1] (numeric) = 0.79611009527133708122699838377808
absolute error = 1.2e-31
relative error = 1.5073292087710628666803413795108e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.385
y[1] (analytic) = 0.7966202513105731679814311559483
y[1] (numeric) = 0.79662025131057316798143115594815
absolute error = 1.5e-31
relative error = 1.8829548929144719090770591041802e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.386
y[1] (analytic) = 0.7971305246748903461921142027108
y[1] (numeric) = 0.79713052467489034619211420271071
absolute error = 9e-32
relative error = 1.1290497254098567676352465038238e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.387
y[1] (analytic) = 0.7976409153474025889735586855218
y[1] (numeric) = 0.79764091534740258897355868552181
absolute error = 1e-32
relative error = 1.2536969716059041759107841120328e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.388
y[1] (analytic) = 0.7981514233112376127390999661562
y[1] (numeric) = 0.79815142331123761273909996615612
absolute error = 8e-32
relative error = 1.0023160726583601396846494413992e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
memory used=270.8MB, alloc=4.4MB, time=10.93
TOP MAIN SOLVE Loop
x[1] = 0.389
y[1] (analytic) = 0.7986620485495368636072745253181
y[1] (numeric) = 0.79866204854953686360727452531802
absolute error = 8e-32
relative error = 1.0016752410520732915547064622509e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 0.7991727910454555038286688430814
y[1] (numeric) = 0.79917279104545550382866884308125
absolute error = 1.5e-31
relative error = 1.8769407777731545808968209676936e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.391
y[1] (analytic) = 0.79968365078216239823320183278
y[1] (numeric) = 0.79968365078216239823320183277994
absolute error = 6e-32
relative error = 7.5029669471564929191032386041149e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.392
y[1] (analytic) = 0.8001946277428401006978025087165
y[1] (numeric) = 0.80019462774284010069780250871648
absolute error = 2e-32
relative error = 2.4993919362362219940312211905920e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.393
y[1] (analytic) = 0.8007057219106848406344446565529
y[1] (numeric) = 0.80070572191068484063444465655286
absolute error = 4e-32
relative error = 4.9955931255930030635372576975982e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.4MB, time=11.09
x[1] = 0.394
y[1] (analytic) = 0.8012169332689065094985003635128
y[1] (numeric) = 0.80121693326890650949850036351271
absolute error = 9e-32
relative error = 1.1232912868279827791769951927924e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.395
y[1] (analytic) = 0.8017282618007286473173743535422
y[1] (numeric) = 0.80172826180072864731737435354198
absolute error = 2.2e-31
relative error = 2.7440719066815370925552099211102e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.396
y[1] (analytic) = 0.8022397074893884292393811603581
y[1] (numeric) = 0.80223970748938842923938116035801
absolute error = 9e-32
relative error = 1.1218592044222701209677762992762e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.397
y[1] (analytic) = 0.8027512703181366521028272588598
y[1] (numeric) = 0.80275127031813665210282725885978
absolute error = 2e-32
relative error = 2.4914317472302276706376035985114e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.398
y[1] (analytic) = 0.803262950270237721025260362678
y[1] (numeric) = 0.80326295027023772102526036267794
absolute error = 6e-32
relative error = 7.4695341021037384173227724297102e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.399
y[1] (analytic) = 0.8037747473289696360128481827122
y[1] (numeric) = 0.80377474732896963601284818271204
absolute error = 1.6e-31
relative error = 1.9906074498072662038888858976907e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.4MB, time=11.24
x[1] = 0.4
y[1] (analytic) = 0.8042866614776239785898490283349
y[1] (numeric) = 0.80428666147762397858984902833491
absolute error = 1e-32
relative error = 1.2433377897413022719926098970569e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.401
y[1] (analytic) = 0.8047986926995058984481367195416
y[1] (numeric) = 0.8047986926995058984481367195416
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.402
y[1] (analytic) = 0.8053108409779341001167423646828
y[1] (numeric) = 0.80531084097793410011674236468278
absolute error = 2e-32
relative error = 2.4835130712648644832899898643507e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.403
y[1] (analytic) = 0.8058231062962408296513756445515
y[1] (numeric) = 0.80582310629624082965137564455131
absolute error = 1.9e-31
