|\^/| 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_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_y2[1]) < min_size) then # if number 1
> min_size := omniabs(array_y2[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> if (omniabs(array_y1[1]) < min_size) then # if number 1
> min_size := omniabs(array_y1[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_1D0, array_y2_init, array_y1_init, array_norms,
array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y2[1]) < min_size then
min_size := omniabs(array_y2[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if omniabs(array_y1[1]) < min_size then
min_size := omniabs(array_y1[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_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[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;
> value3 := omniabs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[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_1D0, array_y2_init, array_y1_init, array_norms,
array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_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_y2[no_terms - 3]
+ array_y2[no_terms - 2]*hn_div_ho
+ array_y2[no_terms - 1]*hn_div_ho_2
+ array_y2[no_terms]*hn_div_ho_3);
if max_value3 < value3 then
max_value3 := value3;
omniout_float(ALWAYS, "value3", 32, value3, 32, "")
end if;
value3 := omniabs(array_y1[no_terms - 3]
+ array_y1[no_terms - 2]*hn_div_ho
+ array_y1[no_terms - 1]*hn_div_ho_2
+ array_y1[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_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_1D0, array_y2_init, array_y1_init, array_norms,
array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_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_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_y2(ind_var);
> omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y2[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," ");
> ;
> analytic_val_y := exact_soln_y1(ind_var);
> omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y1[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[2] := relerr;
> else
> array_last_rel_error[2] := 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_1D0, array_y2_init, array_y1_init, array_norms,
array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_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_y2(ind_var);
omniout_float(ALWAYS, "y2[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y2[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, " ");
analytic_val_y := exact_soln_y1(ind_var);
omniout_float(ALWAYS, "y1[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y1[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[2] := relerr
else array_last_rel_error[2] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 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_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_y2_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y2_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1;
> if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y1_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_1D0, array_y2_init, array_y1_init, array_norms,
array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_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_y2_higher[1, 1]) then
tmp := omniabs(array_y2_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_small_float < omniabs(array_y1_higher[1, 1]) then
tmp := omniabs(array_y1_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_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_1D0, array_y2_init, array_y1_init, array_norms,
array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_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_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_y2_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y2_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_y2_higher[1,m]/array_y2_higher[1,m-1];
> rm1 := array_y2_higher[1,m-1]/array_y2_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
> #IN RADII REAL EQ = 2
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y1_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_y1_higher[1,m]/array_y1_higher[1,m-1];
> rm1 := array_y1_higher[1,m-1]/array_y1_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[2,1] := rcs;
> array_real_pole[2,2] := ord_no;
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[2,1] := glob_large_float;
> array_real_pole[2,2] := glob_large_float;
> fi;# end if 1;
> #BOTTOM RADII REAL EQ = 2
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y2_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_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y2_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y2_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-5]) <= (glob_small_float)))) then # if number 2
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]);
> rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]);
> rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]);
> rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]);
> rm4 := (array_y2_higher[1,m-4])/(array_y2_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
> #TOP RADII COMPLEX EQ = 2
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y1_higher[1,n]) > glob_small_float) then # if number 2
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 2;
> n := n - 1;
> od;# end do number 2;
> m := n + cnt;
> if (m <= 10) then # if number 2
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> elif
> (((omniabs(array_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y1_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y1_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-5]) <= (glob_small_float)))) then # if number 3
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]);
> rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]);
> rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]);
> rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]);
> rm4 := (array_y1_higher[1,m-4])/(array_y1_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 4
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 6
> if (rcs > 0.0) then # if number 7
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> fi;# end if 4;
> array_complex_pole[2,1] := rad_c;
> array_complex_pole[2,2] := ord_no;
> fi;# end if 3;
> #BOTTOM RADII COMPLEX EQ = 2
> found_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 3
> 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 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> 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 3
> 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 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> 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 3
> 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 4
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> 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 3
> 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 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> 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 3
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found_sing := 1;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if (1 <> found_sing ) then # if number 3
> 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 4
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> #BOTTOM WHICH RADII EQ = 1
> #TOP WHICH RADII EQ = 2
> if (2 <> found_sing and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> found_sing := 2;
> array_type_pole[2] := 2;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 2");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if (2 <> found_sing and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0)))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found_sing := 2;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Real estimate of pole used for equation 2");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if (2 <> found_sing and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float)))) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> found_sing := 2;
> array_type_pole[2] := 3;
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"NO POLE for equation 2");
> fi;# end if 4;
> fi;# end if 3;
> if (2 <> found_sing and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > -1.0 * glob_smallish_float))) then # if number 3
> array_poles[2,1] := array_real_pole[2,1];
> array_poles[2,2] := array_real_pole[2,2];
> found_sing := 2;
> array_type_pole[2] := 1;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Real estimate of pole used for equation 2");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if (2 <> found_sing and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3
> array_poles[2,1] := array_complex_pole[2,1];
> array_poles[2,2] := array_complex_pole[2,2];
> array_type_pole[2] := 2;
> found_sing := 2;
> if (glob_display_flag) then # if number 4
> if (reached_interval()) then # if number 5
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 2");
> fi;# end if 5;
> fi;# end if 4;
> fi;# end if 3;
> if (2 <> found_sing ) then # if number 3
> array_poles[2,1] := glob_large_float;
> array_poles[2,2] := glob_large_float;
> array_type_pole[2] := 3;
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"NO POLE for equation 2");
> fi;# end if 4;
> fi;# end if 3;
> #BOTTOM WHICH RADII EQ = 2
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if (array_pole[1] > array_poles[1,1]) then # if number 3
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 3;
> #BOTTOM WHICH RADIUS EQ = 1
> #TOP WHICH RADIUS EQ = 2
> if (array_pole[1] > array_poles[2,1]) then # if number 3
> array_pole[1] := array_poles[2,1];
> array_pole[2] := array_poles[2,2];
> fi;# end if 3;
> #BOTTOM WHICH RADIUS EQ = 2
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 3
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 2
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_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 3;
> #BOTTOM ADJUST ALL SERIES
> if (reached_interval()) then # if number 3
> display_pole();
> fi;# end if 3
> 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_1D0, array_y2_init, array_y1_init, array_norms,
array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_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_y2_higher[1, m]) < glob_small_float*glob_small_float or
omniabs(array_y2_higher[1, m - 1]) < glob_small_float*glob_small_float
or
omniabs(array_y2_higher[1, m - 2]) < glob_small_float*glob_small_float)
do m := m - 1
end do;
if 10 < m then
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_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;
m := n - 2;
while 10 <= m and (
omniabs(array_y1_higher[1, m]) < glob_small_float*glob_small_float or
omniabs(array_y1_higher[1, m - 1]) < glob_small_float*glob_small_float
or
omniabs(array_y1_higher[1, m - 2]) < glob_small_float*glob_small_float)
do m := m - 1
end do;
if 10 < m then
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_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[2, 1] := rcs;
array_real_pole[2, 2] := ord_no
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if
else
array_real_pole[2, 1] := glob_large_float;
array_real_pole[2, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y2_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_y2_higher[1, m]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y2_higher[1, m - 5]) or
omniabs(array_y2_higher[1, m]) <= glob_small_float or
omniabs(array_y2_higher[1, m - 1]) <= glob_small_float or
omniabs(array_y2_higher[1, m - 2]) <= glob_small_float or
omniabs(array_y2_higher[1, m - 3]) <= glob_small_float or
omniabs(array_y2_higher[1, m - 4]) <= glob_small_float or
omniabs(array_y2_higher[1, m - 5]) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1];
rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2];
rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3];
rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4];
rm4 := array_y2_higher[1, m - 4]/array_y2_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;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y1_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_y1_higher[1, m]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y1_higher[1, m - 5]) or
omniabs(array_y1_higher[1, m]) <= glob_small_float or
omniabs(array_y1_higher[1, m - 1]) <= glob_small_float or
omniabs(array_y1_higher[1, m - 2]) <= glob_small_float or
omniabs(array_y1_higher[1, m - 3]) <= glob_small_float or
omniabs(array_y1_higher[1, m - 4]) <= glob_small_float or
omniabs(array_y1_higher[1, m - 5]) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1];
rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2];
rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3];
rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4];
rm4 := array_y1_higher[1, m - 4]/array_y1_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[2, 1] := rad_c;
array_complex_pole[2, 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;
if 2 <> found_sing and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and
array_complex_pole[2, 1] <> glob_large_float and
array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
found_sing := 2;
array_type_pole[2] := 2;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 2")
end if
end if
end if;
if 2 <> found_sing and array_real_pole[2, 1] <> glob_large_float and
array_real_pole[2, 2] <> glob_large_float and
0. < array_real_pole[2, 1] and
-1.0*glob_smallish_float < array_real_pole[2, 2] and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float or
array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found_sing := 2;
array_type_pole[2] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 2")
end if
end if
end if;
if 2 <> found_sing and (array_real_pole[2, 1] = glob_large_float or
array_real_pole[2, 2] = glob_large_float) and (
array_complex_pole[2, 1] = glob_large_float or
array_complex_pole[2, 2] = glob_large_float) then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
found_sing := 2;
array_type_pole[2] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 2")
end if
end if;
if 2 <> found_sing and array_real_pole[2, 1] < array_complex_pole[2, 1]
and 0. < array_real_pole[2, 1] and
-1.0*glob_smallish_float < array_real_pole[2, 2] then
array_poles[2, 1] := array_real_pole[2, 1];
array_poles[2, 2] := array_real_pole[2, 2];
found_sing := 2;
array_type_pole[2] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 2")
end if
end if
end if;
if 2 <> found_sing and array_complex_pole[2, 1] <> glob_large_float
and array_complex_pole[2, 2] <> glob_large_float and
0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then
array_poles[2, 1] := array_complex_pole[2, 1];
array_poles[2, 2] := array_complex_pole[2, 2];
array_type_pole[2] := 2;
found_sing := 2;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 2")
end if
end if
end if;
if 2 <> found_sing then
array_poles[2, 1] := glob_large_float;
array_poles[2, 2] := glob_large_float;
array_type_pole[2] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 2")
end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_poles[2, 1] < array_pole[1] then
array_pole[1] := array_poles[2, 1];
array_pole[2] := array_poles[2, 2]
end if;
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_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_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_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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 3
> 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_y2[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_y2[iii]);
> fi;# end if 4;
> iii := iii + 1;
> od;# end do number 2
> ;
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4
> array_norms[iii] := omniabs(array_y1[iii]);
> fi;# end if 4;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 3;
> 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_1D0, array_y2_init, array_y1_init, array_norms,
array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_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_y2[iii]) then
array_norms[iii] := omniabs(array_y2[iii])
end if;
iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y1[iii]) then
array_norms[iii] := omniabs(array_y1[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_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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 FULL FULL $eq_no = 1 i = 1
> array_tmp1[1] := (array_m1[1] * (array_y1[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y2[2] := temporary;
> array_y2_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y2_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre sub FULL - CONST $eq_no = 2 i = 1
> array_tmp5[1] := array_y2[1] - array_const_1D0[1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[2,2]) 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_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y1_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp1[2] := ats(2,array_m1,array_y1,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y2_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre sub FULL CONST $eq_no = 2 i = 2
> array_tmp5[2] := array_y2[2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[2,3]) 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_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y1_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp1[3] := ats(3,array_m1,array_y1,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y2_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre sub FULL CONST $eq_no = 2 i = 3
> array_tmp5[3] := array_y2[3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[2,4]) 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_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y1_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp1[4] := ats(4,array_m1,array_y1,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre add FULL CONST $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y2_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre sub FULL CONST $eq_no = 2 i = 4
> array_tmp5[4] := array_y2[4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[2,5]) 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_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y1_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp1[5] := ats(5,array_m1,array_y1,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre add FULL CONST $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y2_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre sub FULL CONST $eq_no = 2 i = 5
> array_tmp5[5] := array_y2[5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[2,6]) 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_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y1_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 mult FULL FULL $eq_no = 1
> array_tmp1[kkk] := ats(kkk,array_m1,array_y1,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y2_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y2[kkk + order_d] := temporary;
> array_y2_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_y2_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;
> #emit FULL - NOT FULL sub $eq_no = 2
> array_tmp5[kkk] := array_y2[kkk];
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y1_set_initial[2,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_y1[kkk + order_d] := temporary;
> array_y1_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_y1_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_1D0, array_y2_init, array_y1_init, array_norms,
array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
array_tmp1[1] := array_m1[1]*array_y1[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
if not array_y2_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y2[2] := temporary;
array_y2_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y2_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp5[1] := array_y2[1] - array_const_1D0[1];
if not array_y1_set_initial[2, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y1_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := ats(2, array_m1, array_y1, 1);
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2];
if not array_y2_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y2_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp5[2] := array_y2[2];
if not array_y1_set_initial[2, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y1_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := ats(3, array_m1, array_y1, 1);
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := array_tmp2[3];
if not array_y2_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y2_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp5[3] := array_y2[3];
if not array_y1_set_initial[2, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y1_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := ats(4, array_m1, array_y1, 1);
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := array_tmp2[4];
if not array_y2_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y2_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp5[4] := array_y2[4];
if not array_y1_set_initial[2, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y1_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := ats(5, array_m1, array_y1, 1);
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := array_tmp2[5];
if not array_y2_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y2_higher[2, 5] := temporary
end if
end if;
kkk := 6;
array_tmp5[5] := array_y2[5];
if not array_y1_set_initial[2, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y1_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := ats(kkk, array_m1, array_y1, 1);
array_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] := array_tmp2[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y2_set_initial[1, kkk + order_d] then
temporary := array_tmp3[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y2[kkk + order_d] := temporary;
array_y2_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_y2_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
array_tmp5[kkk] := array_y2[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y1_set_initial[2, kkk + order_d] then
temporary := array_tmp5[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y1[kkk + order_d] := temporary;
array_y1_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_y1_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_y1 := proc(x)
> return(1.0 + cos(x));
> end;
exact_soln_y1 := proc(x) return 1.0 + cos(x) end proc
> exact_soln_y2 := proc(x)
> return(1.0 - sin(x));
> end;
exact_soln_y2 := proc(x) return 1.0 - sin(x) 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_1D0,
> #END CONST
> array_y2_init,
> array_y1_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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 := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/mtest3postode.ode#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = y2 - 1.0;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 0.5;");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"glob_max_iter := 20;");
> 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_y1 := proc(x)");
> omniout_str(ALWAYS,"return(1.0 + cos(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(1.0 - sin(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> 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_y2_init:= Array(0..(max_terms + 1),[]);
> array_y1_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_y2:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_y1:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y2_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_pole := Array(0..(2+ 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_y2_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y1_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_y2[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_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_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_y2_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_y2_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y2_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 <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_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_y1_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_y1_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=3) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y1_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 <=2) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= 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_y2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y2[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_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_y1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_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_1D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1D0[1] := 1.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 2
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 3
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 3;
> iiif := iiif + 1;
> od;# end do number 2;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1;
> x_end := 0.5;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> glob_max_iter := 20;
> #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_y2_set_initial[1,1] := true;
> array_y2_set_initial[1,2] := false;
> array_y2_set_initial[1,3] := false;
> array_y2_set_initial[1,4] := false;
> array_y2_set_initial[1,5] := false;
> array_y2_set_initial[1,6] := false;
> array_y2_set_initial[1,7] := false;
> array_y2_set_initial[1,8] := false;
> array_y2_set_initial[1,9] := false;
> array_y2_set_initial[1,10] := false;
> array_y2_set_initial[1,11] := false;
> array_y2_set_initial[1,12] := false;
> array_y2_set_initial[1,13] := false;
> array_y2_set_initial[1,14] := false;
> array_y2_set_initial[1,15] := false;
> array_y2_set_initial[1,16] := false;
> array_y2_set_initial[1,17] := false;
> array_y2_set_initial[1,18] := false;
> array_y2_set_initial[1,19] := false;
> array_y2_set_initial[1,20] := false;
> array_y2_set_initial[1,21] := false;
> array_y2_set_initial[1,22] := false;
> array_y2_set_initial[1,23] := false;
> array_y2_set_initial[1,24] := false;
> array_y2_set_initial[1,25] := false;
> array_y2_set_initial[1,26] := false;
> array_y2_set_initial[1,27] := false;
> array_y2_set_initial[1,28] := false;
> array_y2_set_initial[1,29] := false;
> array_y2_set_initial[1,30] := false;
> array_y1_set_initial[2,1] := true;
> array_y1_set_initial[2,2] := false;
> array_y1_set_initial[2,3] := false;
> array_y1_set_initial[2,4] := false;
> array_y1_set_initial[2,5] := false;
> array_y1_set_initial[2,6] := false;
> array_y1_set_initial[2,7] := false;
> array_y1_set_initial[2,8] := false;
> array_y1_set_initial[2,9] := false;
> array_y1_set_initial[2,10] := false;
> array_y1_set_initial[2,11] := false;
> array_y1_set_initial[2,12] := false;
> array_y1_set_initial[2,13] := false;
> array_y1_set_initial[2,14] := false;
> array_y1_set_initial[2,15] := false;
> array_y1_set_initial[2,16] := false;
> array_y1_set_initial[2,17] := false;
> array_y1_set_initial[2,18] := false;
> array_y1_set_initial[2,19] := false;
> array_y1_set_initial[2,20] := false;
> array_y1_set_initial[2,21] := false;
> array_y1_set_initial[2,22] := false;
> array_y1_set_initial[2,23] := false;
> array_y1_set_initial[2,24] := false;
> array_y1_set_initial[2,25] := false;
> array_y1_set_initial[2,26] := false;
> array_y1_set_initial[2,27] := false;
> array_y1_set_initial[2,28] := false;
> array_y1_set_initial[2,29] := false;
> array_y1_set_initial[2,30] := 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 3
> glob_h := glob_display_interval;
> fi;# end if 3;
> if (glob_max_h < glob_h) then # if number 3
> glob_h := glob_max_h;
> fi;# end if 3;
> 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_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y2[term_no] := array_y2_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_y2_higher[r_order,term_no] := array_y2_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
> ;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y1[term_no] := array_y1_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_y1_higher[r_order,term_no] := array_y1_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
> ;
> if (glob_subiter_method = 1 ) then # if number 3
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 4
> subiter := 1;
> while (subiter <= 2) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3;
> else
> subiter := 1;
> while (subiter <= 2 + glob_max_terms) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3;
> fi;# end if 4;
> 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 4
> best_h := glob_h;
> found_h := 1.0;
> fi;# end if 4;
> 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 4
