|\^/| Maple 12 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> #BEGIN OUTFILE1
> # Begin Function number 3
> 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_2D0,
> array_const_1D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 1
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> if (min_size < 1.0) then # if number 1
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 1;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_1D0, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6_g, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y[1]) < min_size then
min_size := omniabs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 4
> # Begin Function number 5
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms;
> max_value3 := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> value3 := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (value3 > max_value3) then # if number 1
> max_value3 := value3;
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> fi;# end if 1;
> omniout_float(ALWAYS,"max_value3",32,max_value3,32,"");
> max_value3;
> end;
test_suggested_h := proc()
local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_1D0, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6_g, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
max_value3 := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
value3 := omniabs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_value3 < value3 then
max_value3 := value3;
omniout_float(ALWAYS, "value3", 32, value3, 32, "")
end if;
omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, "");
max_value3
end proc
> # End Function number 5
> # Begin Function number 6
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1
> ret := true;
> else
> ret := false;
> fi;# end if 1;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_1D0, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6_g, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 6
> # Begin Function number 7
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 1
> if (iter >= 0) then # if number 2
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 3
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 4
> glob_good_digits := -trunc(log10(relerr)) + 2;
> else
> glob_good_digits := Digits;
> fi;# end if 4;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 3;
> if (glob_iter = 1) then # if number 3
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 2;
> #BOTTOM DISPLAY ALOT
> fi;# end if 1;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_1D0, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6_g, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 2
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 7
> # Begin Function number 8
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 1
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 2
> glob_normmax := tmp;
> fi;# end if 2
> fi;# end if 1;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 2
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 2
> fi;# end if 1;
> if ( not glob_reached_optimal_h) then # if number 1
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 1;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_1D0, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6_g, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 8
> # Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 1
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 1;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_1D0, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6_g, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # End Function number 9
> # Begin Function number 10
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term;
> #TOP CHECK FOR POLE
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2
> m := m - 1;
> od;# end do number 2;
> if (m > 10) then # if number 1
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > glob_small_float * glob_small_float) then # if number 2
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_pole[1,1] := rcs;
> array_real_pole[1,2] := ord_no;
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 2
> else
> array_real_pole[1,1] := glob_large_float;
> array_real_pole[1,2] := glob_large_float;
> fi;# end if 1;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 2
> if (omniabs(array_y_higher[1,n]) > glob_small_float) then # if number 1
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 1;
> n := n - 1;
> od;# end do number 2;
> m := n + cnt;
> if (m <= 10) then # if number 1
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> elif
> (((omniabs(array_y_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y_higher[1,m-5]) <= (glob_small_float)))) then # if number 2
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) > glob_small_float) then # if number 5
> if (rcs > 0.0) then # if number 6
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 6
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 5
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 4
> fi;# end if 3;
> array_complex_pole[1,1] := rad_c;
> array_complex_pole[1,2] := ord_no;
> fi;# end if 2;
> #BOTTOM RADII COMPLEX EQ = 1
> found_sing := 0;
> #TOP WHICH RADII EQ = 1
> if (1 <> found_sing and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 2;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> found_sing := 1;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float))) then # if number 2
> array_poles[1,1] := array_real_pole[1,1];
> array_poles[1,2] := array_real_pole[1,2];
> found_sing := 1;
> array_type_pole[1] := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Real estimate of pole used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 2
> array_poles[1,1] := array_complex_pole[1,1];
> array_poles[1,2] := array_complex_pole[1,2];
> array_type_pole[1] := 2;
> found_sing := 1;
> if (glob_display_flag) then # if number 3
> if (reached_interval()) then # if number 4
> omniout_str(ALWAYS,"Complex estimate of poles used for equation 1");
> fi;# end if 4;
> fi;# end if 3;
> fi;# end if 2;
> if (1 <> found_sing ) then # if number 2
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> array_type_pole[1] := 3;
> if (reached_interval()) then # if number 3
> omniout_str(ALWAYS,"NO POLE for equation 1");
> fi;# end if 3;
> fi;# end if 2;
> #BOTTOM WHICH RADII EQ = 1
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> #TOP WHICH RADIUS EQ = 1
> if (array_pole[1] > array_poles[1,1]) then # if number 2
> array_pole[1] := array_poles[1,1];
> array_pole[2] := array_poles[1,2];
> fi;# end if 2;
> #BOTTOM WHICH RADIUS EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 2
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 2;
> #BOTTOM ADJUST ALL SERIES
> if (reached_interval()) then # if number 2
> display_pole();
> fi;# end if 2
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no,
rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_1D0, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6_g, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (
omniabs(array_y_higher[1, m]) < glob_small_float*glob_small_float or
omniabs(array_y_higher[1, m - 1]) < glob_small_float*glob_small_float
or
omniabs(array_y_higher[1, m - 2]) < glob_small_float*glob_small_float)
do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if glob_small_float*glob_small_float < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_pole[1, 1] := rcs;
array_real_pole[1, 2] := ord_no
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if
else
array_real_pole[1, 1] := glob_large_float;
array_real_pole[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if glob_small_float < omniabs(array_y_higher[1, n]) then
cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
elif glob_large_float <= omniabs(array_y_higher[1, m]) or
glob_large_float <= omniabs(array_y_higher[1, m - 1]) or
glob_large_float <= omniabs(array_y_higher[1, m - 2]) or
glob_large_float <= omniabs(array_y_higher[1, m - 3]) or
glob_large_float <= omniabs(array_y_higher[1, m - 4]) or
glob_large_float <= omniabs(array_y_higher[1, m - 5]) or
omniabs(array_y_higher[1, m]) <= glob_small_float or
omniabs(array_y_higher[1, m - 1]) <= glob_small_float or
omniabs(array_y_higher[1, m - 2]) <= glob_small_float or
omniabs(array_y_higher[1, m - 3]) <= glob_small_float or
omniabs(array_y_higher[1, m - 4]) <= glob_small_float or
omniabs(array_y_higher[1, m - 5]) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or
omniabs(dr1) <= glob_small_float then
rad_c := glob_large_float; ord_no := glob_large_float
else
if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if glob_small_float < omniabs(rcs) then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_pole[1, 1] := rad_c;
array_complex_pole[1, 2] := ord_no
end if;
found_sing := 0;
if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and
array_complex_pole[1, 1] <> glob_large_float and
array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 2;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1")
end if
end if
end if;
if 1 <> found_sing and array_real_pole[1, 1] <> glob_large_float and
array_real_pole[1, 2] <> glob_large_float and
0. < array_real_pole[1, 1] and
-1.0*glob_smallish_float < array_real_pole[1, 2] and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float or
array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 1")
end if
end if
end if;
if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or
array_real_pole[1, 2] = glob_large_float) and (
array_complex_pole[1, 1] = glob_large_float or
array_complex_pole[1, 2] = glob_large_float) then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
array_type_pole[1] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 1")
end if
end if;
if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1]
and 0. < array_real_pole[1, 1] and
-1.0*glob_smallish_float < array_real_pole[1, 2] then
array_poles[1, 1] := array_real_pole[1, 1];
array_poles[1, 2] := array_real_pole[1, 2];
found_sing := 1;
array_type_pole[1] := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Real estimate of pole used for equation 1")
end if
end if
end if;
if 1 <> found_sing and array_complex_pole[1, 1] <> glob_large_float
and array_complex_pole[1, 2] <> glob_large_float and
0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then
array_poles[1, 1] := array_complex_pole[1, 1];
array_poles[1, 2] := array_complex_pole[1, 2];
array_type_pole[1] := 2;
found_sing := 1;
if glob_display_flag then
if reached_interval() then omniout_str(ALWAYS,
"Complex estimate of poles used for equation 1")
end if
end if
end if;
if 1 <> found_sing then
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
array_type_pole[1] := 3;
if reached_interval() then
omniout_str(ALWAYS, "NO POLE for equation 1")
end if
end if;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
if array_poles[1, 1] < array_pole[1] then
array_pole[1] := array_poles[1, 1];
array_pole[2] := array_poles[1, 2]
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_pole() end if
end proc
> # End Function number 10
> # Begin Function number 11
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 2
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 2;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 2
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 3
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 3;
> iii := iii + 1;
> od;# end do number 2
> #BOTTOM GET NORMS
> ;
> fi;# end if 2;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_1D0, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6_g, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 11
> # Begin Function number 12
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre cos 1 $eq_no = 1
> array_tmp1[1] := cos(array_x[1]);
> array_tmp1_g[1] := sin(array_x[1]);
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp2[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp1[1] / array_tmp3[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
> #emit pre sin 1 $eq_no = 1
> array_tmp6[1] := sin(array_x[1]);
> array_tmp6_g[1] := cos(array_x[1]);
> #emit pre mult CONST FULL $eq_no = 1 i = 1
> array_tmp7[1] := array_const_2D0[1] * array_tmp6[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp8[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp9[1] := array_tmp8[1] + array_const_1D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp10[1] := array_tmp7[1] / array_tmp9[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp11[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp12[1] := array_tmp11[1] + array_const_1D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp13[1] := array_tmp10[1] / array_tmp12[1];
> #emit pre sub FULL FULL $eq_no = 1 i = 1
> array_tmp14[1] := array_tmp5[1] - array_tmp13[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp14[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := -array_tmp1_g[1] * array_x[2] / 1;
> array_tmp1_g[2] := array_tmp1[1] * array_x[2] / 1;
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp2[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp4[2] := (array_tmp1[2] - array_tmp4[1] * array_tmp3[2]) / array_tmp3[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp6[2] := array_tmp6_g[1] * array_x[2] / 1;
> array_tmp6_g[2] := -array_tmp6[1] * array_x[2] / 1;
> #emit pre mult CONST FULL $eq_no = 1 i = 2
> array_tmp7[2] := array_const_2D0[1] * array_tmp6[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp8[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp9[2] := array_tmp8[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp10[2] := (array_tmp7[2] - array_tmp10[1] * array_tmp9[2]) / array_tmp9[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp11[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp12[2] := array_tmp11[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp13[2] := (array_tmp10[2] - array_tmp13[1] * array_tmp12[2]) / array_tmp12[1];
> #emit pre sub FULL FULL $eq_no = 1 i = 2
> array_tmp14[2] := array_tmp5[2] - array_tmp13[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp14[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := -array_tmp1_g[2] * array_x[2] / 2;
> array_tmp1_g[3] := array_tmp1[2] * array_x[2] / 2;
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp4[3] := (array_tmp1[3] - array_tmp4[2] * array_tmp3[2]) / array_tmp3[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp6[3] := array_tmp6_g[2] * array_x[2] / 2;
> array_tmp6_g[3] := -array_tmp6[2] * array_x[2] / 2;
> #emit pre mult CONST FULL $eq_no = 1 i = 3
> array_tmp7[3] := array_const_2D0[1] * array_tmp6[3];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp10[3] := (array_tmp7[3] - array_tmp10[2] * array_tmp9[2]) / array_tmp9[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp13[3] := (array_tmp10[3] - array_tmp13[2] * array_tmp12[2]) / array_tmp12[1];
> #emit pre sub FULL FULL $eq_no = 1 i = 3
> array_tmp14[3] := array_tmp5[3] - array_tmp13[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp14[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := -array_tmp1_g[3] * array_x[2] / 3;
> array_tmp1_g[4] := array_tmp1[3] * array_x[2] / 3;
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp4[4] := (array_tmp1[4] - array_tmp4[3] * array_tmp3[2]) / array_tmp3[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp6[4] := array_tmp6_g[3] * array_x[2] / 3;
> array_tmp6_g[4] := -array_tmp6[3] * array_x[2] / 3;
> #emit pre mult CONST FULL $eq_no = 1 i = 4
> array_tmp7[4] := array_const_2D0[1] * array_tmp6[4];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp10[4] := (array_tmp7[4] - array_tmp10[3] * array_tmp9[2]) / array_tmp9[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp13[4] := (array_tmp10[4] - array_tmp13[3] * array_tmp12[2]) / array_tmp12[1];
> #emit pre sub FULL FULL $eq_no = 1 i = 4
> array_tmp14[4] := array_tmp5[4] - array_tmp13[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp14[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := -array_tmp1_g[4] * array_x[2] / 4;
> array_tmp1_g[5] := array_tmp1[4] * array_x[2] / 4;
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp4[5] := (array_tmp1[5] - array_tmp4[4] * array_tmp3[2]) / array_tmp3[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp6[5] := array_tmp6_g[4] * array_x[2] / 4;
> array_tmp6_g[5] := -array_tmp6[4] * array_x[2] / 4;
> #emit pre mult CONST FULL $eq_no = 1 i = 5
> array_tmp7[5] := array_const_2D0[1] * array_tmp6[5];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp10[5] := (array_tmp7[5] - array_tmp10[4] * array_tmp9[2]) / array_tmp9[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp13[5] := (array_tmp10[5] - array_tmp13[4] * array_tmp12[2]) / array_tmp12[1];
> #emit pre sub FULL FULL $eq_no = 1 i = 5
> array_tmp14[5] := array_tmp5[5] - array_tmp13[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp14[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit cos LINEAR $eq_no = 1
> array_tmp1[kkk] := -array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp1_g[kkk] := array_tmp1[kkk - 1] * array_x[2] / (kkk - 1);
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp4[kkk] := -ats(kkk,array_tmp3,array_tmp4,2) / array_tmp3[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit sin LINEAR $eq_no = 1
> array_tmp6[kkk] := array_tmp6_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp6_g[kkk] := -array_tmp6[kkk - 1] * array_x[2] / (kkk - 1);
> #emit mult CONST FULL $eq_no = 1 i = 1
> array_tmp7[kkk] := array_const_2D0[1] * array_tmp6[kkk];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp10[kkk] := -ats(kkk,array_tmp9,array_tmp10,2) / array_tmp9[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp13[kkk] := -ats(kkk,array_tmp12,array_tmp13,2) / array_tmp12[1];
> #emit FULL - FULL sub $eq_no = 1
> array_tmp14[kkk] := array_tmp5[kkk] - array_tmp13[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d + 1 <= glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp14[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 2
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 2
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_1D0, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6_g, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
array_tmp1[1] := cos(array_x[1]);
array_tmp1_g[1] := sin(array_x[1]);
array_tmp2[1] := array_const_2D0[1]*array_x[1];
array_tmp3[1] := array_tmp2[1] + array_const_1D0[1];
array_tmp4[1] := array_tmp1[1]/array_tmp3[1];
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
array_tmp6[1] := sin(array_x[1]);
array_tmp6_g[1] := cos(array_x[1]);
array_tmp7[1] := array_const_2D0[1]*array_tmp6[1];
array_tmp8[1] := array_const_2D0[1]*array_x[1];
array_tmp9[1] := array_tmp8[1] + array_const_1D0[1];
array_tmp10[1] := array_tmp7[1]/array_tmp9[1];
array_tmp11[1] := array_const_2D0[1]*array_x[1];
array_tmp12[1] := array_tmp11[1] + array_const_1D0[1];
array_tmp13[1] := array_tmp10[1]/array_tmp12[1];
array_tmp14[1] := array_tmp5[1] - array_tmp13[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp14[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := -array_tmp1_g[1]*array_x[2];
array_tmp1_g[2] := array_tmp1[1]*array_x[2];
array_tmp2[2] := array_const_2D0[1]*array_x[2];
array_tmp3[2] := array_tmp2[2];
array_tmp4[2] :=
(array_tmp1[2] - array_tmp4[1]*array_tmp3[2])/array_tmp3[1];
array_tmp5[2] := array_tmp4[2];
array_tmp6[2] := array_tmp6_g[1]*array_x[2];
array_tmp6_g[2] := -array_tmp6[1]*array_x[2];
array_tmp7[2] := array_const_2D0[1]*array_tmp6[2];
array_tmp8[2] := array_const_2D0[1]*array_x[2];
array_tmp9[2] := array_tmp8[2];
array_tmp10[2] :=
(array_tmp7[2] - array_tmp10[1]*array_tmp9[2])/array_tmp9[1];
array_tmp11[2] := array_const_2D0[1]*array_x[2];
array_tmp12[2] := array_tmp11[2];
array_tmp13[2] :=
(array_tmp10[2] - array_tmp13[1]*array_tmp12[2])/array_tmp12[1];
array_tmp14[2] := array_tmp5[2] - array_tmp13[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp14[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := -1/2*array_tmp1_g[2]*array_x[2];
array_tmp1_g[3] := 1/2*array_tmp1[2]*array_x[2];
array_tmp4[3] :=
(array_tmp1[3] - array_tmp4[2]*array_tmp3[2])/array_tmp3[1];
array_tmp5[3] := array_tmp4[3];
array_tmp6[3] := 1/2*array_tmp6_g[2]*array_x[2];
array_tmp6_g[3] := -1/2*array_tmp6[2]*array_x[2];
array_tmp7[3] := array_const_2D0[1]*array_tmp6[3];
array_tmp10[3] :=
(array_tmp7[3] - array_tmp10[2]*array_tmp9[2])/array_tmp9[1];
array_tmp13[3] :=
(array_tmp10[3] - array_tmp13[2]*array_tmp12[2])/array_tmp12[1];
array_tmp14[3] := array_tmp5[3] - array_tmp13[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp14[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := -1/3*array_tmp1_g[3]*array_x[2];
array_tmp1_g[4] := 1/3*array_tmp1[3]*array_x[2];
array_tmp4[4] :=
(array_tmp1[4] - array_tmp4[3]*array_tmp3[2])/array_tmp3[1];
array_tmp5[4] := array_tmp4[4];
array_tmp6[4] := 1/3*array_tmp6_g[3]*array_x[2];
array_tmp6_g[4] := -1/3*array_tmp6[3]*array_x[2];
array_tmp7[4] := array_const_2D0[1]*array_tmp6[4];
array_tmp10[4] :=
(array_tmp7[4] - array_tmp10[3]*array_tmp9[2])/array_tmp9[1];
array_tmp13[4] :=
(array_tmp10[4] - array_tmp13[3]*array_tmp12[2])/array_tmp12[1];
array_tmp14[4] := array_tmp5[4] - array_tmp13[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp14[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := -1/4*array_tmp1_g[4]*array_x[2];
array_tmp1_g[5] := 1/4*array_tmp1[4]*array_x[2];
array_tmp4[5] :=
(array_tmp1[5] - array_tmp4[4]*array_tmp3[2])/array_tmp3[1];
array_tmp5[5] := array_tmp4[5];
array_tmp6[5] := 1/4*array_tmp6_g[4]*array_x[2];
array_tmp6_g[5] := -1/4*array_tmp6[4]*array_x[2];
array_tmp7[5] := array_const_2D0[1]*array_tmp6[5];
array_tmp10[5] :=
(array_tmp7[5] - array_tmp10[4]*array_tmp9[2])/array_tmp9[1];
array_tmp13[5] :=
(array_tmp10[5] - array_tmp13[4]*array_tmp12[2])/array_tmp12[1];
array_tmp14[5] := array_tmp5[5] - array_tmp13[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp14[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := -array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp1_g[kkk] := array_tmp1[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp4[kkk] :=
-ats(kkk, array_tmp3, array_tmp4, 2)/array_tmp3[1];
array_tmp5[kkk] := array_tmp4[kkk];
array_tmp6[kkk] := array_tmp6_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp6_g[kkk] := -array_tmp6[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp7[kkk] := array_const_2D0[1]*array_tmp6[kkk];
array_tmp10[kkk] :=
-ats(kkk, array_tmp9, array_tmp10, 2)/array_tmp9[1];
array_tmp13[kkk] :=
-ats(kkk, array_tmp12, array_tmp13, 2)/array_tmp12[1];
array_tmp14[kkk] := array_tmp5[kkk] - array_tmp13[kkk];
order_d := 1;
if kkk + order_d + 1 <= glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp14[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 12
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " | \n")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" Unknown\n")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> display_pole := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6
> omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," ");
> omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," ");
> fi;# end if 6
> end;
display_pole := proc()
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if array_pole[1] <> glob_large_float and 0. < array_pole[1] and
array_pole[2] <> glob_large_float and 0. < array_pole[2] and
glob_display_flag then
omniout_float(ALWAYS, "Radius of convergence ", 4,
array_pole[1], 4, " ");
omniout_float(ALWAYS, "Order of pole ", 4,
array_pole[2], 4, " ")
end if
end proc
> # End Function number 16
> # Begin Function number 17
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 20
> # Begin Function number 21
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 21
> # Begin Function number 22
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> else
> fprintf(file,"No Pole");
> fi;# end if 8
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
else fprintf(file, "No Pole")
end if;
fprintf(file, " | ")
end proc
> # End Function number 23
> # Begin Function number 24
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 24
> # Begin Function number 25
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
> # End Function number 25
> # Begin Function number 26
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 8
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 8;
> if (glob_max_iter < 2) then # if number 8
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 8;
> if (errflag) then # if number 8
> quit;
> fi;# end if 8
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 26
> # Begin Function number 27
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 8
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 9
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 9
> fi;# end if 8;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 27
> # Begin Function number 28
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 8
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 8;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 28
> # Begin Function number 29
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 29
> # Begin Function number 30
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 8
> if (array_fact_1[nnn] = 0) then # if number 9
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 9;
> else
> ret := factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 8
> if (array_fact_2[mmm,nnn] = 0) then # if number 9
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 9;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 8;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 31
> # Begin Function number 32
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 33
> # Begin Function number 34
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 34
> # Begin Function number 35
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 35
> # Begin Function number 36
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 36
> # Begin Function number 37
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 37
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(sin(x)/(2*x+1));
> end;
exact_soln_y := proc(x) return sin(x)/(2*x + 1) 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_2D0,
> array_const_1D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_value3 := 0.0;