relative error = 2.3578375764537983354477526359213e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.404
y[1] (analytic) = 0.8063354886377718613438883294862
y[1] (numeric) = 0.8063354886377718613438883294862
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.4MB, time=11.40
x[1] = 0.405
y[1] (analytic) = 0.8068479879858864844516428418212
y[1] (numeric) = 0.80684798798588648445164284182115
absolute error = 5e-32
relative error = 6.1969541654077481680055189161513e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.406
y[1] (analytic) = 0.8073606043239574899467487614365
y[1] (numeric) = 0.80736060432395748994674876143644
absolute error = 6e-32
relative error = 7.4316234503714648935090518966486e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.407
y[1] (analytic) = 0.807873337635371157285130257373
y[1] (numeric) = 0.80787333763537115728513025737299
absolute error = 1e-32
relative error = 1.2378178031310943857978308654489e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.408
y[1] (analytic) = 0.8083861879035272411953875134378
y[1] (numeric) = 0.80838618790352724119538751343771
absolute error = 9e-32
relative error = 1.1133292644868963862145563737658e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.409
y[1] (analytic) = 0.8088991551118389584874153004696
y[1] (numeric) = 0.80889915511183895848741530046951
absolute error = 9e-32
relative error = 1.1126232414911663190978806265492e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 0.8094122392437329748807419324471
y[1] (numeric) = 0.80941223924373297488074193244716
absolute error = 6e-32
relative error = 7.4127863517433908363896403725499e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.4MB, time=11.55
x[1] = 0.411
y[1] (analytic) = 0.8099254402826493918525519279037
y[1] (numeric) = 0.80992544028264939185255192790359
absolute error = 1.1e-31
relative error = 1.3581497077263307238088872409624e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.412
y[1] (analytic) = 0.8104387582120417335053557821674
y[1] (numeric) = 0.81043875821204173350535578216724
absolute error = 1.6e-31
relative error = 1.9742392423702160709020768972501e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.413
y[1] (analytic) = 0.8109521930153769334542703397805
y[1] (numeric) = 0.81095219301537693345427033978047
absolute error = 3e-32
relative error = 3.6993549383534563859169594057943e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.414
y[1] (analytic) = 0.8114657446761353217338733400484
y[1] (numeric) = 0.81146574467613532173387334004832
absolute error = 8e-32
relative error = 9.8587032816682677916844174697429e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.415
y[1] (analytic) = 0.8119794131778106117245957920491
y[1] (numeric) = 0.81197941317781061172459579204901
absolute error = 9e-32
relative error = 1.1084024858188298376962560430496e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.4MB, time=11.71
x[1] = 0.416
y[1] (analytic) = 0.8124931985039098870986159185909
y[1] (numeric) = 0.81249319850390988709861591859076
absolute error = 1.4e-31
relative error = 1.7230913471988441603820398218167e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.417
y[1] (analytic) = 0.8130071006379535887852184915294
y[1] (numeric) = 0.81300710063795358878521849152927
absolute error = 1.3e-31
relative error = 1.5990020246808557020965961947502e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.418
y[1] (analytic) = 0.8135211195634755019555834635663
y[1] (numeric) = 0.81352111956347550195558346356619
absolute error = 1.1e-31
relative error = 1.3521468263666531664992964364874e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.419
y[1] (analytic) = 0.8140352552640227430269678841331
y[1] (numeric) = 0.81403525526402274302696788413294
absolute error = 1.6e-31
relative error = 1.9655168368365800732705573740765e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 0.8145495077231557466862451692259
y[1] (numeric) = 0.81454950772315574668624516922587
absolute error = 3e-32
relative error = 3.6830173875933667602311799391249e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.421
y[1] (analytic) = 0.8150638769244482529327658770997
y[1] (numeric) = 0.81506387692444825293276587709971
absolute error = 1e-32
relative error = 1.2268977049668639223512374325562e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.4MB, time=11.87
x[1] = 0.422
y[1] (analytic) = 0.8155783628514872941405042235466
y[1] (numeric) = 0.81557836285148729414050422354653
absolute error = 7e-32
relative error = 8.5828662441780161472393118971152e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.423