> glob_h := best_h ;
> else
> omniout_str(ALWAYS,"No increment to obtain desired accuracy found");
> fi;# end if 4;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 4
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 4;
> #BEGIN SOLUTION CODE
> if (found_h > 0.0) then # if number 4
> 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_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y2[term_no] := array_y2_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_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y1[term_no] := array_y1_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_y1_higher[r_order,term_no] := array_y1_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 5
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 5;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> if (glob_subiter_method = 1 ) then # if number 5
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 6
> subiter := 1;
> while (subiter <= 2) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3;
> else
> subiter := 1;
> while (subiter <= 2 + glob_max_terms) do # do number 3
> atomall();
> subiter := subiter + 1;
> od;# end do number 3;
> fi;# end if 6;
> display_alot(current_iter);
> if (glob_look_poles) then # if number 6
> #left paren 0004C
> check_for_pole();
> fi;# end if 6;#was right paren 0004C
> if (reached_interval()) then # if number 6
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 6;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y2;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[2,iii] := array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y2_higher_work[1,iii] := array_y2_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_y2
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y2_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_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y2_higher[ord,term_no] := array_y2_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
> #Jump Series array_y1;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[2,iii] := array_y1_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y1_higher_work[1,iii] := array_y1_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y1_higher[ord,term_no] := array_y1_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 6
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 6;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 6;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;");
> omniout_str(INFO,"diff ( y1 , x , 1 ) = y2 - 1.0;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 6
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-01-28T16:42:51-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest3")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;")
> ;
> 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 7
> 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 7;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 7
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 7;
> log_revs(html_log_file," 165 | ")
> ;
> logitem_str(html_log_file,"mtest3 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest3 maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = y2 - 1.0;")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_float(html_log_file,array_1st_rel_error[2])
> ;
> logitem_float(html_log_file,array_last_rel_error[2])
> ;
> logditto(html_log_file)
> ;
> logitem_pole(html_log_file,array_type_pole[2])
> ;
> if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 7
> 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 7;
> logditto(html_log_file)
> ;
> if (glob_percent_done < 100.0) then # if number 7
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 7;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #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_1D0, array_y2_init, array_y1_init, array_norms,
array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error,
array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_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 := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest3postode.ode#################");
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = y2 - 1.0;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 0.5;");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "glob_max_iter := 20;");
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_y1 := proc(x)");
omniout_str(ALWAYS, "return(1.0 + cos(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(1.0 - sin(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
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_y2_init := Array(0 .. max_terms + 1, []);
array_y1_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_y2 := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_y1 := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y2_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_real_pole := Array(0 .. 3, 0 .. 4, []);
array_complex_pole := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y2_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y1_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_y2[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_y1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y2_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_y2_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_y2_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y2_set_initial[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_y1_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_y1_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_y1_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= max_terms do
array_y1_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 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_y2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y2[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_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_y1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_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_1D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1D0[term] := 0.; term := term + 1
end do;
array_const_1D0[1] := 1.0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 0.5;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
glob_max_iter := 20;
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_y2_set_initial[1, 1] := true;
array_y2_set_initial[1, 2] := false;
array_y2_set_initial[1, 3] := false;
array_y2_set_initial[1, 4] := false;
array_y2_set_initial[1, 5] := false;
array_y2_set_initial[1, 6] := false;
array_y2_set_initial[1, 7] := false;
array_y2_set_initial[1, 8] := false;
array_y2_set_initial[1, 9] := false;
array_y2_set_initial[1, 10] := false;
array_y2_set_initial[1, 11] := false;
array_y2_set_initial[1, 12] := false;
array_y2_set_initial[1, 13] := false;
array_y2_set_initial[1, 14] := false;
array_y2_set_initial[1, 15] := false;
array_y2_set_initial[1, 16] := false;
array_y2_set_initial[1, 17] := false;
array_y2_set_initial[1, 18] := false;
array_y2_set_initial[1, 19] := false;
array_y2_set_initial[1, 20] := false;
array_y2_set_initial[1, 21] := false;
array_y2_set_initial[1, 22] := false;
array_y2_set_initial[1, 23] := false;
array_y2_set_initial[1, 24] := false;
array_y2_set_initial[1, 25] := false;
array_y2_set_initial[1, 26] := false;
array_y2_set_initial[1, 27] := false;
array_y2_set_initial[1, 28] := false;
array_y2_set_initial[1, 29] := false;
array_y2_set_initial[1, 30] := false;
array_y1_set_initial[2, 1] := true;
array_y1_set_initial[2, 2] := false;
array_y1_set_initial[2, 3] := false;
array_y1_set_initial[2, 4] := false;
array_y1_set_initial[2, 5] := false;
array_y1_set_initial[2, 6] := false;
array_y1_set_initial[2, 7] := false;
array_y1_set_initial[2, 8] := false;
array_y1_set_initial[2, 9] := false;
array_y1_set_initial[2, 10] := false;
array_y1_set_initial[2, 11] := false;
array_y1_set_initial[2, 12] := false;
array_y1_set_initial[2, 13] := false;
array_y1_set_initial[2, 14] := false;
array_y1_set_initial[2, 15] := false;
array_y1_set_initial[2, 16] := false;
array_y1_set_initial[2, 17] := false;
array_y1_set_initial[2, 18] := false;
array_y1_set_initial[2, 19] := false;
array_y1_set_initial[2, 20] := false;
array_y1_set_initial[2, 21] := false;
array_y1_set_initial[2, 22] := false;
array_y1_set_initial[2, 23] := false;
array_y1_set_initial[2, 24] := false;
array_y1_set_initial[2, 25] := false;
array_y1_set_initial[2, 26] := false;
array_y1_set_initial[2, 27] := false;
array_y1_set_initial[2, 28] := false;
array_y1_set_initial[2, 29] := false;
array_y1_set_initial[2, 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_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 2 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 2 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
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_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 2 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 2 + glob_max_terms do
atomall(); subiter := subiter + 1
end do
end if;
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_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_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_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 ( y2 , x , 1 ) = m1 * y1 + 1.0;");
omniout_str(INFO, "diff ( y1 , x , 1 ) = y2 - 1.0;");
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, "2013-01-28T16:42:51-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest3");
logitem_str(html_log_file,
"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;");
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,
"mtest3 diffeq.mxt");
logitem_str(html_log_file, "mtest3 maple results");
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( y1 , x , 1 ) = y2 - 1.0;");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_good_digits(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_float(html_log_file, array_1st_rel_error[2]);
logitem_float(html_log_file, array_last_rel_error[2]);
logditto(html_log_file);
logitem_pole(html_log_file, array_type_pole[2]);
if array_type_pole[2] = 1 or array_type_pole[2] = 2 then
logitem_float(html_log_file, array_pole[1]);
logitem_float(html_log_file, array_pole[2]);
0
else
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
0
end if;
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/mtest3postode.ode#################
diff ( y2 , x , 1 ) = m1 * y1 + 1.0;
diff ( y1 , x , 1 ) = y2 - 1.0;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 0.5;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
glob_max_iter := 20;
#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_y1 := proc(x)
return(1.0 + cos(x));
end;
exact_soln_y2 := proc(x)
return(1.0 - sin(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
opt_iter = 1
memory used=3.8MB, alloc=3.1MB, time=0.20
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 0.4
estimated_steps = 400
step_error = 2.5000000000000000000000000000000e-13
est_needed_step_err = 2.5000000000000000000000000000000e-13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 2.4759225582891422933370225621906e-106
value3 = 2.4672040251049429538467757202074e-105
max_value3 = 2.4672040251049429538467757202074e-105
value3 = 2.4672040251049429538467757202074e-105
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y2[1] (analytic) = 0.90016658335317184769318580158938
y2[1] (numeric) = 0.90016658335317184769318580158938
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
y1[1] (analytic) = 1.9950041652780257660955619878039
y1[1] (numeric) = 1.9950041652780257660955619878039
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=4.3MB, time=0.44
x[1] = 0.101
y2[1] (analytic) = 0.89917162927043200487024788047681
y2[1] (numeric) = 0.89917162927043200487024788047681
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
y1[1] (analytic) = 1.994903834375976659378402999829
y1[1] (numeric) = 1.994903834375976659378402999829
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.3MB, time=0.69
x[1] = 0.102
y2[1] (analytic) = 0.89817677601605448925135770391935
y2[1] (numeric) = 0.89817677601605448925135770391935
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
y1[1] (analytic) = 1.9948025085701760853346856764599
y1[1] (numeric) = 1.9948025085701760853346856764599
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.103
y2[1] (analytic) = 0.89718202458489247230959578949541
y2[1] (numeric) = 0.89718202458489247230959578949541
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
y1[1] (analytic) = 1.9947001879619498413211671928266
y1[1] (numeric) = 1.9947001879619498413211671928267
absolute error = 1e-31
relative error = 5.0132847333900969580736126213353e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
memory used=15.2MB, alloc=4.3MB, time=0.92
TOP MAIN SOLVE Loop
x[1] = 0.104
y2[1] (analytic) = 0.89618737597169730231102924533054
y2[1] (numeric) = 0.89618737597169730231102924533054
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
y1[1] (analytic) = 1.9945968726536185270373744944846
y1[1] (numeric) = 1.9945968726536185270373744944847
absolute error = 1e-31
relative error = 5.0135444094504999744422042989207e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.4MB, time=1.16
x[1] = 0.105
y2[1] (analytic) = 0.89519283117111750956344639997322
y2[1] (numeric) = 0.89519283117111750956344639997321
absolute error = 1e-32
relative error = 1.1170777570814219760206128377360e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9944925627484974422050131246041
y1[1] (numeric) = 1.9944925627484974422050131246041
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.4MB, time=1.40
x[1] = 0.106
y2[1] (analytic) = 0.89419839117769781176790938198128
y2[1] (numeric) = 0.89419839117769781176790938198127
absolute error = 1e-32
relative error = 1.1183200617068399222589756982068e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9943872583508964832526761118722
y1[1] (numeric) = 1.9943872583508964832526761118723
absolute error = 1e-31
relative error = 5.0140713435307056092197789941372e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.107
y2[1] (analytic) = 0.89320405698587811947411929758354
y2[1] (numeric) = 0.89320405698587811947411929758352
absolute error = 2e-32
relative error = 2.2391299998670076868448853850700e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9942809595661200390059562343918
y1[1] (numeric) = 1.9942809595661200390059562343919
absolute error = 1e-31
relative error = 5.0143386026087422693494546616177e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.4MB, time=1.64
x[1] = 0.108
y2[1] (analytic) = 0.89220982958999254164058855096841
y2[1] (numeric) = 0.8922098295899925416405885509684
absolute error = 1e-32
relative error = 1.1208125788745698046855410005165e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9941736665004668853830659694533
y1[1] (numeric) = 1.9941736665004668853830659694534
absolute error = 1e-31
relative error = 5.0146083904260896791060449451647e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.4MB, time=1.89
x[1] = 0.109
y2[1] (analytic) = 0.89121570998426839130061474694456
y2[1] (numeric) = 0.89121570998426839130061474694454
absolute error = 2e-32
relative error = 2.2441256113352217567953267159562e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9940653792612300790960704335539
y1[1] (numeric) = 1.994065379261230079096070433554
absolute error = 1e-31
relative error = 5.0148807075246665300616373141045e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.4MB, time=2.13
x[1] = 0.11
y2[1] (analytic) = 0.89022169916282519133505050991655
y2[1] (numeric) = 0.89022169916282519133505050991653
absolute error = 2e-32
relative error = 2.2466313749494347211081974406268e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9939560979566968503578396114198
y1[1] (numeric) = 1.9939560979566968503578396114199
absolute error = 1e-31
relative error = 5.0151555544515163299513758223921e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.111
y2[1] (analytic) = 0.88922779811967368035286344632307
y2[1] (numeric) = 0.88922779811967368035286344632305
absolute error = 2e-32
relative error = 2.2491424629651949362687953771165e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.993845822696148494594827167072
y1[1] (numeric) = 1.993845822696148494594827167072
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.4MB, time=2.37
x[1] = 0.112
y2[1] (analytic) = 0.88823400784871481868048036989479
y2[1] (numeric) = 0.88823400784871481868048036989477
absolute error = 2e-32
relative error = 2.2516588898053570398915774345620e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9937345535898602631657841241467
y1[1] (numeric) = 1.9937345535898602631657841241467
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.4MB, time=2.62
x[1] = 0.113
y2[1] (analytic) = 0.8872403293437387944609098003048
y2[1] (numeric) = 0.88724032934373879446090980030478
absolute error = 2e-32
relative error = 2.2541806699424172072513032681368e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9936222907491012530865166967484
y1[1] (numeric) = 1.9936222907491012530865166967485
absolute error = 1e-31
relative error = 5.0159952797490600140029164077157e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.114
y2[1] (analytic) = 0.88624676359842402986363663600634
y2[1] (numeric) = 0.88624676359842402986363663600631
absolute error = 3e-32
relative error = 3.3850617268480761944203721174969e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9935090342861342957607985460685
y1[1] (numeric) = 1.9935090342861342957607985460686
absolute error = 1e-31
relative error = 5.0162802515620153356578675886210e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.4MB, time=2.86
x[1] = 0.115
y2[1] (analytic) = 0.8852533116063361874062827912803
y2[1] (numeric) = 0.88525331160633618740628279128028
absolute error = 2e-32
relative error = 2.2592403482466509755981957994363e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9933947843142158447175487318465
y1[1] (numeric) = 1.9933947843142158447175487318466
absolute error = 1e-31
relative error = 5.0165677560154160235631469102881e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.4MB, time=3.10
x[1] = 0.116
y2[1] (analytic) = 0.88425997436092717638902747574917
y2[1] (numeric) = 0.88425997436092717638902747574914
absolute error = 3e-32
relative error = 3.3926674134133025114734768757084e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.993279540947595862354387621489
y1[1] (numeric) = 1.9932795409475958623543876214891
absolute error = 1e-31
relative error = 5.0168577936871043750751276314026e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=53.4MB, alloc=4.4MB, time=3.34
x[1] = 0.117
y2[1] (analytic) = 0.88326675285553415944278068185407
y2[1] (numeric) = 0.88326675285553415944278068185404
absolute error = 3e-32
relative error = 3.3964824219877272885762939066605e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.993163304301517705687684013279
y1[1] (numeric) = 1.9931633043015177056876840132791
absolute error = 1e-31
relative error = 5.0171503651600643420268444514782e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.118
y2[1] (analytic) = 0.88227364808337855919210333203896
y2[1] (numeric) = 0.88227364808337855919210333203893
absolute error = 3e-32
relative error = 3.4003055701789332154524433289617e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.99304607449221801110920772362
y1[1] (numeric) = 1.9930460744922180111092077236201
absolute error = 1e-31
relative error = 5.0174454710224240252081801655507e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.4MB, time=3.58
x[1] = 0.119
y2[1] (analytic) = 0.88128066103756506503386742263883
y2[1] (numeric) = 0.8812806610375650650338674226388
absolute error = 3e-32
relative error = 3.4041368801489261055202243212795e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9929278516369265781495028816522
y1[1] (numeric) = 1.9929278516369265781495028816522
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.4MB, time=3.83
x[1] = 0.12
y2[1] (analytic) = 0.88028779271108064003264938572903
y2[1] (numeric) = 0.880287792711080640032649385729
absolute error = 3e-32
relative error = 3.4079763741363506023300343931569e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9928086358538662522480981678576
y1[1] (numeric) = 1.9928086358538662522480981678577
absolute error = 1e-31
relative error = 5.0180432882935908112451694551819e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.4MB, time=4.07
x[1] = 0.121
y2[1] (analytic) = 0.87929504409679352793384977345972
y2[1] (numeric) = 0.87929504409679352793384977345968
absolute error = 4e-32
relative error = 4.5490987659424095213311720332303e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9926884272622528065306712264356
y1[1] (numeric) = 1.9926884272622528065306712264357
absolute error = 1e-31
relative error = 5.0183460009043976231818861055706e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.122
y2[1] (analytic) = 0.87830241618745226029553225167281
y2[1] (numeric) = 0.87830241618745226029553225167277
absolute error = 4e-32
relative error = 4.5542400046708939227102223691582e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.992567225982294822593285474272
y1[1] (numeric) = 1.9925672259822948225932854742721
absolute error = 1e-31
relative error = 5.0186512503086087147802678879264e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.4MB, time=4.31
x[1] = 0.123
y2[1] (analytic) = 0.8773099099756846637399747708799
y2[1] (numeric) = 0.87730990997568466373997477087986
absolute error = 4e-32
relative error = 4.5593922449945460613552099494721e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9924450321351935702938185222573
y1[1] (numeric) = 1.9924450321351935702938185222575
absolute error = 2e-31
relative error = 1.0037918074240222260358253667455e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.4MB, time=4.56
x[1] = 0.124
y2[1] (analytic) = 0.87631752645399686732592566296706
y2[1] (numeric) = 0.87631752645399686732592566296703
absolute error = 3e-32
relative error = 3.4234166377334093976771369684560e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.992321845843142886550702417515
y1[1] (numeric) = 1.9923218458431428865507024175152
absolute error = 2e-31
relative error = 1.0038538723915902996870739417277e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.125
y2[1] (analytic) = 0.87532526661477231004255729128789
y2[1] (numeric) = 0.87532526661477231004255729128786
absolute error = 3e-32
relative error = 3.4272973880922939879124629753081e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9921976672293290531490969077882
y1[1] (numeric) = 1.9921976672293290531490969077884
absolute error = 2e-31
relative error = 1.0039164450892677369081925000522e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.4MB, time=4.80
x[1] = 0.126
y2[1] (analytic) = 0.87433313145027074842610976010826
y2[1] (numeric) = 0.87433313145027074842610976010823
absolute error = 3e-32
relative error = 3.4311864575277510624030639187458e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9920724964179306735546179218037
y1[1] (numeric) = 1.9920724964179306735546179218039
absolute error = 2e-31
relative error = 1.0039795256429292925758083279198e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=80.1MB, alloc=4.4MB, time=5.05
x[1] = 0.127
y2[1] (analytic) = 0.87334112195262726430021706667654
y2[1] (numeric) = 0.8733411219526272643002170666765
absolute error = 4e-32
relative error = 4.5801118250984778739937092177196e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9919463335341185487347444518721
y1[1] (numeric) = 1.9919463335341185487347444518723
absolute error = 2e-31
relative error = 1.0040431141794832426277726888305e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.4MB, time=5.29
x[1] = 0.128
y2[1] (analytic) = 0.87234923911385127264090795551028
y2[1] (numeric) = 0.87234923911385127264090795551025
absolute error = 3e-32
relative error = 3.4389896448439117080901317646250e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9918191787040555519880280173089
y1[1] (numeric) = 1.9918191787040555519880280173091
absolute error = 2e-31
relative error = 1.0041072108268719277418903648233e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.129
y2[1] (analytic) = 0.87135748392582552956727360981603
y2[1] (numeric) = 0.871357483925825529567273609816
absolute error = 3e-32
relative error = 3.4429038085307540283301055523704e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9916910320548965027812298794554
y1[1] (numeric) = 1.9916910320548965027812298794556
absolute error = 2e-31
relative error = 1.0041718157140723015143946141587e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.4MB, time=5.53
x[1] = 0.13
y2[1] (analytic) = 0.87036585738030514045879418929169
y2[1] (numeric) = 0.87036585738030514045879418929165
absolute error = 4e-32
relative error = 4.5957685105428091385734511947828e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9915618937147880395945121711518
y1[1] (numeric) = 1.991561893714788039594512171152
absolute error = 2e-31
relative error = 1.0042369289710964831422071099758e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.4MB, time=5.78
x[1] = 0.131
y2[1] (analytic) = 0.86937436046891656820031609690237
y2[1] (numeric) = 0.86937436046891656820031609690233
absolute error = 4e-32
relative error = 4.6010098547678703667386917818045e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9914317638128684917748100954616
y1[1] (numeric) = 1.9914317638128684917748100954618
absolute error = 2e-31
relative error = 1.0043025507289923146130562707447e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.132
y2[1] (analytic) = 0.86838299418315664155567172956986
y2[1] (numeric) = 0.86838299418315664155567172956982
absolute error = 4e-32
relative error = 4.6062624749608263689261729132492e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.991300642479267750397513340263
y1[1] (numeric) = 1.9913006424792677503975133402633
absolute error = 3e-31
relative error = 1.5065530216797658836113419283996e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
memory used=95.3MB, alloc=4.4MB, time=6.02
TOP MAIN SOLVE Loop
x[1] = 0.133
y2[1] (analytic) = 0.86739175951439156367093333907315
y2[1] (numeric) = 0.86739175951439156367093333907311
absolute error = 4e-32
relative error = 4.6115264021408228794262602231311e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9911685298451071381365858470171
y1[1] (numeric) = 1.9911685298451071381365858470173
absolute error = 2e-31
relative error = 1.0044353202767722837174230762644e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=99.1MB, alloc=4.4MB, time=6.26
x[1] = 0.134
y2[1] (analytic) = 0.86640065745385592070829249982374
y2[1] (numeric) = 0.8664006574538559207082924998237
absolute error = 4e-32
relative error = 4.6168016674352974648062542205788e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9910354260424992781432540635797
y1[1] (numeric) = 1.9910354260424992781432540635799
absolute error = 2e-31
relative error = 1.0045024683339357971838974226552e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=102.9MB, alloc=4.4MB, time=6.51
x[1] = 0.135
y2[1] (analytic) = 0.86540968899265169061155654955344
y2[1] (numeric) = 0.8654096889926516906115565495534
absolute error = 4e-32
relative error = 4.6220883020804317975048604800521e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9909013312045479619333948023605
y1[1] (numeric) = 1.9909013312045479619333948023607
absolute error = 2e-31
relative error = 1.0045701254265308581607595117831e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.136
y2[1] (analytic) = 0.86441885512174725200425323733583
y2[1] (numeric) = 0.86441885512174725200425323733578
absolute error = 5e-32
relative error = 5.7842329217770076716120643201105e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.990766245465348016283754816428
y1[1] (numeric) = 1.9907662454653480162837548164282
absolute error = 2e-31
relative error = 1.0046382916907924385060032496373e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.4MB, time=6.75
x[1] = 0.137
y2[1] (analytic) = 0.86342815683197639322133468075391
y2[1] (numeric) = 0.86342815683197639322133468075386
absolute error = 5e-32
relative error = 5.7908697561423200411247680794535e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9906301689599851691371351973316
y1[1] (numeric) = 1.9906301689599851691371351973318
absolute error = 2e-31
relative error = 1.0047069672639946709065528037444e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=110.6MB, alloc=4.4MB, time=6.99
x[1] = 0.138
y2[1] (analytic) = 0.86243759511403732147547160042766
y2[1] (numeric) = 0.86243759511403732147547160042761
absolute error = 5e-32
relative error = 5.7975209201529140703423883308995e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9904931018245359145166746894438
y1[1] (numeric) = 1.9904931018245359145166746894441
absolute error = 3e-31
relative error = 1.5071642284266771566104470306467e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.4MB, time=7.24
x[1] = 0.139
y2[1] (analytic) = 0.86144717095849167215892866552446