> glob_ratio_of_radius := 0.01;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_sec_in_minute := 60;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_disp_incr := 0.1;
> glob_h := 0.1;
> glob_max_h := 0.1;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.1e-200;
> glob_smallish_float := 0.1e-100;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/div_sin_lin_newpostode.ode#################");
> omniout_str(ALWAYS,"diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 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 := 1.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.001;");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_max_iter:=10000000;");
> omniout_str(ALWAYS,"glob_max_minutes:=3;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(sin(x)/(2*x+1));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1_g:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_tmp6_g:= Array(0..(max_terms + 1),[]);
> array_tmp6:= Array(0..(max_terms + 1),[]);
> array_tmp7:= Array(0..(max_terms + 1),[]);
> array_tmp8:= Array(0..(max_terms + 1),[]);
> array_tmp9:= Array(0..(max_terms + 1),[]);
> array_tmp10:= Array(0..(max_terms + 1),[]);
> array_tmp11:= Array(0..(max_terms + 1),[]);
> array_tmp12:= Array(0..(max_terms + 1),[]);
> array_tmp13:= Array(0..(max_terms + 1),[]);
> array_tmp14:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp6_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1_g[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_tmp6_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp6_g[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp7 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp8 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp9 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp10 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp11 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp12 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp13 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp14 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_0D0[1] := 0.0;
> array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_2D0[1] := 2.0;
> array_const_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 := 1.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.001;
> glob_look_poles:=true;
> glob_max_iter:=10000000;
> glob_max_minutes:=3;
> glob_subiter_method:=3;
> #END OVERRIDE BLOCK
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_terms := max_terms;
> glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours);
> if (glob_h > 0.0) then # if number 1
> glob_neg_h := false;
> glob_display_interval := omniabs(glob_display_interval);
> else
> glob_neg_h := true;
> glob_display_interval := -omniabs(glob_display_interval);
> fi;# end if 1;
> chk_data();
> #AFTER INITS AFTER SECOND INPUT BLOCK
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := check_sign(x_start,x_end);
> glob_h := check_sign(x_start,x_end);
> if (glob_display_interval < glob_h) then # if number 2
> glob_h := glob_display_interval;
> fi;# end if 2;
> if (glob_max_h < glob_h) then # if number 2
> glob_h := glob_max_h;
> fi;# end if 2;
> found_h := -1.0;
> best_h := 0.0;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 3
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 3;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 3
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 4
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 4;
> r_order := r_order + 1;
> od;# end do number 3
> ;
> atomall();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> value3 := test_suggested_h();
> omniout_float(ALWAYS,"value3",32,value3,32,"");
> if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 2
> best_h := glob_h;
> found_h := 1.0;
> fi;# end if 2;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> glob_h := glob_h * 0.5;
> od;# end do number 2;
> if (found_h > 0.0) then # if number 2
> glob_h := best_h ;
> else
> omniout_str(ALWAYS,"No increment to obtain desired accuracy found");
> fi;# end if 2;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 2
> html_log_file := fopen("html/entry.html",WRITE,TEXT);
> fi;# end if 2;
> #BEGIN SOLUTION CODE
> if (found_h > 0.0) then # if number 2
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := x_start;
> array_x[2] := glob_h;
> glob_next_display := x_start;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1);
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := 0;
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2
> #left paren 0001C
> if (reached_interval()) then # if number 3
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 3;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> glob_current_iter := glob_current_iter + 1;
> atomall();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 3
> #left paren 0004C
> check_for_pole();
> fi;# end if 3;#was right paren 0004C
> if (reached_interval()) then # if number 3
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 3;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 3;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := glob_max_terms;
> while (iii >= calc_term) do # do number 3
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 3;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := glob_max_terms;
> while (term_no >= 1) do # do number 3
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 4
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 4;
> term_no := term_no - 1;
> od;# end do number 3;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 2;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 3
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 3;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 3
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 3;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ;");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 3
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-01-28T13:36:37-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"div_sin_lin_new")
> ;
> logitem_str(html_log_file,"diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 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 4
> logitem_float(html_log_file,array_pole[1])
> ;
> logitem_float(html_log_file,array_pole[2])
> ;
> 0;
> else
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> 0;
> fi;# end if 4;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 4
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 4;
> log_revs(html_log_file," 165 | ")
> ;
> logitem_str(html_log_file,"div_sin_lin_new diffeq.mxt")
> ;
> logitem_str(html_log_file,"div_sin_lin_new maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 3;
> if (glob_html_log) then # if number 3
> fclose(html_log_file);
> fi;# end if 3
> ;
> ;;
> fi;# end if 2
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, value3, min_value, est_answer, best_h,
found_h, repeat_it;
global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct,
glob_max_value3, glob_ratio_of_radius, glob_percent_done,
glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec,
glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump,
glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec,
glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h,
glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display,
glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter,
glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs,
glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt,
glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1,
array_const_0D0, array_const_2D0, array_const_1D0, array_y_init,
array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5,
array_tmp6_g, array_tmp6, array_tmp7, array_tmp8, array_tmp9, array_tmp10,
array_tmp11, array_tmp12, array_tmp13, array_tmp14, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_value3 := 0.;
glob_ratio_of_radius := 0.01;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_disp_incr := 0.1;
glob_h := 0.1;
glob_max_h := 0.1;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.1*10^(-200);
glob_smallish_float := 0.1*10^(-100);
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/div_sin_lin_newpostode.ode#################");
omniout_str(ALWAYS, "diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 \
) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 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 := 1.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.001;");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_max_iter:=10000000;");
omniout_str(ALWAYS, "glob_max_minutes:=3;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(sin(x)/(2*x+1));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1_g := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_tmp6_g := Array(0 .. max_terms + 1, []);
array_tmp6 := Array(0 .. max_terms + 1, []);
array_tmp7 := Array(0 .. max_terms + 1, []);
array_tmp8 := Array(0 .. max_terms + 1, []);
array_tmp9 := Array(0 .. max_terms + 1, []);
array_tmp10 := Array(0 .. max_terms + 1, []);
array_tmp11 := Array(0 .. max_terms + 1, []);
array_tmp12 := Array(0 .. max_terms + 1, []);
array_tmp13 := Array(0 .. max_terms + 1, []);
array_tmp14 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp10[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp11[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp12[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp13[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp14[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp6_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp6_g[term] := 0.; term := term + 1
end do;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_tmp7 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1
end do;
array_tmp8 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
end do;
array_tmp9 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1
end do;
array_tmp10 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp10[term] := 0.; term := term + 1
end do;
array_tmp11 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp11[term] := 0.; term := term + 1
end do;
array_tmp12 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp12[term] := 0.; term := term + 1
end do;
array_tmp13 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp13[term] := 0.; term := term + 1
end do;
array_tmp14 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp14[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_const_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 := 1.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_desired_digits_correct := 10;
glob_display_interval := 0.001;
glob_look_poles := true;
glob_max_iter := 10000000;
glob_max_minutes := 3;
glob_subiter_method := 3;
glob_last_good_h := glob_h;
glob_max_terms := max_terms;
glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes)
+ convfloat(3600.0)*convfloat(glob_max_hours);
if 0. < glob_h then
glob_neg_h := false;
glob_display_interval := omniabs(glob_display_interval)
else
glob_neg_h := true;
glob_display_interval := -omniabs(glob_display_interval)
end if;
chk_data();
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := check_sign(x_start, x_end);
glob_h := check_sign(x_start, x_end);
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
found_h := -1.0;
best_h := 0.;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
while opt_iter <= 20 and found_h < 0. do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
value3 := test_suggested_h();
omniout_float(ALWAYS, "value3", 32, value3, 32, "");
if value3 < est_needed_step_err and found_h < 0. then
best_h := glob_h; found_h := 1.0
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1;
glob_h := glob_h*0.5
end do;
if 0. < found_h then glob_h := best_h
else omniout_str(ALWAYS,
"No increment to obtain desired accuracy found")
end if;
if glob_html_log then
html_log_file := fopen("html/entry.html", WRITE, TEXT)
end if;
if 0. < found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.\
0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 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, "2013-01-28T13:36:37-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"div_sin_lin_new");
logitem_str(html_log_file, "diff( y , x , 1 ) = cos ( x ) / (\
2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) /\
( 2.0 * x + 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, "div_sin_lin_new diffeq.mxt");
logitem_str(html_log_file, "div_sin_lin_new maple results");
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/div_sin_lin_newpostode.ode#################
diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 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 := 1.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.001;
glob_look_poles:=true;
glob_max_iter:=10000000;
glob_max_minutes:=3;
glob_subiter_method:=3;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(sin(x)/(2*x+1));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
opt_iter = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 0.9
estimated_steps = 900
step_error = 1.1111111111111111111111111111111e-13
est_needed_step_err = 1.1111111111111111111111111111111e-13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
value3 = 4.5004387586644603261302416132434e-74
max_value3 = 4.5004387586644603261302416132434e-74
value3 = 4.5004387586644603261302416132434e-74
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 0.083194513872356793589011832008852
y[1] (numeric) = 0.083194513872356793589011832008852
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.101
y[1] (analytic) = 0.083883835881504155681990116075865
y[1] (numeric) = 0.083883835881504157105222037934532
absolute error = 1.423231921858667e-18
relative error = 1.6966700519861186407733767791954e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.102
y[1] (analytic) = 0.08457078403982185278126436551549
y[1] (numeric) = 0.084570784039821855611242761471728
absolute error = 2.829978395956238e-18
relative error = 3.3462837409946274295124586992577e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.103
y[1] (analytic) = 0.085255369332593306542623723469809
y[1] (numeric) = 0.085255369332593310763081052136671
absolute error = 4.220457328666862e-18
relative error = 4.9503712923959761789118608860927e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.104
y[1] (analytic) = 0.085937602672436008020671154527699
y[1] (numeric) = 0.08593760267243601361555454598075
absolute error = 5.594883391453051e-18
relative error = 6.5104019864026038061148749567406e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.105
y[1] (analytic) = 0.086617494899902884658308760352711
y[1] (numeric) = 0.086617494899902891611776834489678
absolute error = 6.953468074136967e-18
relative error = 8.0277870910172942589496278226601e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.106
y[1] (analytic) = 0.087295056784077713062781037969241
y[1] (numeric) = 0.087295056784077721359200775177556
absolute error = 8.296419737208315e-18
relative error = 9.5038826284623603822207313639143e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.107
y[1] (analytic) = 0.087970299023164646232191682385881
y[1] (numeric) = 0.087970299023164655856135345573776
absolute error = 9.623943663187895e-18
relative error = 1.0939991985992550234045134604754e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.108
y[1] (analytic) = 0.088643232245071922992937046900979
y[1] (numeric) = 0.088643232245071933929179153966174
absolute error = 1.0936242107065195e-17
relative error = 1.2337368381186472376710863242157e-14 %
Correct digits = 15
h = 0.001
memory used=3.8MB, alloc=3.0MB, time=0.18
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.109
y[1] (analytic) = 0.089313867007989826518378697089852
y[1] (numeric) = 0.089313867007989838751893042918315
absolute error = 1.2233514345828463e-17
relative error = 1.3697217191070765202214234337020e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.5278
Order of pole = 1.901e-27
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 0.089982213800962957922089745970041
y[1] (numeric) = 0.089982213800962971438046473074783
absolute error = 1.3515956727104742e-17
relative error = 1.5020698153750134781830934310451e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.111
y[1] (analytic) = 0.090648283044456890054939896625966
y[1] (numeric) = 0.09064828304445690483870261355354
absolute error = 1.4783762716927574e-17
relative error = 1.6308927450591791191621903261810e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.3119
Order of pole = 2.372e-27
TOP MAIN SOLVE Loop
x[1] = 0.112
y[1] (analytic) = 0.091312085090919265783921266425825
y[1] (numeric) = 0.091312085090919281821044213075059
absolute error = 1.6037122946649234e-17
relative error = 1.7562979676437244674025290578446e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.113
y[1] (analytic) = 0.091973630225335404191753833356607
y[1] (numeric) = 0.091973630225335421467979092370825
absolute error = 1.7276225259014218e-17
relative error = 1.8783889704785452320179670106195e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.114
y[1] (analytic) = 0.0926329286657784773097421530893
y[1] (numeric) = 0.092632928665778495810996906499644
absolute error = 1.8501254753410344e-17
relative error = 1.9972654454403847943933794031994e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.115
y[1] (analytic) = 0.093289990563954319181883909528211
y[1] (numeric) = 0.093289990563954338894277739841628
absolute error = 1.9712393830313417e-17
relative error = 2.1130234563374426909668047541952e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.035
Order of pole = 4.648e-26
TOP MAIN SOLVE Loop
x[1] = 0.116
y[1] (analytic) = 0.093944826005740928255659516437362
y[1] (numeric) = 0.093944826005740949165481751378576
absolute error = 2.0909822234941214e-17
relative error = 2.2257555976167781374085413211230e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.117
y[1] (analytic) = 0.094597445011722723304067518756831
y[1] (numeric) = 0.094597445011722745397784618888719
absolute error = 2.2093717100131888e-17
relative error = 2.3355511448955081203925946710541e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.118
y[1] (analytic) = 0.095247857537719612304123517767832
y[1] (numeric) = 0.095247857537719635568376506229898
absolute error = 2.3264252988462066e-17
relative error = 2.4424961978015164316386960344700e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.6072
Order of pole = 6.399e-27
TOP MAIN SOLVE Loop
x[1] = 0.119
y[1] (analytic) = 0.09589607347531093292902469899933
y[1] (numeric) = 0.095896073475310957350626632618479
absolute error = 2.4421601933619149e-17
relative error = 2.5466738155766772936815725823452e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 0.096542102652354322554315011508847
y[1] (numeric) = 0.096542102652354348120248492551061
absolute error = 2.5565933481042214e-17
relative error = 2.6481641458654050500303737569269e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.121
y[1] (analytic) = 0.097185954833499574932488105104895
y[1] (numeric) = 0.097185954833499601629902832950599
absolute error = 2.6697414727845704e-17
relative error = 2.7470445470833838569449063432502e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.122
y[1] (analytic) = 0.097827639720697539955359926308031
y[1] (numeric) = 0.097827639720697567771570288347564
absolute error = 2.7816210362039533e-17
relative error = 2.8433897047354006433989430261354e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.123
y[1] (analytic) = 0.09846716695370412219905716622801
y[1] (numeric) = 0.098467166953704151121539867287312
absolute error = 2.8922482701059302e-17
relative error = 2.9372717420272342519720844634148e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.124
y[1] (analytic) = 0.099104546110579433232431359802035
y[1] (numeric) = 0.099104546110579463248823089421659
absolute error = 3.0016391729619624e-17
relative error = 3.0287603250942458265658544468749e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.1693
Order of pole = 2.404e-27
TOP MAIN SOLVE Loop
x[1] = 0.125
y[1] (analytic) = 0.099739786708182151965954166969688
y[1] (numeric) = 0.099739786708182183064049303873423
absolute error = 3.1098095136903735e-17
relative error = 3.1179227631487007394393155418986e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
memory used=7.6MB, alloc=4.3MB, time=0.38
TOP MAIN SOLVE Loop
x[1] = 0.126
y[1] (analytic) = 0.10037289820265914662451297115954
y[1] (numeric) = 0.1003728982026591787922613242614
absolute error = 3.216774835310186e-17
relative error = 3.2048241038286219656268360306136e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.127
y[1] (analytic) = 0.1010038899899304112438460393329
y[1] (numeric) = 0.10100388998993044446935062464385
absolute error = 3.322550458531095e-17
relative error = 3.2895272240131908419367370653101e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.128
y[1] (analytic) = 0.10163277140616936891647455771475
y[1] (numeric) = 0.10163277140616940318798941052245
absolute error = 3.427151485280770e-17
relative error = 3.3720929163530939074479197136078e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.129
y[1] (analytic) = 0.1022595517282785933487491177933
y[1] (numeric) = 0.10225955172827862865467713950046
absolute error = 3.530592802170716e-17
relative error = 3.4525799717488639740915093235840e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 0.10288424017436099963587762754628
y[1] (numeric) = 0.10288424017436103596476846656433
absolute error = 3.632889083901805e-17
relative error = 3.5310452579958205363262955730490e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.131
y[1] (analytic) = 0.10350684590418655451638978058449
y[1] (numeric) = 0.10350684590418659185693774669123
absolute error = 3.734054796610674e-17
relative error = 3.6075437948009603221114296529194e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.132
y[1] (analytic) = 0.10412737801965455573127236584663
y[1] (numeric) = 0.1041273780196545940723143774274
absolute error = 3.834104201158077e-17
relative error = 3.6821288253646134621016458532061e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.133
y[1] (analytic) = 0.10474584556525152948583464528187
y[1] (numeric) = 0.10474584556525156881634820888484
absolute error = 3.933051356360297e-17
relative error = 3.7548518847081135216004986137313e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.134
y[1] (analytic) = 0.10536225752850479439409108846708
y[1] (numeric) = 0.105362257528504834703192310114
absolute error = 4.030910122164692e-17
relative error = 3.8257628649178916476326128454251e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.135
y[1] (analytic) = 0.10597662284043173967593972476107
y[1] (numeric) = 0.1059766228404317809528813524653
absolute error = 4.127694162770423e-17
relative error = 3.8949100774662948561773619695523e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.136
y[1] (analytic) = 0.10658895037598486477653047379259
y[1] (numeric) = 0.10658895037598490701069997074662
absolute error = 4.223416949695403e-17
relative error = 3.9623403127600029206436017696694e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.137
y[1] (analytic) = 0.10719924895449262698482364148045
y[1] (numeric) = 0.10719924895449267016574128938511
absolute error = 4.318091764790466e-17
relative error = 4.0280988970580829260328368102081e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.138
y[1] (analytic) = 0.10780752734009614304430125358334
y[1] (numeric) = 0.10780752734009618716161828560086
absolute error = 4.411731703201752e-17
relative error = 4.0922297468934951696866690325066e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.139
y[1] (analytic) = 0.10841379424218179017298226484784
y[1] (numeric) = 0.10841379424218183521647902767064
absolute error = 4.504349676282280e-17
relative error = 4.1547754211241518837118330375063e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 0.10901805831580975134217839976982
y[1] (numeric) = 0.10901805831580979730176254430627
absolute error = 4.595958414453645e-17
relative error = 4.2157771707324025162598987742089e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.141
y[1] (analytic) = 0.10962032816213854910368412706527
y[1] (numeric) = 0.10962032816213859596938882725316
absolute error = 4.686570470018789e-17
relative error = 4.2752749864850980620312815991742e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.142
y[1] (analytic) = 0.11022061232884561170319788484446
y[1] (numeric) = 0.11022061232884565946518008411181
absolute error = 4.776198219926735e-17
relative error = 4.3333076445600238268184844451814e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.143
y[1] (analytic) = 0.11081891931054391467360012191315
memory used=11.4MB, alloc=4.4MB, time=0.60
y[1] (numeric) = 0.11081891931054396332213880681515
absolute error = 4.864853868490200e-17
relative error = 4.3899127502386060043173051865502e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.144
y[1] (analytic) = 0.1114152575491947405651470517554
y[1] (numeric) = 0.11141525754919479009064155232485
absolute error = 4.952549450056945e-17
relative error = 4.4451267797592052532891048669696e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.145
y[1] (analytic) = 0.11200963543451659894055932442552
y[1] (numeric) = 0.11200963543451664933352764078275
absolute error = 5.039296831635723e-17
relative error = 4.4989851204201190977085776009004e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.146
y[1] (analytic) = 0.11260206130439034824127621030696
y[1] (numeric) = 0.11260206130439039949235336508376
absolute error = 5.125107715477680e-17
relative error = 4.5515221090165356760973385931761e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.147
y[1] (analytic) = 0.1131925434452605606166944314349
y[1] (numeric) = 0.11319254344526061271663084757492
absolute error = 5.209993641614002e-17
relative error = 4.6027710686910512608972903926430e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.148
y[1] (analytic) = 0.1137810900925331703009044777236
y[1] (numeric) = 0.11378109009253322324056438123011
absolute error = 5.293965990350651e-17
relative error = 4.6527643442731130854995313847473e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.149
y[1] (analytic) = 0.11436770943096944562116601207703
y[1] (numeric) = 0.11436770943096949939152585928659
absolute error = 5.377035984720956e-17
relative error = 4.7015333361786444855484379085497e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 0.11495240959507632422901956822126