y[1] (analytic) = 0.8160929654878731821394546520879
y[1] (numeric) = 0.81609296548787318213945465208789
absolute error = 1e-32
relative error = 1.2253505939757541060050407035247e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.424
y[1] (analytic) = 0.8166076848172194953162428557894
y[1] (numeric) = 0.8166076848172194953162428557894
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) = 0.8171225208231530657339157285699
y[1] (numeric) = 0.81712252082315306573391572856988
absolute error = 2e-32
relative error = 2.4476133615620330200897135822101e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.426
y[1] (analytic) = 0.8176374734893139662708748048227
y[1] (numeric) = 0.81763747348931396627087480482262
absolute error = 8e-32
relative error = 9.7842873637622667312649987295611e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.427
y[1] (analytic) = 0.8181525427993554977789178268946
y[1] (numeric) = 0.81815254279935549777891782689447
absolute error = 1.3e-31
relative error = 1.5889457429930804818865596321217e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
memory used=297.5MB, alloc=4.4MB, time=12.02
TOP MAIN SOLVE Loop
x[1] = 0.428
y[1] (analytic) = 0.8186677287369441762603531604804
y[1] (numeric) = 0.81866772873694417626035316048027
absolute error = 1.3e-31
relative error = 1.5879458226668641490271361516137e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.429
y[1] (analytic) = 0.8191830312857597200641518582865
y[1] (numeric) = 0.81918303128575972006415185828638
absolute error = 1.2e-31
relative error = 1.4648740930540564251991256101174e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 0.819698450429495037101102252398
y[1] (numeric) = 0.81969845042949503710110225239798
absolute error = 2e-32
relative error = 2.4399216552770909328216773003929e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.431
y[1] (analytic) = 0.8202139861518562120779320356516
y[1] (numeric) = 0.82021398615185621207793203565153
absolute error = 7e-32
relative error = 8.5343582506333959093728084576388e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.432
y[1] (analytic) = 0.8207296384365624937503628719667
y[1] (numeric) = 0.82072963843656249375036287196675
absolute error = 5e-32
relative error = 6.0921401711831443506266115217821e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.4MB, time=12.18
x[1] = 0.433
y[1] (analytic) = 0.8212454072673462821950626550325
y[1] (numeric) = 0.82124540726734628219506265503236
absolute error = 1.4e-31
relative error = 1.7047279505141236306190267664173e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.434
y[1] (analytic) = 0.8217612926279531161004606139672
y[1] (numeric) = 0.82176129262795311610046061396718
absolute error = 2e-32
relative error = 2.4337967946921619165505108063175e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.435
y[1] (analytic) = 0.822277294502141660076390543594
y[1] (numeric) = 0.822277294502141660076390543594
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) = 0.8227934128736836919825275157683
y[1] (numeric) = 0.82279341287368369198252751576823
absolute error = 7e-32
relative error = 8.5076033551992583172342823318696e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.437
y[1] (analytic) = 0.8233096477263640902755835067975
y[1] (numeric) = 0.82330964772636409027558350679746
absolute error = 4e-32
relative error = 4.8584393624516877698308980060271e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.438
y[1] (analytic) = 0.8238259990439808213752274543724
y[1] (numeric) = 0.82382599904398082137522745437236
absolute error = 4e-32
relative error = 4.8553942272298397975006053118622e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.4MB, time=12.33
x[1] = 0.439
y[1] (analytic) = 0.8243424668103449270486953356048
y[1] (numeric) = 0.8243424668103449270486953356047
absolute error = 1.0e-31
relative error = 1.2130880553434696500144302848026e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 0.8248590510092805118140559357349
y[1] (numeric) = 0.82485905100928051181405593573482
absolute error = 8e-32
relative error = 9.6986266807782070157691944187268e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.441
y[1] (analytic) = 0.8253757516246247303620980548297
y[1] (numeric) = 0.82537575162462473036209805482972
absolute error = 2e-32
relative error = 2.4231387898945526287119798039921e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.442
y[1] (analytic) = 0.8258925686402277749968049773448
y[1] (numeric) = 0.82589256864022777499680497734462
absolute error = 1.8e-31
relative error = 2.1794602207930862893387812328336e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.443