y2[1] (numeric) = 0.86144717095849167215892866552441
absolute error = 5e-32
relative error = 5.8041864534034462273004264759941e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9903550441960673764493670065295
y1[1] (numeric) = 1.9903550441960673764493670065297
absolute error = 2e-31
relative error = 1.0048458468915169644797995858842e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.14
y2[1] (analytic) = 0.86045688535576351828201164829463
y2[1] (numeric) = 0.86045688535576351828201164829458
absolute error = 5e-32
relative error = 5.8108663956273715292834160742387e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9902159962126371718989482270114
y1[1] (numeric) = 1.9902159962126371718989482270116
absolute error = 2e-31
relative error = 1.0049160512255864176420440742915e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.4MB, time=7.48
x[1] = 0.141
y2[1] (analytic) = 0.85946673929613838004907694910232
y2[1] (numeric) = 0.85946673929613838004907694910227
absolute error = 5e-32
relative error = 5.8175607866975256767794024678851e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9900759580132932727082913350357
y1[1] (numeric) = 1.9900759580132932727082913350359
absolute error = 2e-31
relative error = 1.0049867654280965072886633500590e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.4MB, time=7.72
x[1] = 0.142
y2[1] (analytic) = 0.85847673376976223457309391585971
y2[1] (numeric) = 0.85847673376976223457309391585966
absolute error = 5e-32
relative error = 5.8242696666267100411457918037568e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9899349297380738665514459649294
y1[1] (numeric) = 1.9899349297380738665514459649296
absolute error = 2e-31
relative error = 1.0050579896415260940810671647313e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.143
y2[1] (analytic) = 0.85748686976664052572975024321969
y2[1] (numeric) = 0.85748686976664052572975024321964
absolute error = 5e-32
relative error = 5.8309930755682795219804128555278e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9897929115280072168954623969991
y1[1] (numeric) = 1.9897929115280072168954623969993
absolute error = 2e-31
relative error = 1.0051297240093968008949722131981e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.4MB, time=7.96
x[1] = 0.144
y2[1] (analytic) = 0.85649714827663717415209059733904
y2[1] (numeric) = 0.85649714827663717415209059733899
absolute error = 5e-32
relative error = 5.8377310538167332902925591359729e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9896499035251115219721398428361
y1[1] (numeric) = 1.9896499035251115219721398428362
absolute error = 1e-31
relative error = 5.0260098433813681449942269421877e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.4MB, time=8.21
x[1] = 0.145
y2[1] (analytic) = 0.85550757028947358736667847149108
y2[1] (numeric) = 0.85550757028947358736667847149103
absolute error = 5e-32
relative error = 5.8444836418083084336704109618459e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.989505905872394772759840048366
y1[1] (numeric) = 1.9895059058723947727598400483661
absolute error = 1e-31
relative error = 5.0263736189388278940040674992332e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.4MB, time=8.46
x[1] = 0.146
y2[1] (analytic) = 0.85451813679472767007227113628341
y2[1] (numeric) = 0.85451813679472767007227113628336
absolute error = 5e-32
relative error = 5.8512508801215765197435828628824e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9893609187138546099755082328197
y1[1] (numeric) = 1.9893609187138546099755082328198
absolute error = 1e-31
relative error = 5.0267399474526313758431314876131e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.147
y2[1] (analytic) = 0.85352884878183283456199740572324
y2[1] (numeric) = 0.85352884878183283456199740572319
absolute error = 5e-32
relative error = 5.8580328094780430943426065257114e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9892149421944781800770443715908
y1[1] (numeric) = 1.989214942194478180077044371591
absolute error = 2e-31
relative error = 1.0054217659322545973272942741022e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.4MB, time=8.70
x[1] = 0.148
y2[1] (analytic) = 0.85253970724007701129002779687021
y2[1] (numeric) = 0.85253970724007701129002779687017
absolute error = 4e-32
relative error = 4.6918635765942001046887591155860e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9890679764602419902761688205978
y1[1] (numeric) = 1.989067976460241990276168820598
absolute error = 2e-31
relative error = 1.0054960532616953133390573973376e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.4MB, time=8.95
x[1] = 0.149
y2[1] (analytic) = 0.85155071315860165958372651632402
y2[1] (numeric) = 0.85155071315860165958372651632397
absolute error = 5e-32
relative error = 5.8716409049248814474296847209873e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9889200216581117625619272692718
y1[1] (numeric) = 1.988920021658111762561927269272
absolute error = 2e-31
relative error = 1.0055708516286397191703756608917e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.15
y2[1] (analytic) = 0.85056186752640077850227456131236
y2[1] (numeric) = 0.85056186752640077850227456131231
absolute error = 5e-32
relative error = 5.8784671531783711086201984236119e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9887710779360422867349809986543
y1[1] (numeric) = 1.9887710779360422867349809986545
memory used=144.9MB, alloc=4.4MB, time=9.19
absolute error = 2e-31
relative error = 1.0056461611839262823506671282776e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.151
y2[1] (analytic) = 0.8495731713323199178427530766738
y2[1] (numeric) = 0.84957317133231991784275307667375
absolute error = 5e-32
relative error = 5.8853082568025148284962872800144e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9886211454429772724528294103012
y1[1] (numeric) = 1.9886211454429772724528294103014
absolute error = 2e-31
relative error = 1.0057219820794412902275539858543e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.4MB, time=9.43
x[1] = 0.152
y2[1] (analytic) = 0.84858462556505518929467596156972
y2[1] (numeric) = 0.84858462556505518929467596156966
absolute error = 6e-32
relative error = 7.0705971086911012703325389936195e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9884702243288492002861127807586
y1[1] (numeric) = 1.9884702243288492002861127807588
absolute error = 2e-31
relative error = 1.0057983144681195028234120157272e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.4MB, time=9.68
x[1] = 0.153
y2[1] (analytic) = 0.84759623121315227774396057131025
y2[1] (numeric) = 0.8475962312131522777439605713102
absolute error = 5e-32
relative error = 5.8990351960904451113133023498748e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9883183147445791717861441852958
y1[1] (numeric) = 1.988318314744579171786144185296
absolute error = 2e-31
relative error = 1.0058751585039448102980538486994e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.154
y2[1] (analytic) = 0.84660798926500545272732521024132
y2[1] (numeric) = 0.84660798926500545272732521024127
absolute error = 5e-32
relative error = 5.9059211150851763355200083163966e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9881654168420767585638205233501
y1[1] (numeric) = 1.9881654168420767585638205233503
absolute error = 2e-31
relative error = 1.0059525143419508950224113614814e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.4MB, time=9.92
x[1] = 0.155
y2[1] (analytic) = 0.84561990070885658003810196121268
y2[1] (numeric) = 0.84561990070885658003810196121262
absolute error = 6e-32
relative error = 7.0953864673364340346239078820797e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9880115307742398503800635667605
y1[1] (numeric) = 1.9880115307742398503800635667606
absolute error = 1e-31
relative error = 5.0301519106911094913405882080405e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.4MB, time=10.16
x[1] = 0.156
y2[1] (analytic) = 0.84463196653279413348445324573189
y2[1] (numeric) = 0.84463196653279413348445324573183
absolute error = 6e-32
relative error = 7.1036856734536589242305957156056e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9878566566949545022479429403361
y1[1] (numeric) = 1.9878566566949545022479429403362
absolute error = 1e-31
relative error = 5.0305438102494654575896202916916e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.4MB, time=10.40
x[1] = 0.157
y2[1] (analytic) = 0.84364418772475220680098035650535
y2[1] (numeric) = 0.84364418772475220680098035650529
absolute error = 6e-32
relative error = 7.1120030070752566281204038530042e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9877007947590947805466339326243
y1[1] (numeric) = 1.9877007947590947805466339326245
absolute error = 2e-31
relative error = 1.0061876542351515524019231486357e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.158
y2[1] (analytic) = 0.84265656527250952571471205067536
y2[1] (numeric) = 0.8426565652725095257147120506753
absolute error = 6e-32
relative error = 7.1203385190022698360612620737539e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9875439451225226081473640229073
y1[1] (numeric) = 1.9875439451225226081473640229074
absolute error = 1e-31
relative error = 5.0313352942661842263229162728394e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.4MB, time=10.65
x[1] = 0.159
y2[1] (analytic) = 0.84166910016368846016646113768246
y2[1] (numeric) = 0.8416691001636884601664611376824
absolute error = 6e-32
relative error = 7.1286922602161768097755335524334e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9873861079420876085515029984672
y1[1] (numeric) = 1.9873861079420876085515029984673
absolute error = 1e-31
relative error = 5.0317348803222085318381806625831e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.4MB, time=10.89
x[1] = 0.16
y2[1] (analytic) = 0.84068179338575403668853684031401
y2[1] (numeric) = 0.84068179338575403668853684031395
absolute error = 6e-32
relative error = 7.1370642818796584109670951466707e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9872272833756269490409525240183
y1[1] (numeric) = 1.9872272833756269490409525240185
absolute error = 2e-31
relative error = 1.0064274060301127337338940958891e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.161
y2[1] (analytic) = 0.83969464592601295093980055114447
y2[1] (numeric) = 0.83969464592601295093980055114441
absolute error = 6e-32
relative error = 7.1454546353373689400207697384388e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9870674715819651828409920129024
y1[1] (numeric) = 1.9870674715819651828409920129025
absolute error = 1e-31
relative error = 5.0325417445632554081855432598379e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.4MB, time=11.13
x[1] = 0.162
y2[1] (analytic) = 0.83870765877161258039905244922922
y2[1] (numeric) = 0.83870765877161258039905244922915
absolute error = 7e-32
relative error = 8.3461739341361626081896158726682e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9869066727209140902957386371875
y1[1] (numeric) = 1.9869066727209140902957386371876
absolute error = 1e-31
relative error = 5.0329490243775657987150902527648e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=179.2MB, alloc=4.4MB, time=11.38
x[1] = 0.163
y2[1] (analytic) = 0.83772083290953999721773628358307
y2[1] (numeric) = 0.837720832909539997217736283583
absolute error = 7e-32
relative error = 8.3560056345833818996751916970906e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9867448869532725190563803011996
y1[1] (numeric) = 1.9867448869532725190563803011997
absolute error = 1e-31
relative error = 5.0333588704160566845338333877699e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.5MB, time=11.63
x[1] = 0.164
y2[1] (analytic) = 0.8367341693266209812329494706565
y2[1] (numeric) = 0.83673416932662098123294947065643
absolute error = 7e-32
relative error = 8.3658589031130327321541650727921e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9865821144408262232823413902376
y1[1] (numeric) = 1.9865821144408262232823413902377
absolute error = 1e-31
relative error = 5.0337712835065732481595740054154e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.165
y2[1] (analytic) = 0.83574766900951903314174549271711
y2[1] (numeric) = 0.83574766900951903314174549271704
absolute error = 7e-32
relative error = 8.3757338004855040910281504549655e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9864183553463477018555420932949
y1[1] (numeric) = 1.9864183553463477018555420932951
absolute error = 2e-31
relative error = 1.0068372528964495151962928113393e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.5MB, time=11.87
x[1] = 0.166
y2[1] (analytic) = 0.83476133294473438783771542275181
y2[1] (numeric) = 0.83476133294473438783771542275174
absolute error = 7e-32
relative error = 8.3856303876780514422098696494668e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9862536098335960356079130855139
y1[1] (numeric) = 1.9862536098335960356079130855141
absolute error = 2e-31
relative error = 1.0069207628363004494499897890260e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.5MB, time=12.11
x[1] = 0.167
y2[1] (analytic) = 0.83377516211860302791083523922592
y2[1] (numeric) = 0.83377516211860302791083523922585
absolute error = 7e-32
relative error = 8.3955487258857232546548302355625e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9860878780673167235623283428443
y1[1] (numeric) = 1.9860878780673167235623283428445
absolute error = 2e-31
relative error = 1.0070047866896107892908019906781e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.5MB, time=12.36
x[1] = 0.168
y2[1] (analytic) = 0.83278915751729569731156543076966
y2[1] (numeric) = 0.83278915751729569731156543076959
absolute error = 7e-32
relative error = 8.4054888765222921488815616077521e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.985921160213241518187119847961
y1[1] (numeric) = 1.9859211602132415181871198479612
absolute error = 2e-31
relative error = 1.0070893246261834198225026534807e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.169
y2[1] (analytic) = 0.83180332012681691518018922661023
y2[1] (numeric) = 0.83180332012681691518018922661016
absolute error = 7e-32
relative error = 8.4154509012211906978885168114016e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9857534564380882596643389329105
y1[1] (numeric) = 1.9857534564380882596643389329106
absolute error = 1e-31
relative error = 5.0358718840844075310066519868860e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.5MB, time=12.60
x[1] = 0.17
y2[1] (analytic) = 0.83081765093300398984237562332915
y2[1] (numeric) = 0.83081765093300398984237562332908
absolute error = 7e-32
relative error = 8.4254348618364519070454817149844e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9855847669095607091719299902125
y1[1] (numeric) = 1.9855847669095607091719299902126
absolute error = 1e-31
relative error = 5.0362997171681461508806471945451e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.5MB, time=12.85
x[1] = 0.171
y2[1] (analytic) = 0.8298321509215260329719532122995
y2[1] (numeric) = 0.82983215092152603297195321229943
absolute error = 7e-32
relative error = 8.4354408204436543997082794139332e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9854150917963483811799832702289
y1[1] (numeric) = 1.985415091796348381179983270229
absolute error = 1e-31
relative error = 5.0367301232470626566380541486165e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.172
y2[1] (analytic) = 0.82884682107788297392188064494727
y2[1] (numeric) = 0.8288468210778829739218806449472
absolute error = 7e-32
relative error = 8.4454688393408723354777266396802e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9852444312681263747612344685321
y1[1] (numeric) = 1.9852444312681263747612344685322
absolute error = 1e-31
relative error = 5.0371631031913992650611999673230e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.5MB, time=13.09
x[1] = 0.173
y2[1] (analytic) = 0.82786166238740457422439940478408
y2[1] (numeric) = 0.82786166238740457422439940478401
absolute error = 7e-32
relative error = 8.4555189810496300881971999765540e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9850727854955552039159797927608
y1[1] (numeric) = 1.9850727854955552039159797927609
absolute error = 1e-31
relative error = 5.0375986578767144650814597912235e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.5MB, time=13.34
x[1] = 0.174
y2[1] (analytic) = 0.82687667583524944226135438597639
y2[1] (numeric) = 0.82687667583524944226135438597632
absolute error = 7e-32
relative error = 8.4655913083158617109578125756920e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9849001546502806269115761840325
y1[1] (numeric) = 1.9849001546502806269115761840326
absolute error = 1e-31
relative error = 5.0380367881838867946282593425039e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.5MB, time=13.58
x[1] = 0.175
y2[1] (analytic) = 0.82589186240640404810566760804859
y2[1] (numeric) = 0.82589186240640404810566760804852
absolute error = 7e-32
relative error = 8.4756858841108752155560965893498e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9847265389049334746366973533995
y1[1] (numeric) = 1.9847265389049334746366973533996
absolute error = 1e-31
relative error = 5.0384774949991186410848730511387e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.176
y2[1] (analytic) = 0.82490722308568173853495022516409
y2[1] (numeric) = 0.82490722308568173853495022516402
absolute error = 7e-32
relative error = 8.4858027716323216940262426055857e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9845519384331294779705172790773
y1[1] (numeric) = 1.9845519384331294779705172790774
absolute error = 1e-31
relative error = 5.0389207792139400653792684886860e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.5MB, time=13.82
x[1] = 0.177
y2[1] (analytic) = 0.82392275885772175221823781629032
y2[1] (numeric) = 0.82392275885772175221823781629025
absolute error = 7e-32
relative error = 8.4959420343051693100473749019003e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9843763534094690941669937952475
y1[1] (numeric) = 1.9843763534094690941669937952476
absolute error = 1e-31
relative error = 5.0393666417252126497384297434273e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.5MB, time=14.07
x[1] = 0.178
y2[1] (analytic) = 0.82293847070698823507683376943031
y2[1] (numeric) = 0.82293847070698823507683376943023
absolute error = 8e-32
relative error = 9.7212614123230653579497718886167e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9841997840095373322544258881378
y1[1] (numeric) = 1.9841997840095373322544258881379
absolute error = 1e-31
relative error = 5.0398150834351333691347745877695e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.179
y2[1] (analytic) = 0.82195435961776925582024539899536
y2[1] (numeric) = 0.82195435961776925582024539899529
absolute error = 7e-32
relative error = 8.5162879399474042292751699499598e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9840222304099035774504592998064
y1[1] (numeric) = 1.9840222304099035774504592998065
absolute error = 1e-31
relative error = 5.0402661052512384864534628324771e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
memory used=225.0MB, alloc=4.5MB, time=14.31
TOP MAIN SOLVE Loop
x[1] = 0.18
y2[1] (analytic) = 0.82097042657417582165819726030079
y2[1] (numeric) = 0.82097042657417582165819726030072
absolute error = 7e-32
relative error = 8.5264947109121478798527931059974e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9838436927881214145927160246115
y1[1] (numeric) = 1.9838436927881214145927160246116
absolute error = 1e-31
relative error = 5.0407197080864074714095761345369e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.5MB, time=14.56
x[1] = 0.181
y2[1] (analytic) = 0.81998667256014089418970594908918
y2[1] (numeric) = 0.81998667256014089418970594908911
absolute error = 7e-32
relative error = 8.5367241130209878848879624904715e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9836641713227284505852242677207
y1[1] (numeric) = 1.9836641713227284505852242677208
absolute error = 1e-31
relative error = 5.0411758928588669432443327284863e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=232.6MB, alloc=4.5MB, time=14.81
x[1] = 0.182
y2[1] (analytic) = 0.81900309855941840547020049692454
y2[1] (numeric) = 0.81900309855941840547020049692447
absolute error = 7e-32
relative error = 8.5469762108502600518055810412083e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.983483666193246135860826419216
y1[1] (numeric) = 1.9834836661932461358608264192161
absolute error = 1e-31
relative error = 5.0416346604921946372296840869981e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.183
y2[1] (analytic) = 0.81801970555558227425767229525488
y2[1] (numeric) = 0.81801970555558227425767229525481
absolute error = 7e-32
relative error = 8.5572510692095650551286560267459e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9833021775801795848597435813723
y1[1] (numeric) = 1.9833021775801795848597435813724
absolute error = 1e-31
relative error = 5.0420960119153233950108243876294e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.5MB, time=15.05
x[1] = 0.184
y2[1] (analytic) = 0.81703649453202542243883830191132
y2[1] (numeric) = 0.81703649453202542243883830191125
absolute error = 7e-32
relative error = 8.5675487531427773106838377389049e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9831197056650173955244761705281
y1[1] (numeric) = 1.9831197056650173955244761705282
absolute error = 1e-31
relative error = 5.0425599480625451788163278710881e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.5MB, time=15.30
x[1] = 0.185
y2[1] (analytic) = 0.81605346647195879163630110379855
y2[1] (numeric) = 0.81605346647195879163630110379848
absolute error = 7e-32
relative error = 8.5778693279290589486651492063135e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9829362506302314678112210986348
y1[1] (numeric) = 1.9829362506302314678112210986349
absolute error = 1e-31
relative error = 5.0430264698735151095658137243275e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.5MB, time=15.54
x[1] = 0.186
y2[1] (analytic) = 0.81507062235841035999768922853466
y2[1] (numeric) = 0.81507062235841035999768922853459
absolute error = 7e-32
relative error = 8.5882128590838789150211367636360e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9827518126592768212179870230509
y1[1] (numeric) = 1.982751812659276821217987023051
absolute error = 1e-31
relative error = 5.0434955782932555289052230114821e-30 %
Correct digits = 31
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.187
y2[1] (analytic) = 0.81408796317422415916776091581804
y2[1] (numeric) = 0.81408796317422415916776091581797
absolute error = 7e-32
relative error = 8.5985794123600372308223807398312e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9825663919365914113295901364508
y1[1] (numeric) = 1.982566391936591411329590136451
absolute error = 2e-31
relative error = 1.0087934548544320170399954818566e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.5MB, time=15.78
x[1] = 0.188
y2[1] (analytic) = 0.81310548990205929144445437633573
y2[1] (numeric) = 0.81310548990205929144445437633566
absolute error = 7e-32
relative error = 8.6089690537486944394594018416325e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9823799886475959453797139518383
y1[1] (numeric) = 1.9823799886475959453797139518385
absolute error = 2e-31
relative error = 1.0088883117531995687032950166730e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.5MB, time=16.03
x[1] = 0.189
y2[1] (analytic) = 0.81212320352438894711986738208099
y2[1] (numeric) = 0.81212320352438894711986738208093
absolute error = 6e-32
relative error = 7.3880415852689196614704226143903e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9821926029786936968302175205875
y1[1] (numeric) = 1.9821926029786936968302175205877
absolute error = 2e-31
relative error = 1.0089836865471834839245129940049e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.19
y2[1] (analytic) = 0.81114110502349942200714884701869
y2[1] (numeric) = 0.81114110502349942200714884701863
absolute error = 6e-32
relative error = 7.3969867423081401933899229936576e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9820042351172703189678775041899
y1[1] (numeric) = 1.9820042351172703189678775041901
absolute error = 2e-31
relative error = 1.0090795794296902276075654013421e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.5MB, time=16.27
x[1] = 0.191
y2[1] (analytic) = 0.81015919538148913515428487112495
y2[1] (numeric) = 0.81015919538148913515428487112488
absolute error = 7e-32
relative error = 8.6402771700984374248641777030803e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9818148852516936575187505029481
y1[1] (numeric) = 1.9818148852516936575187505029483
absolute error = 2e-31
relative error = 1.0091759905951038428329344972188e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.5MB, time=16.52
x[1] = 0.192
y2[1] (analytic) = 0.80917747558026764674576153393323
y2[1] (numeric) = 0.80917747558026764674576153393316
absolute error = 7e-32
relative error = 8.6507598286522297863830222779011e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9816245535713135622803430272392
y1[1] (numeric) = 1.9816245535713135622803430272394
absolute error = 2e-31
relative error = 1.0092729202388867921062931390297e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.5MB, time=16.76
x[1] = 0.193
y2[1] (analytic) = 0.80819594660155467619308653584224
y2[1] (numeric) = 0.80819594660155467619308653584217
absolute error = 7e-32
relative error = 8.6612659088861291946616436022755e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9814332402664616977717774791618
y1[1] (numeric) = 1.981433240266461697771777479162
absolute error = 2e-31
relative error = 1.0093703685575808034358110689189e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.194
y2[1] (analytic) = 0.8072146094268791204151515965821
y2[1] (numeric) = 0.80721460942687912041515159658203
absolute error = 7e-32
relative error = 8.6717954782433720470826866027180e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9812409455284513529021434943852
y1[1] (numeric) = 1.9812409455284513529021434943854
absolute error = 2e-31
relative error = 1.0094683357488077212444583994990e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=267.0MB, alloc=4.5MB, time=17.01
x[1] = 0.195
y2[1] (analytic) = 0.80623346503757807230941733039465
y2[1] (numeric) = 0.80623346503757807230941733039458
absolute error = 7e-32
relative error = 8.6823486044129092015893970037079e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9810476695495772496572249758333
y1[1] (numeric) = 1.9810476695495772496572249758336
absolute error = 3e-31
relative error = 1.5143502330169055431854887313091e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.5MB, time=17.25
x[1] = 0.196
y2[1] (analytic) = 0.80525251441479583941490212666118
y2[1] (numeric) = 0.80525251441479583941490212666111
absolute error = 7e-32
relative error = 8.6929253553304780247660400705220e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9808534125231153508047941324606
y1[1] (numeric) = 1.9808534125231153508047941324609
absolute error = 3e-31
relative error = 1.5144987413171300631520281044339e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.5MB, time=17.50
x[1] = 0.197
y2[1] (analytic) = 0.80427175853948296276795637290694
y2[1] (numeric) = 0.80427175853948296276795637290687
absolute error = 7e-32
relative error = 8.7035257991796799053227491424915e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.980658174643322666618664817809
y1[1] (numeric) = 1.9806581746433226666186648178093
absolute error = 3e-31
relative error = 1.5146480288251861631463304393383e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.198
y2[1] (analytic) = 0.80329119839239523595180316432647
y2[1] (numeric) = 0.8032911983923952359518031643264
absolute error = 7e-32
relative error = 8.7141500043930632648445593440009e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9804619561054370606216984442784
y1[1] (numeric) = 1.9804619561054370606216984442787
absolute error = 3e-31
relative error = 1.5147980958440002173608341602801e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.5MB, time=17.75
x[1] = 0.199
y2[1] (analytic) = 0.8023108349540927243408264502072
y2[1] (numeric) = 0.80231083495409272434082645020713
absolute error = 7e-32
relative error = 8.7247980396532120978734844175872e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9802647571056770543479567300861
y1[1] (numeric) = 1.9802647571056770543479567300864
absolute error = 3e-31
relative error = 1.5149489426781252655753970838099e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=282.2MB, alloc=4.5MB, time=17.99
x[1] = 0.2
y2[1] (analytic) = 0.80133066920493878454058737288161
y2[1] (numeric) = 0.80133066920493878454058737288154
absolute error = 7e-32
relative error = 8.7354699738938400736031231398581e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9800665778412416311241965167482
y1[1] (numeric) = 1.9800665778412416311241965167485