y[1] (numeric) = 0.1149524095950763788211664971897
absolute error = 5.459214692896844e-17
relative error = 4.7491085329373336652299281042846e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.151
y[1] (analytic) = 0.11553519866949315065840777521214
y[1] (numeric) = 0.11553519866949320606353808080674
absolute error = 5.540513030559460e-17
relative error = 4.7955195424114693818846392983031e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.152
y[1] (analytic) = 0.11611608468937485483537119511525
y[1] (numeric) = 0.11611608468937491104478882741475
absolute error = 5.620941763229950e-17
relative error = 4.8407951217668739641976578603561e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.153
y[1] (analytic) = 0.11669507564077160969068868965525
y[1] (numeric) = 0.11669507564077166669580377526616
absolute error = 5.700511508561091e-17
relative error = 4.8849632062532490171441933591943e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.154
y[1] (analytic) = 0.11727217946100500556014892183385
y[1] (numeric) = 0.11727217946100506335247630773915
absolute error = 5.779232738590530e-17
relative error = 4.9280509368483453390725472381752e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.155
y[1] (analytic) = 0.11784740403904077859686873189872
y[1] (numeric) = 0.1178474040390408371680265514617
absolute error = 5.857115781956298e-17
relative error = 4.9700846868174866553214089681741e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.156
y[1] (analytic) = 0.11842075721585812996611795294825
y[1] (numeric) = 0.11842075721585818930782621370135
absolute error = 5.934170826075310e-17
relative error = 5.0110900872373790405442897508521e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.157
y[1] (analytic) = 0.11899224678481567214537263584068
y[1] (numeric) = 0.11899224678481573224945182869576
absolute error = 6.010407919285508e-17
relative error = 5.0510920515306064271604548324572e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.158
y[1] (analytic) = 0.11956188049201403821070512866614
y[1] (numeric) = 0.1195618804920140990690748581894
absolute error = 6.085836972952326e-17
relative error = 5.0901147990548882533541004304064e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.159
y[1] (analytic) = 0.12012966603665518955503707307856
y[1] (numeric) = 0.12012966603665525115971470847955
absolute error = 6.160467763540099e-17
relative error = 5.1281818777889170290121449645400e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 0.12069561107139845705413875733787
y[1] (numeric) = 0.12069561107139851939723810382864
absolute error = 6.234309934649077e-17
relative error = 5.1653161861545412294387174782984e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.4MB, time=0.82
x[1] = 0.161
y[1] (analytic) = 0.12125972320271335027246554376364
y[1] (numeric) = 0.12125972320271341334619553395017
absolute error = 6.307372999018653e-17
relative error = 5.2015399940130467000769491848820e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.162
y[1] (analytic) = 0.1218220099912291688828908993737
y[1] (numeric) = 0.12182200999122923267955430434786
absolute error = 6.379666340497416e-17
relative error = 5.2368749628714330512258197924528e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.163
y[1] (analytic) = 0.12238247895208145006203900182272
y[1] (numeric) = 0.122382478952081514574031161629
absolute error = 6.451199215980628e-17
relative error = 5.2713421653328159236713941729844e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.164
y[1] (analytic) = 0.12294113755525528521615250703577
y[1] (numeric) = 0.12294113755525535043596008019294
absolute error = 6.521980757315717e-17
relative error = 5.3049621038234212359744630755510e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.165
y[1] (analytic) = 0.12349799322592553899116880246834
y[1] (numeric) = 0.12349799322592560491136853423188
absolute error = 6.592019973176354e-17
relative error = 5.3377547286270497200085982645185e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.166
y[1] (analytic) = 0.12405305334479400312483827120735
y[1] (numeric) = 0.12405305334479406973809578026414
absolute error = 6.661325750905679e-17
relative error = 5.3697394552564049954075353535727e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.167
y[1] (analytic) = 0.12460632524842351730821946085013
y[1] (numeric) = 0.12460632524842358460728804414251
absolute error = 6.729906858329238e-17
relative error = 5.4009351811892733818709053025076e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.386
Order of pole = 8.74e-28
TOP MAIN SOLVE Loop
x[1] = 0.168
y[1] (analytic) = 0.12515781622956908883864862966343
y[1] (numeric) = 0.125157816229569156816368085045
absolute error = 6.797771945538157e-17
relative error = 5.4313603019961874719540311258630e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.169
y[1] (analytic) = 0.12570753353750604246622628803421
y[1] (numeric) = 0.12570753353750611111552175446527
absolute error = 6.864929546643106e-17
relative error = 5.4610327268849712546145909534269e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 0.12625548437835523146091371393347
y[1] (numeric) = 0.12625548437835530077479452892902
absolute error = 6.931388081499555e-17
relative error = 5.4899698936863342123092186987825e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.171
y[1] (analytic) = 0.12680167591540534055741191333867
y[1] (numeric) = 0.12680167591540541052897048738706
absolute error = 6.997155857404839e-17
relative error = 5.5181887833035676978234484717625e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.172
y[1] (analytic) = 0.12734611526943231107002928203328
y[1] (numeric) = 0.12734611526943238169243998970876
absolute error = 7.062241070767548e-17
relative error = 5.5457059336483286811094028055745e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.173
y[1] (analytic) = 0.1278888095190159181096586888677
y[1] (numeric) = 0.12788880951901598937617677636484
absolute error = 7.126651808749714e-17
relative error = 5.5725374530834496831339971375456e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.174
y[1] (analytic) = 0.1284297657008535294797074288009
y[1] (numeric) = 0.12842976570085360138366793762376
absolute error = 7.190396050882286e-17
relative error = 5.5986990333927701413457439979983e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.175
y[1] (analytic) = 0.12896899081007107547728325329734
y[1] (numeric) = 0.12896899081007114801209995984101
absolute error = 7.253481670654367e-17
relative error = 5.6242059622970616999968010949208e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.176
y[1] (analytic) = 0.12950649180053125848006640150585
y[1] (numeric) = 0.12950649180053133163923077227265
absolute error = 7.315916437076680e-17
relative error = 5.6490731355342518975734630500284e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.177
y[1] (analytic) = 0.13004227558513903085802229225235
y[1] (numeric) = 0.13004227558513910463510245444946
absolute error = 7.377708016219711e-17
relative error = 5.6733150685213175411859098886576e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.3595
Order of pole = 1.032e-26
TOP MAIN SOLVE Loop
x[1] = 0.178
y[1] (analytic) = 0.13057634903614436941236447682131
y[1] (numeric) = 0.13057634903614444380100420409113
absolute error = 7.438863972726982e-17
relative error = 5.6969459076144461857554726749074e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.4MB, time=1.04
x[1] = 0.179
y[1] (analytic) = 0.13110871898544237421189587702845
y[1] (numeric) = 0.13110871898544244920581359006731
absolute error = 7.499391771303886e-17
relative error = 5.7199794409833103488524210511786e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 0.13163939222487071936897260272001
y[1] (numeric) = 0.1316393922248707949619603845452
absolute error = 7.559298778182519e-17
relative error = 5.7424291091146010102209466533264e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.181
y[1] (analytic) = 0.13216837550650448297378417834862
y[1] (numeric) = 0.13216837550650455915970680397798
absolute error = 7.618592262562936e-17
relative error = 5.7643080149592952866478228672774e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.182
y[1] (analytic) = 0.13269567554294838308636327204946
y[1] (numeric) = 0.13269567554294845985915725236169
absolute error = 7.677279398031223e-17
relative error = 5.7856289337374743019285167785782e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 3.539
Order of pole = 1.165e-25
TOP MAIN SOLVE Loop
x[1] = 0.183
y[1] (analytic) = 0.13322129900762644637066449834928
y[1] (numeric) = 0.13322129900762652372433713789746
absolute error = 7.735367263954818e-17
relative error = 5.8064043224139374953003240920513e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.184
y[1] (analytic) = 0.13374525253506913564412404831044
y[1] (numeric) = 0.13374525253506921357275251686505
absolute error = 7.792862846855461e-17
relative error = 5.8266463288572478454363661107391e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.185
y[1] (analytic) = 0.13426754272119796230926926730033
y[1] (numeric) = 0.13426754272119804080699968490203
absolute error = 7.849773041760170e-17
relative error = 5.8463668006943120804780977203523e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.2734
Order of pole = 7.448e-27
TOP MAIN SOLVE Loop
x[1] = 0.186
y[1] (analytic) = 0.13478817612360760933113029990185
y[1] (numeric) = 0.13478817612360768839217683520811
absolute error = 7.906104653530626e-17
relative error = 5.8655772938720723793866934803816e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.187
y[1] (analytic) = 0.13530715926184559012535595646431
y[1] (numeric) = 0.13530715926184566974399993817766
absolute error = 7.961864398171335e-17
relative error = 5.8842890809373830185420012003983e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.188
y[1] (analytic) = 0.13582449861768946842699536603508
y[1] (numeric) = 0.13582449861768954859758440720465
absolute error = 8.017058904116957e-17
relative error = 5.9025131590456935420127258741610e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.6437
Order of pole = 1.026e-26
TOP MAIN SOLVE Loop
x[1] = 0.189
y[1] (analytic) = 0.13634020063542166391881902606604
y[1] (numeric) = 0.13634020063542174463576616105736
absolute error = 8.071694713499132e-17
relative error = 5.9202602577086697556135368022409e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.6013
Order of pole = 3.135e-27
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 0.13685427172210186811076170505892
y[1] (numeric) = 0.13685427172210194936854453899084
absolute error = 8.125778283393192e-17
relative error = 5.9375408462905031506811698718641e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.191
y[1] (analytic) = 0.13736671824783709467852035374461
y[1] (numeric) = 0.13736671824783717647168022419544
absolute error = 8.179315987045083e-17
relative error = 5.9543651412622069250756737282517e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.192
y[1] (analytic) = 0.13787754654604938818947866045287
y[1] (numeric) = 0.1378775465460494705126198112413
absolute error = 8.232314115078843e-17
relative error = 5.9707431132228280012187891370184e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.193
y[1] (analytic) = 0.13838676291374121486790293229276
y[1] (numeric) = 0.13838676291374129771569169914262
absolute error = 8.284778876684986e-17
relative error = 5.9866844936961400809367343137946e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.194
y[1] (analytic) = 0.13889437361175855877870922436448
y[1] (numeric) = 0.13889437361175864214587323226554
absolute error = 8.336716400790106e-17
relative error = 6.0021987817110065632187294899929e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.9334
Order of pole = 8.706e-27
TOP MAIN SOLVE Loop
x[1] = 0.195
y[1] (analytic) = 0.13940038486505174653998753209018
y[1] (numeric) = 0.13940038486505183042131490417042
absolute error = 8.388132737208024e-17
relative error = 6.0172952501732752356753697525068e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.196
y[1] (analytic) = 0.13990480286293402340883467912272
y[1] (numeric) = 0.13990480286293410779917325685083
absolute error = 8.439033857772811e-17
relative error = 6.0319829520367555508596672325759e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.4MB, time=1.26
x[1] = 0.197
y[1] (analytic) = 0.14040763375933790332284334798641
y[1] (numeric) = 0.1404076337593379882170999225262
absolute error = 8.489425657453979e-17
relative error = 6.0462707262804961877242297141308e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.198
y[1] (analytic) = 0.14090888367306931522077137225898
y[1] (numeric) = 0.14090888367306940061391092680052
absolute error = 8.539313955454154e-17
relative error = 6.0601672036993069491774381325756e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.199
y[1] (analytic) = 0.14140855868805956771042457066724
y[1] (numeric) = 0.14140855868805965359746953356262
absolute error = 8.588704496289538e-17
relative error = 6.0736808125141874774678623007838e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 0.14190666485361515389958044794171
y[1] (numeric) = 0.14190666485361524027560995647608
absolute error = 8.637602950853437e-17
relative error = 6.0868197838090400989543045384295e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.201
y[1] (analytic) = 0.14240320818466541795681215470063
y[1] (numeric) = 0.14240320818466550481696132933224
absolute error = 8.686014917463161e-17
relative error = 6.0995921567998128595422461158879e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.202
y[1] (analytic) = 0.14289819466200810472329606332962
y[1] (numeric) = 0.1428981946620081920627552922353
absolute error = 8.733945922890568e-17
relative error = 6.1120057839419540523707642460606e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.9469
Order of pole = 1.430e-26
TOP MAIN SOLVE Loop
x[1] = 0.203
y[1] (analytic) = 0.14339163023255281345405677484399
y[1] (numeric) = 0.14339163023255290126807100860936
absolute error = 8.781401423376537e-17
relative error = 6.1240683358818389797631479056924e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.204
y[1] (analytic) = 0.14388352080956237652757562856007
y[1] (numeric) = 0.14388352080956246481144368485648
absolute error = 8.828386805629641e-17
relative error = 6.1357873062576002205003439770160e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.205
y[1] (analytic) = 0.14437387227289218372621884491251
y[1] (numeric) = 0.14437387227289227247529272300531
absolute error = 8.874907387809280e-17
relative error = 6.1471700163545752274391003061038e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.206
y[1] (analytic) = 0.14486269046922747245648598029798
y[1] (numeric) = 0.14486269046922756166617018523353
absolute error = 8.920968420493555e-17
relative error = 6.1582236196203991251556061327843e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.207
y[1] (analytic) = 0.14534998121231860404759577363673
y[1] (numeric) = 0.14534998121231869371334664995797
absolute error = 8.966575087632124e-17
relative error = 6.1689551060445509342882734399709e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.208
y[1] (analytic) = 0.14583575028321434603937274210663
y[1] (numeric) = 0.1458357502832144361566978169497
absolute error = 9.011732507484307e-17
relative error = 6.1793713064069962030673423196680e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.209
y[1] (analytic) = 0.14632000343049318014573271414467
y[1] (numeric) = 0.1463200034304932707101900495714
absolute error = 9.056445733542673e-17
relative error = 6.1894788964003701287766140311818e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 0.14680274637049265535824818748425
y[1] (numeric) = 0.14680274637049274636544574190799
absolute error = 9.100719755442374e-17
relative error = 6.1992844006299995307282971463397e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.211
y[1] (analytic) = 0.1472839847875368054352649142871
y[1] (numeric) = 0.14728398478753689688085991285154
absolute error = 9.144559499856444e-17
relative error = 6.2087941964958691834859024031801e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.212
y[1] (analytic) = 0.14776372433416164980580000873602
y[1] (numeric) = 0.14776372433416174168549832250923
absolute error = 9.187969831377321e-17
relative error = 6.2180145179605118111526419258896e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.213
y[1] (analytic) = 0.14824197063133879670394031758548
y[1] (numeric) = 0.14824197063133888901349585143351
absolute error = 9.230955553384803e-17
relative error = 6.2269514592066218400271263563665e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.214
y[1] (analytic) = 0.14871872926869716713863956210221
y[1] (numeric) = 0.14871872926869725987385365110899
absolute error = 9.273521408900678e-17
relative error = 6.2356109781880720267738697374033e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.4MB, time=1.48
x[1] = 0.215
y[1] (analytic) = 0.14919400580474285809564620969025
y[1] (numeric) = 0.1491940058047429512523670239927
absolute error = 9.315672081430245e-17
relative error = 6.2439989000778615682665696314156e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.216
y[1] (analytic) = 0.14966780576707716316274410268667
y[1] (numeric) = 0.14966780576707725673686606059621
absolute error = 9.357412195790954e-17
relative error = 6.2521209206164025754445045281974e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.217
y[1] (analytic) = 0.15014013465261276856651806634236
y[1] (numeric) = 0.15014013465261286255398125562598
absolute error = 9.398746318928362e-17
relative error = 6.2599826093634072427635560668640e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.218
y[1] (analytic) = 0.15061099792778814240843110297295
y[1] (numeric) = 0.15061099792778823680522071016931
absolute error = 9.439678960719636e-17
relative error = 6.2675894128565423497401003454996e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.219
y[1] (analytic) = 0.15108040102878013469008296955393
y[1] (numeric) = 0.15108040102878022949222871720192
absolute error = 9.480214574764799e-17
relative error = 6.2749466576798805956233004969964e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 4.422
Order of pole = 8.480e-26
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 0.15154834936171480552207708712292
y[1] (numeric) = 0.15154834936171490072565267878212
absolute error = 9.520357559165920e-17
relative error = 6.2820595534450728351221368200962e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.476
Order of pole = 3.065e-27
TOP MAIN SOLVE Loop
x[1] = 0.221
y[1] (analytic) = 0.15201484830287649871791952933045
y[1] (numeric) = 0.1520148483028765943190421022751
absolute error = 9.560112257294465e-17
relative error = 6.2889331956880714245696595816314e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.222
y[1] (analytic) = 0.15247990319891517778377649421193
y[1] (numeric) = 0.15247990319891527377860607968176
absolute error = 9.599482958546983e-17
relative error = 6.2955725686841062802193318895496e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.223
y[1] (analytic) = 0.1529435193670520411266919016964
y[1] (numeric) = 0.15294351936705213751143089258974
absolute error = 9.638473899089334e-17
relative error = 6.3019825481835411577292152010775e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.224
y[1] (analytic) = 0.15340570209528343311798180905613
y[1] (numeric) = 0.15340570209528352988887443495256
absolute error = 9.677089262589643e-17
relative error = 6.3081679040711303248391573170259e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.225
y[1] (analytic) = 0.15386645664258306746494492417738
y[1] (numeric) = 0.15386645664258316461827673357911
absolute error = 9.715333180940173e-17
relative error = 6.3141333029511133590228996819678e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.226
y[1] (analytic) = 0.15432578823910257916272683792554
y[1] (numeric) = 0.15432578823910267669482418760843
absolute error = 9.753209734968289e-17
relative error = 6.3198833106604872830042161847559e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.227
y[1] (analytic) = 0.15478370208637042111911838863584
y[1] (numeric) = 0.1547837020863705190263479400028
absolute error = 9.790722955136696e-17
relative error = 6.3254223947127211365726346193696e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.228
y[1] (analytic) = 0.15524020335748912136822498352081
y[1] (numeric) = 0.15524020335748921964699320585221
absolute error = 9.827876822233140e-17
relative error = 6.3307549266741037672162349739147e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.229
y[1] (analytic) = 0.15569529719733091661428336839079
y[1] (numeric) = 0.15569529719733101526103604888796
absolute error = 9.864675268049717e-17
relative error = 6.3358851844748121645879094458289e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 0.15614898872273177767439535093155
y[1] (numeric) = 0.15614898872273187668561711145153
absolute error = 9.901122176051998e-17
relative error = 6.3408173546567564136904010353931e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.231
y[1] (analytic) = 0.15660128302268384221856488632105
y[1] (numeric) = 0.15660128302268394159077870670198
absolute error = 9.937221382038093e-17
relative error = 6.3455555345601333257588749900887e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.232
y[1] (analytic) = 0.15705218515852627003713671230632
y[1] (numeric) = 0.15705218515852636976690346018497
absolute error = 9.972976674787865e-17
relative error = 6.3501037344506110540814962547265e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 2.744
Order of pole = 3.595e-26
TOP MAIN SOLVE Loop
memory used=30.5MB, alloc=4.5MB, time=1.70
x[1] = 0.233
y[1] (analytic) = 0.15750170016413453589951279453848
y[1] (numeric) = 0.15750170016413463598343076156259
absolute error = 1.0008391796702411e-16
relative error = 6.3544658795889427984864894885601e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.234
y[1] (analytic) = 0.1579498330461081749038390608141
y[1] (numeric) = 0.1579498330461082753385435051541
absolute error = 1.0043470444434000e-16
relative error = 6.3586458122447932359476016913171e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.235
y[1] (analytic) = 0.15839658878395699505518153504313
y[1] (numeric) = 0.15839658878395709583734423010924
absolute error = 1.0078216269506611e-16
relative error = 6.3626472936564722408609509641189e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.236
y[1] (analytic) = 0.15884197233028577164952071284472
y[1] (numeric) = 0.15884197233028587277584950211691
absolute error = 1.0112632878927219e-16
relative error = 6.3664740059382171373576288751820e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.237
y[1] (analytic) = 0.15928598861097743788265894294265
y[1] (numeric) = 0.1592859886109775393498973008226
absolute error = 1.0146723835787995e-16
relative error = 6.3701295539366216327527681587192e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.238
y[1] (analytic) = 0.15972864252537478594683118533696
y[1] (numeric) = 0.15972864252537488775175778393243
absolute error = 1.0180492659859547e-16
relative error = 6.3736174670377325786571633057571e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.239
y[1] (analytic) = 0.16016993894646069272340869646172
y[1] (numeric) = 0.16016993894646079486283697821539
absolute error = 1.0213942828175367e-16
relative error = 6.3769412009263093647126183946758e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.7205
Order of pole = 2.140e-27
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 0.16060988272103688402756221924988
y[1] (numeric) = 0.16060988272103698649833997532596
absolute error = 1.0247077775607608e-16
relative error = 6.3801041392986665143601669666016e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.241
y[1] (analytic) = 0.16104847866990125121008079012902
y[1] (numeric) = 0.16104847866990135400908974447247
absolute error = 1.0279900895434345e-16
relative error = 6.3831095955304923486644217753775e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.242
y[1] (analytic) = 0.1614857315880237337726993490737
y[1] (numeric) = 0.16148573158802383689685474805819
absolute error = 1.0312415539898449e-16
relative error = 6.3859608143009760921142468516349e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.243
y[1] (analytic) = 0.16192164624472078150624835617049
y[1] (numeric) = 0.16192164624472088495249856375264
absolute error = 1.0344625020758215e-16
relative error = 6.3886609731745401962271144283157e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.244
y[1] (analytic) = 0.16235622738382840951567734560296
y[1] (numeric) = 0.16235622738382851328100344390168
absolute error = 1.0376532609829872e-16
relative error = 6.3912131841414250693037411781917e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.245
y[1] (analytic) = 0.16278947972387385935249791023181
y[1] (numeric) = 0.16278947972387396343391330545289
absolute error = 1.0408141539522108e-16
relative error = 6.3936204951183365908030282903604e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.246
y[1] (analytic) = 0.16322140795824587933341648377509
y[1] (numeric) = 0.16322140795824598372796651740239
absolute error = 1.0439455003362730e-16
relative error = 6.3958858914103203378789968010558e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.247
y[1] (analytic) = 0.16365201675536363698386029612297
y[1] (numeric) = 0.16365201675536374168862186129902
absolute error = 1.0470476156517605e-16
relative error = 6.3980122971350054237562197032399e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.248
y[1] (analytic) = 0.16408131075884427640671818452614
y[1] (numeric) = 0.16408131075884438141879934754595
absolute error = 1.0501208116301981e-16
relative error = 6.4000025766102962960926369013299e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.249
y[1] (analytic) = 0.164509294587669133239899048625
y[1] (numeric) = 0.16450929458766923855643867546823
absolute error = 1.0531653962684323e-16
relative error = 6.4018595357065787148033857116203e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 0.16493597283634861973123246989959
y[1] (numeric) = 0.16493597283634872534939985772749
absolute error = 1.0561816738782790e-16
relative error = 6.4035859231644674324352216034627e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.5MB, time=1.92
x[1] = 0.251