y[1] (analytic) = 0.8264095020399528630943821067657
y[1] (numeric) = 0.82640950203995286309438210676571
absolute error = 1e-32
relative error = 1.2100538504597868045517102719400e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=309.0MB, alloc=4.4MB, time=12.48
x[1] = 0.444
y[1] (analytic) = 0.826926551807676224580803744691
y[1] (numeric) = 0.82692655180767622458080374469095
absolute error = 5e-32
relative error = 6.0464862194470725590441601737611e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.445
y[1] (analytic) = 0.8274437179272870894278450706394
y[1] (numeric) = 0.82744371792728708942784507063936
absolute error = 4e-32
relative error = 4.8341656517978498384468490224472e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.446
y[1] (analytic) = 0.8279610003826876751675654556086
y[1] (numeric) = 0.82796100038268767516756545560849
absolute error = 1.1e-31
relative error = 1.3285649921814850600850193500519e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.447
y[1] (analytic) = 0.8284783991577931744252093189246
y[1] (numeric) = 0.82847839915779317442520931892446
absolute error = 1.4e-31
relative error = 1.6898449029246856784750692861218e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.448
y[1] (analytic) = 0.8289959142365317424704908142506
y[1] (numeric) = 0.82899591423653174247049081425065
absolute error = 5e-32
relative error = 6.0313928140463478185124328195464e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.449
y[1] (analytic) = 0.8295135456028444847872287067398
y[1] (numeric) = 0.82951354560284448478722870673972
absolute error = 8e-32
relative error = 9.6442065863867759377552615573596e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=312.8MB, alloc=4.4MB, time=12.64
x[1] = 0.45
y[1] (analytic) = 0.8300312932406854446612978792303
y[1] (numeric) = 0.83003129324068544466129787923028
absolute error = 2e-32
relative error = 2.4095477077634191540346544800750e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.451
y[1] (analytic) = 0.8305491571340215907868639811044
y[1] (numeric) = 0.83054915713402159078686398110431
absolute error = 9e-32
relative error = 1.0836203881124058160667020232849e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.452
y[1] (analytic) = 0.8310671372668328048908678089355
y[1] (numeric) = 0.83106713726683280489086780893552
absolute error = 2e-32
relative error = 2.4065444418575956715812356856918e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.453
y[1] (analytic) = 0.8315852336231118693757260833726
y[1] (numeric) = 0.83158523362311186937572608337248
absolute error = 1.2e-31
relative error = 1.4430270662355938049685995831817e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.454
y[1] (analytic) = 0.8321034461868644549802153618143
y[1] (numeric) = 0.83210344618686445498021536181421
absolute error = 9e-32
relative error = 1.0815962896491695322531866854047e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.4MB, time=12.79
x[1] = 0.455
y[1] (analytic) = 0.832621774942109108458505901351
y[1] (numeric) = 0.83262177494210910845850590135081
absolute error = 1.9e-31
relative error = 2.2819484875135580406769014526009e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.456
y[1] (analytic) = 0.8331402198728772402773123611579
y[1] (numeric) = 0.83314021987287724027731236115794
absolute error = 4e-32
relative error = 4.8011125913598681892383142042491e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.457
y[1] (analytic) = 0.8336587809632131123311283080525
y[1] (numeric) = 0.83365878096321311233112830805244
absolute error = 6e-32
relative error = 7.1971892301878868972682660697851e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.458
y[1] (analytic) = 0.8341774581971738256755115632374
y[1] (numeric) = 0.83417745819717382567551156323733
absolute error = 7e-32
relative error = 8.3914998316166628840319627484565e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.459
y[1] (analytic) = 0.8346962515588293082783875023893
y[1] (numeric) = 0.83469625155882930827838750238916
absolute error = 1.4e-31
relative error = 1.6772568432953219511418213509334e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 0.8352151610322623027893374951687
y[1] (numeric) = 0.83521516103226230278933749516863
absolute error = 7e-32
relative error = 8.3810739155507346634919188334035e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.4MB, time=12.95
x[1] = 0.461
y[1] (analytic) = 0.8357341866015683543268397439686
y[1] (numeric) = 0.83573418660156835432683974396855
absolute error = 5e-32
relative error = 5.9827635151937637714849068545730e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.462