absolute error = 3e-31
relative error = 1.5151005696337423332428237405056e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.201
y2[1] (analytic) = 0.80035070212509908402454935910971
y2[1] (numeric) = 0.80035070212509908402454935910964
absolute error = 7e-32
relative error = 8.7461658763008902316774485151913e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.979867418510310038870902875571
y1[1] (numeric) = 1.9798674185103100388709028755713
absolute error = 3e-31
relative error = 1.5152529770186617588947844467261e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.5MB, time=18.24
x[1] = 0.202
y2[1] (analytic) = 0.79937093469454062096849232708521
y2[1] (numeric) = 0.79937093469454062096849232708513
absolute error = 8e-32
relative error = 1.0007869504358446062627600297492e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9796672793120415919230577021024
y1[1] (numeric) = 1.9796672793120415919230577021028
absolute error = 4e-31
relative error = 2.0205415535230993718374045891190e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.5MB, time=18.48
x[1] = 0.203
y2[1] (analytic) = 0.79839136789303074428359617456935
y2[1] (numeric) = 0.79839136789303074428359617456927
absolute error = 8e-32
relative error = 1.0020148415572358515506493107896e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9794661604465754718708419777594
y1[1] (numeric) = 1.9794661604465754718708419777597
absolute error = 3e-31
relative error = 1.5155601343158036194310507188101e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.5MB, time=18.73
x[1] = 0.204
y2[1] (analytic) = 0.79741200270013617384917351498742
y2[1] (numeric) = 0.79741200270013617384917351498734
absolute error = 8e-32
relative error = 1.0032454957927652776214875850103e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.979264062115030527420470857911
y1[1] (numeric) = 1.9792640621150305274204708579113
absolute error = 3e-31
relative error = 1.5157148848518053461107296031697e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.205
y2[1] (analytic) = 0.79643284009522202094603142867336
y2[1] (numeric) = 0.79643284009522202094603142867328
absolute error = 8e-32
relative error = 1.0044789211659723714166366201908e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9790609845195050732753617255673
y1[1] (numeric) = 1.9790609845195050732753617255676
absolute error = 3e-31
relative error = 1.5158704170646707205799096779146e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=297.5MB, alloc=4.5MB, time=18.97
x[1] = 0.206
y2[1] (analytic) = 0.79545388105745080889144179581925
y2[1] (numeric) = 0.79545388105745080889144179581917
absolute error = 8e-32
relative error = 1.0057151257298609528218033809172e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9788569278630766880378363294873
y1[1] (numeric) = 1.9788569278630766880378363294876
absolute error = 3e-31
relative error = 1.5160267312703768147652123105131e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.5MB, time=19.22
x[1] = 0.207
y2[1] (analytic) = 0.79447512656578149387669957607767
y2[1] (numeric) = 0.79447512656578149387669957607759
absolute error = 8e-32
relative error = 1.0069541175670287695043994205744e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9786518923498020111315591049884
y1[1] (numeric) = 1.9786518923498020111315591049887
absolute error = 3e-31
relative error = 1.5161838277865381323958138136096e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.208
y2[1] (analytic) = 0.79349657759896848600824819717701
y2[1] (numeric) = 0.79349657759896848600824819717693
absolute error = 8e-32
relative error = 1.0081959047897977577644155233324e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9784458781847165387449147550011
y1[1] (numeric) = 1.9784458781847165387449147550014
absolute error = 3e-31
relative error = 1.5163417069324079879332891639242e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.5MB, time=19.46
x[1] = 0.209
y2[1] (analytic) = 0.79251823513556067055335101134286
y2[1] (numeric) = 0.79251823513556067055335101134278
absolute error = 8e-32
relative error = 1.0094404955403449733126252978759e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9782388855738344187955291479752
y1[1] (numeric) = 1.9782388855738344187955291479756
absolute error = 4e-31
relative error = 2.0220004920385065238705029532612e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=308.9MB, alloc=4.5MB, time=19.70
x[1] = 0.21
y2[1] (analytic) = 0.79154010015390042939128757377236
y2[1] (numeric) = 0.79154010015390042939128757377228
absolute error = 8e-32
relative error = 1.0106878979908341959158263286153e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9780309147241482449161385680994
y1[1] (numeric) = 1.9780309147241482449161385680997
absolute error = 3e-31
relative error = 1.5166598143984889496365564690110e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=312.8MB, alloc=4.5MB, time=19.95
x[1] = 0.211
y2[1] (analytic) = 0.79056217363212266267105329188374
y2[1] (numeric) = 0.79056217363212266267105329188366
absolute error = 8e-32
relative error = 1.0119381203435482118749128956175e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9778219658436288494620133319462
y1[1] (numeric) = 1.9778219658436288494620133319466
absolute error = 4e-31
relative error = 2.0224267244872176699178382986142e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.212
y2[1] (analytic) = 0.78958445654815381067654078755991
y2[1] (numeric) = 0.78958445654815381067654078755983
absolute error = 8e-32
relative error = 1.0131911708310217783278517242668e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.977612039141225095540142764105
y1[1] (numeric) = 1.9776120391412250955401427641054
absolute error = 4e-31
relative error = 2.0226414083406337282434217059670e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.5MB, time=20.19
x[1] = 0.213
y2[1] (analytic) = 0.7886069498797108759001811071231
y2[1] (numeric) = 0.78860694987971087590018110712303
absolute error = 7e-32
relative error = 8.8764117550165336422159036658806e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9774011348268636680603895025966
y1[1] (numeric) = 1.977401134826863668060389502597
absolute error = 4e-31
relative error = 2.0228571378615245231399158388189e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.5MB, time=20.44
x[1] = 0.214
y2[1] (analytic) = 0.78762965460430044532602270531804
y2[1] (numeric) = 0.78762965460430044532602270531796
absolute error = 8e-32
relative error = 1.0157057892924490362196973135299e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9771892531114488638088220829006
y1[1] (numeric) = 1.9771892531114488638088220829009
absolute error = 3e-31
relative error = 1.5173054351165330925482791767462e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.5MB, time=20.68
x[1] = 0.215
y2[1] (analytic) = 0.78665257169921771292322592014294
y2[1] (numeric) = 0.78665257169921771292322592014286
absolute error = 8e-32
relative error = 1.0169673738839384009530344473092e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9769763942068623805434357272442
y1[1] (numeric) = 1.9769763942068623805434357272446
absolute error = 4e-31
relative error = 2.0232917356632114925631470015457e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.216
y2[1] (analytic) = 0.78567570214154550235095044495269
y2[1] (numeric) = 0.78567570214154550235095044495262
absolute error = 7e-32
relative error = 8.9095284236483825021797836668276e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9767625583259631051124722434151
y1[1] (numeric) = 1.9767625583259631051124722434155
absolute error = 4e-31
relative error = 2.0235106048282457401857407345363e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=328.0MB, alloc=4.5MB, time=20.92
x[1] = 0.217
y2[1] (analytic) = 0.78469904690815328987561309286506
y2[1] (numeric) = 0.78469904690815328987561309286499
absolute error = 7e-32
relative error = 8.9206174361765592456378501992139e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9765477456825869005955509147589
y1[1] (numeric) = 1.9765477456825869005955509147593
absolute error = 4e-31
relative error = 2.0237305214292347163802008447365e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.5MB, time=21.17
x[1] = 0.218
y2[1] (analytic) = 0.78372260697569622750149293613085
y2[1] (numeric) = 0.78372260697569622750149293613078
absolute error = 7e-32
relative error = 8.9317316327166695774787889836935e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.976331956491546392467823240215
y1[1] (numeric) = 1.9763319564915463924678232402155
absolute error = 5e-31
relative error = 2.5299393573922545204807052838998e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.219
y2[1] (analytic) = 0.78274638332061416631566068978145
y2[1] (numeric) = 0.78274638332061416631566068978137
absolute error = 8e-32
relative error = 1.0220424099645040771654154339040e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9761151909686307537873653602166
y1[1] (numeric) = 1.9761151909686307537873653602171
absolute error = 5e-31
relative error = 2.5302168734147294939111215318674e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=335.6MB, alloc=4.5MB, time=21.41
x[1] = 0.22
y2[1] (analytic) = 0.78177037691913068004820899454299
y2[1] (numeric) = 0.78177037691913068004820899454291
absolute error = 8e-32
relative error = 1.0233183855759669721224204264164e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9758974493306054894060229810447
y1[1] (numeric) = 1.9758974493306054894060229810452
absolute error = 5e-31
relative error = 2.5304957004190171564532112113104e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=339.5MB, alloc=4.5MB, time=21.66
x[1] = 0.221
y2[1] (analytic) = 0.78079458874725208884876003870549
y2[1] (numeric) = 0.78079458874725208884876003870542
absolute error = 7e-32
relative error = 8.9652260669879490691883504238521e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9756787317952122192039245867742
y1[1] (numeric) = 1.9756787317952122192039245867747
absolute error = 5e-31
relative error = 2.5307758389729287057768418451278e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=343.3MB, alloc=4.5MB, time=21.90
x[1] = 0.222
y2[1] (analytic) = 0.77981901978076648328022674235797
y2[1] (numeric) = 0.7798190197807664832802267423579
absolute error = 7e-32
relative error = 8.9764417415311784657753618179398e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9754590385811684603478797042797
y1[1] (numeric) = 1.9754590385811684603478797042802
absolute error = 5e-31
relative error = 2.5310572896470401690624942535257e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.223
y2[1] (analytic) = 0.778843670995242748530803510147
y2[1] (numeric) = 0.77884367099524274853080351014693
absolute error = 7e-32
relative error = 8.9876829724443593353990716366432e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.975238369908167408573879962885
y1[1] (numeric) = 1.9752383699081674085738799628855
absolute error = 5e-31
relative error = 2.5313400530146948881157424609929e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.5MB, time=22.15
x[1] = 0.224
y2[1] (analytic) = 0.77786854336602958884516234048672
y2[1] (numeric) = 0.77786854336602958884516234048665
absolute error = 7e-32
relative error = 8.9989498350315961958692336179813e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9750167259968777184939216661375
y1[1] (numeric) = 1.975016725996877718493921666138
absolute error = 5e-31
relative error = 2.5316241296520060170874492718091e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=350.9MB, alloc=4.5MB, time=22.39
x[1] = 0.225
y2[1] (analytic) = 0.7768936378682545521758298599428
y2[1] (numeric) = 0.77689363786825455217582985994273
absolute error = 7e-32
relative error = 9.0102424048773822249203416004664e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9747941070689432829273695688655
y1[1] (numeric) = 1.974794107068943282927369568866
absolute error = 5e-31
relative error = 2.5319095201378590328184704602865e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.226
y2[1] (analytic) = 0.77591895547682305505572063133211
y2[1] (numeric) = 0.77591895547682305505572063133204
absolute error = 7e-32
relative error = 9.0215607578478500220067260327423e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9745705133469830112570825281373
y1[1] (numeric) = 1.9745705133469830112570825281378
absolute error = 5e-31
relative error = 2.5321962250539142578277607380671e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
memory used=354.7MB, alloc=4.5MB, time=22.64
TOP MAIN SOLVE Loop
x[1] = 0.227
y2[1] (analytic) = 0.77494449716641740769280186292349
y2[1] (numeric) = 0.77494449716641740769280186292342
absolute error = 7e-32
relative error = 9.0329049700920288888016435712117e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9743459450545906068105226719777
y1[1] (numeric) = 1.9743459450545906068105226719782
absolute error = 5e-31
relative error = 2.5324842449846093959628750955369e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.5MB, time=22.88
x[1] = 0.228
y2[1] (analytic) = 0.7739702639114958392878644239937
y2[1] (numeric) = 0.77397026391149583928786442399362
absolute error = 8e-32
relative error = 1.0336314420620695619714116779233e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9741204024163343432660707047136
y1[1] (numeric) = 1.9741204024163343432660707047141
absolute error = 5e-31
relative error = 2.5327735805171620807319597690100e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=362.4MB, alloc=4.5MB, time=23.13
x[1] = 0.229
y2[1] (analytic) = 0.77299625668629152357637484888623
y2[1] (numeric) = 0.77299625668629152357637484888615
absolute error = 8e-32
relative error = 1.0349338603908240199181536019696e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9738938856577568400847709426156
y1[1] (numeric) = 1.9738938856577568400847709426162
absolute error = 6e-31
relative error = 3.0396770786898869236037135532063e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.23
y2[1] (analytic) = 0.77202247646481160459538278763993
y2[1] (numeric) = 0.77202247646481160459538278763985
absolute error = 8e-32
relative error = 1.0362392603688185454373180720842e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9736663950053748369677306480716
y1[1] (numeric) = 1.9736663950053748369677306480722
absolute error = 6e-31
relative error = 3.0400274409007507817083398467313e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=366.2MB, alloc=4.5MB, time=23.37
x[1] = 0.231
y2[1] (analytic) = 0.77104892422083622267645813619863
y2[1] (numeric) = 0.77104892422083622267645813619855
absolute error = 8e-32
relative error = 1.0375476508295754990820320901213e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9734379306866789673393992048733
y1[1] (numeric) = 1.9734379306866789673393992048739
absolute error = 6e-31
relative error = 3.0403793839678734786945855109978e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=370.0MB, alloc=4.5MB, time=23.61
x[1] = 0.232
y2[1] (analytic) = 0.77007560092791754066563185318355
y2[1] (numeric) = 0.77007560092791754066563185318348
absolute error = 7e-32
relative error = 9.0900166055971831164687038687941e-30 %
Correct digits = 31
h = 0.001
y1[1] (analytic) = 1.9732084929301335308569536513194
y1[1] (numeric) = 1.97320849293013353085695365132
absolute error = 6e-31
relative error = 3.0407329086092907222914515314984e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=373.8MB, alloc=4.5MB, time=23.86
x[1] = 0.233
y2[1] (analytic) = 0.76910250755937877037131424320659
y2[1] (numeric) = 0.76910250755937877037131424320651
absolute error = 8e-32
relative error = 1.0401734386989185316590020402005e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9729780819651762649460180617296
y1[1] (numeric) = 1.9729780819651762649460180617302
absolute error = 6e-31
relative error = 3.0410880155463896548898545640705e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.234
y2[1] (analytic) = 0.7681296450883131992411642587249
y2[1] (numeric) = 0.76812964508831319924116425872482
absolute error = 8e-32
relative error = 1.0414908539404472674767121851664e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.972746698022218115362945240631
y1[1] (numeric) = 1.9727466980222181153629452406316
absolute error = 6e-31
relative error = 3.0414447055039120033357141473492e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=377.6MB, alloc=4.5MB, time=24.10
x[1] = 0.235
y2[1] (analytic) = 0.7671570144875832172688831434866
y2[1] (numeric) = 0.76715701448758321726888314348651
absolute error = 9e-32
relative error = 1.1731627072472879102432275613040e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9725143413326430057838901673172
y1[1] (numeric) = 1.9725143413326430057838901673178
absolute error = 6e-31
relative error = 3.0418029792099572441046236479964e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=381.4MB, alloc=4.5MB, time=24.35
x[1] = 0.236
y2[1] (analytic) = 0.76618461672981934413190551069257
y2[1] (numeric) = 0.76618461672981934413190551069248
absolute error = 9e-32
relative error = 1.1746516183544939857015372627874e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9722810121288076064209056016861
y1[1] (numeric) = 1.9722810121288076064209056016867
absolute error = 6e-31
relative error = 3.0421628373959857838819940014039e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.237
y2[1] (analytic) = 0.76521245278741925656096071810253
y2[1] (numeric) = 0.76521245278741925656096071810244
absolute error = 9e-32
relative error = 1.1761439541680139857425552861063e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9720467106440411016652912352422
y1[1] (numeric) = 1.9720467106440411016652912352428
absolute error = 6e-31
relative error = 3.0425242807968221555726825378280e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=385.2MB, alloc=4.5MB, time=24.59
x[1] = 0.238
y2[1] (analytic) = 0.76424052363254681594247717044265
y2[1] (numeric) = 0.76424052363254681594247717044256
absolute error = 9e-32
relative error = 1.1776397248894478495140004241396e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9718114371126449567584287438953
y1[1] (numeric) = 1.9718114371126449567584287438959
absolute error = 6e-31
relative error = 3.0428873101506582297642426900502e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=389.1MB, alloc=4.5MB, time=24.84
x[1] = 0.239
y2[1] (analytic) = 0.76326883023713109615480194662958
y2[1] (numeric) = 0.7632688302371310961548019466295
absolute error = 8e-32
relative error = 1.0481235028966888702274104850782e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9715751917698926834903360717
y1[1] (numeric) = 1.9715751917698926834903360717007
absolute error = 7e-31
relative error = 3.5504605805655658486127298594102e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=392.9MB, alloc=4.5MB, time=25.08
x[1] = 0.24
y2[1] (analytic) = 0.76229737357286541163920791551018
y2[1] (numeric) = 0.7622973735728654116392079155101
absolute error = 8e-32
relative error = 1.0494592107151353350592167892287e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9713379748520296049261752469634
y1[1] (numeric) = 1.9713379748520296049261752469641
absolute error = 7e-31
relative error = 3.5508878179681118724898367705815e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.241
y2[1] (analytic) = 0.76132615461120634570666026902879
y2[1] (numeric) = 0.76132615461120634570666026902871
absolute error = 8e-32
relative error = 1.0507979991946337296542918682897e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9710997865962726191609490041922
y1[1] (numeric) = 1.9710997865962726191609490041929
absolute error = 7e-31
relative error = 3.5513169082564381982249223134855e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=396.7MB, alloc=4.5MB, time=25.33
x[1] = 0.242
y2[1] (analytic) = 0.76035517432337277908131416597463
y2[1] (numeric) = 0.76035517432337277908131416597454
absolute error = 9e-32
relative error = 1.1836573622332415788816331685131e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9708606272408099621026224571645
y1[1] (numeric) = 1.9708606272408099621026224571652
absolute error = 7e-31
relative error = 3.5517478523075207460054227492605e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=400.5MB, alloc=4.5MB, time=25.57
x[1] = 0.243
y2[1] (analytic) = 0.75938443368034491868171494273065
y2[1] (numeric) = 0.75938443368034491868171494273057
absolute error = 8e-32
relative error = 1.0534848549934219312566315117634e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9706204970248009692839070399837
y1[1] (numeric) = 1.9706204970248009692839070399844
absolute error = 7e-31
relative error = 3.5521806510022830016182478925237e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=404.3MB, alloc=4.5MB, time=25.82
x[1] = 0.244
y2[1] (analytic) = 0.7584139336528633266406721097428
y2[1] (numeric) = 0.75841393365286332664067210974272
absolute error = 8e-32
relative error = 1.0548329408280243939042358740000e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9703793961883758367029449043108
y1[1] (numeric) = 1.9703793961883758367029449043115
absolute error = 7e-31
relative error = 3.5526153052255998719316894591292e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.245
y2[1] (analytic) = 0.7574436752114279495647781137546
y2[1] (numeric) = 0.75744367521142794956477811375452
absolute error = 8e-32
relative error = 1.0561841443546190441108024012494e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9701373249726353806931329320715
y1[1] (numeric) = 1.9701373249726353806931329320722
absolute error = 7e-31
relative error = 3.5530518158663015586077250173530e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=408.1MB, alloc=4.5MB, time=26.07
x[1] = 0.246
y2[1] (analytic) = 0.75647365932629714803454260620757
y2[1] (numeric) = 0.75647365932629714803454260620749
absolute error = 8e-32
relative error = 1.0575384749185671403493930180178e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9698942836196507968223264937931
y1[1] (numeric) = 1.9698942836196507968223264937938
absolute error = 7e-31
relative error = 3.5534901838171774500740406235301e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=411.9MB, alloc=4.5MB, time=26.31
x[1] = 0.247
y2[1] (analytic) = 0.75550388696748672634611271759229
y2[1] (numeric) = 0.75550388696748672634611271759221
absolute error = 8e-32
relative error = 1.0588959419005982871005465532089e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9696502723724634178216640533481
y1[1] (numeric) = 1.9696502723724634178216640533489
absolute error = 8e-31
relative error = 4.0616347542571200363259912261665e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.248
y2[1] (analytic) = 0.75453435910476896249554959594889
y2[1] (numeric) = 0.75453435910476896249554959594881
absolute error = 8e-32
relative error = 1.0602565547169708421233035642242e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9694052914750844705442546902599
y1[1] (numeric) = 1.9694052914750844705442546902607
absolute error = 8e-31
relative error = 4.0621399945604900740604275880829e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=415.8MB, alloc=4.5MB, time=26.55
x[1] = 0.249
y2[1] (analytic) = 0.75356507670767163840663122515975
y2[1] (numeric) = 0.75356507670767163840663122515967
absolute error = 8e-32
relative error = 1.0616203228196331736377515469281e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9691593411724948319539715808613
y1[1] (numeric) = 1.9691593411724948319539715808621
absolute error = 8e-31
relative error = 4.0626473605922448945417233921748e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=419.6MB, alloc=4.5MB, time=26.80
x[1] = 0.25
y2[1] (analytic) = 0.75259604074547707040315129515061
y2[1] (numeric) = 0.75259604074547707040315129515053
absolute error = 8e-32
relative error = 1.0629872556963857725687379856705e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9689124217106447841445954494942
y1[1] (numeric) = 1.968912421710644784144595449495
absolute error = 8e-31
relative error = 4.0631568533908592651295073313858e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=423.4MB, alloc=4.5MB, time=27.04
x[1] = 0.251
y2[1] (analytic) = 0.75162725218722113992668365162059
y2[1] (numeric) = 0.75162725218722113992668365162051
absolute error = 8e-32
relative error = 1.0643573628710442250355289438266e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9686645333364537683895529705847
y1[1] (numeric) = 1.9686645333364537683895529705855
absolute error = 8e-31
relative error = 4.0636684739993552921070949963022e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.252
y2[1] (analytic) = 0.75065871200169232450078160745575
y2[1] (numeric) = 0.75065871200169232450078160745566
absolute error = 9e-32
relative error = 1.1989469856415534315960360758547e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9684156762978101382224960718362
y1[1] (numeric) = 1.968415676297810138222496071837
absolute error = 8e-31
relative error = 4.0641822234653069945722102173436e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=427.2MB, alloc=4.5MB, time=27.29
x[1] = 0.253
y2[1] (analytic) = 0.74969042115743072894258115154618
y2[1] (numeric) = 0.74969042115743072894258115154609
absolute error = 9e-32
relative error = 1.2004955306892004606676018473445e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9681658508435709115489690579392
y1[1] (numeric) = 1.96816585084357091154896905794
absolute error = 8e-31
relative error = 4.0646981028408448994352703009504e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=431.0MB, alloc=4.5MB, time=27.53
x[1] = 0.254
y2[1] (analytic) = 0.7487223806227271168227768433228
y2[1] (numeric) = 0.74872238062272711682277684332271
absolute error = 9e-32
relative error = 1.2020476792098191514485771961473e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9679150572235615217894114431114
y1[1] (numeric) = 1.9679150572235615217894114431123
absolute error = 9e-31
relative error = 4.5733681273304932397551161825195e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.255
y2[1] (analytic) = 0.74775459136562194217493893295701
y2[1] (numeric) = 0.74775459136562194217493893295692
absolute error = 9e-32
relative error = 1.2036034420816229691295541449292e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9676632956885755680537453494437
y1[1] (numeric) = 1.9676632956885755680537453494445
absolute error = 8e-31
relative error = 4.0657362555520116810821365590172e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
memory used=434.8MB, alloc=4.5MB, time=27.78
TOP MAIN SOLVE Loop
x[1] = 0.256
y2[1] (analytic) = 0.7467870543539043814551399978256
y2[1] (numeric) = 0.74678705435390438145513999782551
absolute error = 9e-32
relative error = 1.2051628302242738048546198820295e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9674105664903745643477972964435
y1[1] (numeric) = 1.9674105664903745643477972964443
absolute error = 8e-31
relative error = 4.0662585310147258019392682440068e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=438.6MB, alloc=4.5MB, time=28.02
x[1] = 0.257
y2[1] (analytic) = 0.74581977055511136575285913553355
y2[1] (numeric) = 0.74581977055511136575285913553346
absolute error = 9e-32
relative error = 1.2067258545990712511740248536306e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.967156869881687687811805175334
y1[1] (numeric) = 1.9671568698816876878118051753349
absolute error = 9e-31
relative error = 4.5751308082213566956071547353065e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=442.5MB, alloc=4.5MB, time=28.27
x[1] = 0.258
y2[1] (analytic) = 0.74485274093652661325413150250981
y2[1] (numeric) = 0.74485274093652661325413150250972
absolute error = 9e-32
relative error = 1.2082925262091428872357675518884e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9669022061162115259912621695806
y1[1] (numeric) = 1.9669022061162115259912621695815
absolute error = 9e-31
relative error = 4.5757231711947392201775190876811e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.259
y2[1] (analytic) = 0.74388596646517966195791073494597
y2[1] (numeric) = 0.74388596646517966195791073494588
absolute error = 9e-32
relative error = 1.2098628560996355798761488142652e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9666465754486098231403503507787
y1[1] (numeric) = 1.9666465754486098231403503507796
absolute error = 9e-31
relative error = 4.5763179375262272629805618744130e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=446.3MB, alloc=4.5MB, time=28.51
x[1] = 0.26
y2[1] (analytic) = 0.74291944810784490264661153563478
y2[1] (numeric) = 0.74291944810784490264661153563469
absolute error = 9e-32
relative error = 1.2114368553579078068116601684141e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9663899781345132255582176464501
y1[1] (numeric) = 1.966389978134513225558217646451
absolute error = 9e-31
relative error = 4.5769151084354969112124928792545e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=450.1MB, alloc=4.5MB, time=28.76
x[1] = 0.261
y2[1] (analytic) = 0.74195318683104061211179945608533
y2[1] (numeric) = 0.74195318683104061211179945608524
absolute error = 9e-32