y[1] (analytic) = 0.16536135007508579232577653021266
y[1] (numeric) = 0.16536135007508589824277104375716
absolute error = 1.0591699451354450e-16
relative error = 6.4051844318790736283879573358373e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.252
y[1] (analytic) = 0.16578543084993861402873563334059
y[1] (numeric) = 0.16578543084993872024178634611431
absolute error = 1.0621305071277372e-16
relative error = 6.4066577001517650482100981893309e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.253
y[1] (analytic) = 0.16620821968298092367690494585247
y[1] (numeric) = 0.16620821968298103018327028610926
absolute error = 1.0650636534025679e-16
relative error = 6.4080083129103288419161646346853e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.254
y[1] (analytic) = 0.16662972107246212412282702697427
y[1] (numeric) = 0.16662972107246223091979442835142
absolute error = 1.0679696740137715e-16
relative error = 6.4092388028984603672926539805465e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.255
y[1] (analytic) = 0.1670499394929656012086497132735
y[1] (numeric) = 0.16704993949296570829353527004741
absolute error = 1.0708488555677391e-16
relative error = 6.4103516518354205684211061715070e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.256
y[1] (analytic) = 0.16746887939556588528099206493016
y[1] (numeric) = 0.16746887939556599265114019181863
absolute error = 1.0737014812688847e-16
relative error = 6.4113492915467215950233940300975e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.257
y[1] (analytic) = 0.16788654520798456687393716279158
y[1] (numeric) = 0.16788654520798467452672025923687
absolute error = 1.0765278309644529e-16
relative error = 6.4122341050666518091930734619294e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.258
y[1] (analytic) = 0.16830294133474497806455705639195
y[1] (numeric) = 0.16830294133474508599737517525969
absolute error = 1.0793281811886774e-16
relative error = 6.4130084277134232285177393564097e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.259
y[1] (analytic) = 0.16871807215732565088411677539791
y[1] (numeric) = 0.16871807215732575909439729602817
absolute error = 1.0821028052063026e-16
relative error = 6.4136745481377186265816258711442e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 0.1691319420343125640482818844508
y[1] (numeric) = 0.16913194203431267253347918999839
absolute error = 1.0848519730554759e-16
relative error = 6.4142347093453645835561590166479e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 4.572
Order of pole = 9.488e-26
TOP MAIN SOLVE Loop
x[1] = 0.261
y[1] (analytic) = 0.16954455530155018915124871479282
y[1] (numeric) = 0.1695445553015502979088438737951
absolute error = 1.0875759515900228e-16
relative error = 6.4146911096948615219443702547367e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.262
y[1] (analytic) = 0.16995591627229134735170954846157
y[1] (numeric) = 0.1699559162722914563792100005729
absolute error = 1.0902750045211133e-16
relative error = 6.4150459038704590166313910640370e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.6073
Order of pole = 1.076e-27
TOP MAIN SOLVE Loop
x[1] = 0.263
y[1] (analytic) = 0.17036602923734588746293833339402
y[1] (numeric) = 0.17036602923734599675787757922688
absolute error = 1.0929493924583286e-16
relative error = 6.4153012038314471861909073526477e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.264
y[1] (analytic) = 0.17077489846522819624501790557314
y[1] (numeric) = 0.17077489846522830580495520058712
absolute error = 1.0955993729501398e-16
relative error = 6.4154590797383310060569543832700e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.265
y[1] (analytic) = 0.17118252820230355158430938221292
y[1] (numeric) = 0.17118252820230366140682943459339
absolute error = 1.0982252005238047e-16
relative error = 6.4155215608565022650735567507120e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.266
y[1] (analytic) = 0.1715889226729333291336708184291
y[1] (numeric) = 0.17158892267293343921638349089851
absolute error = 1.1008271267246941e-16
relative error = 6.4154906364380366466540270772621e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.267
y[1] (analytic) = 0.17199408607961907287664809109444
y[1] (numeric) = 0.17199408607961918321718810660002
absolute error = 1.1034054001550558e-16
relative error = 6.4153682565822067117391843002003e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.268
y[1] (analytic) = 0.17239802260314543996986923759083
y[1] (numeric) = 0.17239802260314555056589588881332
absolute error = 1.1059602665122249e-16
relative error = 6.4151563330752867397272874600069e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 1.474
Order of pole = 9.226e-27
TOP MAIN SOLVE Loop
memory used=38.1MB, alloc=4.5MB, time=2.14
x[1] = 0.269
y[1] (analytic) = 0.17280073640272203011015732779846
y[1] (numeric) = 0.17280073640272214095935419042734
absolute error = 1.1084919686262888e-16
relative error = 6.4148567402102076157633905306214e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 0.17320223161612410956641981884451
y[1] (numeric) = 0.17320223161612422066649446856616
absolute error = 1.1110007464972165e-16
relative error = 6.4144713155866108465130446229907e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.271
y[1] (analytic) = 0.17360251235983223991115790416149
y[1] (numeric) = 0.17360251235983235125984163730736
absolute error = 1.1134868373314587e-16
relative error = 6.4140018608918173004372330231411e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.272
y[1] (analytic) = 0.17400158272917082138245152424622
y[1] (numeric) = 0.17400158272917093297749908204907
absolute error = 1.1159504755780285e-16
relative error = 6.4134501426632304502774655423552e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.273
y[1] (analytic) = 0.17439944679844556070449858819817
y[1] (numeric) = 0.17439944679844567254368788460518
absolute error = 1.1183918929640701e-16
relative error = 6.4128178930326654919631576751874e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.274
y[1] (analytic) = 0.17479610862107987309320492019731
y[1] (numeric) = 0.17479610862107998517433677318969
absolute error = 1.1208113185299238e-16
relative error = 6.4121068104530869526209461107871e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.1896
Order of pole = 7.1e-29
TOP MAIN SOLVE Loop
x[1] = 0.275
y[1] (analytic) = 0.17519157222975022807291907312599
y[1] (numeric) = 0.17519157222975034039381693949535
absolute error = 1.1232089786636936e-16
relative error = 6.4113185604082124367151292680440e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.276
y[1] (analytic) = 0.17558584163652044863116824070321
y[1] (numeric) = 0.17558584163652056118967795423599
absolute error = 1.1255850971353278e-16
relative error = 6.4104547761054506096738370808986e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.277
y[1] (analytic) = 0.17597892083297497314016306315514
y[1] (numeric) = 0.17597892083297508593415257617683
absolute error = 1.1279398951302169e-16
relative error = 6.4095170591525939573384761149237e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.278
y[1] (analytic) = 0.17637081379035108937688538485371
y[1] (numeric) = 0.17637081379035120240424451308564
absolute error = 1.1302735912823193e-16
relative error = 6.4085069802187101496479939425858e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.3832
Order of pole = 2.042e-27
TOP MAIN SOLVE Loop
x[1] = 0.279
y[1] (analytic) = 0.17676152445967014987773941941088
y[1] (numeric) = 0.17676152445967026313637959009283
absolute error = 1.1325864017068195e-16
relative error = 6.4074260796796309225254684638359e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 0.17715105677186777776901894772939
y[1] (numeric) = 0.17715105677186789125687295096215
absolute error = 1.1348785400323276e-16
relative error = 6.4062758682484494012825808380754e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.281
y[1] (analytic) = 0.17753941463792307212080695905855
y[1] (numeric) = 0.1775394146379231858358287023212
absolute error = 1.1371502174326265e-16
relative error = 6.4050578275914120878615972076370e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.282
y[1] (analytic) = 0.17792660194898682177936558491948
y[1] (numeric) = 0.17792660194898693571952985071685
absolute error = 1.1394016426579737e-16
relative error = 6.4037734109295839544910255329050e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.283
y[1] (analytic) = 0.17831262257650873654157950769037
y[1] (numeric) = 0.17831262257650885070488171428686
absolute error = 1.1416330220659649e-16
relative error = 6.4024240436266564674561611374225e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.7022
Order of pole = 7.134e-27
TOP MAIN SOLVE Loop
x[1] = 0.284
y[1] (analytic) = 0.17869748037236370444457167962655
y[1] (numeric) = 0.17869748037236381882902764482307
absolute error = 1.1438445596519652e-16
relative error = 6.4010111237632505268938618951212e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.285
y[1] (analytic) = 0.17908117916897708385420278423262
y[1] (numeric) = 0.17908117916897719845784849214421
absolute error = 1.1460364570791159e-16
relative error = 6.3995360226980690408820516831280e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.286
y[1] (analytic) = 0.17946372277944903894778221755712
y[1] (numeric) = 0.17946372277944915376867358834929
absolute error = 1.1482089137079217e-16
relative error = 6.3980000856162265601434693382216e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.5MB, time=2.36
x[1] = 0.287
y[1] (analytic) = 0.17984511499767792709894545388989
y[1] (numeric) = 0.17984511499767804213515811643253
absolute error = 1.1503621266254264e-16
relative error = 6.3964046320650928876233203601542e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.288
y[1] (analytic) = 0.18022535959848274658627766184383
y[1] (numeric) = 0.18022535959848286183590672924203
absolute error = 1.1524962906739820e-16
relative error = 6.3947509564779609279726490460686e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.289
y[1] (analytic) = 0.18060446033772465296187370505453
y[1] (numeric) = 0.18060446033772476842303355301627
absolute error = 1.1546115984796174e-16
relative error = 6.3930403286858479221571217324781e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.632
Order of pole = 5.503e-27
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 0.18098242095242755233160772500277
y[1] (numeric) = 0.18098242095242766800243177300421
absolute error = 1.1567082404800144e-16
relative error = 6.3912739944177393208470471558136e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.5852
Order of pole = 7.21e-28
TOP MAIN SOLVE Loop
x[1] = 0.291
y[1] (analytic) = 0.1813592451608977797154290634627
y[1] (numeric) = 0.18135924516089789559406955867218
absolute error = 1.1587864049520948e-16
relative error = 6.3894531757895549819903778845433e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.4796
Order of pole = 5.757e-27
TOP MAIN SOLVE Loop
x[1] = 0.292
y[1] (analytic) = 0.18173493666284287057349321131756
y[1] (numeric) = 0.18173493666284298665812101524011
absolute error = 1.1608462780392255e-16
relative error = 6.3875790717821269766467230366422e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.293
y[1] (analytic) = 0.1821094991394894335023648097066
y[1] (numeric) = 0.18210949913948954979116918751139
absolute error = 1.1628880437780479e-16
relative error = 6.3856528587084674819516112963780e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.294
y[1] (analytic) = 0.18248293625370013202488268509479
y[1] (numeric) = 0.18248293625370024851607109758839
absolute error = 1.1649118841249360e-16
relative error = 6.3836756906705876020804365229876e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.295
y[1] (analytic) = 0.18285525165008978331754284149487
y[1] (numeric) = 0.18285525165008990000934073970383
absolute error = 1.1669179789820896e-16
relative error = 6.3816487000061320601853246681048e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.296
y[1] (analytic) = 0.18322644895514058164042279104645
y[1] (numeric) = 0.18322644895514069853107341337331
absolute error = 1.1689065062232686e-16
relative error = 6.3795729977250857165299957435788e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.297
y[1] (analytic) = 0.18359653177731645415672826709704
y[1] (numeric) = 0.18359653177731657124449243901422
absolute error = 1.1708776417191718e-16
relative error = 6.3774496739367871438293883739615e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.298
y[1] (analytic) = 0.18396550370717655675198007638341
y[1] (numeric) = 0.18396550370717667403513601263023
absolute error = 1.1728315593624682e-16
relative error = 6.3752797982675033586635469283340e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.299
y[1] (analytic) = 0.18433336831748791738666360700863
y[1] (numeric) = 0.18433336831748803486350671625701
absolute error = 1.1747684310924838e-16
relative error = 6.3730644202687863319343157171447e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 0.18470012916333723444082546605314
y[1] (numeric) = 0.18470012916333735210966815800815
absolute error = 1.1766884269195501e-16
relative error = 6.3708045698168434977278440495689e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.301
y[1] (analytic) = 0.18506578978224183743461017326206
y[1] (numeric) = 0.185065789782241955293781668164
absolute error = 1.1785917149490194e-16
relative error = 6.3685012575031427047065742791289e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.302
y[1] (analytic) = 0.18543035369425981743507423050909
y[1] (numeric) = 0.18543035369425993548292037100425
absolute error = 1.1804784614049516e-16
relative error = 6.3661554750164643333865152342240e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.303
y[1] (analytic) = 0.18579382440209933438678481042927
y[1] (numeric) = 0.18579382440209945262166787577696
absolute error = 1.1823488306534769e-16
relative error = 6.3637681955166063237440117286333e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.304
y[1] (analytic) = 0.18615620539122710853169549394721
y[1] (numeric) = 0.18615620539122722695199401653128
absolute error = 1.1842029852258407e-16
relative error = 6.3613403739999528841601816532171e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.5MB, time=2.58
x[1] = 0.305
y[1] (analytic) = 0.18651750012997610301258180791829
y[1] (numeric) = 0.18651750012997622161669039203161
absolute error = 1.1860410858411332e-16
relative error = 6.3588729476570920943686360328528e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.306
y[1] (analytic) = 0.18687771206965240468390478147614
y[1] (numeric) = 0.18687771206965252347023392434724
absolute error = 1.1878632914287110e-16
relative error = 6.3563668362226885825960122455361e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.307
y[1] (analytic) = 0.18723684464464131008434149983343
y[1] (numeric) = 0.18723684464464142905131741486474
absolute error = 1.1896697591503131e-16
relative error = 6.3538229423177863135757449419801e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 4.893
Order of pole = 1.956e-25
TOP MAIN SOLVE Loop
x[1] = 0.308
y[1] (analytic) = 0.18759490127251262345636796824256
y[1] (numeric) = 0.18759490127251274260243241043025
absolute error = 1.1914606444218769e-16
relative error = 6.3512421517847291542880253989094e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.309
y[1] (analytic) = 0.18795188535412517363019191976836
y[1] (numeric) = 0.18795188535412529295380201327419
absolute error = 1.1932361009350583e-16
relative error = 6.3486253340148743455217139784790e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 0.18830780027373055652200205182652
y[1] (numeric) = 0.18830780027373067602163011967256
absolute error = 1.1949962806784604e-16
relative error = 6.3459733422692718270132347973667e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.311
y[1] (analytic) = 0.18866264939907610992991622973392
y[1] (numeric) = 0.18866264939907622960404962559143
absolute error = 1.1967413339585751e-16
relative error = 6.3432870139924770922034925026404e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.312
y[1] (analytic) = 0.18901643608150712724516524880645
y[1] (numeric) = 0.18901643608150724709230619085063
absolute error = 1.1984714094204418e-16
relative error = 6.3405671711196606456860310257549e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.313
y[1] (analytic) = 0.18936916365606831663093172233375
y[1] (numeric) = 0.18936916365606843664959712913649
absolute error = 1.2001866540680274e-16
relative error = 6.3378146203771731878555137698776e-14 %
Correct digits = 15
h = 0.001
Complex estimate of poles used for equation 1
Radius of convergence = 0.08005
Order of pole = 3.622e-27
TOP MAIN SOLVE Loop
x[1] = 0.31460101075085529751805348293588
y[1] (analytic) = 0.18993168739068738639018182112069
y[1] (numeric) = 0.1899316873906875064980748008519
absolute error = 1.2010789297973121e-16
relative error = 6.3237416899619597805295671649649e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31540151612628294627708022440382
y[1] (analytic) = 0.19021193865102394353139995025362
y[1] (numeric) = 0.19021193865102406368344898244471
absolute error = 1.2015204903219109e-16
relative error = 6.3167459353132612050165814215665e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31620202150171059503610696587176
y[1] (analytic) = 0.19049151841810286215005433893288
y[1] (numeric) = 0.19049151841810298234595745225684
absolute error = 1.2019590311332396e-16
relative error = 6.3097771549865212999725711317614e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.3005
Order of pole = 1.015e-27
TOP MAIN SOLVE Loop
x[1] = 0.3170025268771382437951337073397
y[1] (analytic) = 0.19077042836731705456614635066835
y[1] (numeric) = 0.19077042836731717480560393603967
absolute error = 1.2023945758537132e-16
relative error = 6.3028352252717823206719199004468e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31860353762799354131318719027558
y[1] (analytic) = 0.19132624548134601973047182684363
y[1] (numeric) = 0.19132624548134614005614887439145
absolute error = 1.2032567704754782e-16
relative error = 6.2890314261291123707199652898052e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.5MB, time=2.79
x[1] = 0.31940404300342119007221393174352
y[1] (analytic) = 0.19160315596466518902566119853719
y[1] (numeric) = 0.19160315596466530939400785767516
absolute error = 1.2036834665913797e-16
relative error = 6.2821693125626749340610759588718e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32020454837884883883124067321146
y[1] (analytic) = 0.19187940326719163180252298502085
y[1] (numeric) = 0.19187940326719175221324888998422
absolute error = 1.2041072590496337e-16
relative error = 6.2753335613250635642451854170848e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3210050537542764875902674146794
y[1] (analytic) = 0.19215498903222645460302824145954
y[1] (numeric) = 0.1921549890322265750558452868994
absolute error = 1.2045281704543986e-16
relative error = 6.2685240519692480855192491596020e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32260606450513178510832089761528
y[1] (analytic) = 0.19270418249143564740589603227148
y[1] (numeric) = 0.1927041824914357679420399856008
absolute error = 1.2053614395332932e-16
relative error = 6.2549832803284541179222092992217e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32340656988055943386734763908322
y[1] (analytic) = 0.19297779344071491395632473929205
y[1] (numeric) = 0.19297779344071503453370888275993
absolute error = 1.2057738414346788e-16
relative error = 6.2482517803537169390467574427257e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32420707525598708262637438055116
y[1] (analytic) = 0.19325074936277373500520252829425
y[1] (numeric) = 0.19325074936277385562354760238085
absolute error = 1.2061834507408660e-16
relative error = 6.2415460468750733192147822085847e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3250075806314147313854011220191
y[1] (analytic) = 0.19352305186960004714124052616628
y[1] (numeric) = 0.19352305186960016780026943479529
absolute error = 1.2065902890862901e-16
relative error = 6.2348659626312441972432217042225e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32660859138227002890345460495498
y[1] (analytic) = 0.19406570305468103585050707799959
y[1] (numeric) = 0.19406570305468115659008092726764
absolute error = 1.2073957384926805e-16
relative error = 6.2215822759391850734309812645523e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32740909675769767766248134642292
y[1] (analytic) = 0.19433605492617576577540446159171
y[1] (numeric) = 0.19433605492617588655484365039652
absolute error = 1.2077943918880481e-16
relative error = 6.2149784420953905038880303929126e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32820960213312532642150808789086
y[1] (analytic) = 0.19460575976897771083108637947656
y[1] (numeric) = 0.1946057597689778316501222789804
absolute error = 1.2081903589950384e-16
relative error = 6.2083997946891044368105560561514e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.4427
Order of pole = 1.726e-27
TOP MAIN SOLVE Loop
x[1] = 0.3290101075085529751805348293588
y[1] (analytic) = 0.19487481916451784215469487846347
y[1] (numeric) = 0.19487481916451796301306093089996
absolute error = 1.2085836605243649e-16
relative error = 6.2018462195674985724117753476585e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33061111825940827269858831229468
y[1] (analytic) = 0.1954110079094529099443585372604
y[1] (numeric) = 0.19541100790945303088059341700273
absolute error = 1.2093623487974233e-16
relative error = 6.1888138326260636424350862324383e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33141162363483592145761505376262
memory used=53.4MB, alloc=4.5MB, time=2.99
y[1] (analytic) = 0.19567814039171360774464192981714
y[1] (numeric) = 0.19567814039171372871941953704545
absolute error = 1.2097477760722831e-16
relative error = 6.1823347955503789690035268676430e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33221212901026357021664179523056
y[1] (analytic) = 0.1959446336925019266242785764334
y[1] (numeric) = 0.19594463369250204763734045994658
absolute error = 1.2101306188351318e-16
relative error = 6.1758803802415080084468225624022e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.377
Order of pole = 5.841e-27
TOP MAIN SOLVE Loop
x[1] = 0.3330126343856912189756685366985
y[1] (analytic) = 0.19621048936342639547329905349636
y[1] (numeric) = 0.19621048936342651652438874515373
absolute error = 1.2105108969165737e-16
relative error = 6.1694504755779521634527613509500e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33461364513654651649372201963438
y[1] (analytic) = 0.19674029399275526209027494101716
y[1] (numeric) = 0.196740293992755383216658691452
absolute error = 1.2112638375043484e-16
relative error = 6.1566637566829691497536920578913e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33541415051197416525274876110232
y[1] (analytic) = 0.19700424602509904595627134532794
y[1] (numeric) = 0.19700424602509916711992522767536
absolute error = 1.2116365388234742e-16
relative error = 6.1503067231815265997348211284151e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.5261
Order of pole = 4.073e-27
TOP MAIN SOLVE Loop
x[1] = 0.33621465588740181401177550257026
y[1] (analytic) = 0.19726756657551401554181722329784
y[1] (numeric) = 0.19726756657551413674249253229802
absolute error = 1.2120067530900018e-16
relative error = 6.1439737617792617209807958983004e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3370151612628294627708022440382
y[1] (analytic) = 0.19753025716649982089571050688946
y[1] (numeric) = 0.19753025716649994213316043646794
absolute error = 1.2123744992957848e-16
relative error = 6.1376647643093215639596151495997e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33861617201368476028885572697408
y[1] (analytic) = 0.19805375453152039274543120171689
y[1] (numeric) = 0.19805375453152051405569746963699
absolute error = 1.2131026626792010e-16
relative error = 6.1251182314048728004998130682948e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.5569
Order of pole = 3.188e-27
TOP MAIN SOLVE Loop
x[1] = 0.33941667738911240904788246844202
y[1] (analytic) = 0.19831456432197486788709147178372
y[1] (numeric) = 0.19831456432197498923340317496891
absolute error = 1.2134631170318519e-16
relative error = 6.1188804825334268693417663857013e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34021718276454005780690920990996
y[1] (analytic) = 0.19857475018589426552460499656896
y[1] (numeric) = 0.19857475018589438690672276425397
absolute error = 1.2138211776768501e-16
relative error = 6.1126662707143808223780912936746e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3410176881399677065659359513779
y[1] (analytic) = 0.19883431361736265465918156584342
y[1] (numeric) = 0.19883431361736277607686784649625
absolute error = 1.2141768628065283e-16
relative error = 6.1064754906594938695275728324333e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.654
Order of pole = 3.179e-27
TOP MAIN SOLVE Loop
x[1] = 0.34261869889082300408398943431378
y[1] (analytic) = 0.19935157913130119306375968480389
y[1] (numeric) = 0.1993515791313013145518775361893
absolute error = 1.2148811785138541e-16
relative error = 6.0941638075195939197787492014136e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34341920426625065284301617578172
y[1] (analytic) = 0.19960928417403821426093637086183
y[1] (numeric) = 0.1996092841740383357839208413786
absolute error = 1.2152298447051677e-16
relative error = 6.0880426966794571575416891876057e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.9997
Order of pole = 4.60e-28
memory used=57.2MB, alloc=4.5MB, time=3.19
TOP MAIN SOLVE Loop
x[1] = 0.34421970964167830160204291724966
y[1] (analytic) = 0.19986637270491109855037597857861
y[1] (numeric) = 0.19986637270491122010799663971801
absolute error = 1.2155762066113940e-16
relative error = 6.0819446020872573262106450520733e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3450202150171059503610696587176
y[1] (analytic) = 0.20012284619026203409881114796668
y[1] (numeric) = 0.20012284619026215569083931422336
absolute error = 1.2159202816625668e-16
relative error = 6.0758694212581782141587799597328e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34662122576796124787912314165348
y[1] (analytic) = 0.20063395386244679491906615640035