y[1] (analytic) = 0.8362533282508557982834298552511
y[1] (numeric) = 0.83625332825085579828342985525106
absolute error = 4e-32
relative error = 4.7832395577624494934824591124256e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.463
y[1] (analytic) = 0.8367725859642457481487485501695
y[1] (numeric) = 0.83677258596424574814874855016954
absolute error = 4e-32
relative error = 4.7802713271140971926474577818606e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.464
y[1] (analytic) = 0.837291959725872083350443994321
y[1] (numeric) = 0.83729195972587208335044399432089
absolute error = 1.1e-31
relative error = 1.3137591818750272814116432787667e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.465
y[1] (analytic) = 0.8378114495198814371128962994305
y[1] (numeric) = 0.83781144951988143711289629943038
absolute error = 1.2e-31
relative error = 1.4323031759564462176529616304221e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.466
y[1] (analytic) = 0.8383310553304331843337318225359
y[1] (numeric) = 0.83833105533043318433373182253576
absolute error = 1.4e-31
relative error = 1.6699846571330721512577672959117e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
memory used=324.2MB, alloc=4.4MB, time=13.10
TOP MAIN SOLVE Loop
x[1] = 0.467
y[1] (analytic) = 0.8388507771416994294780949608097
y[1] (numeric) = 0.83885077714169942947809496080961
absolute error = 9e-32
relative error = 1.0728964251146794713789271307661e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.468
y[1] (analytic) = 0.8393706149378649944906452125399
y[1] (numeric) = 0.83937061493786499449064521253995
absolute error = 5e-32
relative error = 5.9568442247291782411538385075344e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.469
y[1] (analytic) = 0.8398905687031274067252473469794
y[1] (numeric) = 0.83989056870312740672524734697937
absolute error = 3e-32
relative error = 3.5718939011689240736578523796011e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 0.840410638421696886892322597773
y[1] (numeric) = 0.84041063842169688689232259777285
absolute error = 1.5e-31
relative error = 1.7848417564263837742134445012405e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.471
y[1] (analytic) = 0.8409308240777963370238288664851
y[1] (numeric) = 0.8409308240777963370238288664851
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.4MB, time=13.26
x[1] = 0.472
y[1] (analytic) = 0.8414511256556613284558379943694
y[1] (numeric) = 0.84145112565566132845583799436941
absolute error = 1e-32
relative error = 1.1884231531817096288476700448060e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.473
y[1] (analytic) = 0.8419715431395400898286782319531
y[1] (numeric) = 0.84197154313954008982867823195306
absolute error = 4e-32
relative error = 4.7507543842691121764730487374018e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.474
y[1] (analytic) = 0.8424920765136934951046101072593
y[1] (numeric) = 0.84249207651369349510461010725927
absolute error = 3e-32
relative error = 3.5608643495073147094005232843583e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.475
y[1] (analytic) = 0.8430127257623950516030039645435
y[1] (numeric) = 0.84301272576239505160300396454348
absolute error = 2e-32
relative error = 2.3724434268667307141167190269304e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.476
y[1] (analytic) = 0.8435334908699308880529875162926
y[1] (numeric) = 0.84353349086993088805298751629264
absolute error = 4e-32
relative error = 4.7419575432326043904979961369886e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.477
y[1] (analytic) = 0.8440543718205997426635318219209
y[1] (numeric) = 0.84405437182059974266353182192094
absolute error = 4e-32
relative error = 4.7390311969738643996534646091340e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.4MB, time=13.41
x[1] = 0.478
y[1] (analytic) = 0.8445753685987129512109441770946
y[1] (numeric) = 0.84457536859871295121094417709462
absolute error = 2e-32
relative error = 2.3680539053824447526178321319207e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.479
y[1] (analytic) = 0.8450964811885944351437364679326
y[1] (numeric) = 0.84509648118859443514373646793257
absolute error = 3e-32
relative error = 3.5498905353157072247589182923453e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 0.845617709574580689704837614459
y[1] (numeric) = 0.84561770957458068970483761445897
absolute error = 3e-32
relative error = 3.5477024263236647673084893329906e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.481
y[1] (analytic) = 0.8461390537410207720711187976299
y[1] (numeric) = 0.84613905374102077207111879762991