relative error = 1.2130145351137230081772056390046e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9661324144305190259583528434479
y1[1] (numeric) = 1.9661324144305190259583528434489
absolute error = 1.0e-30
relative error = 5.0861274279415472643861018365973e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=453.9MB, alloc=4.5MB, time=29.00
x[1] = 0.262
y2[1] (analytic) = 0.74098718360102798663599464814456
y2[1] (numeric) = 0.74098718360102798663599464814446
absolute error = 1.0e-31
relative error = 1.3495510072660488585540191055455e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9658738845941909068713142575752
y1[1] (numeric) = 1.9658738845941909068713142575761
absolute error = 9e-31
relative error = 4.5781166688919321870132857776241e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.263
y2[1] (analytic) = 0.74002143938381017573155610324072
y2[1] (numeric) = 0.74002143938381017573155610324062
absolute error = 1.0e-31
relative error = 1.3513122009446980720341260000518e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9656143888840586830810686666656
y1[1] (numeric) = 1.9656143888840586830810686666665
absolute error = 9e-31
relative error = 4.5787210609043129820137333389625e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=457.7MB, alloc=4.5MB, time=29.25
x[1] = 0.264
y2[1] (analytic) = 0.73905595514513131613761264028424
y2[1] (numeric) = 0.73905595514513131613761264028414
absolute error = 1.0e-31
relative error = 1.3530775214491385547064128916372e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9653539275596180430951980707674
y1[1] (numeric) = 1.9653539275596180430951980707684
absolute error = 1.0e-30
relative error = 5.0881420693610183994884272638175e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=461.5MB, alloc=4.5MB, time=29.49
x[1] = 0.265
y2[1] (analytic) = 0.73809073185047556607600664521424
y2[1] (numeric) = 0.73809073185047556607600664521413
absolute error = 1.1e-31
relative error = 1.4903316794700532843592920579860e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9650925008813302896492328092017
y1[1] (numeric) = 1.9650925008813302896492328092027
absolute error = 1.0e-30
relative error = 5.0888189718881272517875497956842e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.266
y2[1] (analytic) = 0.73712577046506613976721630616662
y2[1] (numeric) = 0.73712577046506613976721630616652
absolute error = 1.0e-31
relative error = 1.3566205932117685935553328035733e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9648301091106220792453705301393
y1[1] (numeric) = 1.9648301091106220792453705301404
absolute error = 1.1e-30
relative error = 5.5984484098623348184619508822390e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=465.3MB, alloc=4.5MB, time=29.73
x[1] = 0.267
y2[1] (analytic) = 0.73616107195386434220722182826113
y2[1] (numeric) = 0.73616107195386434220722182826103
absolute error = 1.0e-31
relative error = 1.3583983697288880854217183325161e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9645667525098851607258414739579
y1[1] (numeric) = 1.9645667525098851607258414739589
absolute error = 1.0e-30
relative error = 5.0901808183530698046296009585882e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=469.2MB, alloc=4.5MB, time=29.98
x[1] = 0.268
y2[1] (analytic) = 0.73519663728156860420628085106048
y2[1] (numeric) = 0.73519663728156860420628085106038
absolute error = 1.0e-31
relative error = 1.3601803235901035885966479327048e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9643024313424761128811814969892
y1[1] (numeric) = 1.9643024313424761128811814969902
absolute error = 1.0e-30
relative error = 5.0908657650877285309294985431725e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=473.0MB, alloc=4.5MB, time=30.22
x[1] = 0.269
y2[1] (analytic) = 0.73423246741261351769057802984597
y2[1] (numeric) = 0.73423246741261351769057802984587
absolute error = 1.0e-31
relative error = 1.3619664675466254270787734059393e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9640371458727160810936752273647
y1[1] (numeric) = 1.9640371458727160810936752273658
absolute error = 1.1e-30
relative error = 5.6007087356345143975828083854236e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.27
y2[1] (analytic) = 0.73326856331116887126771347897946
y2[1] (numeric) = 0.73326856331116887126771347897936
absolute error = 1.0e-31
relative error = 1.3637568143987666513120147986682e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9637708963658905130162327094922
y1[1] (numeric) = 1.9637708963658905130162327094933
absolute error = 1.1e-30
relative error = 5.6014680838565987023130090620512e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=476.8MB, alloc=4.5MB, time=30.46
x[1] = 0.271
y2[1] (analytic) = 0.73230492594113868605699451178298
y2[1] (numeric) = 0.73230492594113868605699451178288
absolute error = 1.0e-31
relative error = 1.3655513769961696916219774096800e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9635036830882488932869638582654
y1[1] (numeric) = 1.9635036830882488932869638582665
absolute error = 1.1e-30
relative error = 5.6022303878233211179242761750288e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=480.6MB, alloc=4.5MB, time=30.71
x[1] = 0.272
y2[1] (analytic) = 0.73134155626616025178549484656383
y2[1] (numeric) = 0.73134155626616025178549484656372
absolute error = 1.1e-31
relative error = 1.5040851850618376572014576961615e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9632355063070044772797160084106
y1[1] (numeric) = 1.9632355063070044772797160084117
absolute error = 1.1e-30
relative error = 5.6029956491016392862380455200351e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.273
y2[1] (analytic) = 0.73037845524960316315084518264563
y2[1] (numeric) = 0.73037845524960316315084518264552
absolute error = 1.1e-31
relative error = 1.5060685211806809569586583129631e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9629663662903340238908408084099
y1[1] (numeric) = 1.9629663662903340238908408084109
absolute error = 1.0e-30
relative error = 5.0943307902408259819559099334717e-29 %
Correct digits = 30
h = 0.001
memory used=484.4MB, alloc=4.5MB, time=30.95
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.274
y2[1] (analytic) = 0.72941562385456835645171878353456
y2[1] (numeric) = 0.72941562385456835645171878353445
absolute error = 1.1e-31
relative error = 1.5080565373512195850506182811150e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9626962633073775273624576722117
y1[1] (numeric) = 1.9626962633073775273624576722127
absolute error = 1.0e-30
relative error = 5.0950318635389900388027846286740e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=488.2MB, alloc=4.5MB, time=31.20
x[1] = 0.275
y2[1] (analytic) = 0.72845306304388714648697543665472
y2[1] (numeric) = 0.72845306304388714648697543665461
absolute error = 1.1e-31
relative error = 1.5100492479276296864903882305940e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9624251976282379481424819654439
y1[1] (numeric) = 1.9624251976282379481424819654449
absolute error = 1.0e-30
relative error = 5.0957356296106839601371289578471e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=492.1MB, alloc=4.5MB, time=31.44
x[1] = 0.276
y2[1] (analytic) = 0.72749077378012026372442689042862
y2[1] (numeric) = 0.72749077378012026372442689042851
absolute error = 1.1e-31
relative error = 1.5120466673196166504877167537258e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9621531695239809427816870660775
y1[1] (numeric) = 1.9621531695239809427816870660785
absolute error = 1.0e-30
relative error = 5.0964420899037171286702841213958e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.277
y2[1] (analytic) = 0.72652875702555689174018659985692
y2[1] (numeric) = 0.72652875702555689174018659985681
absolute error = 1.1e-31
relative error = 1.5140488099926726210421137044400e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9618801792666345928680704024572
y1[1] (numeric) = 1.9618801792666345928680704024582
absolute error = 1.0e-30
relative error = 5.0971512458717404437215687212819e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=495.9MB, alloc=4.5MB, time=31.69
x[1] = 0.278
y2[1] (analytic) = 0.72556701374221370492956634116763
y2[1] (numeric) = 0.72556701374221370492956634116752
absolute error = 1.1e-31
relative error = 1.5160556904683354025328945666618e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9616062271291891329987945343101
y1[1] (numeric) = 1.9616062271291891329987945343111
absolute error = 1.0e-30
relative error = 5.0978630989742527393072801447340e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=499.7MB, alloc=4.5MB, time=31.93
x[1] = 0.279
y2[1] (analytic) = 0.72460554489183390649048198455785
y2[1] (numeric) = 0.72460554489183390649048198455774
absolute error = 1.1e-31
relative error = 1.5180673233244487689484297896225e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9613313133855966777899753047686
y1[1] (numeric) = 1.9613313133855966777899753047696
absolute error = 1.0e-30
relative error = 5.0985776506766072298183325934940e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=503.5MB, alloc=4.5MB, time=32.18
x[1] = 0.28
y2[1] (analytic) = 0.72364435143588626668033044154215
y2[1] (numeric) = 0.72364435143588626668033044154204
absolute error = 1.1e-31
relative error = 1.5200837231954241854571040974414e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9610554383107709479245900535965
y1[1] (numeric) = 1.9610554383107709479245900535975
absolute error = 1.0e-30
relative error = 5.0992949024500179833358581186582e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.281
y2[1] (analytic) = 0.72268343433556416134729952995054
y2[1] (numeric) = 0.72268343433556416134729952995043
absolute error = 1.1e-31
relative error = 1.5221049047725039510832394392794e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9607786021805869952387798436879
y1[1] (numeric) = 1.9607786021805869952387798436889
absolute error = 1.0e-30
relative error = 5.1000148557715664226343253735826e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=507.3MB, alloc=4.5MB, time=32.43
x[1] = 0.282
y2[1] (analytic) = 0.72172279455178461073707222518593
y2[1] (numeric) = 0.72172279455178461073707222518582
absolute error = 1.1e-31
relative error = 1.5241308828040257713124554468255e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9605008052718809268468206145129
y1[1] (numeric) = 1.9605008052718809268468206145139
absolute error = 1.0e-30
relative error = 5.1007375121242078539219597347593e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=511.1MB, alloc=4.5MB, time=32.67
x[1] = 0.283
y2[1] (analytic) = 0.72076243304518731857588649095688
y2[1] (numeric) = 0.72076243304518731857588649095677
absolute error = 1.1e-31
relative error = 1.5261616720956887695126370371844e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9602220478624496283050391375165
y1[1] (numeric) = 1.9602220478624496283050391375174
absolute error = 9e-31
relative error = 4.5913165856971002210316301693582e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.284
y2[1] (analytic) = 0.71980235077613371143091160634557
y2[1] (numeric) = 0.71980235077613371143091160634546
absolute error = 1.1e-31
relative error = 1.5281972875108209461188542083226e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9599423302310504858149506095312
y1[1] (numeric) = 1.9599423302310504858149506095322
absolute error = 1.0e-30
relative error = 5.1021909398839997014703807171879e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=514.9MB, alloc=4.5MB, time=32.91
x[1] = 0.285
y2[1] (analytic) = 0.71884254870470597834890162875478
y2[1] (numeric) = 0.71884254870470597834890162875467
absolute error = 1.1e-31
relative error = 1.5302377439706480945932382260050e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.959661652657401107465895681044
y1[1] (numeric) = 1.9596616526574011074658956810449
absolute error = 9e-31
relative error = 4.5926295428578403657738491742749e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=518.8MB, alloc=4.5MB, time=33.16
x[1] = 0.286
y2[1] (analytic) = 0.71788302779070611077408635400021
y2[1] (numeric) = 0.7178830277907061107740863540001
absolute error = 1.1e-31
relative error = 1.5322830564545641832339654388605e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9593800154221790435174556766546
y1[1] (numeric) = 1.9593800154221790435174556766556
absolute error = 1.0e-30
relative error = 5.1036551977107634887189449698404e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=522.6MB, alloc=4.5MB, time=33.41
x[1] = 0.287
y2[1] (analytic) = 0.71692378899365494274625985557732
y2[1] (numeric) = 0.71692378899365494274625985557721
absolute error = 1.1e-31
relative error = 1.5343332400004032119711390638666e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9590974188070215057219257252902
y1[1] (numeric) = 1.9590974188070215057219257252912
absolute error = 1.0e-30
relative error = 5.1043913916692459105170691646961e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.288
y2[1] (analytic) = 0.71596483327279119138002640493412
y2[1] (numeric) = 0.71596483327279119138002640493401
absolute error = 1.1e-31
relative error = 1.5363883097047125533514946792627e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9588138630945250856871264776764
y1[1] (numeric) = 1.9588138630945250856871264776774
absolute error = 1.0e-30
relative error = 5.1051302976802738306778190357374e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=526.4MB, alloc=4.5MB, time=33.65
x[1] = 0.289
y2[1] (analytic) = 0.71500616158707049762616329342395
y2[1] (numeric) = 0.71500616158707049762616329342384
absolute error = 1.1e-31
relative error = 1.5384482807230277869784911063637e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9585293485682454722798360482323
y1[1] (numeric) = 1.9585293485682454722798360482333
absolute error = 1.0e-30
relative error = 5.1058719172681048846716764997670e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=530.2MB, alloc=4.5MB, time=33.90
x[1] = 0.29
y2[1] (analytic) = 0.71404777489516446731605979449563
y2[1] (numeric) = 0.71404777489516446731605979449552
absolute error = 1.1e-31
relative error = 1.5405131682701490367394891565550e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9582438755126971680701247779319
y1[1] (numeric) = 1.9582438755126971680701247779329
absolute error = 1.0e-30
relative error = 5.1066162519629238259191461445522e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=534.0MB, alloc=4.5MB, time=34.14
x[1] = 0.291
y2[1] (analytic) = 0.71308967415545971249019122160201
y2[1] (numeric) = 0.7130896741554597124901912216019
absolute error = 1.1e-31
relative error = 1.5425829876204188202173707058413e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9579574442133532048168763737751
y1[1] (numeric) = 1.9579574442133532048168763737761
absolute error = 1.0e-30
relative error = 5.1073633033008493064452199655655e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.292
y2[1] (analytic) = 0.71213186032605689301158675327299
y2[1] (numeric) = 0.71213186032605689301158675327288
absolute error = 1.1e-31
relative error = 1.5446577541080014197501141184002e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9576700549566448579947799393226
y1[1] (numeric) = 1.9576700549566448579947799393236
absolute error = 1.0e-30
relative error = 5.1081130728239406857817023459649e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=537.8MB, alloc=4.5MB, time=34.39
x[1] = 0.293
y2[1] (analytic) = 0.71117433436476975846524941180534
y2[1] (numeric) = 0.71117433436476975846524941180523
absolute error = 1.1e-31
relative error = 1.5467374831271637846685235955069e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9573817080299613603630783692788
y1[1] (numeric) = 1.9573817080299613603630783692798
absolute error = 1.0e-30
relative error = 5.1088655620802048681697367000869e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=541.6MB, alloc=4.5MB, time=34.63
x[1] = 0.294
y2[1] (analytic) = 0.71021709722912419034448629606947
y2[1] (numeric) = 0.71021709722912419034448629606936
absolute error = 1.1e-31
relative error = 1.5488221901325579743095140413936e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9570924037216496145763595393507
y1[1] (numeric) = 1.9570924037216496145763595393517
absolute error = 1.0e-30
relative error = 5.1096207726236031681151113904122e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.295
y2[1] (analytic) = 0.70926014987635724452510688202316
y2[1] (numeric) = 0.70926014987635724452510688202305
absolute error = 1.1e-31
relative error = 1.5509118906395051514700840195485e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.956802142321013904837677680568
y1[1] (numeric) = 1.9568021423210139048376776805691
absolute error = 1.1e-30
relative error = 5.6214165766154640247840752758266e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=545.5MB, alloc=4.5MB, time=34.88
x[1] = 0.296
y2[1] (analytic) = 0.70830349326341619402844691665405
y2[1] (numeric) = 0.70830349326341619402844691665393
absolute error = 1.2e-31
relative error = 1.6941890184264885120385874951074e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9565109241183156075942932849186
y1[1] (numeric) = 1.9565109241183156075942932849196
absolute error = 1.0e-30
relative error = 5.1111393638174608222483032164338e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=549.3MB, alloc=4.5MB, time=35.12
x[1] = 0.297
y2[1] (analytic) = 0.70734712834695757207417514224732
y2[1] (numeric) = 0.7073471283469575720741751422472
absolute error = 1.2e-31
relative error = 1.6964796376629856675450785460380e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9562187494047729012763208465347
y1[1] (numeric) = 1.9562187494047729012763208465357
absolute error = 1.0e-30
relative error = 5.1119027476056770447655360877536e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=553.1MB, alloc=4.5MB, time=35.37
x[1] = 0.298
y2[1] (analytic) = 0.70639105608334621542383979809208
y2[1] (numeric) = 0.70639105608334621542383979809196
absolute error = 1.2e-31
relative error = 1.6987757555333677241838120339354e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9559256184725604750785746997598
y1[1] (numeric) = 1.9559256184725604750785746997607
absolute error = 9e-31
relative error = 4.6014019730608995467346296232009e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.299
y2[1] (analytic) = 0.70543527742865430801611155600021
y2[1] (numeric) = 0.70543527742865430801611155600008
absolute error = 1.3e-31
relative error = 1.8428338383339189546092109836442e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9556315316148092367859041722236
y1[1] (numeric) = 1.9556315316148092367859041722245
absolute error = 9e-31
relative error = 4.6020939295085389700549947208734e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=556.9MB, alloc=4.5MB, time=35.61
x[1] = 0.3
y2[1] (analytic) = 0.70447979333866042489467925431497
y2[1] (numeric) = 0.70447979333866042489467925431485
absolute error = 1.2e-31
relative error = 1.7033845560182463068885016686102e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.955336489125606019642310227568
y1[1] (numeric) = 1.955336489125606019642310227569
absolute error = 1.0e-30
relative error = 5.1142092706876420030287293303903e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=560.7MB, alloc=4.5MB, time=35.86
x[1] = 0.301
y2[1] (analytic) = 0.70352460476884857642975450243418
y2[1] (numeric) = 0.70352460476884857642975450243406
absolute error = 1.2e-31
relative error = 1.7056972732236910930578500289110e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9550404912999932882641367286816
y1[1] (numeric) = 1.9550404912999932882641367286825
absolute error = 9e-31
relative error = 4.6034852168281691779694066047728e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.302
y2[1] (analytic) = 0.70256971267440725283414093426342
y2[1] (numeric) = 0.70256971267440725283414093426329
absolute error = 1.3e-31
relative error = 1.8503501880993560577270904947907e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9547435384339688435976304082261
y1[1] (numeric) = 1.9547435384339688435976304082271
absolute error = 1.0e-30
relative error = 5.1157606117534172829147181954506e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
memory used=564.5MB, alloc=4.5MB, time=36.10
TOP MAIN SOLVE Loop
x[1] = 0.303
y2[1] (analytic) = 0.7016151180102284689748235944506
y2[1] (numeric) = 0.70161511801022846897482359445048
absolute error = 1.2e-31
relative error = 1.7103394285504917615225243466929e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9544456308244855269211645888734
y1[1] (numeric) = 1.9544456308244855269211645888744
absolute error = 1.0e-30
relative error = 5.1165403847951945866249120314287e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=568.3MB, alloc=4.5MB, time=36.34
x[1] = 0.304
y2[1] (analytic) = 0.70066082173090680948103364573289
y2[1] (numeric) = 0.70066082173090680948103364573277
absolute error = 1.2e-31
relative error = 1.7126689016741791494859958702460e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9541467687694509228924226510006
y1[1] (numeric) = 1.9541467687694509228924226510016
absolute error = 1.0e-30
relative error = 5.1173228949927425183599670247306e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=572.2MB, alloc=4.5MB, time=36.59
x[1] = 0.305
y2[1] (analytic) = 0.69970682479073847414974328925156
y2[1] (numeric) = 0.69970682479073847414974328925144
absolute error = 1.2e-31
relative error = 1.7150039952216906743468985878332e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9538469525677270616408382006383
y1[1] (numeric) = 1.9538469525677270616408382006394
absolute error = 1.1e-30
relative error = 5.6299189583625804138689588181426e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.306
y2[1] (analytic) = 0.69875312814372032364954549226047
y2[1] (numeric) = 0.69875312814372032364954549226035
absolute error = 1.2e-31
relative error = 1.7173447268678025295891328248236e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9535461825191301199055898452054
y1[1] (numeric) = 1.9535461825191301199055898452065
absolute error = 1.1e-30
relative error = 5.6307857466749611349428242894647e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=576.0MB, alloc=4.5MB, time=36.83
x[1] = 0.307
y2[1] (analytic) = 0.69779973274354892552387281926885
y2[1] (numeric) = 0.69779973274354892552387281926873
absolute error = 1.2e-31
relative error = 1.7196911143573289874617729620330e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9532444589244301212194494390108
y1[1] (numeric) = 1.9532444589244301212194494390118
absolute error = 1.0e-30
relative error = 5.1196868647494236233558366378330e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=579.8MB, alloc=4.5MB, time=37.08
x[1] = 0.308
y2[1] (analytic) = 0.69684663954361960049450936332003
y2[1] (numeric) = 0.69684663954361960049450936331992
absolute error = 1.1e-31
relative error = 1.5785395775466672595794914374929e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9529417820853506351387836146492
y1[1] (numeric) = 1.9529417820853506351387836146503
absolute error = 1.1e-30
relative error = 5.6325283738126609069895302046525e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=583.6MB, alloc=4.5MB, time=37.32
x[1] = 0.309
y2[1] (analytic) = 0.6958938494970254690663494738148
y2[1] (numeric) = 0.69589384949702546906634947381468
absolute error = 1.2e-31
relative error = 1.7244009281980718007523370767769e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9526381523045684755200093702652
y1[1] (numeric) = 1.9526381523045684755200093702662
absolute error = 1.0e-30
relative error = 5.1212765602257988685123627472396e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.31
y2[1] (analytic) = 0.69494136355655649843435667604104
y2[1] (numeric) = 0.69494136355655649843435667604092
absolute error = 1.2e-31
relative error = 1.7267643903921114812995092166152e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9523335698857133978428054362022
y1[1] (numeric) = 1.9523335698857133978428054362032
absolute error = 1.0e-30
relative error = 5.1220755275879339656289087204656e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=587.4MB, alloc=4.5MB, time=37.57
x[1] = 0.311
y2[1] (analytic) = 0.69398918267469854969367587537158
y2[1] (numeric) = 0.69398918267469854969367587537146
absolute error = 1.2e-31
relative error = 1.7291335801158872837720651212833e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9520280351333677955803820978034
y1[1] (numeric) = 1.9520280351333677955803820978044
absolute error = 1.0e-30
relative error = 5.1228772435723614773779875479121e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=591.2MB, alloc=4.5MB, time=37.81
x[1] = 0.312
y2[1] (analytic) = 0.69303730780363242535385163593833
y2[1] (numeric) = 0.69303730780363242535385163593821
absolute error = 1.2e-31
relative error = 1.7315085154694328918608309651923e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9517215483530663956171131040662
y1[1] (numeric) = 1.9517215483530663956171131040672
absolute error = 1.0e-30
relative error = 5.1236817098414287561152445723890e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.313
y2[1] (analytic) = 0.69208573989523291715810501948532
y2[1] (numeric) = 0.6920857398952329171581050194852
absolute error = 1.2e-31
relative error = 1.7338892146248447699374203806172e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9514141098512959527138342444951
y1[1] (numeric) = 1.9514141098512959527138342444961
absolute error = 1.0e-30
relative error = 5.1244889280635734687171030518765e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=595.1MB, alloc=4.5MB, time=38.06
x[1] = 0.314
y2[1] (analytic) = 0.69113447990106785420862116504429
y2[1] (numeric) = 0.69113447990106785420862116504417
absolute error = 1.2e-31
relative error = 1.7362756958266262164688231399390e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9511057199354949430211141288279
y1[1] (numeric) = 1.9511057199354949430211141288289
absolute error = 1.0e-30
relative error = 5.1252988999133310406023157435978e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=598.9MB, alloc=4.5MB, time=38.30
x[1] = 0.315
y2[1] (analytic) = 0.69018352877239715139879948406602
y2[1] (numeric) = 0.69018352877239715139879948406589
absolute error = 1.3e-31
relative error = 1.8835569755080361141569501174454e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9507963789140532566408036563392
y1[1] (numeric) = 1.9507963789140532566408036563402
absolute error = 1.0e-30
relative error = 5.1261116270713421292661180597210e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=602.7MB, alloc=4.5MB, time=38.55
x[1] = 0.316
y2[1] (analytic) = 0.68923288746017185815341803867781
y2[1] (numeric) = 0.68923288746017185815341803867768
absolute error = 1.3e-31
relative error = 1.8861549175207081882024134629991e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9504860870963118892361716131461
y1[1] (numeric) = 1.9504860870963118892361716131471
absolute error = 1.0e-30
relative error = 5.1269271112243601273849199863454e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.317
y2[1] (analytic) = 0.6882825569150332074776633628236
y2[1] (numeric) = 0.68828255691503320747766336282347
absolute error = 1.3e-31
relative error = 1.8887591831859859404259487646677e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9501748447925626326909347873552
y1[1] (numeric) = 1.9501748447925626326909347873562
absolute error = 1.0e-30
relative error = 5.1277453540652586955497252956420e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=606.5MB, alloc=4.5MB, time=38.79
x[1] = 0.318
y2[1] (analytic) = 0.68733253808731166531597667717754
y2[1] (numeric) = 0.68733253808731166531597667717741
absolute error = 1.3e-31
relative error = 1.8913697925862799087811531812464e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9498626523140477648174919429938
y1[1] (numeric) = 1.9498626523140477648174919429948
absolute error = 1.0e-30
relative error = 5.1285663572930393246867186166926e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=610.3MB, alloc=4.5MB, time=39.04
x[1] = 0.319
y2[1] (analytic) = 0.6863828319270259802216671389056
y2[1] (numeric) = 0.68638283192702598022166713890547
absolute error = 1.3e-31
relative error = 1.8939867658843364364823510872486e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9495495099729597381146719444671
y1[1] (numeric) = 1.9495495099729597381146719444681
absolute error = 1.0e-30
relative error = 5.1293901226128389282237136670064e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.32
y2[1] (analytic) = 0.68543343938388223333824245658285
y2[1] (numeric) = 0.68543343938388223333824245658272
absolute error = 1.3e-31
relative error = 1.8966101233236230689448580102761e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9492354180824408675753072737661
y1[1] (numeric) = 1.9492354180824408675753072737671
absolute error = 1.0e-30
relative error = 5.1302166517359374640614093872705e-29 %
Correct digits = 30
h = 0.001
memory used=614.1MB, alloc=4.5MB, time=39.29
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.321