y[1] (numeric) = 0.20063395386244691657923017444775
absolute error = 1.2166016401804740e-16
relative error = 6.0637873937058898362418137604750e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34742173114338889663814988312142
y[1] (analytic) = 0.20088859095472294983616671689372
y[1] (numeric) = 0.20088859095472307153006249409796
absolute error = 1.2169389577720424e-16
relative error = 6.0577803447599511738881158737203e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34822223651881654539717662458936
y[1] (analytic) = 0.20114261881241345181071590519587
y[1] (numeric) = 0.2011426188124135735381215812937
absolute error = 1.2172740567609783e-16
relative error = 6.0517958051257838371386383644318e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3490227418942441941562033660573
y[1] (analytic) = 0.20139603887477335378800486023144
y[1] (numeric) = 0.20139603887477347554870024526547
absolute error = 1.2176069538503403e-16
relative error = 6.0458336750477986048264686274447e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35062375264509949167425684899318
y[1] (analytic) = 0.20190106134384447155917568355793
y[1] (numeric) = 0.20190106134384459338579652729051
absolute error = 1.2182662084373258e-16
relative error = 6.0339762472202977966218745677932e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35142425802052714043328359046112
y[1] (analytic) = 0.20215266660246448457152995178153
y[1] (numeric) = 0.20215266660246460643078981575982
absolute error = 1.2185925986397829e-16
relative error = 6.0280807526331526906961856294238e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35222476339595478919231033192906
y[1] (analytic) = 0.2024036697696216858814732702325
y[1] (numeric) = 0.2024036697696218077731585057272
absolute error = 1.2189168523549470e-16
relative error = 6.0222072739211347256612477492360e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.353025268771382437951337073397
y[1] (analytic) = 0.2026540722581204032069517212866
y[1] (numeric) = 0.20265407225812052513085028052996
absolute error = 1.2192389855924336e-16
relative error = 6.0163557139848117005504458706025e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35462627952223773546939055633288
y[1] (analytic) = 0.20315308082430756677406587465054
y[1] (numeric) = 0.20315308082430768876176127465228
absolute error = 1.2198769540000174e-16
relative error = 6.0047179646514980003926220646259e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.5261
Order of pole = 7.962e-27
TOP MAIN SOLVE Loop
x[1] = 0.35542678489766538422841729780082
y[1] (analytic) = 0.20340168970162621781173013588766
y[1] (numeric) = 0.20340168970162633983101218791721
absolute error = 1.2201928205202955e-16
relative error = 5.9989315836570453554462602927457e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=61.0MB, alloc=4.5MB, time=3.39
x[1] = 0.35622729027309303298744403926876
y[1] (analytic) = 0.20364970349959559244716544634264
y[1] (numeric) = 0.20364970349959571449782837291656
absolute error = 1.2205066292657392e-16
relative error = 5.9931667382376664343846694512741e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3570277956485206817464707807367
y[1] (analytic) = 0.20389712360518796353101420763731
y[1] (numeric) = 0.20389712360518808561285376607321
absolute error = 1.2208183955843590e-16
relative error = 5.9874233338782444015757374034440e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.7249
Order of pole = 8.507e-27
TOP MAIN SOLVE Loop
x[1] = 0.35862880639937597926452426367258
y[1] (analytic) = 0.2043901882616862553756896092347
y[1] (numeric) = 0.20439018826168637751927577834989
absolute error = 1.2214358616911519e-16
relative error = 5.9760004728177788756912580665709e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35942931177480362802355100514052
y[1] (analytic) = 0.2046358355611638283697391954037
y[1] (numeric) = 0.20463583556116395054389834909446
absolute error = 1.2217415915369076e-16
relative error = 5.9703208296170585501629957922367e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36022981715023127678257774660846
y[1] (analytic) = 0.20488089466545514945739228544055
y[1] (numeric) = 0.20488089466545527166192619277669
absolute error = 1.2220453390733614e-16
relative error = 5.9646622544713524531374786787696e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3610303225256589255416044880764
y[1] (analytic) = 0.205125366936301941293309366851
y[1] (numeric) = 0.20512536693630206352802126856669
absolute error = 1.2223471190171569e-16
relative error = 5.9590246553793378579694142925729e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36263133327651422305965797101228
y[1] (analytic) = 0.20561255639977508693907719415316
y[1] (numeric) = 0.20561255639977520923356063221187
absolute error = 1.2229448343805871e-16
relative error = 5.9478120198204239661268628043405e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.5759
Order of pole = 7.325e-27
TOP MAIN SOLVE Loop
x[1] = 0.36343183865194187181868471248022
y[1] (analytic) = 0.205855276291100806684131699478
y[1] (numeric) = 0.20585527629110092900821156189279
absolute error = 1.2232407986241479e-16
relative error = 5.9422368018119582880372914026728e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36423234402736952057771145394816
y[1] (analytic) = 0.20609741474642686881679597565909
y[1] (numeric) = 0.20609741474642699117028126817332
absolute error = 1.2235348529251423e-16
relative error = 5.9366821967685785553117714570602e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3650328494027971693367381954161
y[1] (analytic) = 0.2063389731028493375968209315276
y[1] (numeric) = 0.20633897310284945997952207128476
absolute error = 1.2238270113975716e-16
relative error = 5.9311481151336201773664646244305e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36663386015365246685479167835198
y[1] (analytic) = 0.20682035484308853240547701180187
y[1] (numeric) = 0.20682035484308865484604668457946
absolute error = 1.2244056967277759e-16
relative error = 5.9201411662634170546953354528705e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36743436552908011561381841981992
y[1] (analytic) = 0.20706018087688591591802813441596
y[1] (numeric) = 0.20706018087688603838725325759793
absolute error = 1.2246922512318197e-16
relative error = 5.9146681223078745812878929404499e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.4369
Order of pole = 2.235e-27
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.5MB, time=3.59
x[1] = 0.36823487090450776437284516128786
y[1] (analytic) = 0.20729943211178589521992838377913
y[1] (numeric) = 0.20729943211178601771762490397561
absolute error = 1.2249769652019648e-16
relative error = 5.9092152483148042751022984153328e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3690353762799354131318719027558
y[1] (analytic) = 0.20753810986080768766932812958284
y[1] (numeric) = 0.20753810986080781019531334726918
absolute error = 1.2252598521768634e-16
relative error = 5.9037824571045025499250779683824e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37063638703079071064992538569168
y[1] (analytic) = 0.20801375012957313385104428861627
y[1] (numeric) = 0.20801375012957325643306416231462
absolute error = 1.2258201987369835e-16
relative error = 5.8929767766477554072186327382426e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37143689240621835940895212715962
y[1] (analytic) = 0.20825071525170067154997614223237
y[1] (numeric) = 0.20825071525170079415974462663562
absolute error = 1.2260976848440325e-16
relative error = 5.8876037153683659190396907287109e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37223739778164600816797886862756
y[1] (analytic) = 0.20848711209276143920235472829497
y[1] (numeric) = 0.20848711209276156183969442844627
absolute error = 1.2263733970015130e-16
relative error = 5.8822503928006206341195709492481e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3730379031570736569270056100955
y[1] (analytic) = 0.20872294194225105158795324058208
y[1] (numeric) = 0.20872294194225117425268806044896
absolute error = 1.2266473481986688e-16
relative error = 5.8769167240755669337036019473570e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37463891390792895444505909303138
y[1] (analytic) = 0.20919290580132234630544739672801
y[1] (numeric) = 0.20919290580132246902444931028234
absolute error = 1.2271900191355433e-16
relative error = 5.8663080109468320664013071424908e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37543941928335660320408583449932
y[1] (analytic) = 0.2094270423667824385658307156542
y[1] (numeric) = 0.20942704236678256131170714797722
absolute error = 1.2274587643232302e-16
relative error = 5.8610327990666377145508368084847e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37623992465878425196311257596726
y[1] (analytic) = 0.20966061705247065782140596313977
y[1] (numeric) = 0.20966061705247078059398590798504
absolute error = 1.2277257994484527e-16
relative error = 5.8557769060709967942289201605233e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 2.703
Order of pole = 6.934e-26
TOP MAIN SOLVE Loop
x[1] = 0.3770404300342119007221393174352
y[1] (analytic) = 0.20989363112489718793302802917552
y[1] (numeric) = 0.20989363112489731073214172674602
absolute error = 1.2279911369757050e-16
relative error = 5.8505402493370033460844346849834e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37864144078506719824019280037108
y[1] (analytic) = 0.21035798247335775204949513145632
y[1] (numeric) = 0.21035798247335787490117198992757
absolute error = 1.2285167685847125e-16
relative error = 5.8401243163677258603601681281948e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37944194616049484699921954183902
y[1] (analytic) = 0.21058932225982635693030527757558
y[1] (numeric) = 0.21058932225982647980801398644236
absolute error = 1.2287770870886678e-16
relative error = 5.8349448770844864095150559370237e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.5MB, time=3.80
x[1] = 0.38024245153592249575824628330696
y[1] (analytic) = 0.21082010645394372778965415821714
y[1] (numeric) = 0.21082010645394385069322984230536
absolute error = 1.2290357568408822e-16
relative error = 5.8297843479619925856424471176849e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3810429569113501445172730247749
y[1] (analytic) = 0.21105033629975819319774092246427
y[1] (numeric) = 0.21105033629975831612701990291907
absolute error = 1.2292927898045480e-16
relative error = 5.8246426485602166662510558148795e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38264396766220544203532650771078
y[1] (analytic) = 0.21150913790053801766039217475588
y[1] (numeric) = 0.21150913790053814064059144797023
absolute error = 1.2298019927321435e-16
relative error = 5.8144154193019158526841075902838e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 4.285
Order of pole = 1.721e-25
TOP MAIN SOLVE Loop
x[1] = 0.38344447303763309079435324917872
y[1] (analytic) = 0.21173771212152701497565848655489
y[1] (numeric) = 0.21173771212152713798107710037861
absolute error = 1.2300541861382372e-16
relative error = 5.8093297307011927040117353846188e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38424497841306073955337999064666
y[1] (analytic) = 0.21196573692630058378661045676499
y[1] (numeric) = 0.21196573692630070681708942095002
absolute error = 1.2303047896418503e-16
relative error = 5.8042625543279245258548802410065e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.6042
Order of pole = 9.428e-27
TOP MAIN SOLVE Loop
x[1] = 0.3850454837884883883124067321146
y[1] (analytic) = 0.21219321353695463645220131477757
y[1] (numeric) = 0.21219321353695475950758278749493
absolute error = 1.2305538147271736e-16
relative error = 5.7992138118633363449863857838442e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.546
Order of pole = 2.616e-26
TOP MAIN SOLVE Loop
x[1] = 0.38664649453934368583046021505048
y[1] (analytic) = 0.21264652704265474777025051760974
y[1] (numeric) = 0.21264652704265487087496802905451
absolute error = 1.2310471751144477e-16
relative error = 5.7891713174676587013088068614561e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 4.901
Order of pole = 2.239e-25
TOP MAIN SOLVE Loop
x[1] = 0.38744699991477133458948695651842
y[1] (analytic) = 0.21287236636031859230054954735373
y[1] (numeric) = 0.21287236636031871542970283955637
absolute error = 1.2312915329220264e-16
relative error = 5.7841774109744227565031091996319e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38824750529019898334851369798636
y[1] (analytic) = 0.21309766232913761472127890229361
y[1] (numeric) = 0.21309766232913773787471463471618
absolute error = 1.2315343573242257e-16
relative error = 5.7792016292608271823825197586522e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3890480106656266321075404394543
y[1] (analytic) = 0.21332241614975105673395358323808
y[1] (numeric) = 0.2133224161497511799115195179829
absolute error = 1.2317756593474482e-16
relative error = 5.7742438960692676325400605104241e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39064902141648192962559392239018
y[1] (analytic) = 0.21377030212777226284011745949084
y[1] (numeric) = 0.21377030212777238606549145127626
absolute error = 1.2322537399178542e-16
relative error = 5.7643822722453095154431638227696e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39144952679190957838462066385812
y[1] (analytic) = 0.21399343666537008454896737293843
y[1] (numeric) = 0.21399343666537020779802138048984
absolute error = 1.2324905400755141e-16
relative error = 5.7594782311141991402278725523292e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.5MB, time=4.00
x[1] = 0.39225003216733722714364740532606
y[1] (analytic) = 0.21421603381518051877653998555937
y[1] (numeric) = 0.2142160338151806420491260932319
absolute error = 1.2327258610767253e-16
relative error = 5.7545919375030815692443693032931e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 2.643
Order of pole = 2.724e-26
TOP MAIN SOLVE Loop
x[1] = 0.393050537542764875902674146794
y[1] (analytic) = 0.21443809475686861581959874976809
y[1] (numeric) = 0.21443809475686873911557010079678
absolute error = 1.2329597135102869e-16
relative error = 5.7497233171569869092276092427191e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.2657
Order of pole = 8.381e-27
TOP MAIN SOLVE Loop
x[1] = 0.39465154829362017342072762972988
y[1] (analytic) = 0.21488061271386628721769389212878
y[1] (numeric) = 0.21488061271386641055999935257804
absolute error = 1.2334230546044926e-16
relative error = 5.7400388012059106221162199320770e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39545205366904782217975437119782
y[1] (analytic) = 0.21510107206789019806714624901631
y[1] (numeric) = 0.21510107206789032143240265100075
absolute error = 1.2336525640198444e-16
relative error = 5.7352227590501222184930915412598e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39625255904447547093878111266576
y[1] (analytic) = 0.21532099989125751020543903417579
y[1] (numeric) = 0.21532099989125763359350367202192
absolute error = 1.2338806463784613e-16
relative error = 5.7304240970532455445233804003167e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3970530644199031196978078541337
y[1] (analytic) = 0.21554039734312870753288065737587
y[1] (numeric) = 0.2155403973431288309436118424508
absolute error = 1.2341073118507493e-16
relative error = 5.7256427429059477227912151731351e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39865407517075841721586133706958
y[1] (analytic) = 0.21597760574881457452825622806068
y[1] (numeric) = 0.21597760574881469798389946920156
absolute error = 1.2345564324114088e-16
relative error = 5.7161316708326592238947732679961e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39945458054618606597488807853752
y[1] (analytic) = 0.21619541900079455913969038157459
y[1] (numeric) = 0.216195419000794682617581125195
absolute error = 1.2347789074362041e-16
relative error = 5.7114018101912975940127034541078e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.40025508592161371473391482000546
y[1] (analytic) = 0.21641270647764514333109247226955
y[1] (numeric) = 0.21641270647764526683109301716411
absolute error = 1.2350000054489456e-16
relative error = 5.7066889719643971737967213478307e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4010555912970413634929415614734
y[1] (analytic) = 0.21662946931847941286234191187981
y[1] (numeric) = 0.21662946931847953638431553387308
absolute error = 1.2352197362199327e-16
relative error = 5.7019930857327877672575033809771e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.40265660204789666101099504440928
y[1] (analytic) = 0.21706142562879061641723162464535
y[1] (numeric) = 0.21706142562879073998274509754607
absolute error = 1.2356551347290072e-16
relative error = 5.6926518894341595214072539453891e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.40345710742332430977002178587722
y[1] (analytic) = 0.21727662135678601669291559712466
y[1] (numeric) = 0.21727662135678614027999775921681
absolute error = 1.2358708216209215e-16
relative error = 5.6880064403777723476929655033083e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.5MB, time=4.20
x[1] = 0.40425761279875195852904852734516
y[1] (analytic) = 0.21749129696583716846988746358202
y[1] (numeric) = 0.21749129696583729207840542159141
absolute error = 1.2360851795800939e-16
relative error = 5.6833776653336807941459783798599e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4050581181741796072880752688131
y[1] (analytic) = 0.21770545357545485437546994744402
y[1] (numeric) = 0.21770545357545497800529174685688
absolute error = 1.2362982179941286e-16
relative error = 5.6787654957189126017373103718445e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.40665912892503490480612875174898
y[1] (analytic) = 0.21813221425510977436774828726453
y[1] (numeric) = 0.21813221425510989803978562378875
absolute error = 1.2367203733652422e-16
relative error = 5.6695907002478514966262002512067e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.40745963430046255356515549321692
y[1] (analytic) = 0.21834482054489702560611916439498
y[1] (numeric) = 0.21834482054489714929907003714823
absolute error = 1.2369295087275325e-16
relative error = 5.6650279390217529596144456339613e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.40826013967589020232418223468486
y[1] (analytic) = 0.21855691227478505716811239536852
y[1] (numeric) = 0.21855691227478518088184853100886
absolute error = 1.2371373613564034e-16
relative error = 5.6604815124812326411063182082335e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4090606450513178510832089761528
y[1] (analytic) = 0.21876849054511574037568157180387
y[1] (numeric) = 0.2187684905451158641100755991384
absolute error = 1.2373439402733453e-16
relative error = 5.6559513538270396720740484267000e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41066165580217314860126245908868
y[1] (analytic) = 0.21919011108957543947250739811111
y[1] (numeric) = 0.2191901110895755632478386682627
absolute error = 1.2377533127015159e-16
relative error = 5.6469395747314932739768194063780e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41146216117760079736028920055662
y[1] (analytic) = 0.21940015554554137683763262728975
y[1] (numeric) = 0.21940015554554150063324501746049
absolute error = 1.2379561239017074e-16
relative error = 5.6424578224364207527554599031519e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41226266655302844611931594202456
y[1] (analytic) = 0.21960969090565712699460275359642
y[1] (numeric) = 0.21960969090565725081037243050933
absolute error = 1.2381576967691291e-16
relative error = 5.6379920743162170847581178132721e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4130631719284560948783426834925
y[1] (analytic) = 0.21981871825151769576463987748261
y[1] (numeric) = 0.21981871825151781960044387497785
absolute error = 1.2383580399749524e-16
relative error = 5.6335422653043442389557644312888e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41466418267931139239639616642838
y[1] (analytic) = 0.22023525320837115851983199685495
y[1] (numeric) = 0.22023525320837128239533917144622
absolute error = 1.2387550717459127e-16
relative error = 5.6246902060402177550214782840313e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41546468805473904115542290789632
y[1] (analytic) = 0.22044276296412088735604465261074
y[1] (numeric) = 0.22044276296412101125122238407045
absolute error = 1.2389517773145971e-16
relative error = 5.6202878273497599013896096873169e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41626519343016668991444964936426
y[1] (analytic) = 0.22064976899516155610065498837996
y[1] (numeric) = 0.22064976899516168001538371137532
absolute error = 1.2391472872299536e-16
relative error = 5.6159011308873195446946808399090e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=80.1MB, alloc=4.5MB, time=4.40
TOP MAIN SOLVE Loop
x[1] = 0.4170656988055943386734763908322
y[1] (analytic) = 0.22085627236475234960946213732822
y[1] (numeric) = 0.2208562723647524735436231201165
absolute error = 1.2393416098278828e-16
relative error = 5.6115300532695038344477635952014e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41866670955644963619152987376808
y[1] (analytic) = 0.22126777535454306358192027593353
y[1] (numeric) = 0.22126777535454318755459288484106
absolute error = 1.2397267260890753e-16
relative error = 5.6028345026863003014113300646092e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.41946721493187728495055661523602
y[1] (analytic) = 0.22147277708323107442009966673741
y[1] (numeric) = 0.22147277708323119841185327672245
absolute error = 1.2399175360998504e-16
relative error = 5.5985099046005117165642878254604e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42026772030730493370958335670396
y[1] (analytic) = 0.22167728036747700192425922409147
y[1] (numeric) = 0.22167728036747712593497837302571
absolute error = 1.2401071914893424e-16
relative error = 5.5942006751147537886885086802121e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.9573
Order of pole = 5.282e-27
TOP MAIN SOLVE Loop
x[1] = 0.4210682256827325824686100981719
y[1] (analytic) = 0.22188128625260458608167648389734
y[1] (numeric) = 0.22188128625260471011124651114952
absolute error = 1.2402957002725218e-16
relative error = 5.5899067524806292972110420997917e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42266923643358787998666358110778
y[1] (analytic) = 0.22228780998911540363439307628657
y[1] (numeric) = 0.22228780998911552770132405306077
absolute error = 1.2406693097677420e-16
relative error = 5.5813645823785519352072648156742e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42346974180901552874569032257572
y[1] (analytic) = 0.22249032991350831226622277507926
y[1] (numeric) = 0.22249032991350843635166539500519
absolute error = 1.2408544261992593e-16
relative error = 5.5771162130130936205223601321151e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42427024718444317750471706404366
y[1] (analytic) = 0.2226923565848330239985908447627
y[1] (numeric) = 0.22269235658483314810243359121125
absolute error = 1.2410384274644855e-16
relative error = 5.5728829067005763650201137529714e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4250707525598708262637438055116
y[1] (analytic) = 0.22289389103086786297921323018642
y[1] (numeric) = 0.22289389103086798710134535729935
absolute error = 1.2412213212711293e-16
relative error = 5.5686646032808343053634090196477e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42667176331072612378179728844748
y[1] (analytic) = 0.22329548734088049789008973656375
y[1] (numeric) = 0.22329548734088062204847144063139
absolute error = 1.2415838170406764e-16
relative error = 5.5602727660379802082980157327312e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42747226868615377254082402991542
y[1] (analytic) = 0.22349555124315950206639416184451
y[1] (numeric) = 0.2234955512431596262427375740158
absolute error = 1.2417634341217129e-16
relative error = 5.5560991134480999406669440673510e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42827277406158142129985077138336
y[1] (analytic) = 0.22369512699678105517649851197088
y[1] (numeric) = 0.22369512699678117937069591011601
absolute error = 1.2419419739814513e-16
relative error = 5.5519402262138803285221356231693e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.5MB, time=4.60
x[1] = 0.4290732794370090700588775128513
y[1] (analytic) = 0.22389421561235805784163479761061
y[1] (numeric) = 0.22389421561235818205357920094754
absolute error = 1.2421194440333693e-16
relative error = 5.5477960457179819860135072224219e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43067429018786436757693099578718
y[1] (analytic) = 0.2242909354549030089243789081539
y[1] (numeric) = 0.22429093545490313317149931630054
absolute error = 1.2424712040814664e-16
relative error = 5.5395515719862138958567279166612e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43147479556329201633595773725512
y[1] (analytic) = 0.22448856868621387556359010878027
y[1] (numeric) = 0.22448856868621399982814097076866
absolute error = 1.2426455086198839e-16
relative error = 5.5354511630248383268574435708530e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43227530093871966509498447872306
y[1] (analytic) = 0.22468571878819526618031300809404
y[1] (numeric) = 0.22468571878819539046219025168692
absolute error = 1.2428187724359288e-16
relative error = 5.5313652293473006179862143247307e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.433075806314147313854011220191
y[1] (analytic) = 0.22488238675466491322332848558319
y[1] (numeric) = 0.22488238675466503752242875171055
absolute error = 1.2429910026612736e-16
relative error = 5.5272937138350131570057726309882e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43467681706500261137206470312688
y[1] (analytic) = 0.22527428023977706685282784979123
y[1] (numeric) = 0.2252742802397771911860669090329
absolute error = 1.2433323905924167e-16
relative error = 5.5191937103030164861739504015131e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43547732244043026013109144459482
y[1] (analytic) = 0.22546950772953519664951810216539
y[1] (numeric) = 0.2254695077295353209996743310482
absolute error = 1.2435015622888281e-16
relative error = 5.5151651095122190393463815205679e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 3.258
Order of pole = 4.330e-26
TOP MAIN SOLVE Loop