absolute error = 1e-32
relative error = 1.1818388426567906780575313821632e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.482
y[1] (analytic) = 0.8466605136722762895102002340184
y[1] (numeric) = 0.84666051367227628951020023401825
absolute error = 1.5e-31
relative error = 1.7716664185671673976790735052162e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=335.7MB, alloc=4.4MB, time=13.57
x[1] = 0.483
y[1] (analytic) = 0.8471820893527213875545083318205
y[1] (numeric) = 0.84718208935272138755450833182035
absolute error = 1.5e-31
relative error = 1.7705756753498598705860231566948e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.484
y[1] (analytic) = 0.8477037807667427381925521312454
y[1] (numeric) = 0.84770378076674273819255213124541
absolute error = 1e-32
relative error = 1.1796573551854473143391269183306e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.485
y[1] (analytic) = 0.8482255878987395280773880015639
y[1] (numeric) = 0.84822558789873952807738800156382
absolute error = 8e-32
relative error = 9.4314532762657395919901603671269e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.486
y[1] (analytic) = 0.848747510733123446752241636125
y[1] (numeric) = 0.84874751073312344675224163612496
absolute error = 4e-32
relative error = 4.7128267823076337336275086045323e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.487
y[1] (analytic) = 0.8492695492543186748932564555087
y[1] (numeric) = 0.84926954925431867489325645550864
absolute error = 6e-32
relative error = 7.0648947737124922194627586457860e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.488
y[1] (analytic) = 0.8497917034467618725693375976481
y[1] (numeric) = 0.849791703446761872569337597648
absolute error = 1.0e-31
relative error = 1.1767589586294995446430489690191e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=339.5MB, alloc=4.4MB, time=13.72
x[1] = 0.489
y[1] (analytic) = 0.8503139732949021675190607422556
y[1] (numeric) = 0.85031397329490216751906074225549
absolute error = 1.1e-31
relative error = 1.2936398019399627323529547015024e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 0.8508363587832011434446150851991
y[1] (numeric) = 0.85083635878320114344461508519894
absolute error = 1.6e-31
relative error = 1.8805026177868014891516719972584e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.491
y[1] (analytic) = 0.851358859896132828322749846611
y[1] (numeric) = 0.85135885989613282832274984661094
absolute error = 6e-32
relative error = 7.0475568912644073517131748534814e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.492
y[1] (analytic) = 0.8518814766181836827326937644736
y[1] (numeric) = 0.85188147661818368273269376447361
absolute error = 1e-32
relative error = 1.1738722198419200608143280522385e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.493
y[1] (analytic) = 0.8524042089338525882010170932022
y[1] (numeric) = 0.8524042089338525882010170932022
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.4MB, time=13.88
x[1] = 0.494
y[1] (analytic) = 0.8529270568276508355634056943552
y[1] (numeric) = 0.8529270568276508355634056943551
absolute error = 1.0e-31
relative error = 1.1724332016378604374137076257869e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.495
y[1] (analytic) = 0.8534500202841021133433168740263
y[1] (numeric) = 0.8534500202841021133433168740263
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) = 0.8539730992877424961474866887285
y[1] (numeric) = 0.85397309928774249614748668872844
absolute error = 6e-32
relative error = 7.0259824402013467578421400088706e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.497
y[1] (analytic) = 0.8544962938231204330782585086519
y[1] (numeric) = 0.85449629382312043307825850865177
absolute error = 1.3e-31
relative error = 1.5213641175477096056804153792371e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.498
y[1] (analytic) = 0.8550196038747967361627026940869
y[1] (numeric) = 0.85501960387479673616270269408673
absolute error = 1.7e-31
relative error = 1.9882585057651338416260015471403e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.499
y[1] (analytic) = 0.8555430294273445687984973075261
y[1] (numeric) = 0.85554302942734456879849730752593
absolute error = 1.7e-31
relative error = 1.9870420791551424814414285656502e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
Finished!
diff ( y , x , 1 ) = arcsin(sqrt(0.1 * x + 0.2));
Iterations = 500
Total Elapsed Time = 13 Seconds
Elapsed Time(since restart) = 13 Seconds
Time to Timeout = 2 Minutes 46 Seconds
Percent Done = 100.2 %
> quit
memory used=346.8MB, alloc=4.4MB, time=14.01