y2[1] (analytic) = 0.68448436140727288869340688885654
y2[1] (numeric) = 0.6844843614072728886934068888564
absolute error = 1.4e-31
relative error = 2.0453352610155404264959056933236e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9489203769565830175439451328269
y1[1] (numeric) = 1.9489203769565830175439451328279
absolute error = 1.0e-30
relative error = 5.1310459463797655864086548699288e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=617.9MB, alloc=4.5MB, time=39.53
x[1] = 0.322
y2[1] (analytic) = 0.68353559894627584380667633277783
y2[1] (numeric) = 0.68353559894627584380667633277769
absolute error = 1.4e-31
relative error = 2.0481742313907434575596653774170e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9486043869104272876250092733052
y1[1] (numeric) = 1.9486043869104272876250092733061
absolute error = 9e-31
relative error = 4.6186902074411210947870609479681e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=621.8MB, alloc=4.5MB, time=39.77
x[1] = 0.323
y2[1] (analytic) = 0.68258715294965348061155989410811
y2[1] (numeric) = 0.68258715294965348061155989410797
absolute error = 1.4e-31
relative error = 2.0510201429227041508525712343220e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.948287448259963697641726645576
y1[1] (numeric) = 1.9482874482599636976417266455769
absolute error = 9e-31
relative error = 4.6194415552171195285891454534450e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.324
y2[1] (analytic) = 0.68163902436585171669325701733906
y2[1] (numeric) = 0.68163902436585171669325701733892
absolute error = 1.4e-31
relative error = 2.0538730177639991318646694035178e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9479695613221308716461339080079
y1[1] (numeric) = 1.9479695613221308716461339080088
absolute error = 9e-31
relative error = 4.6201953966321203874845556098588e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=625.6MB, alloc=4.5MB, time=40.02
x[1] = 0.325
y2[1] (analytic) = 0.68069121414299905684281893765035
y2[1] (numeric) = 0.68069121414299905684281893765021
absolute error = 1.4e-31
relative error = 2.0567328781562459512604203953597e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9476507264148157209804797864775
y1[1] (numeric) = 1.9476507264148157209804797864784
absolute error = 9e-31
relative error = 4.6209517332540231729178297576778e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=629.4MB, alloc=4.5MB, time=40.26
x[1] = 0.326
y2[1] (analytic) = 0.67974372322890564492872290056454
y2[1] (numeric) = 0.6797437232289056449287229005644
absolute error = 1.4e-31
relative error = 2.0595997464305323077595890507731e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9473309438568531263903402226954
y1[1] (numeric) = 1.9473309438568531263903402226963
absolute error = 9e-31
relative error = 4.6217105666562978513145725157266e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=633.2MB, alloc=4.5MB, time=40.51
x[1] = 0.327
y2[1] (analytic) = 0.67879655257106231608680727764583
y2[1] (numeric) = 0.67879655257106231608680727764569
absolute error = 1.4e-31
relative error = 2.0624736450078476877911703636575e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9470102139680256191897641982033
y1[1] (numeric) = 1.9470102139680256191897641982042
absolute error = 9e-31
relative error = 4.6224718984179919031306275914817e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.328
y2[1] (analytic) = 0.67784970311663964922951538822866
y2[1] (numeric) = 0.67784970311663964922951538822852
absolute error = 1.4e-31
relative error = 2.0653545963995174374833250613670e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9466885370690630614787690688678
y1[1] (numeric) = 1.9466885370690630614787690688687
absolute error = 9e-31
relative error = 4.6232357301237373991582827719637e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=637.0MB, alloc=4.5MB, time=40.76
x[1] = 0.329
y2[1] (analytic) = 0.67690317581248701987539551785335
y2[1] (numeric) = 0.67690317581248701987539551785321
absolute error = 1.4e-31
relative error = 2.0682426232076392826651383619391e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9463659134816423254135051923513
y1[1] (numeric) = 1.9463659134816423254135051923522
absolute error = 9e-31
relative error = 4.6240020633637581041446410510263e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=640.8MB, alloc=4.5MB, time=41.00
x[1] = 0.33
y2[1] (analytic) = 0.67595697160513165329980430382978
y2[1] (numeric) = 0.67595697160513165329980430382964
absolute error = 1.4e-31
relative error = 2.0711377481255223126697646272715e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9460423435283869715294105783662
y1[1] (numeric) = 1.9460423435283869715294105783671
absolute error = 9e-31
relative error = 4.6247708997338766077775264504044e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.331
y2[1] (analytic) = 0.67501109144077767800776033714693
y2[1] (numeric) = 0.67501109144077767800776033714679
absolute error = 1.4e-31
relative error = 2.0740399939381284438431877843736e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9457178275328669261176772385331
y1[1] (numeric) = 1.945717827532866926117677238534
absolute error = 9e-31
relative error = 4.6255422408355214830945283609599e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=644.6MB, alloc=4.5MB, time=41.25
x[1] = 0.332
y2[1] (analytic) = 0.67406553626530517952989450779567
y2[1] (numeric) = 0.67406553626530517952989450779553
absolute error = 1.4e-31
relative error = 2.0769493835225163787784205455945e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9453923658195981576553518593481
y1[1] (numeric) = 1.945392365819598157655351859349
absolute error = 9e-31
relative error = 4.6263160882757344723710241703554e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=648.5MB, alloc=4.5MB, time=41.50
x[1] = 0.333
y2[1] (analytic) = 0.67312030702426925454244329747574
y2[1] (numeric) = 0.6731203070242692545424432974756
absolute error = 1.4e-31
relative error = 2.0798659398482880774114928558608e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9450659587140423522893943681328
y1[1] (numeric) = 1.9450659587140423522893943681338
absolute error = 1.0e-30
relative error = 5.1412138262968641117147295077744e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=652.3MB, alloc=4.5MB, time=41.74
x[1] = 0.334
y2[1] (analytic) = 0.67217540466289906531223089961467
y2[1] (numeric) = 0.67217540466289906531223089961452
absolute error = 1.5e-31
relative error = 2.2315603778336118816782677959266e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9447386065426065883750189078808
y1[1] (numeric) = 1.9447386065426065883750189078818
absolute error = 1.0e-30
relative error = 5.1420792318090454624697545785867e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.335
y2[1] (analytic) = 0.67123083012609689446758572163781
y2[1] (numeric) = 0.67123083012609689446758572163766
absolute error = 1.5e-31
relative error = 2.2347006911440751057012156121542e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9444103096326430100686426826321
y1[1] (numeric) = 1.9444103096326430100686426826331
absolute error = 1.0e-30
relative error = 5.1429474275361652892875799906416e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=656.1MB, alloc=4.5MB, time=41.99
x[1] = 0.336
y2[1] (analytic) = 0.67028658435843720009613649849422
y2[1] (numeric) = 0.67028658435843720009613649849407
absolute error = 1.5e-31
relative error = 2.2378487575366296710929732998316e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9440810683124484999757690804005
y1[1] (numeric) = 1.9440810683124484999757690804015
absolute error = 1.0e-30
relative error = 5.1438184152888534028948530134037e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=659.9MB, alloc=4.5MB, time=42.23
x[1] = 0.337
y2[1] (analytic) = 0.66934266830416567117043291956346
y2[1] (numeric) = 0.66934266830416567117043291956331
absolute error = 1.5e-31
relative error = 2.2410046020230154087975168552408e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.943750882911264350854132425743
y1[1] (numeric) = 1.943750882911264350854132425744
absolute error = 1.0e-30
relative error = 5.1446921968840168504999633659405e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=663.7MB, alloc=4.5MB, time=42.48
x[1] = 0.338
y2[1] (analytic) = 0.66839908290719828330233534324402
y2[1] (numeric) = 0.66839908290719828330233534324387
absolute error = 1.5e-31
relative error = 2.2441682497165584324000187292031e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9434197537592759363724326587988
y1[1] (numeric) = 1.9434197537592759363724326587998
absolute error = 1.0e-30
relative error = 5.1455687741448480846239602934521e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.339
y2[1] (analytic) = 0.66745582911112035482711784475499
y2[1] (numeric) = 0.66745582911112035482711784475484
absolute error = 1.5e-31
relative error = 2.2473397258326660178862508920657e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9430876811876123809249891820363
y1[1] (numeric) = 1.9430876811876123809249891820373
absolute error = 1.0e-30
relative error = 5.1464481489008331629053807184733e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=667.5MB, alloc=4.5MB, time=42.73
x[1] = 0.34
y2[1] (analytic) = 0.66651290785918560321822851296921
y2[1] (numeric) = 0.66651290785918560321822851296906
absolute error = 1.5e-31
relative error = 2.2505190556893242992869002225079e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9427546655283462285026440600266
y1[1] (numeric) = 1.9427546655283462285026440600275
absolute error = 9e-31
relative error = 4.6325972906889839810488414304234e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=671.3MB, alloc=4.5MB, time=42.97
x[1] = 0.341
y2[1] (analytic) = 0.66557032009431520183365058143904
y2[1] (numeric) = 0.66557032009431520183365058143888
absolute error = 1.6e-31
relative error = 2.4039533490214387184337828447604e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9424207071144931106202457013121
y1[1] (numeric) = 1.942420707114493110620245701313
absolute error = 9e-31
relative error = 4.6333937684229538718178387131858e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.342
y2[1] (analytic) = 0.66462806675909683699480764717492
y2[1] (numeric) = 0.66462806675909683699480764717476
absolute error = 1.6e-31
relative error = 2.4073614703062803285038117116300e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9420858062800114133010450948604
y1[1] (numeric) = 1.9420858062800114133010450948612
absolute error = 8e-31
relative error = 4.1192824612233193450602104149994e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=675.2MB, alloc=4.5MB, time=43.22
x[1] = 0.343
y2[1] (analytic) = 0.66368614879578376539895589819304
y2[1] (numeric) = 0.66368614879578376539895589819289
absolute error = 1.5e-31
relative error = 2.2601044224316786441691507525808e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9417499633598019431183376166772
y1[1] (numeric) = 1.9417499633598019431183376166781
absolute error = 9e-31
relative error = 4.6349942937180939432714298071154e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=679.0MB, alloc=4.5MB, time=43.46
x[1] = 0.344
y2[1] (analytic) = 0.66274456714629387186600593736127
y2[1] (numeric) = 0.66274456714629387186600593736112
absolute error = 1.5e-31
relative error = 2.2633154224995567916718881939262e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9414131786897075922946843649114
y1[1] (numeric) = 1.9414131786897075922946843649122
absolute error = 8e-31
relative error = 4.1207096396653362347172264617922e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=682.8MB, alloc=4.5MB, time=43.71
x[1] = 0.345
y2[1] (analytic) = 0.66180332275220872742071645564298
y2[1] (numeric) = 0.66180332275220872742071645564282
absolute error = 1.6e-31
relative error = 2.4176366980844991527078433300136e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9410754526065130028590479241997
y1[1] (numeric) = 1.9410754526065130028590479242005
absolute error = 8e-31
relative error = 4.1214265984650148353438824984369e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.346
y2[1] (analytic) = 0.66086241655477264771120167246664
y2[1] (numeric) = 0.66086241655477264771120167246649
absolute error = 1.5e-31
relative error = 2.2697613942397330424748419159145e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9407367854479442298621784020909
y1[1] (numeric) = 1.9407367854479442298621784020917
absolute error = 8e-31
relative error = 4.1221458056474714430219008162702e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=686.6MB, alloc=4.5MB, time=43.95
x[1] = 0.347
y2[1] (analytic) = 0.65992184949489175176469412463536
y2[1] (numeric) = 0.65992184949489175176469412463521
absolute error = 1.5e-31
relative error = 2.2729964179063160871151403135282e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9403971775526684036505865221322
y1[1] (numeric) = 1.940397177552668403650586522133
absolute error = 8e-31
relative error = 4.1228672627168131215287969763994e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=690.4MB, alloc=4.5MB, time=44.20
x[1] = 0.348
y2[1] (analytic) = 0.65898162251313302108150404793491
y2[1] (numeric) = 0.65898162251313302108150404793476
absolute error = 1.5e-31
relative error = 2.2762395016108451471099901627448e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9400566292602933911994414996184
y1[1] (numeric) = 1.9400566292602933911994414996193
absolute error = 9e-31
relative error = 4.6390398425800222285498671195137e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.349
y2[1] (analytic) = 0.65804173654972335906811625740272
y2[1] (numeric) = 0.65804173654972335906811625740257
absolute error = 1.5e-31
relative error = 2.2794906716173861820734940919544e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9397151409113674565047323670778
y1[1] (numeric) = 1.9397151409113674565047323670787
absolute error = 9e-31
relative error = 4.6398565491278197366003722221219e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
memory used=694.2MB, alloc=4.5MB, time=44.44
TOP MAIN SOLVE Loop
x[1] = 0.35
y2[1] (analytic) = 0.65710219254454865081036509308237
y2[1] (numeric) = 0.65710219254454865081036509308222
absolute error = 1.5e-31
relative error = 2.2827499542977199385902429468145e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9393727128473789200350323573037
y1[1] (numeric) = 1.9393727128473789200350323573045
absolute error = 8e-31
relative error = 4.1250451483636858024863402852388e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=698.0MB, alloc=4.5MB, time=44.68
x[1] = 0.351
y2[1] (analytic) = 0.65616299143715282318762765801042
y2[1] (numeric) = 0.65616299143715282318762765801027
absolute error = 1.5e-31
relative error = 2.2860173761318718601244295254951e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9390293454107558172432068921403
y1[1] (numeric) = 1.9390293454107558172432068921411
absolute error = 8e-31
relative error = 4.1257756201236416375091089051730e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=701.9MB, alloc=4.5MB, time=44.93
x[1] = 0.352
y2[1] (analytic) = 0.65522413416673690532897523416392
y2[1] (numeric) = 0.65522413416673690532897523416377
absolute error = 1.5e-31
relative error = 2.2892929637086450418198767311851e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9386850389448655561384066652863
y1[1] (numeric) = 1.9386850389448655561384066652871
absolute error = 8e-31
relative error = 4.1265083493675801471600478076042e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.353
y2[1] (analytic) = 0.65428562167215808941222242013895
y2[1] (numeric) = 0.6542856216721580894122224201388
absolute error = 1.5e-31
relative error = 2.2925767437261562502015194704945e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9383397937940145739186882470937
y1[1] (numeric) = 1.9383397937940145739186882470945
absolute error = 8e-31
relative error = 4.1272433376302813383002901515126e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=705.7MB, alloc=4.5MB, time=45.18
x[1] = 0.354
y2[1] (analytic) = 0.65334745489192879180681319143277
y2[1] (numeric) = 0.65334745489192879180681319143262
absolute error = 1.5e-31
relative error = 2.2958687429923750279369482803084e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9379936103034479926646055787134
y1[1] (numeric) = 1.9379936103034479926646055787142
absolute error = 8e-31
relative error = 4.1279805864516615084622399676628e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=709.5MB, alloc=4.5MB, time=45.42
x[1] = 0.355
y2[1] (analytic) = 0.65240963476421571456148274036527
y2[1] (numeric) = 0.65240963476421571456148274036512
absolute error = 1.5e-31
relative error = 2.2991689884256659039659096926995e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.937646488819349274094116661967
y1[1] (numeric) = 1.9376464888193492740941166619678
absolute error = 8e-31
relative error = 4.1287200973767802092889012463146e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=713.3MB, alloc=4.5MB, time=45.67
x[1] = 0.356
y2[1] (analytic) = 0.65147216222683890723763360789966
y2[1] (numeric) = 0.65147216222683890723763360789951
absolute error = 1.5e-31
relative error = 2.3024775070553337294561747846112e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9372984296888398733791506900099
y1[1] (numeric) = 1.9372984296888398733791506900107
absolute error = 8e-31
relative error = 4.1294618719558472356547312362800e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.357
y2[1] (analytic) = 0.65053503821727082908936427390812
y2[1] (numeric) = 0.65053503821727082908936427390797
absolute error = 1.5e-31
relative error = 2.3057943260221721601959443522657e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9369494332599788920241818021889
y1[1] (numeric) = 1.9369494332599788920241818021897
absolute error = 8e-31
relative error = 4.1302059117442296405230985543782e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=717.1MB, alloc=4.5MB, time=45.91
x[1] = 0.358
y2[1] (analytic) = 0.64959826367263541159108802577568
y2[1] (numeric) = 0.64959826367263541159108802577553
absolute error = 1.5e-31
relative error = 2.3091194725790153061859679560464e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9365994998817627298071565844923
y1[1] (numeric) = 1.9365994998817627298071565844931
absolute error = 8e-31
relative error = 4.1309522183024587755956529447573e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=720.9MB, alloc=4.5MB, time=46.16
x[1] = 0.359
y2[1] (analytic) = 0.64866183952970712131367957764527
y2[1] (numeric) = 0.64866183952970712131367957764512
absolute error = 1.5e-31
relative error = 2.3124529740912925693488260678829e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9362486299041247357831233746356
y1[1] (numeric) = 1.9362486299041247357831233746364
absolute error = 8e-31
relative error = 4.1317007931962373578091404436683e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.36
y2[1] (analytic) = 0.64772576672491002315008656407927
y2[1] (numeric) = 0.64772576672491002315008656407912
absolute error = 1.5e-31
relative error = 2.3157948580375866904283712005704e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9358968236779348583509123681247
y1[1] (numeric) = 1.9358968236779348583509123681255
absolute error = 8e-31
relative error = 4.1324516379964465617354253002022e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=724.8MB, alloc=4.5MB, time=46.41
x[1] = 0.361
y2[1] (analytic) = 0.64679004619431684389134268244803
y2[1] (numeric) = 0.64679004619431684389134268244788
absolute error = 1.5e-31
relative error = 2.3191451520101950263091568015476e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.935544081554999294383216458587
y1[1] (numeric) = 1.9355440815549992943832164585877
absolute error = 7e-31
relative error = 3.6165541599942589956981197453045e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=728.6MB, alloc=4.5MB, time=46.66
x[1] = 0.362
y2[1] (analytic) = 0.64585467887364803615391890795416
y2[1] (numeric) = 0.645854678873648036153918907954
absolute error = 1.6e-31
relative error = 2.4773374759634070177534011329665e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9351904038880601374204236822605
y1[1] (numeric) = 1.9351904038880601374204236822612
absolute error = 7e-31
relative error = 3.6172151256724144876901399506773e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=732.4MB, alloc=4.5MB, time=46.90
x[1] = 0.363
y2[1] (analytic) = 0.64491966569827084265934885386328
y2[1] (numeric) = 0.64491966569827084265934885386312
absolute error = 1.6e-31
relative error = 2.4809291530405411187581583503053e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9348357910307950249285530727796
y1[1] (numeric) = 1.9348357910307950249285530727803
absolute error = 7e-31
relative error = 3.6178780816695091590263649902181e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.364
y2[1] (analytic) = 0.64398500760319836086706399723811
y2[1] (numeric) = 0.64398500760319836086706399723795
absolute error = 1.6e-31
relative error = 2.4845298898415745926245378075512e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9344802433378167846216466682912
y1[1] (numeric) = 1.9344802433378167846216466682919
absolute error = 7e-31
relative error = 3.6185430293782511527052935933073e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=736.2MB, alloc=4.5MB, time=47.15
x[1] = 0.365
y2[1] (analytic) = 0.64305070552308860796137413726246
y2[1] (numeric) = 0.6430507055230886079613741372623
absolute error = 1.6e-31
relative error = 2.4881397162895303246618805909746e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9341237611646730798489713484808
y1[1] (numeric) = 1.9341237611646730798489713484815
absolute error = 7e-31
relative error = 3.6192099701959111331075444616641e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=740.0MB, alloc=4.5MB, time=47.39
x[1] = 0.366
y2[1] (analytic) = 0.64211676039224358619352809909695
y2[1] (numeric) = 0.64211676039224358619352809909679
absolute error = 1.6e-31
relative error = 2.4917586624317727609523424595834e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9337663448678460540473851142766
y1[1] (numeric) = 1.9337663448678460540473851142773
absolute error = 7e-31
relative error = 3.6198789055243286288735534135592e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.367
y2[1] (analytic) = 0.64118317314460834857978934112779
y2[1] (numeric) = 0.64118317314460834857978934112763
absolute error = 1.6e-31
relative error = 2.4953867584406277639385697329250e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9334079948047519742592233578357
y1[1] (numeric) = 1.9334079948047519742592233578364
absolute error = 7e-31
relative error = 3.6205498367699183987937412546215e-29 %
Correct digits = 30
h = 0.001
memory used=743.8MB, alloc=4.5MB, time=47.64
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.368
y2[1] (analytic) = 0.64024994471377006495646076745515
y2[1] (numeric) = 0.64024994471377006495646076745498
absolute error = 1.7e-31
relative error = 2.6552130367773814569301500553064e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9330487113337408737160616048967
y1[1] (numeric) = 1.9330487113337408737160616048974
absolute error = 7e-31
relative error = 3.6212227653436768207615584332622e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=747.6MB, alloc=4.5MB, time=47.88
x[1] = 0.369
y2[1] (analytic) = 0.63931707603295708839279269051843
y2[1] (numeric) = 0.63931707603295708839279269051826
absolute error = 1.7e-31
relative error = 2.6590874289620323242539738551970e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9326884948140961934887121457059
y1[1] (numeric) = 1.9326884948140961934887121457066
absolute error = 7e-31
relative error = 3.6218976926611883038400171538870e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=751.5MB, alloc=4.5MB, time=48.13
x[1] = 0.37
y2[1] (analytic) = 0.63838456803503802196270753087285
y2[1] (numeric) = 0.63838456803503802196270753087268
absolute error = 1.7e-31
relative error = 2.6629716398575203985767477246961e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9323273456060344232038129044909
y1[1] (numeric) = 1.9323273456060344232038129044916
absolute error = 7e-31
relative error = 3.6225746201426317234925268579095e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.371
y2[1] (analytic) = 0.63745242165252078587627448231464
y2[1] (numeric) = 0.63745242165252078587627448231447
absolute error = 1.7e-31
relative error = 2.6668657020596909714545236121616e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9319652640707047408273678308622
y1[1] (numeric) = 1.9319652640707047408273678308629
absolute error = 7e-31
relative error = 3.6232535492127868800290548439675e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=755.3MB, alloc=4.5MB, time=48.38
x[1] = 0.372
y2[1] (analytic) = 0.63652063781755168497186701080265
y2[1] (numeric) = 0.63652063781755168497186701080247
absolute error = 1.8e-31
relative error = 2.8278737452593654943437466578091e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9316022505701886515155990295735
y1[1] (numeric) = 1.9316022505701886515155990295742
absolute error = 7e-31
relative error = 3.6239344813010409803188402875072e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=759.1MB, alloc=4.5MB, time=48.62
x[1] = 0.373
y2[1] (analytic) = 0.63558921746191447656993569494098
y2[1] (numeric) = 0.6355892174619144765699356949408
absolute error = 1.8e-31
relative error = 2.8320178356516233405644108541358e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9312383054674996255334717777569
y1[1] (numeric) = 1.9312383054674996255334717777576
absolute error = 7e-31
relative error = 3.6246174178413951428210970389125e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=762.9MB, alloc=4.5MB, time=48.87
x[1] = 0.374
y2[1] (analytic) = 0.6346581615170294386893285541723
y2[1] (numeric) = 0.63465816151702943868932855417212
absolute error = 1.8e-31
relative error = 2.8361724612466069656914651398097e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9308734291265827352412545110794
y1[1] (numeric) = 1.9308734291265827352412545110801
absolute error = 7e-31
relative error = 3.6253023602724709259853483314666e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.375
y2[1] (analytic) = 0.63372747091395243862709064828374
y2[1] (numeric) = 0.63372747091395243862709064828356
absolute error = 1.8e-31
relative error = 2.8403376571384328214997087573487e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9305076219123142911494767922296
y1[1] (numeric) = 1.9305076219123142911494767922302
absolute error = 6e-31
relative error = 3.1079908371750144686342099301732e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=766.7MB, alloc=4.5MB, time=49.11
x[1] = 0.376
y2[1] (analytic) = 0.63279714658337400190267436834815
y2[1] (numeric) = 0.63279714658337400190267436834797
absolute error = 1.8e-31
relative error = 2.8445134585682609892950061844809e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9301408841905014770426492067458
y1[1] (numeric) = 1.9301408841905014770426492067464
absolute error = 6e-31
relative error = 3.1085813730723558192462233025772e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=770.5MB, alloc=4.5MB, time=49.36
x[1] = 0.377
y2[1] (analytic) = 0.63186718945561838156749147481296
y2[1] (numeric) = 0.63186718945561838156749147481278
absolute error = 1.8e-31
relative error = 2.8486999009250343612462246934049e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.929773216327881984172110062437
y1[1] (numeric) = 1.9297732163278819841721100624376
absolute error = 6e-31
relative error = 3.1091736320277325169358869635125e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.378
y2[1] (analytic) = 0.6309376004606426278807375731069
y2[1] (numeric) = 0.63093760046064262788073757310672
absolute error = 1.8e-31
relative error = 2.8528970197462221616701489222190e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9294046186921236445183646995176
y1[1] (numeric) = 1.9294046186921236445183646995182
absolute error = 6e-31
relative error = 3.1097676152901466230968665829421e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=774.3MB, alloc=4.5MB, time=49.60
x[1] = 0.379
y2[1] (analytic) = 0.63000838052803565835241935086267
y2[1] (numeric) = 0.63000838052803565835241935086249
absolute error = 1.8e-31
relative error = 2.8571048507185678374134169807661e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.929035091651824063123284149087
y1[1] (numeric) = 1.9290350916518240631232841490876
absolute error = 6e-31
relative error = 3.1103633241125888571444799942848e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=778.2MB, alloc=4.5MB, time=49.85
x[1] = 0.38
y2[1] (analytic) = 0.6290795305870173281545145336508
y2[1] (numeric) = 0.62907953058701732815451453365062
absolute error = 1.8e-31
relative error = 2.8613234296788413466958853345073e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9286646355765102494925308077246
y1[1] (numeric) = 1.9286646355765102494925308077251
absolute error = 5e-31