x[1] = 0.43627782781585790889011818606276
y[1] (analytic) = 0.22566425702604132282520626877756
y[1] (numeric) = 0.22566425702604144719217910644669
absolute error = 1.2436697283766913e-16
relative error = 5.5111507013411239753755680138161e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4370783331912855576491449275307
y[1] (analytic) = 0.22585852910667881761802888774132
y[1] (numeric) = 0.22585852910667894200171845951377
absolute error = 1.2438368957177245e-16
relative error = 5.5071504301271182177469145473626e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43867934394214085516719841046658
y[1] (analytic) = 0.22624564551367346145870167182164
y[1] (numeric) = 0.22624564551367358587552780617499
absolute error = 1.2441682613435335e-16
relative error = 5.4991920773491329320473885006616e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43947984931756850392622515193452
y[1] (analytic) = 0.22643849177863132100596735853024
y[1] (numeric) = 0.22643849177863144543921466757482
absolute error = 1.2443324730904458e-16
relative error = 5.4952338858842005805330579514681e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44028035469299615268525189340246
y[1] (analytic) = 0.22663086470494974125266913402179
y[1] (numeric) = 0.22663086470494986570224043559027
absolute error = 1.2444957130156848e-16
relative error = 5.4912896115711830370086950036010e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.5MB, time=4.80
x[1] = 0.4410808600684238014442786348704
y[1] (analytic) = 0.22682276525392937456073760654375
y[1] (numeric) = 0.2268227652539294990265363787756
absolute error = 1.2446579877223185e-16
relative error = 5.4873592001619273546584815860677e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44268187081927909896233211780628
y[1] (analytic) = 0.22720515304921285503034206917764
y[1] (numeric) = 0.22720515304921297952830883321509
absolute error = 1.2449796676403745e-16
relative error = 5.4795397504506013762288120095544e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44348237619470674772135885927422
y[1] (analytic) = 0.2273956422022968195808207745756
y[1] (numeric) = 0.22739564220229694409472935532977
absolute error = 1.2451390858075417e-16
relative error = 5.4756506050359355500112584911429e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44428288157013439648038560074216
y[1] (analytic) = 0.22758566279162930186342632506426
y[1] (numeric) = 0.22758566279162942639318279190795
absolute error = 1.2452975646684369e-16
relative error = 5.4717751082966702492243687857820e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4450833869455620452394123422101
y[1] (analytic) = 0.22777521576277097740555655371301
y[1] (numeric) = 0.22777521576277110195106761153954
absolute error = 1.2454551105782653e-16
relative error = 5.4679132073588419111102344014716e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44668439769641734275746582514598
y[1] (analytic) = 0.22815292261719975263347891304888
y[1] (numeric) = 0.22815292261719987721022178548286
absolute error = 1.2457674287243398e-16
relative error = 5.4602299827406427226497255941194e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44748490307184499151649256661392
y[1] (analytic) = 0.22834107837612316500918344401013
y[1] (numeric) = 0.22834107837612328960140478711147
absolute error = 1.2459222134310134e-16
relative error = 5.4564085546566953881129510114863e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44828540844727264027551930808186
y[1] (analytic) = 0.22852877026815478527269267031962
y[1] (numeric) = 0.2285287702681549098803016831476
absolute error = 1.2460760901282798e-16
relative error = 5.4526005135639546832877276411340e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4490859138227002890345460495498
y[1] (analytic) = 0.22871599922344941912623873946694
y[1] (numeric) = 0.22871599922344954374914523284439
absolute error = 1.2462290649337745e-16
relative error = 5.4488058079235725319233209590421e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45068692457355558655259953248568
y[1] (analytic) = 0.22908907202925079658577703929687
y[1] (numeric) = 0.22908907202925092123901035017479
absolute error = 1.2465323331087792e-16
relative error = 5.4412561981551792299226928213800e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45148742994898323531162627395362
y[1] (analytic) = 0.2292749177249098191130620580496
y[1] (numeric) = 0.22927491772490994378132590640082
absolute error = 1.2466826384835122e-16
relative error = 5.4375011922556456286707570813277e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.198
Order of pole = 4.756e-27
TOP MAIN SOLVE Loop
x[1] = 0.45228793532441088407065301542156
y[1] (analytic) = 0.22946030417416214153785177834863
y[1] (numeric) = 0.22946030417416226622105837611746
absolute error = 1.2468320659776883e-16
relative error = 5.4337593182624439499136863748975e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.5MB, time=5.00
x[1] = 0.4530884406998385328296797568895
y[1] (analytic) = 0.22964523229208242324182023437066
y[1] (numeric) = 0.2296452322920825479398823824905
absolute error = 1.2469806214811984e-16
relative error = 5.4300305259339411223140869941248e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45468945145069383034773323982538
y[1] (analytic) = 0.23001371717934982608863011565746
y[1] (numeric) = 0.23001371717934995081614410106862
absolute error = 1.2472751398541116e-16
relative error = 5.4226119865780312713311312147886e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.671
Order of pole = 9.419e-27
TOP MAIN SOLVE Loop
x[1] = 0.45548995682612147910675998129332
y[1] (analytic) = 0.23019727576400844240590356160624
y[1] (numeric) = 0.23019727576400856714801498987961
absolute error = 1.2474211142827337e-16
relative error = 5.4189221403365067464097493253276e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45629046220154912786578672276126
y[1] (analytic) = 0.23038037964798309523365639547464
y[1] (numeric) = 0.23038037964798321999028037946079
absolute error = 1.2475662398398615e-16
relative error = 5.4152451773285526565850208492345e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4570909675769767766248134642292
y[1] (analytic) = 0.23056302973158588175451950491791
y[1] (numeric) = 0.23056302973158600652557172462016
absolute error = 1.2477105221970225e-16
relative error = 5.4115810485729965270957517188164e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45869197832783207414286694716508
y[1] (analytic) = 0.23092697208436105946131596357431
y[1] (numeric) = 0.23092697208436118426097394207271
absolute error = 1.2479965797849840e-16
relative error = 5.4042910991318600810297575247833e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45949248370325972290189368863302
y[1] (analytic) = 0.23110826613963137126520715859955
y[1] (numeric) = 0.2311082661396314960790437733327
absolute error = 1.2481383661473315e-16
relative error = 5.4006651817171663385357789951332e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46029298907868737166092043010096
y[1] (analytic) = 0.2312891099667501218640747350294
y[1] (numeric) = 0.23128910996675024669200789238008
absolute error = 1.2482793315735068e-16
relative error = 5.3970519050938373974357607337265e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4610934944541150204199471715689
y[1] (analytic) = 0.23146950445157652700919795916585
y[1] (numeric) = 0.23146950445157665185114611172885
absolute error = 1.2484194815256300e-16
relative error = 5.3934512215055078218814791356922e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46269450520497031793800065450478
y[1] (analytic) = 0.23182894892353071345634623750738
y[1] (numeric) = 0.23182894892353083832608190274022
absolute error = 1.2486973566523284e-16
relative error = 5.3862874436109096881251312589406e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46349501058039796669702739597272
y[1] (analytic) = 0.23200800066815447337493243858468
y[1] (numeric) = 0.23200800066815459825844169341322
absolute error = 1.2488350925482854e-16
relative error = 5.3827242549903197738201585301769e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46429551595582561545605413744066
y[1] (analytic) = 0.23218660658550170387669298633098
y[1] (numeric) = 0.23218660658550182877389642769327
absolute error = 1.2489720344136229e-16
relative error = 5.3791734707733643663058272293439e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.5MB, time=5.20
x[1] = 0.4650960213312532642150808789086
y[1] (analytic) = 0.23236476754728074493284090424382
y[1] (numeric) = 0.23236476754728086984365965520466
absolute error = 1.2491081875096084e-16
relative error = 5.3756350443939155733408266678040e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46669703208210856173313436184448
y[1] (analytic) = 0.23271975807700637003350373548408
y[1] (numeric) = 0.23271975807700649497131855978697
absolute error = 1.2493781482430289e-16
relative error = 5.3685950800516597336161473748003e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46749753745753621049216110331242
y[1] (analytic) = 0.23289658937444349551640181881089
y[1] (numeric) = 0.23289658937444362046759843965106
absolute error = 1.2495119662084017e-16
relative error = 5.3650934501212353726848804883151e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46829804283296385925118784478036
y[1] (analytic) = 0.23307297917531678553737599924304
y[1] (numeric) = 0.23307297917531691050187760533683
absolute error = 1.2496450160609379e-16
relative error = 5.3616039940904463336854961882707e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4690985482083915080102145862483
y[1] (analytic) = 0.23324892833747825555621236332445
y[1] (numeric) = 0.23324892833747838053394265024686
absolute error = 1.2497773028692241e-16
relative error = 5.3581266665498795326661629444322e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47069955895924680552826806918418
y[1] (analytic) = 0.23359950816340243413112787567503
y[1] (numeric) = 0.2335995081634025591350886196515
absolute error = 1.2500396074397647e-16
relative error = 5.3512082164375288491258997488616e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47150006433467445428729481065212
y[1] (analytic) = 0.23377414052923205821407377259377
y[1] (numeric) = 0.23377414052923218323103728784258
absolute error = 1.2501696351524881e-16
relative error = 5.3477670041788127700058512040557e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47230056971010210304632155212006
y[1] (analytic) = 0.23394833566050639355654456728965
y[1] (numeric) = 0.2339483356605065185864365395407
absolute error = 1.2502989197225105e-16
relative error = 5.3443377410338964486392725575085e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.106
Order of pole = 3.999e-27
TOP MAIN SOLVE Loop
x[1] = 0.473101075085529751805348293588
y[1] (analytic) = 0.23412209440150844149939496893265
y[1] (numeric) = 0.23412209440150856654214157228719
absolute error = 1.2504274660335454e-16
relative error = 5.3409203827175780384174811365738e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47470208583638504932340177652388
y[1] (analytic) = 0.23446830607643909486653539902206
y[1] (numeric) = 0.2344683060764392199347717223681
absolute error = 1.2506823632334604e-16
relative error = 5.3341212045338230200590139871083e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47550259121181269808242851799182
y[1] (analytic) = 0.23464076068557852760484181544187
y[1] (numeric) = 0.23464076068557865268571418650234
absolute error = 1.2508087237106047e-16
relative error = 5.3307392971961235617503640214163e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47630309658724034684145525945976
y[1] (analytic) = 0.2348127822548894731317506412036
y[1] (numeric) = 0.234812782254889598225187151791
absolute error = 1.2509343651058740e-16
relative error = 5.3273691197440167115352748899293e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.9436
Order of pole = 8.739e-27
TOP MAIN SOLVE Loop
x[1] = 0.4771036019626679956004820009277
y[1] (analytic) = 0.23498437161536619472991475867593
y[1] (numeric) = 0.23498437161536631983584397123287
absolute error = 1.2510592921255694e-16
relative error = 5.3240106289849942341053996378463e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
memory used=99.1MB, alloc=4.5MB, time=5.40
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47870461271352329311853548386358
y[1] (analytic) = 0.23532625702068130576173641231428
y[1] (numeric) = 0.23532625702068143089243858137861
absolute error = 1.2513070216906433e-16
relative error = 5.3173285358491636686104995507597e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.49
Order of pole = 3.386e-27
TOP MAIN SOLVE Loop
x[1] = 0.47950511808895094187756222533152
y[1] (analytic) = 0.23549655471442810474843763998322
y[1] (numeric) = 0.23549655471442822989142098765017
absolute error = 1.2514298334766695e-16
relative error = 5.3140048481566956929119343028441e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48030562346437859063658896679946
y[1] (analytic) = 0.23566642349717910554949023384731
y[1] (numeric) = 0.23566642349717923070468517074482
absolute error = 1.2515519493689751e-16
relative error = 5.3106926765235863287905680010577e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4811061288398062393956157082674
y[1] (analytic) = 0.23583586418691327495493187818492
y[1] (numeric) = 0.23583586418691340012226926854289
absolute error = 1.2516733739035797e-16
relative error = 5.3073919788194626910914524132326e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 5.366
Order of pole = 1.197e-25
TOP MAIN SOLVE Loop
x[1] = 0.48270713959066153691366919120328
y[1] (analytic) = 0.23617346454640343562998328414902
y[1] (numeric) = 0.23617346454640356082139997193833
absolute error = 1.2519141668778931e-16
relative error = 5.3008248377197202688156203607813e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48350764496608918567269593267122
y[1] (analytic) = 0.23634162583930561504894912595941
y[1] (numeric) = 0.23634162583930574025230354841714
absolute error = 1.2520335442245773e-16
relative error = 5.2975583111028658766399570033281e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.9429
Order of pole = 7.229e-27
TOP MAIN SOLVE Loop
x[1] = 0.48430815034151683443172267413916
y[1] (analytic) = 0.23650936228550442230183183021154
y[1] (numeric) = 0.23650936228550454751705663301602
absolute error = 1.2521522480280448e-16
relative error = 5.2943030919701937813195225282135e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4851086557169444831907494156071
y[1] (analytic) = 0.23667667469023032812945143385688
y[1] (numeric) = 0.23667667469023045335647969994195
absolute error = 1.2522702826608507e-16
relative error = 5.2910591392238392456926134589513e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48670966646779978070880289854298
y[1] (analytic) = 0.23701003058360440933961308521461
y[1] (numeric) = 0.23701003058360453459004925975967
absolute error = 1.2525043617454506e-16
relative error = 5.2846048695126189239115532409875e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48751017184322742946782964001092
y[1] (analytic) = 0.23717607567016365419193583203846
y[1] (numeric) = 0.23717607567016377945397731042637
absolute error = 1.2526204147838791e-16
relative error = 5.2813944713625962561466424970130e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48831067721865507822685638147886
y[1] (analytic) = 0.23734169991109271051095615559108
y[1] (numeric) = 0.23734169991109283578453773813362
absolute error = 1.2527358158254254e-16
relative error = 5.2781951772263172742140772957960e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4891111825940827269858831229468
y[1] (analytic) = 0.23750690409913389945302594977794
y[1] (numeric) = 0.23750690409913402473808285834776
absolute error = 1.2528505690856982e-16
relative error = 5.2750069470097012072589136029709e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=102.9MB, alloc=4.5MB, time=5.61
TOP MAIN SOLVE Loop
x[1] = 0.49071219334493802450393660588268
y[1] (analytic) = 0.23783605547519735551981873684574
y[1] (numeric) = 0.23783605547519748082763363404015
absolute error = 1.2530781489719441e-16
relative error = 5.2686635189449687461121420215561e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49151269872036567326296334735062
y[1] (analytic) = 0.2380000042364099507553460429406
y[1] (numeric) = 0.23800000423641007607444443063648
absolute error = 1.2531909838769588e-16
relative error = 5.2655082418912070935621959526844e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 5.084
Order of pole = 1.062e-25
TOP MAIN SOLVE Loop
x[1] = 0.49231320409579332202199008881856
y[1] (analytic) = 0.23816353609113541406570253497779
y[1] (numeric) = 0.23816353609113553939602129090493
absolute error = 1.2533031875592714e-16
relative error = 5.2623638703436267830346649060901e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4931137094712209707810168302865
y[1] (analytic) = 0.23832665181988199064786272630792
y[1] (numeric) = 0.23832665181988211598933913468567
absolute error = 1.2534147640837775e-16
relative error = 5.2592303651840819049531681992814e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49471472022207626829907031322238
y[1] (analytic) = 0.23865163800939700517051778867464
y[1] (numeric) = 0.23865163800939713053412296588423
absolute error = 1.2536360517720959e-16
relative error = 5.2529957985150450604518620631120e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49551522559750391705809705469032
y[1] (analytic) = 0.23881351001913703821846886288607
y[1] (numeric) = 0.23881351001913716359304595484099
absolute error = 1.2537457709195492e-16
relative error = 5.2498946597245765754789801965537e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49631573097293156581712379615826
y[1] (analytic) = 0.23897496900086097306259921341465
y[1] (numeric) = 0.23897496900086109844808710110913
absolute error = 1.2538548788769448e-16
relative error = 5.2468042327580653139068459187505e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4971162363483592145761505376262
y[1] (analytic) = 0.23913601572309095507625415676841
y[1] (numeric) = 0.23913601572309108047259211321114
absolute error = 1.2539633795644273e-16
relative error = 5.2437244794462998724823668466847e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49871724709921451209420402056208
y[1] (analytic) = 0.2394568754513273399211787478649
y[1] (numeric) = 0.23945687545132746533903621478179
absolute error = 1.2541785746691689e-16
relative error = 5.2375968420422184566699925300572e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.3556
Order of pole = 3.886e-27
TOP MAIN SOLVE Loop
x[1] = 0.49951775247464216085323076203002
y[1] (analytic) = 0.23961668998257658931771519548896
y[1] (numeric) = 0.23961668998257671474624287412205
absolute error = 1.2542852767863309e-16
relative error = 5.2345488825404215162015499282507e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.50031825785006980961225750349796
y[1] (analytic) = 0.2397760953048367097661661442505
y[1] (numeric) = 0.23977609530483683520530484763374
absolute error = 1.2543913870338324e-16
relative error = 5.2315114458723487999762220025677e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.7458
Order of pole = 1.380e-27
TOP MAIN SOLVE Loop
x[1] = 0.5011187632254974583712842449659
y[1] (analytic) = 0.23993509217488579523158555777549
y[1] (numeric) = 0.23993509217488592068127647705253
absolute error = 1.2544969091927704e-16
relative error = 5.2284844947915444201566225950654e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=106.8MB, alloc=4.5MB, time=5.80
TOP MAIN SOLVE Loop
x[1] = 0.50271977397635275588933772790178
y[1] (analytic) = 0.24025186357387127023822930692314
y[1] (numeric) = 0.24025186357387139570884973030581
absolute error = 1.2547062042338267e-16
relative error = 5.2224619013123151304060587879459e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.50352027935178040464836446936972
y[1] (analytic) = 0.24040963960480005247795577196485
y[1] (numeric) = 0.24040963960480017795895422629167
absolute error = 1.2548099845432682e-16
relative error = 5.2194661853243528942236619009109e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.50432078472720805340739121083766
y[1] (analytic) = 0.24056701018752126126619229144239
y[1] (numeric) = 0.24056701018752138675751145336437
absolute error = 1.2549131916192198e-16
relative error = 5.2164808077425858997092940931820e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5051212901026357021664179523056
y[1] (analytic) = 0.24072397606730522424125158302896
y[1] (numeric) = 0.24072397606730534974283449394785
absolute error = 1.2550158291091889e-16
relative error = 5.2135057322179354814662139203543e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.50672230085349099968447143524148
y[1] (analytic) = 0.24103669668778343114310423018569
y[1] (numeric) = 0.2410366966877835566650452092852
absolute error = 1.2552194097909951e-16
relative error = 5.2075863428251750395621554794249e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.50752280622891864844349817670942
y[1] (analytic) = 0.24119245290768654232850264092193
y[1] (numeric) = 0.24119245290768666786053865574723
absolute error = 1.2553203601482530e-16
relative error = 5.2046419571374876103835248724549e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.50832331160434629720252491817736
y[1] (analytic) = 0.241347807383088376267618243005
y[1] (numeric) = 0.24134780738308850180969376808289
absolute error = 1.2554207552507789e-16
relative error = 5.2017077298658244362957179698183e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5091238169797739459615516596453
y[1] (analytic) = 0.24150276084798217521531390305605
y[1] (numeric) = 0.24150276084798230076737376482733
absolute error = 1.2555205986177128e-16
relative error = 5.1987836255338736201028506584872e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51072482773062924347960514258118
y[1] (analytic) = 0.24181146767108651495505473702746
y[1] (numeric) = 0.24181146767108664052691914665034
absolute error = 1.2557186440962288e-16
relative error = 5.1929656446412426886950701361080e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51152533310605689223863188404912
y[1] (analytic) = 0.24196522248617827308457057500546
y[1] (numeric) = 0.2419652224861783986662558871603
absolute error = 1.2558168531215484e-16
relative error = 5.1900716979824823944730857948843e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51232583848148454099765862551706
y[1] (analytic) = 0.24211857920454223500148609247044
y[1] (numeric) = 0.24211857920454236059293851638471
absolute error = 1.2559145242391427e-16
relative error = 5.1871877340653966398091634863659e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.513126343856912189756685366985
y[1] (analytic) = 0.24227153854911978857038013571365
y[1] (numeric) = 0.24227153854911991417154622019196
absolute error = 1.2560116608447831e-16
relative error = 5.1843137182625795983725129131917e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=110.6MB, alloc=4.5MB, time=6.00
TOP MAIN SOLVE Loop
x[1] = 0.51472735460776748727473884992088
y[1] (analytic) = 0.24257626799777091624066909166349
y[1] (numeric) = 0.24257626799777104186110348996497
absolute error = 1.2562043439830148e-16
relative error = 5.1785953933241248599281965379038e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 3.565
Order of pole = 5.589e-26
TOP MAIN SOLVE Loop
x[1] = 0.51552785998319513603376559138882
y[1] (analytic) = 0.24272803953684318387291071769355
y[1] (numeric) = 0.24272803953684330950290043643782
absolute error = 1.2562998971874427e-16
relative error = 5.1757510157649155883606467155765e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51632836535862278479279233285676
y[1] (analytic) = 0.24287941657214381613636463932223
y[1] (numeric) = 0.24287941657214394177585756171874
absolute error = 1.2563949292239651e-16
relative error = 5.1729164494710121587458075748858e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5171288707340504335518190743247
y[1] (analytic) = 0.24303039981578227690560646036409
y[1] (numeric) = 0.24303039981578240255455079734117
absolute error = 1.2564894433697708e-16
relative error = 5.1700916606407812105504360262698e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51872988148490573106987255726058
y[1] (analytic) = 0.24333118776581684260386779394728
y[1] (numeric) = 0.2433311877658169682715608921841
absolute error = 1.2566769309823682e-16
relative error = 5.1644712809761171710575570047731e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51953038686033337982889929872852
y[1] (analytic) = 0.24348099388576378798066980468322
y[1] (numeric) = 0.24348099388576391365766089352935
absolute error = 1.2567699108884613e-16
relative error = 5.1616756233470591584806943804653e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52033089223576102858792604019646
y[1] (analytic) = 0.2436304090411672218832173764475
y[1] (numeric) = 0.24363040904116734756945595472748
absolute error = 1.2568623857827998e-16
relative error = 5.1588896095906592956175543048761e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5211313976111886773469527816644
y[1] (analytic) = 0.2437794339335194586994439861271
y[1] (numeric) = 0.2437794339335195843948798689843
absolute error = 1.2569543588285720e-16
relative error = 5.1561132067086233245948669339762e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52273240836204397486500626460028
y[1] (analytic) = 0.24407631572455744529427056161083
y[1] (numeric) = 0.24407631572455757100795175321179
absolute error = 1.2571368119160096e-16
relative error = 5.1505891023637910881716700813897e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52353291373747162362403300606822
y[1] (analytic) = 0.2442241740157706826255229230895
y[1] (numeric) = 0.24422417401577080834825274043045
absolute error = 1.2572272981734095e-16
relative error = 5.1478413356911364887583449307304e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52433341911289927238305974753616
y[1] (analytic) = 0.24437164482900428134670185741877
y[1] (numeric) = 0.24437164482900440707843135882441
absolute error = 1.2573172950140564e-16
relative error = 5.1451030494714188034771425481380e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 5.073
Order of pole = 1.048e-25
TOP MAIN SOLVE Loop
x[1] = 0.5251339244883269211420864890041
y[1] (analytic) = 0.24451872885534316516325656680745
y[1] (numeric) = 0.24451872885534329090393711596011
absolute error = 1.2574068054915266e-16
relative error = 5.1423742114879313681527374265368e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=114.4MB, alloc=4.5MB, time=6.20
TOP MAIN SOLVE Loop
x[1] = 0.52673493523918221866013997193998
y[1] (analytic) = 0.24481173930140094499485634144548
y[1] (numeric) = 0.2448117393014010707532942878804
absolute error = 1.2575843794643492e-16
relative error = 5.1369447521308167224832456504063e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52753544061460986741916671340792
y[1] (analytic) = 0.2449576670930385813367565810477
y[1] (numeric) = 0.24495766709303870710400147709357
absolute error = 1.2576724489604587e-16
relative error = 5.1342440670892571644281549872048e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52833594599003751617819345487586
y[1] (analytic) = 0.24510321084163518174373233567152
y[1] (numeric) = 0.24510321084163530751973674519504
absolute error = 1.2577600440952352e-16
relative error = 5.1315527029464033058896411147155e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5291364513654651649372201963438
y[1] (analytic) = 0.24524837122807315819988593757489
y[1] (numeric) = 0.24524837122807328398460271925953
absolute error = 1.2578471678168464e-16
relative error = 5.1288706282460431829628414373036e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53073746211632046245527367927968
y[1] (analytic) = 0.24553754462792916975477615082169
y[1] (numeric) = 0.2455375446279292955567774218655
absolute error = 1.2580200127104381e-16
relative error = 5.1235342220952634017938143688496e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53153796749174811121430042074762
y[1] (analytic) = 0.24568155899306217659135110688509
y[1] (numeric) = 0.24568155899306230240192507452769
absolute error = 1.2581057396764260e-16
relative error = 5.1208798284772922657450561315460e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53233847286717575997332716221556
y[1] (analytic) = 0.24582519269948232658293031250782
y[1] (numeric) = 0.24582519269948245240203099426571
absolute error = 1.2581910068175789e-16
relative error = 5.1182345999651014368745300655072e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5331389782426034087323539036835
y[1] (analytic) = 0.24596844641806965077570778592253
y[1] (numeric) = 0.24596844641806977660328948399074
absolute error = 1.2582758169806821e-16
relative error = 5.1155985058425161540992405412062e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53473998899345870625040738661938
y[1] (analytic) = 0.24625381656538938307781790461032
y[1] (numeric) = 0.24625381656538950892222567070968
absolute error = 1.2584440776609936e-16
relative error = 5.1103535986287170127012489960527e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53554049436888635500943412808732
y[1] (analytic) = 0.24639593432602860519077024176217
y[1] (numeric) = 0.24639593432602873104352361909638
absolute error = 1.2585275337733421e-16
relative error = 5.1077447248300420886537308676922e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.1567
Order of pole = 1.498e-27
TOP MAIN SOLVE Loop
x[1] = 0.53634099974431400376846086955526
y[1] (analytic) = 0.24653767476266408850756624629625
y[1] (numeric) = 0.24653767476266421436862065611867
absolute error = 1.2586105440982242e-16
relative error = 5.1051448640044910361040057537990e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5371415051197416525274876110232
y[1] (analytic) = 0.24667903853636899336157637534818
y[1] (numeric) = 0.24667903853636911923088751383827
absolute error = 1.2586931113849009e-16
relative error = 5.1025539861560881994049289925205e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.6957
Order of pole = 1.745e-27
memory used=118.2MB, alloc=4.5MB, time=6.40
TOP MAIN SOLVE Loop
x[1] = 0.53874251587059695004554109395908
y[1] (analytic) = 0.24696063872959575991230344866963
y[1] (numeric) = 0.24696063872959588579799622322453
absolute error = 1.2588569277455490e-16
relative error = 5.0973990601146254698265253977570e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.851
Order of pole = 4.679e-27
TOP MAIN SOLVE Loop
x[1] = 0.53954302124602459880456783542702
y[1] (analytic) = 0.24710087646160277225049733769473
y[1] (numeric) = 0.24710087646160289814431556002945
absolute error = 1.2589381822233472e-16
relative error = 5.0948349526351224335801067272254e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54034352662145224756359457689496
y[1] (analytic) = 0.24724074015566461151353099710103
y[1] (numeric) = 0.24724074015566473741543144418937
absolute error = 1.2590190044708834e-16
relative error = 5.0922797095583667048293108503499e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.48
Order of pole = 7.475e-27
TOP MAIN SOLVE Loop
x[1] = 0.5411440319968798963226213183629
y[1] (analytic) = 0.24738023046323858070139134321883
y[1] (numeric) = 0.24738023046323870661133105757799
absolute error = 1.2590993971435916e-16
relative error = 5.0897333015893419179986477890512e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54274504274773519384067480129878
y[1] (analytic) = 0.24765809351525636599668922161324
y[1] (numeric) = 0.24765809351525649192257965108568
absolute error = 1.2592589042947244e-16
relative error = 5.0846668744833524335906273119964e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54354554812316284259970154276672
y[1] (analytic) = 0.24779646755314129089407924110639
y[1] (numeric) = 0.2477964675531414168278816403965
absolute error = 1.2593380239929011e-16
relative error = 5.0821467974430638672065207414431e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54434605349859049135872828423466
y[1] (analytic) = 0.24793447079143532195757657202756
y[1] (numeric) = 0.24793447079143544789924902763076
absolute error = 1.2594167245560320e-16
relative error = 5.0796354397023902741398673505096e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.1801
Order of pole = 9.657e-27
TOP MAIN SOLVE Loop
x[1] = 0.5451465588740181401177550257026
y[1] (analytic) = 0.24807210387216654132768193487998
y[1] (numeric) = 0.24807210387216666727718278980675
absolute error = 1.2594950085492677e-16
relative error = 5.0771327726486132534525048135119e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54674756962487343763580850863848
y[1] (analytic) = 0.24834626211974101100958798575072
y[1] (numeric) = 0.24834626211974113697462168560753
absolute error = 1.2596503369985681e-16
relative error = 5.0721533968215045019235164888628e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54754807500030108639483525010642
y[1] (analytic) = 0.24848278856135031311516291138926
y[1] (numeric) = 0.24848278856135043908790156111418
absolute error = 1.2597273864972492e-16
relative error = 5.0696766314912107132337250203932e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54834858037572873515386199157436
y[1] (analytic) = 0.24861894739494332949395746784999
y[1] (numeric) = 0.24861894739494345547436041900344
absolute error = 1.2598040295115345e-16
relative error = 5.0672084437324655147558220182248e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5491490857511563839128887330423
y[1] (analytic) = 0.24875473925330129729177511907947
y[1] (numeric) = 0.24875473925330142327980197104822
absolute error = 1.2598802685196875e-16
relative error = 5.0647488055967450617508675121947e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=122.0MB, alloc=4.5MB, time=6.61
TOP MAIN SOLVE Loop
x[1] = 0.55075009650201168143094221597818
y[1] (analytic) = 0.24902522456630487759487147991181
y[1] (numeric) = 0.24902522456630500359802591449904
absolute error = 1.2600315443458723e-16
relative error = 5.0598550670531740816932746834108e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55155060187743933018996895744612
y[1] (analytic) = 0.24915991927740206214187757451619
y[1] (numeric) = 0.24915991927740218815253617811988
absolute error = 1.2601065860360369e-16
relative error = 5.0574209113990678013442630586685e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55235110725286697894899569891406
y[1] (analytic) = 0.24929424952618143717237585045828
y[1] (numeric) = 0.24929424952618156319049919691737
absolute error = 1.2601812334645909e-16
relative error = 5.0549951948740954046705439647604e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.553151612628294627708022440382
y[1] (analytic) = 0.24942821593635562286998082416498
y[1] (numeric) = 0.24942821593635574889552972678182
absolute error = 1.2602554890261684e-16
relative error = 5.0525778901763727192804108215302e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55475262337914992522607592331788
y[1] (analytic) = 0.24969505972678237595097978979092
y[1] (numeric) = 0.24969505972678250199126319432291
absolute error = 1.2604028340453199e-16
relative error = 5.0477684076908016966734817847500e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55555312875457757398510266478582
y[1] (analytic) = 0.2498279383455244273822993681102
y[1] (numeric) = 0.2498279383455245534298921892024
absolute error = 1.2604759282109220e-16
relative error = 5.0453761759328185540342471812939e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55635363413000522274412940625376
y[1] (analytic) = 0.2499604556026540337764547105311
y[1] (numeric) = 0.24996045560265415983131870311595
absolute error = 1.2605486399258485e-16
relative error = 5.0429922480604737233454147639353e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5571541395054328715031561477217
y[1] (analytic) = 0.25009261211298938793170593418939
y[1] (numeric) = 0.25009261211298951399380308461208
absolute error = 1.2606209715042269e-16
relative error = 5.0406165974014886767674992564439e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55875515025628816902120963065758
y[1] (analytic) = 0.25035584534376523668381852848118
y[1] (numeric) = 0.25035584534376536276026887140916
absolute error = 1.2607645034292798e-16
relative error = 5.0358900216534424222954505068059e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55955565563171581778023637212552
y[1] (analytic) = 0.25048692328507754904800536064847
y[1] (numeric) = 0.25048692328507767513157619324787
absolute error = 1.2608357083259940e-16
relative error = 5.0335390438368114983214567450532e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56035616100714346653926311359346
y[1] (analytic) = 0.25061764292135271048525894642619
y[1] (numeric) = 0.25061764292135283657591316507369
absolute error = 1.2609065421864750e-16
relative error = 5.0311962377771023371963151742913e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5611566663825711152982898550614
y[1] (analytic) = 0.25074800485868474362093475170123
y[1] (numeric) = 0.25074800485868486971863547643514
absolute error = 1.2609770072473391e-16
relative error = 5.0288615774151182702620023602395e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.5MB, time=6.81
x[1] = 0.56275767713342641281634333799728
y[1] (analytic) = 0.25100765805227843244498824616064
y[1] (numeric) = 0.25100765805227855855667223026335
absolute error = 1.2611168398410271e-16
relative error = 5.0242165901502851056553785364637e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56355818250885406157537007946522
y[1] (analytic) = 0.25113695051213090027007161371956
y[1] (numeric) = 0.25113695051213102638869279089657
absolute error = 1.2611862117717701e-16
relative error = 5.0219062117298818461994968827248e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56435868788428171033439682093316
y[1] (analytic) = 0.25126588768023502753067589142825
y[1] (numeric) = 0.25126588768023515365619826132419
absolute error = 1.2612552236989594e-16
relative error = 5.0196038759708317239096362873021e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5651591932597093590934235624011
y[1] (analytic) = 0.25139447015412709444389274620565
y[1] (numeric) = 0.25139447015412722057628052466297
absolute error = 1.2613238777845732e-16
relative error = 5.0173095574109878232033941125963e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56676020401056465661147704533698
y[1] (analytic) = 0.2516505734009671109558053791333
y[1] (numeric) = 0.25165057340096723710181747974627
absolute error = 1.2614601210061297e-16
relative error = 5.0127448706273514873579027201000e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56756070938599230537050378680492
y[1] (analytic) = 0.25177809536055396938719362621631
y[1] (numeric) = 0.25177809536055409553996506556618
absolute error = 1.2615277143934987e-16
relative error = 5.0104744520644349453634716099822e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56836121476141995412953052827286
y[1] (analytic) = 0.25190526499921945415426414153683
y[1] (numeric) = 0.25190526499921958031375998577297
absolute error = 1.2615949584423614e-16
relative error = 5.0082119500212531843356024018930e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5691617201368476028885572697408
y[1] (analytic) = 0.25203208290610480123102250342865
y[1] (numeric) = 0.25203208290610492739720802771002
absolute error = 1.2616618552428137e-16
relative error = 5.0059573396171512792376286733374e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57076273088770290040661075267668
y[1] (analytic) = 0.25228466587280732781973572306494
y[1] (numeric) = 0.25228466587280745399919726193499
absolute error = 1.2617946153887005e-16
relative error = 5.0014716947753417946235021721109e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57156323626313054916563749414462
y[1] (analytic) = 0.25241043210263325357044844730379
y[1] (numeric) = 0.25241043210263337975649673175067
absolute error = 1.2618604828444688e-16
relative error = 4.9992406111462955330488820137884e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57236374163855819792466423561256
y[1] (analytic) = 0.25253584894070911631442978416191
y[1] (numeric) = 0.25253584894070924250703091143214
absolute error = 1.2619260112727023e-16
relative error = 4.9970173207724653490312971596346e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5731642470139858466836909770805
y[1] (analytic) = 0.25266091696794017323095870112942
y[1] (numeric) = 0.25266091696794029943007897055545
absolute error = 1.2619912026942603e-16
relative error = 4.9948017993395978232459406631872e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.5MB, time=7.01
x[1] = 0.57476525776484114420174446001638
y[1] (analytic) = 0.25291000890535298654039555271773
y[1] (numeric) = 0.25291000890535311275245380603683
absolute error = 1.2621205825331910e-16
relative error = 4.9903939665966991639512638357703e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57556576314026879296077120148432
y[1] (analytic) = 0.25303403396922789654674957638172
y[1] (numeric) = 0.25303403396922802276522706888043
absolute error = 1.2621847749249871e-16
relative error = 4.9882016072133780861385631033628e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57636626851569644171979794295226
y[1] (analytic) = 0.25315771252965661075587531996875
y[1] (numeric) = 0.25315771252965673698073914588413
absolute error = 1.2622486382591538e-16
relative error = 4.9860169206232871019596808935988e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5771667738911240904788246844202
y[1] (analytic) = 0.25328104515946393429954703056745
y[1] (numeric) = 0.25328104515946406053076447955262
absolute error = 1.2623121744898517e-16
relative error = 4.9838398830639260207080713262909e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57876778464197938799687816735608
y[1] (analytic) = 0.25352667491053102489896628661461
y[1] (numeric) = 0.25352667491053115114279362585062
absolute error = 1.2624382733923601e-16
relative error = 4.9795086605299881614600879705302e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57956829001740703675590490882402
y[1] (analytic) = 0.25364897316947593740711187598674
y[1] (numeric) = 0.25364897316947606365719586675244
absolute error = 1.2625008399076570e-16
relative error = 4.9773544285713121827244189064652e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58036879539283468551493165029196
y[1] (analytic) = 0.25377092777318178074605467897185
y[1] (numeric) = 0.25377092777318190700236337963673
absolute error = 1.2625630870066488e-16
relative error = 4.9752077516740474017304788744859e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5811693007682623342739583917599
y[1] (analytic) = 0.25389253928654498728996252183417
y[1] (numeric) = 0.25389253928654511355246417975759
absolute error = 1.2626250165792342e-16
relative error = 4.9730686066132345831789057334494e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58277031151911763179201187469578
y[1] (analytic) = 0.25413473529399653083343342555323
y[1] (numeric) = 0.25413473529399665710822648975599
absolute error = 1.2627479306420276e-16
relative error = 4.9688128196297679208163246845334e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58357081689454528055103861616372
y[1] (analytic) = 0.25425532091006278387004107978549
y[1] (numeric) = 0.25425532091006291015093296474136
absolute error = 1.2628089188495587e-16
relative error = 4.9666961317841978357499402439677e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58437132226997292931006535763166
y[1] (analytic) = 0.25437556567975399754529939862051
y[1] (numeric) = 0.25437556567975412383225909517183
absolute error = 1.2628695969655132e-16
relative error = 4.9645868839281611796670452016718e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5851718276454005780690920990996
y[1] (analytic) = 0.25449547016018695187189747743527
y[1] (numeric) = 0.25449547016018707816489415922183
absolute error = 1.2629299668178656e-16
relative error = 4.9624850533604399543628050426864e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.799
Order of pole = 1.030e-26
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.5MB, time=7.21
x[1] = 0.58677283839625587558714558203548
y[1] (analytic) = 0.25473426047405912675126907749983
y[1] (numeric) = 0.25473426047405925305624797581886
absolute error = 1.2630497889831903e-16
relative error = 4.9583035538001886637383147700883e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58757334377168352434617232350342
y[1] (analytic) = 0.25485314741406318146716925977544
y[1] (numeric) = 0.25485314741406330777809374896603
absolute error = 1.2631092448919059e-16
relative error = 4.9562238399187438277142982526964e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58837384914711117310519906497136
y[1] (analytic) = 0.2549716962779501520645096870529
y[1] (numeric) = 0.25497169627795027838134965992111
absolute error = 1.2631683997286821e-16
relative error = 4.9541514535467299481589309894433e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5891743545225388218642258064393
y[1] (analytic) = 0.25508990761520261366840395392547
y[1] (numeric) = 0.255089907615202739991129480107
absolute error = 1.2632272552618153e-16
relative error = 4.9520863724932826155699178580161e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59077536527339411938227928937518
y[1] (analytic) = 0.25532531990019162836401276707896
y[1] (numeric) = 0.25532531990019175469842031028434
absolute error = 1.2633440754320538e-16
relative error = 4.9479780380806080292837871116163e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59157587064882176814130603084312
y[1] (analytic) = 0.25544252193936761949820241692197
y[1] (numeric) = 0.25544252193936774583840677169428
absolute error = 1.2634020435477231e-16
relative error = 4.9459347408400818135661667902200e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59237637602424941690033277231106
y[1] (analytic) = 0.25555938863479923275087222784848
y[1] (numeric) = 0.25555938863479935909684415955313
absolute error = 1.2634597193170465e-16
relative error = 4.9438986611545001160397945977075e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.593176881399677065659359513779
y[1] (analytic) = 0.2556759205284770963758155004306
y[1] (numeric) = 0.25567592052847722272752594551046
absolute error = 1.2635171044507986e-16
relative error = 4.9418697773303548077936169941124e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59477789215053236317741299671488
y[1] (analytic) = 0.25590798207113166224106475491973
y[1] (numeric) = 0.25590798207113178860416571477002
absolute error = 1.2636310095985029e-16
relative error = 4.9378335109815628747924265848000e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59557839752596001193643973818282
y[1] (analytic) = 0.25602351279670379485311685227981
y[1] (numeric) = 0.25602351279670392122187015008639
absolute error = 1.2636875329780658e-16
relative error = 4.9358260855576202973937756542590e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59637890290138766069546647965076
y[1] (analytic) = 0.25613871087372404811912205394598
y[1] (numeric) = 0.25613871087372417449349929929014
absolute error = 1.2637437724534416e-16
relative error = 4.9338257701955295056741589322506e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 2.046
Order of pole = 1.419e-26
TOP MAIN SOLVE Loop
x[1] = 0.5971794082768153094544932211187
y[1] (analytic) = 0.2562535768368302530197158527659
y[1] (numeric) = 0.25625357683683037939968882076126
absolute error = 1.2637997296799536e-16
relative error = 4.9318325436865198112042767723289e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.5MB, time=7.41
x[1] = 0.59878041902767060697254670405458
y[1] (analytic) = 0.25648231455258661494194016981667
y[1] (numeric) = 0.25648231455258674133302056516804
absolute error = 1.2639108039535137e-16
relative error = 4.9278672728695055550764787845192e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59958092440309825573157344552252
y[1] (analytic) = 0.25659618736726344552563003136096
y[1] (numeric) = 0.25659618736726357192222245708882
absolute error = 1.2639659242572786e-16
relative error = 4.9258951866193450546638987669637e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.60038142977852590449060018699046
y[1] (analytic) = 0.25670973019209034512091523107868
y[1] (numeric) = 0.25670973019209047152299211365563
absolute error = 1.2640207688257695e-16
relative error = 4.9239301053369892396153166816034e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6011819351539535532496269284584
y[1] (analytic) = 0.25682294355448846730886037634637
y[1] (numeric) = 0.25682294355448859371639430243114
absolute error = 1.2640753392608477e-16
relative error = 4.9219720082861560580601862474486e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.60278294590480885076768041139428
y[1] (analytic) = 0.25704838399455198541821906083442
y[1] (numeric) = 0.25704838399455211183658546943283
absolute error = 1.2641836640859841e-16
relative error = 4.9180766843987544908701751199754e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.60358345128023649952670715286222
y[1] (analytic) = 0.25716061211994456646335899736058
y[1] (numeric) = 0.25716061211994469288710116013701
absolute error = 1.2642374216277643e-16
relative error = 4.9161394165530298590521171517204e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.60438395665566414828573389433016
y[1] (analytic) = 0.25727251287837327734107633942138
y[1] (numeric) = 0.25727251287837340377016747339397
absolute error = 1.2642909113397259e-16
relative error = 4.9142090509195789653757845940554e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6051844620310917970447606357981
y[1] (analytic) = 0.25738408679017576080549019783538
y[1] (numeric) = 0.25738408679017588723990367505329
absolute error = 1.2643441347721791e-16
relative error = 4.9122855672227152172336017720721e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.60678547278194709456281411873398
y[1] (analytic) = 0.25760625614825292101068174437422
y[1] (numeric) = 0.2576062561482530474556606393179
absolute error = 1.2644497889494368e-16
relative error = 4.9084591649891584586699843931531e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.60758597815737474332184086020192
y[1] (analytic) = 0.25771685262821873095194700225436
y[1] (numeric) = 0.25771685262821885740216927672582
absolute error = 1.2645022227447146e-16
relative error = 4.9065562063528701130518253175523e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.60838648353280239208086760166986
y[1] (analytic) = 0.25782712432895088946495295890908
y[1] (numeric) = 0.2578271243289510159203925950666
absolute error = 1.2645543963615752e-16
relative error = 4.9046600494530704000297204016994e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6091869889082300408398943431378
y[1] (analytic) = 0.25793707176383381597564759824663
y[1] (numeric) = 0.25793707176383394243627872830801
absolute error = 1.2646063113006138e-16
relative error = 4.9027706744631203743153897191788e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61078799965908533835794782607368
y[1] (analytic) = 0.25815599588271843545043302465557
y[1] (numeric) = 0.25815599588271856192137013455863
absolute error = 1.2647093710990306e-16
relative error = 4.8990121913480344440603272298192e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
memory used=141.1MB, alloc=4.5MB, time=7.62
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61158850503451298711697456754162
y[1] (analytic) = 0.25826497358663296066241860196862
y[1] (numeric) = 0.25826497358663308713847049309196
absolute error = 1.2647605189112334e-16
relative error = 4.8971430440101061528966318973441e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61238901040994063587600130900956
y[1] (analytic) = 0.25837362906453400622829458384287
y[1] (numeric) = 0.25837362906453413270943597898307
absolute error = 1.2648114139514020e-16
relative error = 4.8952806001555597272673344701931e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6131895157853682846350280504775
y[1] (analytic) = 0.2584819628229802487721400920529
y[1] (numeric) = 0.25848196282298037525834585927099
absolute error = 1.2648620576721809e-16
relative error = 4.8934248403955897994285093752231e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61479052653622358215308153341338
y[1] (analytic) = 0.25869766720099753446593513535311
y[1] (numeric) = 0.25869766720099766096219482728238
absolute error = 1.2649625969192927e-16
relative error = 4.8897332960349749242268176981662e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61559103191165123091210827488132
y[1] (analytic) = 0.25880503882695531646657429235818
y[1] (numeric) = 0.25880503882695544296782382278426
absolute error = 1.2650124953042608e-16
relative error = 4.8878974730862387550886881514634e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.467