relative error = 2.5924672997933702611780904299166e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=782.0MB, alloc=4.5MB, time=50.09
x[1] = 0.381
y2[1] (analytic) = 0.62815105156643750090119414798726
y2[1] (numeric) = 0.62815105156643750090119414798709
absolute error = 1.7e-31
relative error = 2.7063554152471183273352650171172e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9282932508366382480685797257438
y1[1] (numeric) = 1.9282932508366382480685797257443
absolute error = 5e-31
relative error = 2.5929666028912484986693435674535e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.382
y2[1] (analytic) = 0.6272229443947751197990363113152
y2[1] (numeric) = 0.62722294439477511979903631131502
absolute error = 1.8e-31
relative error = 2.8697929756649290148311997185643e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9279209378035927677747050360532
y1[1] (numeric) = 1.9279209378035927677747050360537
absolute error = 5e-31
relative error = 2.5934673471082846570092162805357e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=785.8MB, alloc=4.5MB, time=50.34
x[1] = 0.383
y2[1] (analytic) = 0.62629521000013727916816039866944
y2[1] (numeric) = 0.62629521000013727916816039866926
absolute error = 1.8e-31
relative error = 2.8740440151212484183430810252598e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.927547696849686810630301979607
y1[1] (numeric) = 1.9275476968496868106303019796075
absolute error = 5e-31
relative error = 2.5939695335019810063400524528633e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=789.6MB, alloc=4.5MB, time=50.59
x[1] = 0.384
y2[1] (analytic) = 0.62536784931025829633521006481245
y2[1] (numeric) = 0.62536784931025829633521006481227
absolute error = 1.8e-31
relative error = 2.8783059474280419881634704680006e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9271735283481612994379159120923
y1[1] (numeric) = 1.9271735283481612994379159120928
absolute error = 5e-31
relative error = 2.5944731631331876888289996180427e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.385
memory used=793.4MB, alloc=4.5MB, time=50.84
y2[1] (analytic) = 0.6244408632524987838991132287812
y2[1] (numeric) = 0.62444086325249878389911322878102
absolute error = 1.8e-31
relative error = 2.8825788091836526018441777635526e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9267984326731847045423506047928
y1[1] (numeric) = 1.9267984326731847045423506047933
absolute error = 5e-31
relative error = 2.5949782370661075679071460507444e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.386
y2[1] (analytic) = 0.62351425275384472237054675500772
y2[1] (numeric) = 0.62351425275384472237054675500754
absolute error = 1.8e-31
relative error = 2.8868626371410574217034819451156e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9264224101998526696622290804899
y1[1] (numeric) = 1.9264224101998526696622290804904
absolute error = 5e-31
relative error = 2.5954847563683010946556496898321e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=797.2MB, alloc=4.5MB, time=51.08
x[1] = 0.387
y2[1] (analytic) = 0.62258801874090653318603319147135
y2[1] (numeric) = 0.62258801874090653318603319147118
absolute error = 1.7e-31
relative error = 2.7305376088637267132286756370451e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9260454613041876367943811528091
y1[1] (numeric) = 1.9260454613041876367943811528096
absolute error = 5e-31
relative error = 2.5959927221106911913777180698096e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=801.0MB, alloc=4.5MB, time=51.32
x[1] = 0.388
y2[1] (analytic) = 0.62166216213991815209759655070879
y2[1] (numeric) = 0.62166216213991815209759655070861
absolute error = 1.8e-31
relative error = 2.8954633394510379096832900802494e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9256675863631384701914327645926
y1[1] (numeric) = 1.9256675863631384701914327645931
absolute error = 5e-31
relative error = 2.5965021353675681523954533819911e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.389
y2[1] (analytic) = 0.62073668387673610293890374394874
y2[1] (numeric) = 0.62073668387673610293890374394856
absolute error = 1.8e-31
relative error = 2.8997802880898178380108422135832e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9252887857545800794129731476774
y1[1] (numeric) = 1.9252887857545800794129731476779
absolute error = 5e-31
relative error = 2.5970129972165945621107322157865e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=804.9MB, alloc=4.5MB, time=51.57
x[1] = 0.39
y2[1] (analytic) = 0.61981158487683857176881790215284
y2[1] (numeric) = 0.61981158487683857176881790215266
absolute error = 1.8e-31
relative error = 2.9041083515043916649434435576127e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9249090598573130414506767528811
y1[1] (numeric) = 1.9249090598573130414506767528816
absolute error = 5e-31
relative error = 2.5975253087388102303694454455841e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=808.7MB, alloc=4.5MB, time=51.82
x[1] = 0.391
y2[1] (analytic) = 0.61888686606532448139328944033205
y2[1] (numeric) = 0.61888686606532448139328944033187
absolute error = 1.8e-31
relative error = 2.9084475672327600679943103307167e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9245284090510632219277578250411
y1[1] (numeric) = 1.9245284090510632219277578250416
absolute error = 5e-31
relative error = 2.5980390710186371451685801321093e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=812.5MB, alloc=4.5MB, time=52.06
x[1] = 0.392
y2[1] (analytic) = 0.61796252836691256626651034317064
y2[1] (numeric) = 0.61796252836691256626651034317045
absolute error = 1.9e-31
relative error = 3.0746200825819057676023407624978e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9241468337164813953731364236214
y1[1] (numeric) = 1.9241468337164813953731364236219
absolute error = 5e-31
relative error = 2.5985542851438844427457822010188e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.393
y2[1] (analytic) = 0.6170385727059404477722567707261
y2[1] (numeric) = 0.61703857270594044777225677072591
absolute error = 1.9e-31
relative error = 3.0792240291685544903952260533862e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9237643342351428645706956146894
y1[1] (numeric) = 1.9237643342351428645706956146898
absolute error = 4e-31
relative error = 2.0792567617646027160729568384690e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=816.3MB, alloc=4.5MB, time=52.30
x[1] = 0.394
y2[1] (analytic) = 0.61611500000636370988634470278558
y2[1] (numeric) = 0.6161150000063637098863447027854
absolute error = 1.8e-31
relative error = 2.9215325060766386384162091155548e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9233809109895470789840104849733
y1[1] (numeric) = 1.9233809109895470789840104849738
absolute error = 5e-31
relative error = 2.5995890732988424149215351018451e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=820.1MB, alloc=4.5MB, time=52.55
x[1] = 0.395
y2[1] (analytic) = 0.61519181119175497522112295934603
y2[1] (numeric) = 0.61519181119175497522112295934584
absolute error = 1.9e-31
relative error = 3.0884676379539307044074158891491e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9229965643631172522569305532408
y1[1] (numeric) = 1.9229965643631172522569305532413
absolute error = 5e-31
relative error = 2.6001086495211520781564957532072e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.396
y2[1] (analytic) = 0.61426900718530298145292755264793
y2[1] (numeric) = 0.61426900718530298145292755264775
absolute error = 1.8e-31
relative error = 2.9303122556157296121670552620689e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9226112947401999787903980783825
y1[1] (numeric) = 1.922611294740199978790398078383
absolute error = 5e-31
relative error = 2.6006296819740901639377859396193e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=823.9MB, alloc=4.5MB, time=52.80
x[1] = 0.397
y2[1] (analytic) = 0.61334658890981165813342094323165
y2[1] (numeric) = 0.61334658890981165813342094323147
absolute error = 1.8e-31
relative error = 2.9347191825088595331122261122609e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9222251025060648493958856873514
y1[1] (numeric) = 1.9222251025060648493958856873519
absolute error = 5e-31
relative error = 2.6011521717624767122311990509709e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=827.8MB, alloc=4.5MB, time=53.05
x[1] = 0.398
y2[1] (analytic) = 0.61242455728769920388573938859978
y2[1] (numeric) = 0.6124245572876992038857393885996
absolute error = 1.8e-31
relative error = 2.9391375289910402348522716935286e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9218379880469040660258376694886
y1[1] (numeric) = 1.9218379880469040660258376694891
absolute error = 5e-31
relative error = 2.6016761199945490990523237080029e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=831.6MB, alloc=4.5MB, time=53.29
x[1] = 0.399
y2[1] (analytic) = 0.6115029132409971639863711882616
y2[1] (numeric) = 0.61150291324099716398637118826142
absolute error = 1.8e-31
relative error = 2.9435673338985526967187563690628e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9214499517498320555815002067615
y1[1] (numeric) = 1.921449951749832055581500206762
absolute error = 5e-31
relative error = 2.6022015277819671293566403536325e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.4
y2[1] (analytic) = 0.61058165769134950833368824320429
y2[1] (numeric) = 0.61058165769134950833368824320411
absolute error = 1.8e-31
relative error = 2.9480086362337211168077230824998e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9210609940028850827985267320518
y1[1] (numeric) = 1.9210609940028850827985267320523
absolute error = 5e-31
relative error = 2.6027283962398181476349164956869e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=835.4MB, alloc=4.5MB, time=53.53
x[1] = 0.401
y2[1] (analytic) = 0.60966079156001170980405296118265
y2[1] (numeric) = 0.60966079156001170980405296118246
absolute error = 1.9e-31
relative error = 3.1164871126749739158616674176345e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9206711151950208622107455298569
y1[1] (numeric) = 1.9206711151950208622107455298574
absolute error = 5e-31
relative error = 2.6032567264866221662549738482904e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=839.2MB, alloc=4.5MB, time=53.78
x[1] = 0.402
y2[1] (analytic) = 0.60874031576784982299642215164349
y2[1] (numeric) = 0.6087403157678498229964221516433
absolute error = 1.9e-31
relative error = 3.1211995505889690869968875307353e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9202803157161181691924776156028
y1[1] (numeric) = 1.9202803157161181691924776156034
absolute error = 6e-31
relative error = 3.1245438235732044139092750490653e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=843.0MB, alloc=4.5MB, time=54.03
x[1] = 0.403
y2[1] (analytic) = 0.60782023123533956336636916560423
y2[1] (numeric) = 0.60782023123533956336636916560404
absolute error = 1.9e-31
relative error = 3.1259242492445868457222076121952e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9198885959569764500797938512206
y1[1] (numeric) = 1.9198885959569764500797938512212
absolute error = 6e-31
relative error = 3.1251813322060361855786880010576e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.404
y2[1] (analytic) = 0.60690053888256538675044514638653
y2[1] (numeric) = 0.60690053888256538675044514638634
absolute error = 1.9e-31
relative error = 3.1306612505210643636787229018820e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9194959563093154313711011756945
y1[1] (numeric) = 1.9194959563093154313711011756951
absolute error = 6e-31
relative error = 3.1258205990370606714735780845361e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=846.8MB, alloc=4.5MB, time=54.27
x[1] = 0.405
y2[1] (analytic) = 0.60598123962921956928179986676729
y2[1] (numeric) = 0.6059812396292195692817998667671
absolute error = 1.9e-31
relative error = 3.1354105964774567797516639594851e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9191023971657747280074487499645
y1[1] (numeric) = 1.9191023971657747280074487499651
absolute error = 6e-31
relative error = 3.1264616254250406599952976710700e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=850.6MB, alloc=4.5MB, time=54.52
x[1] = 0.406
y2[1] (analytic) = 0.60506233439460128769798223684934
y2[1] (numeric) = 0.60506233439460128769798223684914
absolute error = 2.0e-31
relative error = 3.3054445572142775645144676158960e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9187079189199134507329457358444
y1[1] (numeric) = 1.918707918919913450732945735845
absolute error = 6e-31
relative error = 3.1271044127328892322216737175451e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.407
y2[1] (analytic) = 0.60414382409761570004184017477465
y2[1] (numeric) = 0.60414382409761570004184017477446
absolute error = 1.9e-31
relative error = 3.1449464915708611905485293422738e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9183125219662098125356833485036
y1[1] (numeric) = 1.9183125219662098125356833485042
absolute error = 6e-31
relative error = 3.1277489623276760447369764152206e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=854.5MB, alloc=4.5MB, time=54.76
x[1] = 0.408
y2[1] (analytic) = 0.60322570965677302675643913930379
y2[1] (numeric) = 0.60322570965677302675643913930359
absolute error = 2.0e-31
relative error = 3.3155085534036206207919448092281e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9179162067000607341695547415594
y1[1] (numeric) = 1.91791620670006073416955474156
absolute error = 6e-31
relative error = 3.1283952755806336341080247848297e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=858.3MB, alloc=4.5MB, time=55.01
x[1] = 0.409
y2[1] (analytic) = 0.60230799199018763217491822926617
y2[1] (numeric) = 0.60230799199018763217491822926597
absolute error = 2.0e-31
relative error = 3.3205602890831017878006892715868e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9175189735177814487573672029263
y1[1] (numeric) = 1.917518973517781448757367202927
absolute error = 7e-31
relative error = 3.6505505795116910335668372039443e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=862.1MB, alloc=4.5MB, time=55.26
x[1] = 0.41
y2[1] (analytic) = 0.60139067201557710640620235994886
y2[1] (numeric) = 0.60139067201557710640620235994866
absolute error = 2.0e-31
relative error = 3.3256252433995124914681303394039e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.917120822816605105475642058277
y1[1] (numeric) = 1.9171208228166051054756420582777
absolute error = 7e-31
relative error = 3.6513087316613176131147236089912e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.411
y2[1] (analytic) = 0.6004737506502613476174886306349
y2[1] (numeric) = 0.60047375065026134761748863063471
absolute error = 1.9e-31
relative error = 3.1641682886928257305270718787422e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9167217549946823723214985972821
y1[1] (numeric) = 1.9167217549946823723214985972828
absolute error = 7e-31
relative error = 3.6520689462406714024656775733182e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=865.9MB, alloc=4.5MB, time=55.50
x[1] = 0.412
y2[1] (analytic) = 0.59955722881116164471442460072855
y2[1] (numeric) = 0.59955722881116164471442460072836
absolute error = 1.9e-31
relative error = 3.1690052403628507287691968960335e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9163217704510810379620192557123
y1[1] (numeric) = 1.916321770451081037962019255713
absolute error = 7e-31
relative error = 3.6528312248690245269123077650111e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=869.7MB, alloc=4.5MB, time=55.75
x[1] = 0.413
y2[1] (analytic) = 0.59864110741479976041989579421255
y2[1] (numeric) = 0.59864110741479976041989579421235
absolute error = 2.0e-31
relative error = 3.3408998734431972993610369974950e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.915920869585785612666494204004
y1[1] (numeric) = 1.9159208695857856126664942040047
absolute error = 7e-31
relative error = 3.6535955691705429620631398258279e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.414
y2[1] (analytic) = 0.59772538737729701475233935357361
y2[1] (numeric) = 0.59772538737729701475233935357341
absolute error = 2.0e-31
relative error = 3.3460181585654439292974824631816e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9155190527996969283219444100102
y1[1] (numeric) = 1.9155190527996969283219444100109
absolute error = 7e-31
relative error = 3.6543619807742940418419292138193e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
memory used=873.5MB, alloc=4.5MB, time=55.99
TOP MAIN SOLVE Loop
x[1] = 0.415
y2[1] (analytic) = 0.5968100696143733689045003648061
y2[1] (numeric) = 0.5968100696143733689045003648059
absolute error = 2.0e-31
relative error = 3.3511498914425030444493367401644e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9151163204946317375323231603814
y1[1] (numeric) = 1.9151163204946317375323231603821
absolute error = 7e-31
relative error = 3.6551304613142539921610655201482e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=877.3MB, alloc=4.5MB, time=56.24
x[1] = 0.416
y2[1] (analytic) = 0.59589515504134650952354697466115
y2[1] (numeric) = 0.59589515504134650952354697466095
absolute error = 2.0e-31
relative error = 3.3562951184948448052398054443799e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9147126730733223118017969413405
y1[1] (numeric) = 1.9147126730733223118017969413412
absolute error = 7e-31
relative error = 3.6559010124293154903300483949382e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=881.2MB, alloc=4.5MB, time=56.48
x[1] = 0.417
y2[1] (analytic) = 0.59498064457313093339346001994986
y2[1] (numeric) = 0.59498064457313093339346001994966
absolute error = 2.0e-31
relative error = 3.3614538863443208020736986298913e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9143081109394160388025074955377
y1[1] (numeric) = 1.9143081109394160388025074955384
absolute error = 7e-31
relative error = 3.6566736357632952502602530732324e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.418
y2[1] (analytic) = 0.59406653912423703252061248643465
y2[1] (numeric) = 0.59406653912423703252061248643445
absolute error = 2.0e-31
relative error = 3.3666262418152124641224003568403e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9139026344974750187272177871901
y1[1] (numeric) = 1.9139026344974750187272177871908
absolute error = 7e-31
relative error = 3.6574483329649416335274421196241e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=885.0MB, alloc=4.5MB, time=56.72
x[1] = 0.419
y2[1] (analytic) = 0.59315283960877017962345371165307
y2[1] (numeric) = 0.59315283960877017962345371165287
absolute error = 2.0e-31
relative error = 3.3718122319352858427576331133281e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9134962441529756597272455228257
y1[1] (numeric) = 1.9134962441529756597272455228264
absolute error = 7e-31
relative error = 3.6582251056879422863537194122608e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=888.8MB, alloc=4.5MB, time=56.97
x[1] = 0.42
y2[1] (analytic) = 0.59223954694042981402721284191366
y2[1] (numeric) = 0.59223954694042981402721284191345
absolute error = 2.1e-31
relative error = 3.5458624991336954546659581337707e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9130889403123082724360887896657
y1[1] (numeric) = 1.9130889403123082724360887896664
absolute error = 7e-31
relative error = 3.6590039555909318025708625671599e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=892.6MB, alloc=4.5MB, time=57.22
x[1] = 0.421
y2[1] (analytic) = 0.59132666203250852796453564868418
y2[1] (numeric) = 0.59132666203250852796453564868397
absolute error = 2.1e-31
relative error = 3.5513365705207306816578967309148e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.912680723382776663579149287984
y1[1] (numeric) = 1.9126807233827766635791492879847
absolute error = 7e-31
relative error = 3.6597848843374994126272109655865e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.422
y2[1] (analytic) = 0.59041418579789115328296840365935
y2[1] (numeric) = 0.59041418579789115328296840365914
absolute error = 2.1e-31
relative error = 3.5568251077199994996317225597356e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9122715937725977286699595476886
y1[1] (numeric) = 1.9122715937725977286699595476893
absolute error = 7e-31
relative error = 3.6605678935961966987005282940820e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=896.4MB, alloc=4.5MB, time=57.46
x[1] = 0.423
y2[1] (analytic) = 0.58950211914905384856020210494802
y2[1] (numeric) = 0.58950211914905384856020210494781
absolute error = 2.1e-31
relative error = 3.5623281609765024063841662704058e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9118615518909010437933214328626
y1[1] (numeric) = 1.9118615518909010437933214328632
absolute error = 6e-31
relative error = 3.1383025586061817165538580360963e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=900.2MB, alloc=4.5MB, time=57.71
x[1] = 0.424
y2[1] (analytic) = 0.58859046299806318662798993905953
y2[1] (numeric) = 0.58859046299806318662798993905932
absolute error = 2.1e-31
relative error = 3.5678457807545384088519202971251e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.911450598147728456475764151092
y1[1] (numeric) = 1.9114505981477284564757641510927
absolute error = 7e-31
relative error = 3.6621401603490448601767777297078e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.425
y2[1] (analytic) = 0.58767921825657524250565045469569
y2[1] (numeric) = 0.58767921825657524250565045469548
absolute error = 2.1e-31
relative error = 3.5733780177388536964298320662527e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9110387329540336756437308970901
y1[1] (numeric) = 1.9110387329540336756437308970908
absolute error = 7e-31
relative error = 3.6629294212051804613366977604212e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=904.0MB, alloc=4.5MB, time=57.96
x[1] = 0.426
y2[1] (analytic) = 0.58676838583583468174406851476933
y2[1] (numeric) = 0.58676838583583468174406851476912
absolute error = 2.1e-31
relative error = 3.5789249228357973412893170139994e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9106259567216818606699041723951
y1[1] (numeric) = 1.9106259567216818606699041723958
absolute error = 7e-31
relative error = 3.6637207692974308040011037169770e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=907.9MB, alloc=4.5MB, time=58.20
x[1] = 0.427
y2[1] (analytic) = 0.58585796664667384918110568257234
y2[1] (numeric) = 0.58585796664667384918110568257213
absolute error = 2.1e-31
relative error = 3.5844865471744840748666809557717e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.910212269863449209508080734783
y1[1] (numeric) = 1.9102122698634492095080807347837
absolute error = 7e-31
relative error = 3.6645142063192758737968766416440e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=911.7MB, alloc=4.5MB, time=58.45
x[1] = 0.428
y2[1] (analytic) = 0.58494796159951185810933128660698
y2[1] (numeric) = 0.58494796159951185810933128660677
absolute error = 2.1e-31
relative error = 3.5900629421079641900784431511984e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9097976727930225459170080424865
y1[1] (numeric) = 1.9097976727930225459170080424872
absolute error = 7e-31
relative error = 3.6653097339692048505090803742320e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.429
y2[1] (analytic) = 0.58403837160435367985698499627348
y2[1] (numeric) = 0.58403837160435367985698499627327
absolute error = 2.1e-31
relative error = 3.5956541592144006192115476086837e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9093821659249989057735949693482
y1[1] (numeric) = 1.9093821659249989057735949693489
absolute error = 7e-31
relative error = 3.6661073539507240077038483612368e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=915.5MB, alloc=4.5MB, time=58.69
x[1] = 0.43
y2[1] (analytic) = 0.58312919757078923378308132737543
y2[1] (numeric) = 0.58312919757078923378308132737523
absolute error = 2.0e-31
relative error = 3.4297716669507173693624509670906e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9089657496748851224759104776634
y1[1] (numeric) = 1.9089657496748851224759104776642
absolute error = 8e-31
relative error = 4.1907509348255595873890222898837e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=919.3MB, alloc=4.5MB, time=58.94
x[1] = 0.431
y2[1] (analytic) = 0.58222044040799247768756608226273
y2[1] (numeric) = 0.58222044040799247768756608226252
absolute error = 2.1e-31
relative error = 3.6068812673914704454417392527214e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.90854842445909741143638484568
y1[1] (numeric) = 1.9085484244590974114363848456807
absolute error = 7e-31
relative error = 3.6677088777476910108117785818848e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.432
y2[1] (analytic) = 0.58131210102472049863743431437966
y2[1] (numeric) = 0.58131210102472049863743431437946
absolute error = 2.0e-31
relative error = 3.4404926311949410229092111422243e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9081301906949609536656289565175
y1[1] (numeric) = 1.9081301906949609536656289565182
absolute error = 7e-31
relative error = 3.6685127849953083423543065878650e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
memory used=923.1MB, alloc=4.5MB, time=59.18
TOP MAIN SOLVE Loop
x[1] = 0.433
y2[1] (analytic) = 0.58040418032931260420971899102467
y2[1] (numeric) = 0.58040418032931260420971899102447
absolute error = 2.0e-31
relative error = 3.4458745608366054058929687914527e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9077110488007094784472880646543
y1[1] (numeric) = 1.9077110488007094784472880646549
absolute error = 6e-31
relative error = 3.1451303926618892672277402085502e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=926.9MB, alloc=4.5MB, time=59.43
x[1] = 0.434
y2[1] (analytic) = 0.57949667922968941415225911125708
y2[1] (numeric) = 0.57949667922968941415225911125688
absolute error = 2.0e-31
relative error = 3.4512708556993811850190829864171e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9072909991954848451043473650912
y1[1] (numeric) = 1.9072909991954848451043473650918
absolute error = 6e-31
relative error = 3.1458230561203625053906240802957e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=930.7MB, alloc=4.5MB, time=59.68
x[1] = 0.435
y2[1] (analytic) = 0.57858959863335195246315561810729
y2[1] (numeric) = 0.57858959863335195246315561810709
absolute error = 2.0e-31
relative error = 3.4566815662156165845794215192102e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9068700422993366238573075988539
y1[1] (numeric) = 1.9068700422993366238573075988546
absolute error = 7e-31
relative error = 3.6709371088337408991866695089977e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.436
y2[1] (analytic) = 0.5776829394473807398898230255586
y2[1] (numeric) = 0.57768293944738073988982302555839
absolute error = 2.1e-31
relative error = 3.6352120801921002030964178040802e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9064481785332216757746498366219
y1[1] (numeric) = 1.9064481785332216757746498366226
absolute error = 7e-31
relative error = 3.6717494232576741036943826998590e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=934.6MB, alloc=4.5MB, time=59.92
x[1] = 0.437
y2[1] (analytic) = 0.57677670257843488684854426117356
y2[1] (numeric) = 0.57677670257843488684854426117335
absolute error = 2.1e-31
relative error = 3.6409237589037753426703394543572e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9060254083190037318160094899842
y1[1] (numeric) = 1.906025408319003731816009489985
absolute error = 8e-31
relative error = 4.1972158215117940808166496833238e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=938.4MB, alloc=4.5MB, time=60.17
x[1] = 0.438
y2[1] (analytic) = 0.57587088893275118676543580473445
y2[1] (numeric) = 0.57587088893275118676543580473424
absolute error = 2.1e-31
relative error = 3.6466507343197772481323623171922e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9056017320794529709684805071144
y1[1] (numeric) = 1.9056017320794529709684805071151
absolute error = 7e-31
relative error = 3.6733803722781980636472229087095e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=942.2MB, alloc=4.5MB, time=60.42
x[1] = 0.439
y2[1] (analytic) = 0.57496549941614320983972978185704
y2[1] (numeric) = 0.57496549941614320983972978185682
absolute error = 2.2e-31
relative error = 3.8263165393993568185062609609989e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9051771502382455974764716165229
y1[1] (numeric) = 1.9051771502382455974764716165237
absolute error = 8e-31
relative error = 4.1990845832890587547725193712747e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.44
y2[1] (analytic) = 0.57406053493400039723027924922008
y2[1] (numeric) = 0.57406053493400039723027924921987
absolute error = 2.1e-31
relative error = 3.6581507910858852178079235939356e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9047516632199634171655373889984
y1[1] (numeric) = 1.9047516632199634171655373889991
absolute error = 7e-31
relative error = 3.6750197598812281994924040423398e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=946.0MB, alloc=4.5MB, time=60.66
x[1] = 0.441
y2[1] (analytic) = 0.57315599639128715566619248482993
y2[1] (numeric) = 0.57315599639128715566619248482971
absolute error = 2.2e-31
relative error = 3.8383965514653444034775540774152e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9043252714500934128606077938682
y1[1] (numeric) = 1.904325271450093412860607793869
absolute error = 8e-31
relative error = 4.2009629972027894321252582649955e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=949.8MB, alloc=4.5MB, time=60.91
x[1] = 0.442
y2[1] (analytic) = 0.57225188469254195248250167261022
y2[1] (numeric) = 0.57225188469254195248250167261
absolute error = 2.2e-31
relative error = 3.8444609075984265991671863026723e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9038979753550273188990408313166
y1[1] (numeric) = 1.9038979753550273188990408313174
absolute error = 8e-31
relative error = 4.2019058287554555749504898863915e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.443
y2[1] (analytic) = 0.57134820074187641108177094557285
y2[1] (numeric) = 0.57134820074187641108177094557263
absolute error = 2.2e-31
relative error = 3.8505415736732417054996251521254e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9034697753620611947389237276696
y1[1] (numeric) = 1.9034697753620611947389237276704
absolute error = 8e-31
relative error = 4.2028510794075050216544381603657e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=953.6MB, alloc=4.5MB, time=61.15
x[1] = 0.444
y2[1] (analytic) = 0.57044494544297440682254832588658
y2[1] (numeric) = 0.57044494544297440682254832588636
absolute error = 2.2e-31
relative error = 3.8566386074147923259298818814658e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9030406718993949976630490853117
y1[1] (numeric) = 1.9030406718993949976630490853125
absolute error = 8e-31
relative error = 4.2037987511929136442480796405939e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=957.5MB, alloc=4.5MB, time=61.40
x[1] = 0.445
y2[1] (analytic) = 0.56954211969909116333556567331613
y2[1] (numeric) = 0.56954211969909116333556567331591
absolute error = 2.2e-31
relative error = 3.8627520668047101252938845537424e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9026106653961321545789932832218
y1[1] (numeric) = 1.9026106653961321545789932832226
absolute error = 8e-31
relative error = 4.2047488461515397739612978566835e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=961.3MB, alloc=4.5MB, time=61.65
x[1] = 0.446
y2[1] (analytic) = 0.56863972441305234926859032575643
y2[1] (numeric) = 0.56863972441305234926859032575621
absolute error = 2.2e-31
relative error = 3.8688820100826251749735052065926e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9021797562822791329157253280146
y1[1] (numeric) = 1.9021797562822791329157253280154
absolute error = 8e-31
relative error = 4.2057013663291337566995591733307e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.447
y2[1] (analytic) = 0.56773776048725317546083168693519
y2[1] (numeric) = 0.56773776048725317546083168693497
absolute error = 2.2e-31
relative error = 3.8750284957475438315848488763392e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9017479449887450106171752588427
y1[1] (numeric) = 1.9017479449887450106171752588435
absolute error = 8e-31
relative error = 4.2066563137773475402118847613498e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=965.1MB, alloc=4.5MB, time=61.89
x[1] = 0.448
y2[1] (analytic) = 0.56683622882365749254780558680187
y2[1] (numeric) = 0.56683622882365749254780558680165
absolute error = 2.2e-31
relative error = 3.8811915825592352100183881562062e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9013152319473410452331921125551
y1[1] (numeric) = 1.9013152319473410452331921125559
absolute error = 8e-31
relative error = 4.2076136905537442930489662329141e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=968.9MB, alloc=4.5MB, time=62.14
x[1] = 0.449
y2[1] (analytic) = 0.56593513032379688899755880966357
y2[1] (numeric) = 0.56593513032379688899755880966334
absolute error = 2.3e-31
relative error = 4.0640700263368820536090252844992e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9008816175907802421083223581184
y1[1] (numeric) = 1.9008816175907802421083223581192
absolute error = 8e-31
relative error = 4.2085734987218080553905745623625e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.45
y2[1] (analytic) = 0.5650344658887697895791557537681
y2[1] (numeric) = 0.56503446588876978957915575376788
absolute error = 2.2e-31
relative error = 3.8935677959742058730166624527440e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9004471023526769216688406114864
y1[1] (numeric) = 1.9004471023526769216688406114873
absolute error = 9e-31
relative error = 4.7357277078948225995494293730509e-29 %
Correct digits = 30
h = 0.001
memory used=972.7MB, alloc=4.5MB, time=62.38
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.451
y2[1] (analytic) = 0.56413423641924055426432875377253
y2[1] (numeric) = 0.56413423641924055426432875377231
absolute error = 2.2e-31
relative error = 3.8997810414134369868101915231804e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.9000116866675462858084653438511
y1[1] (numeric) = 1.9000116866675462858084653438519
absolute error = 8e-31
relative error = 4.2105004175165352561372847766060e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=976.5MB, alloc=4.5MB, time=62.63
x[1] = 0.452
y2[1] (analytic) = 0.56323444281543857756319316437161
y2[1] (numeric) = 0.56323444281543857756319316437139
absolute error = 2.2e-31
relative error = 3.9060111256741785754185836719084e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8995753709708039833731931975225
y1[1] (numeric) = 1.8995753709708039833731931975233
absolute error = 8e-31
relative error = 4.2114675322998584382552955733283e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=980.3MB, alloc=4.5MB, time=62.87
x[1] = 0.453
y2[1] (analytic) = 0.56233508597715738829492786929617
y2[1] (numeric) = 0.56233508597715738829492786929595
absolute error = 2.2e-31
relative error = 3.9122581088411157629070248496676e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.899138155698765674745686424569
y1[1] (numeric) = 1.8991381556987656747456864245699
absolute error = 9e-31
relative error = 4.7389917226367110987339073908685e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.454
y2[1] (analytic) = 0.56143616680375374979432144492579
y2[1] (numeric) = 0.56143616680375374979432144492557
absolute error = 2.2e-31
relative error = 3.9185220512681992197158324405799e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.898700041288646595529648863792
y1[1] (numeric) = 1.8987000412886465955296488637928
absolute error = 8e-31
relative error = 4.2134090830747571530687989719032e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=984.2MB, alloc=4.5MB, time=63.12
x[1] = 0.455
y2[1] (analytic) = 0.56053768619414676055508377189468
y2[1] (numeric) = 0.56053768619414676055508377189446
absolute error = 2.2e-31
relative error = 3.9248030135800935409302602676563e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8982610281785611193346267716233
y1[1] (numeric) = 1.8982610281785611193346267716241
absolute error = 8e-31
relative error = 4.2143835232587806995643088337900e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=988.0MB, alloc=4.5MB, time=63.36
x[1] = 0.456
y2[1] (analytic) = 0.55963964504681695531082245130418
y2[1] (numeric) = 0.55963964504681695531082245130396
absolute error = 2.2e-31
relative error = 3.9311010566736347234788620572167e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8978211168075223196616717221096
y1[1] (numeric) = 1.8978211168075223196616717221104
absolute error = 8e-31
relative error = 4.2153604094454613413388887449742e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=991.8MB, alloc=4.5MB, time=63.61
x[1] = 0.457
y2[1] (analytic) = 0.55874204425980540655458294449053
y2[1] (numeric) = 0.55874204425980540655458294449031
absolute error = 2.2e-31
relative error = 3.9374162417192968076436719013723e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8973803076154415308903036902821
y1[1] (numeric) = 1.8973803076154415308903036902828
absolute error = 7e-31
relative error = 3.6892972757777512005588207477881e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.458
y2[1] (analytic) = 0.55784488473071282649785091673299
y2[1] (numeric) = 0.55784488473071282649785091673276
absolute error = 2.3e-31
relative error = 4.1230099315336981010124324672754e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8969386010431279083672133319129
y1[1] (numeric) = 1.8969386010431279083672133319136
absolute error = 7e-31
relative error = 3.6901563372429107290999220741487e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=995.6MB, alloc=4.5MB, time=63.85
x[1] = 0.459
y2[1] (analytic) = 0.55694816735669866946991482582499
y2[1] (numeric) = 0.55694816735669866946991482582476
absolute error = 2.3e-31
relative error = 4.1296482057134770669658773067565e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8964959975322879875971433709198
y1[1] (numeric) = 1.8964959975322879875971433709206
absolute error = 8e-31
relative error = 4.2183057651635246310470748777093e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=999.4MB, alloc=4.5MB, time=64.10
x[1] = 0.46
y2[1] (analytic) = 0.5560518930344802347584863560711
y2[1] (numeric) = 0.55605189303448023475848635607087
absolute error = 2.3e-31
relative error = 4.1363045946098042445568083182261e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8960524975255252425363899035004
y1[1] (numeric) = 1.8960524975255252425363899035012
absolute error = 8e-31
relative error = 4.2192924565329982571935800869880e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.461
y2[1] (analytic) = 0.55515606266033176989247585701442
y2[1] (numeric) = 0.55515606266033176989247585701418
absolute error = 2.4e-31
relative error = 4.3231086921740467023111874984078e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.895608101466339642989365325457
y1[1] (numeric) = 1.8956081014663396429893653254578
absolute error = 8e-31
relative error = 4.2202816045213321143286969510917e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1003.2MB, alloc=4.5MB, time=64.35
x[1] = 0.462
y2[1] (analytic) = 0.55426067713008357436781950404435
y2[1] (numeric) = 0.55426067713008357436781950404412
absolute error = 2.3e-31
relative error = 4.1496719772891192076039236200940e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8951628097991272111086654861145
y1[1] (numeric) = 1.8951628097991272111086654861153
absolute error = 8e-31
relative error = 4.2212732112698744455733907136123e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1007.0MB, alloc=4.5MB, time=64.59
x[1] = 0.463
y2[1] (analytic) = 0.55336573733912110381725445498295
y2[1] (numeric) = 0.55336573733912110381725445498272
absolute error = 2.3e-31
relative error = 4.1563831021769292783343675560966e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8947166229691795769990845687246
y1[1] (numeric) = 1.8947166229691795769990845687254
absolute error = 8e-31
relative error = 4.2222672789260328685887211505412e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1010.9MB, alloc=4.5MB, time=64.84
x[1] = 0.464
y2[1] (analytic) = 0.55247124418238407462493783279988
y2[1] (numeric) = 0.55247124418238407462493783279964
absolute error = 2.4e-31
relative error = 4.3441174998199583211851988428678e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8942695414226835334260220933066
y1[1] (numeric) = 1.8942695414226835334260220933074
absolute error = 8e-31
relative error = 4.2232638096432845141491579012118e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.465
y2[1] (analytic) = 0.55157719855436556898680491976248
y2[1] (numeric) = 0.55157719855436556898680491976224
absolute error = 2.4e-31
relative error = 4.3511588337773661146903463990661e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8938215656067205896287273334791
y1[1] (numeric) = 1.8938215656067205896287273334799
absolute error = 8e-31
relative error = 4.2242628055811861978935067903440e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1014.7MB, alloc=4.5MB, time=65.09
x[1] = 0.466
y2[1] (analytic) = 0.55068360134911114041756150258825
y2[1] (numeric) = 0.550683601349111140417561502588
absolute error = 2.5e-31
relative error = 4.5398119607616589786504487934958e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8933726959692665242388273340021
y1[1] (numeric) = 1.893372695969266524238827334003
absolute error = 9e-31
relative error = 4.7534223025185577035051273691963e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1018.5MB, alloc=4.5MB, time=65.33
x[1] = 0.467
y2[1] (analytic) = 0.54979045346021791970520486153262
y2[1] (numeric) = 0.54979045346021791970520486153237
absolute error = 2.5e-31
relative error = 4.5471869950919338001095276159535e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8929229329591909373045856104637
y1[1] (numeric) = 1.8929229329591909373045856104646
absolute error = 9e-31
relative error = 4.7545517270110799590149959493848e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.468
memory used=1022.3MB, alloc=4.5MB, time=65.58
y2[1] (analytic) = 0.54889775578083372131396744881682
y2[1] (numeric) = 0.54889775578083372131396744881658
absolute error = 2.4e-31
relative error = 4.3723990027721709584983190086431e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.892472277026256801421339506815
y1[1] (numeric) = 1.8924722770262568014213395068159
absolute error = 9e-31
relative error = 4.7556839322064906271646267091554e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.469
y2[1] (analytic) = 0.54800550920365615023657685337748
y2[1] (numeric) = 0.54800550920365615023657685337724
absolute error = 2.4e-31
relative error = 4.3795180152250699748486073596932e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8920207286211200119685650802794
y1[1] (numeric) = 1.8920207286211200119685650802803
absolute error = 9e-31
relative error = 4.7568189205617648894639275675040e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1026.1MB, alloc=4.5MB, time=65.82
x[1] = 0.47
y2[1] (analytic) = 0.54711371462093170929672519960359
y2[1] (numeric) = 0.54711371462093170929672519960335
absolute error = 2.4e-31
relative error = 4.3866566234093444872570581529678e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8915682881953289364540192765334
y1[1] (numeric) = 1.8915682881953289364540192765343
absolute error = 9e-31
relative error = 4.7579566945407753522039746130520e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1029.9MB, alloc=4.5MB, time=66.07
x[1] = 0.471
y2[1] (analytic) = 0.54622237292445490690264067751721
y2[1] (numeric) = 0.54622237292445490690264067751696
absolute error = 2.5e-31
relative error = 4.5768905191764483443588386915254e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8911149562013239629654100509787
y1[1] (numeric) = 1.8911149562013239629654100509796
absolute error = 9e-31
relative error = 4.7590972566143037156333490204689e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.472
y2[1] (analytic) = 0.54533148500556736525265345075175
y2[1] (numeric) = 0.5453314850055673652526534507515
absolute error = 2.5e-31
relative error = 4.5843676162847577946608135263850e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.890660733092437047730045984399
y1[1] (numeric) = 1.8906607330924370477300459843999
absolute error = 9e-31
relative error = 4.7602406092600524811319098528164e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1033.7MB, alloc=4.5MB, time=66.31
x[1] = 0.473
y2[1] (analytic) = 0.54444105175515692899364773668793
y2[1] (numeric) = 0.54444105175515692899364773668768
absolute error = 2.5e-31
relative error = 4.5918653487655931089476746763029e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8902056193228912617829178333128
y1[1] (numeric) = 1.8902056193228912617829178333137
absolute error = 9e-31
relative error = 4.7613867549626566964795564760217e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1037.6MB, alloc=4.5MB, time=66.56
x[1] = 0.474
y2[1] (analytic) = 0.54355107406365677433329140022077
y2[1] (numeric) = 0.54355107406365677433329140022051
absolute error = 2.6e-31
relative error = 4.7833591433498055905905456014791e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8897496153478003367436653469044
y1[1] (numeric) = 1.8897496153478003367436653469053
absolute error = 9e-31
relative error = 4.7625356962136957393179042575935e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1041.4MB, alloc=4.5MB, time=66.81
x[1] = 0.475
y2[1] (analytic) = 0.54266155282104451860693394885391
y2[1] (numeric) = 0.54266155282104451860693394885365
absolute error = 2.6e-31
relative error = 4.7911999412595413626779102435504e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8892927216231682097028835735269
y1[1] (numeric) = 1.8892927216231682097028835735278
absolute error = 9e-31
relative error = 4.7636874355117051389031684424808e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.476
y2[1] (analytic) = 0.54177248891684133030006336214914
y2[1] (numeric) = 0.54177248891684133030006336214887
absolute error = 2.7e-31
relative error = 4.9836417596583296037282506644920e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8888349386058885672182237704341
y1[1] (numeric) = 1.8888349386058885672182237704349
absolute error = 8e-31
relative error = 4.2354150892108341655545987557524e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1045.2MB, alloc=4.5MB, time=67.05
x[1] = 0.477
y2[1] (analytic) = 0.54088388324011103952721173299992
y2[1] (numeric) = 0.54088388324011103952721173299965
absolute error = 2.7e-31
relative error = 4.9918292699459242065286713390704e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8883762667537443884207449206015
y1[1] (numeric) = 1.8883762667537443884207449206024
absolute error = 9e-31
relative error = 4.7659993182776290827577798248870e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1049.0MB, alloc=4.5MB, time=67.30
x[1] = 0.478
y2[1] (analytic) = 0.53999573667945924896819924174937
y2[1] (numeric) = 0.5399957366794592489681992417491
absolute error = 2.7e-31
relative error = 5.0000394755018527278966556395156e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8879167065254074872319727502484
y1[1] (numeric) = 1.8879167065254074872319727502493
absolute error = 9e-31
relative error = 4.7671594667775023774413919484385e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.479
y2[1] (analytic) = 0.53910805012303244526260552683451
y2[1] (numeric) = 0.53910805012303244526260552683424
absolute error = 2.7e-31
relative error = 5.0082724592664123505391736488419e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8874562583804380536921240299613
y1[1] (numeric) = 1.8874562583804380536921240299622
absolute error = 9e-31
relative error = 4.7683224233882874428285944046580e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1052.8MB, alloc=4.5MB, time=67.54
x[1] = 0.48
y2[1] (analytic) = 0.53822082445851711086335705741136
y2[1] (numeric) = 0.53822082445851711086335705741109
absolute error = 2.7e-31
relative error = 5.0165283045604269210302760644521e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8869949227792841943999548311587
y1[1] (numeric) = 1.8869949227792841943999548311596
absolute error = 9e-31
relative error = 4.7694881906434792396618320604904e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1056.6MB, alloc=4.5MB, time=67.79
x[1] = 0.481
y2[1] (analytic) = 0.53733406057313883635031865429955
y2[1] (numeric) = 0.53733406057313883635031865429928
absolute error = 2.7e-31
relative error = 5.0248070950873427019251588589409e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8865327001832814720646922980094
y1[1] (numeric) = 1.8865327001832814720646922980102
absolute error = 8e-31
relative error = 4.2405837965187561070954989512688e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1060.5MB, alloc=4.5MB, time=68.04
x[1] = 0.482
y2[1] (analytic) = 0.5364477593536614332047768455809
y2[1] (numeric) = 0.53644775935366143320477684558063
absolute error = 2.7e-31
relative error = 5.0331089149353376041752263774543e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8860695910546524441705103828338
y1[1] (numeric) = 1.8860695910546524441705103828347
absolute error = 9e-31
relative error = 4.7718281672562144222056761107191e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.483
y2[1] (analytic) = 0.53556192168638604704570228229476
y2[1] (numeric) = 0.53556192168638604704570228229448
absolute error = 2.8e-31
relative error = 5.2281536207490530360286420642499e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8856055958565062007540108804759
y1[1] (numeric) = 1.8856055958565062007540108804768
absolute error = 9e-31
relative error = 4.7730023817159355977868949807309e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1064.3MB, alloc=4.5MB, time=68.28
x[1] = 0.484
y2[1] (analytic) = 0.53467654845715027132867797789364
y2[1] (numeric) = 0.53467654845715027132867797789336
absolute error = 2.8e-31
relative error = 5.2368109431386365134667965573386e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8851407150528379012951719841238
y1[1] (numeric) = 1.8851407150528379012951719841246
absolute error = 8e-31
relative error = 4.2437150373550607885159364395646e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1068.1MB, alloc=4.5MB, time=68.53
x[1] = 0.485
y2[1] (analytic) = 0.53379164055132726150837967245725
y2[1] (numeric) = 0.53379164055132726150837967245697
absolute error = 2.8e-31
relative error = 5.2454924118107526624684342565940e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8846749491085283107222274715935
y1[1] (numeric) = 1.8846749491085283107222274715943
absolute error = 8e-31
relative error = 4.2447638006671053573274492309867e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1071.9MB, alloc=4.5MB, time=68.78
x[1] = 0.486
y2[1] (analytic) = 0.53290719885382484966549415911054
y2[1] (numeric) = 0.53290719885382484966549415911026
absolute error = 2.8e-31
relative error = 5.2541981155860369591912122944866e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.884208298489343334530940517158
y1[1] (numeric) = 1.8842082984893433345309405171588
absolute error = 8e-31
relative error = 4.2458150759732715564770858203023e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.487
y2[1] (analytic) = 0.53202322424908465959896094565383
y2[1] (numeric) = 0.53202322424908465959896094565355
absolute error = 2.8e-31
relative error = 5.2629281436952559327257408564244e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8837407636619335530187370096079
y1[1] (numeric) = 1.8837407636619335530187370096087
absolute error = 8e-31
relative error = 4.2468688655695109585569448230878e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1075.7MB, alloc=4.5MB, time=69.02
x[1] = 0.488
y2[1] (analytic) = 0.53113971762108122238442215908945
y2[1] (numeric) = 0.53113971762108122238442215908917
absolute error = 2.8e-31
relative error = 5.2716825857815805847562036180166e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8832723450938337546341641423728
y1[1] (numeric) = 1.8832723450938337546341641423736
absolute error = 8e-31
relative error = 4.2479251717580981266567481239489e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1079.5MB, alloc=4.5MB, time=69.27
x[1] = 0.489
y2[1] (analytic) = 0.53025667985332109239976513452147
y2[1] (numeric) = 0.53025667985332109239976513452118
absolute error = 2.9e-31
relative error = 5.4690494437565486172128612928248e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.882803043253462468442140926205
y1[1] (numeric) = 1.8828030432534624684421409262058
absolute error = 8e-31
relative error = 4.2489839968476416084631550163386e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.49
y2[1] (analytic) = 0.52937411182884196381864166281204
y2[1] (numeric) = 0.52937411182884196381864166281176
absolute error = 2.8e-31
relative error = 5.2892650725339969451652535265374e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8823328586101214957054681591367
y1[1] (numeric) = 1.8823328586101214957054681591375
absolute error = 8e-31
relative error = 4.2500453431530949657466873062150e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1083.3MB, alloc=4.5MB, time=69.51
x[1] = 0.491
y2[1] (analytic) = 0.52849201443021178757284740340174
y2[1] (numeric) = 0.52849201443021178757284740340146
absolute error = 2.8e-31
relative error = 5.2980932985691205000778973692830e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8818617916339954405830662721614
y1[1] (numeric) = 1.8818617916339954405830662721622
absolute error = 8e-31
relative error = 4.2511092129957678393290764513930e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1087.2MB, alloc=4.5MB, time=69.76
x[1] = 0.492
y2[1] (analytic) = 0.52761038853952788878444449984064
y2[1] (numeric) = 0.52761038853952788878444449984036
absolute error = 2.8e-31
relative error = 5.3069463013240642755392662223678e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8813898427961512399454103523624
y1[1] (numeric) = 1.8813898427961512399454103523632
absolute error = 8e-31
relative error = 4.2521756087033370496241938272228e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1091.0MB, alloc=4.5MB, time=70.01
x[1] = 0.493
y2[1] (analytic) = 0.52672923503841608466850996583417
y2[1] (numeric) = 0.52672923503841608466850996583389
absolute error = 2.8e-31
relative error = 5.3158241725386418859109720843588e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8809170125685376923076325280146
y1[1] (numeric) = 1.8809170125685376923076325280154
absolute error = 8e-31
relative error = 4.2532445326098577328460764542696e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.494
y2[1] (analytic) = 0.52584855480802980290739193898176
y2[1] (numeric) = 0.52584855480802980290739193898148
absolute error = 2.8e-31
relative error = 5.3247270043790248553501756936015e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8804433014239849858807627825173
y1[1] (numeric) = 1.8804433014239849858807627825182
absolute error = 9e-31
relative error = 4.7861054854377463271001521254031e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1094.8MB, alloc=4.5MB, time=70.25
x[1] = 0.495
y2[1] (analytic) = 0.52496834872904920049735542787856
y2[1] (numeric) = 0.52496834872904920049735542787828
absolute error = 2.8e-31
relative error = 5.3336548894401213825654663058728e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8799687098362042257415801458792
y1[1] (numeric) = 1.8799687098362042257415801458801
absolute error = 9e-31
relative error = 4.7873137211864242982957346559727e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1098.6MB, alloc=4.5MB, time=70.50
x[1] = 0.496
y2[1] (analytic) = 0.52408861768168028306849870586105
y2[1] (numeric) = 0.52408861768168028306849870586077
absolute error = 2.8e-31
relative error = 5.3426079207479706056285517404878e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8794932382797869601215470938628
y1[1] (numeric) = 1.8794932382797869601215470938636
absolute error = 8e-31
relative error = 4.2564664969595895816447018551466e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
x[1] = 0.497
y2[1] (analytic) = 0.52320936254565402467882103140682
y2[1] (numeric) = 0.52320936254565402467882103140653
absolute error = 2.9e-31
relative error = 5.5427142700393722138868816637830e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8790168872302047058153008658165
y1[1] (numeric) = 1.8790168872302047058153008658173
absolute error = 8e-31
relative error = 4.2575455571304256072529640589527e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
memory used=1102.4MB, alloc=4.5MB, time=70.74
TOP MAIN SOLVE Loop
x[1] = 0.498
y2[1] (analytic) = 0.52233058420022548808332190104733
y2[1] (numeric) = 0.52233058420022548808332190104704
absolute error = 2.9e-31
relative error = 5.5520394319631495958454714840017e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8785396571638084727091762926628
y1[1] (numeric) = 1.8785396571638084727091762926636
absolute error = 8e-31
relative error = 4.2586271572665557996949671946829e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
TOP MAIN SOLVE Loop
memory used=1106.2MB, alloc=4.5MB, time=70.99
x[1] = 0.499
y2[1] (analytic) = 0.52145228352417294547901156562125
y2[1] (numeric) = 0.52145228352417294547901156562096
absolute error = 2.9e-31
relative error = 5.5613909299633257819697074880329e-29 %
Correct digits = 30
h = 0.001
y1[1] (analytic) = 1.8780615485578282874302356064793
y1[1] (numeric) = 1.87806154855782828743023560648
absolute error = 7e-31
relative error = 3.7272473872729734271353587670508e-29 %
Correct digits = 30
h = 0.001
NO POLE for equation 1
NO POLE for equation 2
Finished!
diff ( y2 , x , 1 ) = m1 * y1 + 1.0;
diff ( y1 , x , 1 ) = y2 - 1.0;
Iterations = 400
Total Elapsed Time = 1 Minutes 11 Seconds
Elapsed Time(since restart) = 1 Minutes 10 Seconds
Time to Timeout = 1 Minutes 48 Seconds
Percent Done = 100.2 %
> quit
memory used=1108.0MB, alloc=4.5MB, time=71.09