Order of pole = 1.090e-27
TOP MAIN SOLVE Loop
x[1] = 0.61639153728707887967113501634926
y[1] (analytic) = 0.25891209074624164480612834134069
y[1] (numeric) = 0.25891209074624177131234315006497
absolute error = 1.2650621480872428e-16
relative error = 4.8860682575350389657819340705438e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6171920426625065284301617578172
y[1] (analytic) = 0.25901882345871419690453234979759
y[1] (numeric) = 0.25901882345871432341568801726043
absolute error = 1.2651115566746284e-16
relative error = 4.8842456304195142920468030299916e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61879305341336182594821524075308
y[1] (analytic) = 0.25923133325602621057488050852579
y[1] (numeric) = 0.25923133325602633709584519282248
absolute error = 1.2652096468429669e-16
relative error = 4.8806200660681717793305604465900e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.71
Order of pole = 9.047e-27
TOP MAIN SOLVE Loop
x[1] = 0.61959355878878947470724198222102
y[1] (analytic) = 0.259337111333973119821051531605
y[1] (numeric) = 0.25933711133397324634688465077408
absolute error = 1.2652583311916908e-16
relative error = 4.8788170913275001161445293129808e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62039406416421712346626872368896
y[1] (analytic) = 0.25944257219133080899930038780959
y[1] (numeric) = 0.2594425721913309355299780758584
absolute error = 1.2653067768804881e-16
relative error = 4.8770206300119619433680824933535e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6211945695396447722252954651569
y[1] (analytic) = 0.25954771632137803104679728276498
y[1] (numeric) = 0.25954771632137815758229580987734
absolute error = 1.2653549852711236e-16
relative error = 4.8752306635760630944675848199734e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62279558029050006974334894809278
y[1] (analytic) = 0.259757056366154013087614327928
y[1] (numeric) = 0.25975705636615413963268388406357
absolute error = 1.2654506955613557e-16
relative error = 4.8716701415709536191566981062807e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=144.9MB, alloc=4.5MB, time=7.82
TOP MAIN SOLVE Loop
x[1] = 0.62359608566592771850237568956072
y[1] (analytic) = 0.25986125326095246062612205206488
y[1] (numeric) = 0.25986125326095258717594206617041
absolute error = 1.2654982001410553e-16
relative error = 4.8698995493192785828793468844033e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62439659104135536726140243102866
y[1] (analytic) = 0.25996513538858927132852042400183
y[1] (numeric) = 0.25996513538858939788306770229407
absolute error = 1.2655454727829224e-16
relative error = 4.8681353785815056334705106249628e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 4.544
Order of pole = 1.477e-25
TOP MAIN SOLVE Loop
x[1] = 0.6251970964167830160204291724966
y[1] (analytic) = 0.2600687032358837456183075010769
y[1] (numeric) = 0.26006870323588387217755898164327
absolute error = 1.2655925148056637e-16
relative error = 4.8663776112182338275158438129749e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62679810716763831353848265543248
y[1] (analytic) = 0.26027489803033865196647081079933
y[1] (numeric) = 0.26027489803033877853506203345065
absolute error = 1.2656859122265132e-16
relative error = 4.8628812144572617958735775964151e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62759861254306596229750939690042
y[1] (analytic) = 0.26037752594476740168185710122865
y[1] (numeric) = 0.26037752594476752825508412324161
absolute error = 1.2657322702201296e-16
relative error = 4.8611425491792372809704399166274e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62839911791849361105653613836836
y[1] (analytic) = 0.26047984151339970494974205168424
y[1] (numeric) = 0.2604798415133998315275823302598
absolute error = 1.2657784027857556e-16
relative error = 4.8594102155142816949324126084336e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6291996232939212598155628798363
y[1] (analytic) = 0.26058184521671234315389349303267
y[1] (numeric) = 0.26058184521671246973632461308737
absolute error = 1.2658243112005470e-16
relative error = 4.8576841957191103457114406346172e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63000012866934890857458962130424
y[1] (analytic) = 0.26068353753392740691577387118373
y[1] (numeric) = 0.26068353753392753350277354453627
absolute error = 1.2658699967335254e-16
relative error = 4.8559644721284907275188239608282e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63160113942020420609264310424012
y[1] (analytic) = 0.26088598992070705190507828661374
y[1] (numeric) = 0.26088598992070717850114870559382
absolute error = 1.2659607041898008e-16
relative error = 4.8525438432879178644056769630957e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63240164479563185485166984570806
y[1] (analytic) = 0.26098675094248329087690247767491
y[1] (numeric) = 0.26098675094248341747747533877325
absolute error = 1.2660057286109834e-16
relative error = 4.8508429030942950826615582198222e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.633202150171059503610696587176
y[1] (analytic) = 0.26108720248259429137134774045039
y[1] (numeric) = 0.26108720248259441797640125507409
absolute error = 1.2660505351462370e-16
relative error = 4.8491481892171251115943532097638e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.8777
Order of pole = 1.716e-27
TOP MAIN SOLVE Loop
x[1] = 0.63400265554648715236972332864394
y[1] (analytic) = 0.26118734501405668213001920270806
y[1] (numeric) = 0.26118734501405680873953170518446
absolute error = 1.2660951250247640e-16
relative error = 4.8474596843756913263873779764208e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.5MB, time=8.02
x[1] = 0.63560366629734244988777681157982
y[1] (analytic) = 0.26138670493696845005975065751133
y[1] (numeric) = 0.26138670493696857667811662646355
absolute error = 1.2661836596895222e-16
relative error = 4.8441012330556498992057404590557e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63640417167277009864680355304776
y[1] (analytic) = 0.26148592326833069706482762608057
y[1] (numeric) = 0.26148592326833082368758831562025
absolute error = 1.2662276068953968e-16
relative error = 4.8424312523929781357938948643353e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6372046770481977474058302945157
y[1] (analytic) = 0.2615848344708789045785599277103
y[1] (numeric) = 0.26158483447087903120569415610428
absolute error = 1.2662713422839398e-16
relative error = 4.8407674123971749200522390253352e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63800518242362539616485703598364
y[1] (analytic) = 0.26168343901153580560763095905505
y[1] (numeric) = 0.26168343901153593223911766364681
absolute error = 1.2663148670459176e-16
relative error = 4.8391096961626775748352391439143e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.6114
Order of pole = 8.90e-28
TOP MAIN SOLVE Loop
x[1] = 0.63960619317448069368291051891952
y[1] (analytic) = 0.26187972996884297762604937233531
y[1] (numeric) = 0.26187972996884310426617831390183
absolute error = 1.2664012894156652e-16
relative error = 4.8358125677246372614208368019378e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64040669854990834244193726038746
y[1] (analytic) = 0.26197741731332810420344236412312
y[1] (numeric) = 0.26197741731332823084786130087797
absolute error = 1.2664441893675485e-16
relative error = 4.8341731220781759225758340455156e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6412072039253359912009640018554
y[1] (analytic) = 0.26207479985160028077644549088717
y[1] (numeric) = 0.26207479985160040742513382900693
absolute error = 1.2664868833811976e-16
relative error = 4.8325397333064649464937124316821e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64200770930076363995999074332334
y[1] (analytic) = 0.26217187804459756601890738139921
y[1] (numeric) = 0.26217187804459769267184464242648
absolute error = 1.2665293726102727e-16
relative error = 4.8309123848699964913254465343207e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64360872005161893747804422625922
y[1] (analytic) = 0.26236512323260380333433135366845
y[1] (numeric) = 0.26236512323260392999570548297465
absolute error = 1.2666137412930620e-16
relative error = 4.8276757432051144269872928534578e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64440922542704658623707096772716
y[1] (analytic) = 0.26246129114358573835138931703761
y[1] (numeric) = 0.26246129114358586501695161883452
absolute error = 1.2666556230179691e-16
relative error = 4.8260664172569919658945466765188e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6452097308024742349960977091951
y[1] (analytic) = 0.26255715654124721245702955363739
y[1] (numeric) = 0.26255715654124733912676000371621
absolute error = 1.2666973045007882e-16
relative error = 4.8244630662039964121762246577821e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64601023617790188375512445066304
y[1] (analytic) = 0.26265271988064854368926032243082
y[1] (numeric) = 0.26265271988064867036313900836612
absolute error = 1.2667387868593530e-16
relative error = 4.8228656738638345027103679645786e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.5MB, time=8.22
x[1] = 0.64761124692875718127317793359892
y[1] (analytic) = 0.26284294219910165257453787175009
y[1] (numeric) = 0.26284294219910177925665373575249
absolute error = 1.2668211586400240e-16
relative error = 4.8196887009445207577501482541047e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.187
Order of pole = 5.293e-27
TOP MAIN SOLVE Loop
x[1] = 0.64841175230418483003220467506686
y[1] (analytic) = 0.26293760208247616254952915853848
y[1] (numeric) = 0.26293760208247628923573418482977
absolute error = 1.2668620502629129e-16
relative error = 4.8181090883514399421949656836297e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6492122576796124787912314165348
y[1] (analytic) = 0.26303196171624428242713652913611
y[1] (numeric) = 0.26303196171624440911741124545708
absolute error = 1.2669027471632097e-16
relative error = 4.8165353704426580304907363565124e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65001276305504012755025815800274
y[1] (analytic) = 0.26312602154969329105784605897608
y[1] (numeric) = 0.26312602154969341775217110139138
absolute error = 1.2669432504241530e-16
relative error = 4.8149675313845058727072009523314e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65161377380589542506831164093862
y[1] (analytic) = 0.26331324360707599212338386067316
y[1] (numeric) = 0.26331324360707611882575189338357
absolute error = 1.2670236803271041e-16
relative error = 4.8118494268286606278274233099255e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65241427918132307382733838240656
y[1] (analytic) = 0.26340640672388937806863818012282
y[1] (numeric) = 0.26340640672388950477499909031289
absolute error = 1.2670636091019007e-16
relative error = 4.8102991300058824478852288821300e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6532147845567507225863651238745
y[1] (analytic) = 0.26349927182615115577499178740658
y[1] (numeric) = 0.26349927182615128248532663770792
absolute error = 1.2671033485030134e-16
relative error = 4.8087546493829016649307936466399e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65401528993217837134539186534244
y[1] (analytic) = 0.26359183935747808802928363464475
y[1] (numeric) = 0.26359183935747821474357359267187
absolute error = 1.2671428995802712e-16
relative error = 4.8072159694663264081227435085049e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65561630068303366886344534827832
y[1] (analytic) = 0.26377608347618852418427798023085
y[1] (numeric) = 0.26377608347618865090642207321707
absolute error = 1.2672214409298622e-16
relative error = 4.8041559501138633109665277833855e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65641680605846131762247208974626
y[1] (analytic) = 0.26386776094521159073590963321765
y[1] (numeric) = 0.26386776094521171746195296014911
absolute error = 1.2672604332693146e-16
relative error = 4.8026345800252699643602813945250e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6572173114338889663814988312142
y[1] (analytic) = 0.26395914260658688511637656803818
y[1] (numeric) = 0.26395914260658701184630070996212
absolute error = 1.2672992414192394e-16
relative error = 4.8011189493370288779330897041354e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65801781680931661514052557268214
y[1] (analytic) = 0.26405022889836105128781684928308
y[1] (numeric) = 0.26405022889836117802160348900265
absolute error = 1.2673378663971957e-16
relative error = 4.7996090428879079568933626527277e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.5MB, time=8.42
x[1] = 0.65961882756017191265857905561802
y[1] (analytic) = 0.26423151711978569339009715767263
y[1] (numeric) = 0.26423151711978582013155424526038
absolute error = 1.2674145708758775e-16
relative error = 4.7966063423891733678294519718360e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 5.233
Order of pole = 9.606e-26
TOP MAIN SOLVE Loop
x[1] = 0.66041933293559956141760579708596
y[1] (analytic) = 0.26432171992003430863511583408804
y[1] (numeric) = 0.26432171992003443538038107211709
absolute error = 1.2674526523802905e-16
relative error = 4.7951135183432336459804319155804e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6612198383110272101766325385539
y[1] (analytic) = 0.26441162909188585829396757029364
y[1] (numeric) = 0.26441162909188598504302304231325
absolute error = 1.2674905547201961e-16
relative error = 4.7936263585431396729705760695525e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66202034368645485893565928002184
y[1] (analytic) = 0.26450124506791518985873884197072
y[1] (numeric) = 0.26450124506791531661156673016883
absolute error = 1.2675282788819811e-16
relative error = 4.7921448481519309022805710974961e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66362135443731015645371276295772
y[1] (analytic) = 0.26467959915739672596679849479006
y[1] (numeric) = 0.26467959915739685272711815341487
absolute error = 1.2676031965862481e-16
relative error = 4.7891987165676637662121302060343e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.726
Order of pole = 3.085e-27
TOP MAIN SOLVE Loop
x[1] = 0.66442185981273780521273950442566
y[1] (analytic) = 0.26476833813060025417719594922879
y[1] (numeric) = 0.26476833813060038094123515634282
absolute error = 1.2676403920711403e-16
relative error = 4.7877340660191061593062720522813e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6652223651881654539717662458936
y[1] (analytic) = 0.26485678562749183555143225522617
y[1] (numeric) = 0.26485678562749196231917358150767
absolute error = 1.2676774132628150e-16
relative error = 4.7862750061678295722188347297856e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 5.474
Order of pole = 1.078e-25
TOP MAIN SOLVE Loop
x[1] = 0.66602287056359310273079298736154
y[1] (analytic) = 0.26494494207527081818791361146553
y[1] (numeric) = 0.26494494207527094495933972321995
absolute error = 1.2677142611175442e-16
relative error = 4.7848215224934800571462778252327e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66762388131444840024884647029742
y[1] (analytic) = 0.26512038352697354149439311372248
y[1] (numeric) = 0.26512038352697366827313717490205
absolute error = 1.2677874406117957e-16
relative error = 4.7819312259059480413534170222724e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66842438668987604900787321176536
y[1] (analytic) = 0.26520766937999239589114647633021
y[1] (numeric) = 0.26520766937999252267352388978269
absolute error = 1.2678237741345248e-16
relative error = 4.7804943842629727475178779622645e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6692248920653036977668999532333
y[1] (analytic) = 0.26529466588209634666381735625731
y[1] (numeric) = 0.26529466588209647344981116493747
absolute error = 1.2678599380868016e-16
relative error = 4.7790630613367499611002504593686e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67002539744073134652592669470124
y[1] (analytic) = 0.26538137345520356256939231809656
y[1] (numeric) = 0.26538137345520368935898565767662
absolute error = 1.2678959333958006e-16
relative error = 4.7776372429160772574659654826862e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.5MB, time=8.62
x[1] = 0.67162640819158664404398017763712
y[1] (analytic) = 0.26555392349687870443662455657436
y[1] (numeric) = 0.26555392349687883123336673299411
absolute error = 1.2679674217641975e-16
relative error = 4.7748020630510513564127293373790e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67242691356701429280300691910506
y[1] (analytic) = 0.26563976680407223309648200020916
y[1] (numeric) = 0.26563976680407235989677366516876
absolute error = 1.2680029166495960e-16
relative error = 4.7733926734879125498935569178920e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.673227418942441941562033660573
y[1] (analytic) = 0.26572532285952754738630390251391
y[1] (numeric) = 0.26572532285952767419012855689333
absolute error = 1.2680382465437942e-16
relative error = 4.7719887321921786169245056397402e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67402792431786959032106040204094
y[1] (analytic) = 0.26581059207997402669343230983839
y[1] (numeric) = 0.26581059207997415350077354442328
absolute error = 1.2680734123458489e-16
relative error = 4.7705902252545511428756957551587e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67562893506872488783911388497682
y[1] (analytic) = 0.26598027167762741465466315779145
y[1] (numeric) = 0.26598027167762754146898868201608
absolute error = 1.2681432552422463e-16
relative error = 4.7678094591137848064478364021326e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67642944044415253659814062644476
y[1] (analytic) = 0.26606468288317329970249736220806
y[1] (numeric) = 0.2660646828831734265202907729387
absolute error = 1.2681779341073064e-16
relative error = 4.7664271723885742428975923239369e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6772299458195801853571673679127
y[1] (analytic) = 0.26614880891039546870021011118045
y[1] (numeric) = 0.26614880891039559552145535335361
absolute error = 1.2682124524217316e-16
relative error = 4.7650502649767698025399883461756e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67803045119500783411619410938064
y[1] (analytic) = 0.26623265017092501722978313697237
y[1] (numeric) = 0.26623265017092514405446424271283
absolute error = 1.2682468110574046e-16
relative error = 4.7636787232639299956221050628139e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67963146194586313163424759231652
y[1] (analytic) = 0.26639948003338937329310593484058
y[1] (numeric) = 0.26639948003338950012461121018438
absolute error = 1.2683150527534380e-16
relative error = 4.7609516827678222458753459913896e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68043196732129078039327433378446
y[1] (analytic) = 0.26648246945355569155731991158949
y[1] (numeric) = 0.26648246945355581839221366469799
absolute error = 1.2683489375310850e-16
relative error = 4.7595961570452991917369134603142e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6812324726967184291523010752524
y[1] (analytic) = 0.26656517574349943151077595970712
y[1] (numeric) = 0.26656517574349955834904256616952
absolute error = 1.2683826660646240e-16
relative error = 4.7582459431426886362217232953546e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68203297807214607791132781672034
y[1] (analytic) = 0.26664759930984207052781857244213
y[1] (numeric) = 0.26664759930984219736944249240943
absolute error = 1.2684162391996730e-16
relative error = 4.7569010277335553142225259762229e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68363398882300137542938129965622
y[1] (analytic) = 0.26681159989325620255511829706393
y[1] (numeric) = 0.26681159989325632940341056017116
absolute error = 1.2684829226310723e-16
relative error = 4.7542270393736874562346034519902e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 7.783
Order of pole = 2.070e-25
memory used=164.0MB, alloc=4.5MB, time=8.82
TOP MAIN SOLVE Loop
x[1] = 0.68443449419842902418840804112416
y[1] (analytic) = 0.26689317771862726486915855646113
y[1] (numeric) = 0.26689317771862739172076201576738
absolute error = 1.2685160345930625e-16
relative error = 4.7528979400529990061808713701586e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6852349995738566729474347825921
y[1] (analytic) = 0.26697447443700324351492315576908
y[1] (numeric) = 0.26697447443700337036982260456022
absolute error = 1.2685489944879114e-16
relative error = 4.7515740864853548223656840958394e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68603550494928432170646152406004
y[1] (analytic) = 0.26705549045008286653641574461088
y[1] (numeric) = 0.26705549045008299339459605819561
absolute error = 1.2685818031358473e-16
relative error = 4.7502554656256596831277529025586e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68763651570013961922451500699592
y[1] (analytic) = 0.26721668196227994480065831292505
y[1] (numeric) = 0.26721668196228007166535530763
absolute error = 1.2686469699470495e-16
relative error = 4.7476338701269051445203225160784e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68843702107556726798354174846386
y[1] (analytic) = 0.26729685825993700107747844100503
y[1] (numeric) = 0.26729685825993712794541141360787
absolute error = 1.2686793297260284e-16
relative error = 4.7463308696740512663095611473250e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6892375264509949167425684899318
y[1] (analytic) = 0.26737675544938364374433933399888
y[1] (numeric) = 0.26737675544938377061549348295742
absolute error = 1.2687115414895854e-16
relative error = 4.7450330503010448988671414468201e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69003803182642256550159523139974
y[1] (analytic) = 0.26745637392748096575913369603411
y[1] (numeric) = 0.26745637392748109263349429937446
absolute error = 1.2687436060334035e-16
relative error = 4.7437403992376527636693980297018e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69163904257727786301964871433562
y[1] (analytic) = 0.26761477633228801794654605555802
y[1] (numeric) = 0.2676147763322881448272757176113
absolute error = 1.2688072966205328e-16
relative error = 4.7411705512295727452111690452486e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69243954795270551177867545580356
y[1] (analytic) = 0.26769356104794588600341992052731
y[1] (numeric) = 0.26769356104794601288731234365586
absolute error = 1.2688389242312855e-16
relative error = 4.7398933290144663389146735810743e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6932400533281331605377021972715
y[1] (analytic) = 0.26777206863015731364144349505209
y[1] (numeric) = 0.26777206863015744052848427077664
absolute error = 1.2688704077572455e-16
relative error = 4.7386212245676374234900790863690e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69404055870356080929672893873944
y[1] (analytic) = 0.26785029947102915930696633442535
y[1] (numeric) = 0.26785029947102928619714113146163
absolute error = 1.2689017479703628e-16
relative error = 4.7373542253874087401204064010032e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69564156945441610681478242167532
y[1] (analytic) = 0.26800593249247986016476203390453
y[1] (numeric) = 0.26800593249247998706116218616875
absolute error = 1.2689640015226422e-16
relative error = 4.7348354930846496280631566654219e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.5MB, time=9.02
x[1] = 0.69644207482984375557380916314326
y[1] (analytic) = 0.26808333545258050800287620691434
y[1] (numeric) = 0.26808333545258063490236784517138
absolute error = 1.2689949163825704e-16
relative error = 4.7335837352226413791770559152488e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6972425802052714043328359046112
y[1] (analytic) = 0.26816046323039163129043543785734
y[1] (numeric) = 0.26816046323039175819300453498229
absolute error = 1.2690256909712495e-16
relative error = 4.7323370331477934952586221268025e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69804308558069905309186264607914
y[1] (analytic) = 0.26823731621334758074026034885533
y[1] (numeric) = 0.26823731621334770764589295262334
absolute error = 1.2690563260376801e-16
relative error = 4.7310953746208538247273735264932e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69964409633155435060991612901502
y[1] (analytic) = 0.26839019933981035721654786652818
y[1] (numeric) = 0.26839019933981048412826592426181
absolute error = 1.2691171805773363e-16
relative error = 4.7286271395122734067441540557300e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.70044460170698199936894287048296
y[1] (analytic) = 0.26846623025357444103412314169357
y[1] (numeric) = 0.26846623025357456794886329431266
absolute error = 1.2691474015261909e-16
relative error = 4.7274005387100006986062975343925e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7012451070824096481279696119509
y[1] (analytic) = 0.26854198791300420745569332570837
y[1] (numeric) = 0.26854198791300433437344191611979
absolute error = 1.2691774859041142e-16
relative error = 4.7261789330139012822968675803472e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.70204561245783729688699635341884
y[1] (analytic) = 0.26861747270094159125736699471835
y[1] (numeric) = 0.26861747270094171817811043850962
absolute error = 1.2692074344379127e-16
relative error = 4.7249623104411841813784588739813e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.70364662320869259440504983635472
y[1] (analytic) = 0.2687676251891650102808658309344
y[1] (numeric) = 0.26876762518916513720755851679794
absolute error = 1.2692669268586354e-16
relative error = 4.7225439669874499279181342213323e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.8022
Order of pole = 8.270e-27
TOP MAIN SOLVE Loop
x[1] = 0.70444712858412024316407657782266
y[1] (analytic) = 0.26884229365060234389204907030481
y[1] (numeric) = 0.26884229365060247082169628805825
absolute error = 1.2692964721775344e-16
relative error = 4.7213422223928810330251706092878e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7052476339595478919231033192906
y[1] (analytic) = 0.26891669076285610823360939752644
y[1] (numeric) = 0.26891669076285623516619784915791
absolute error = 1.2693258845163147e-16
relative error = 4.7201454134941306155640488936689e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.70604813933497554068213006075854
y[1] (analytic) = 0.26899081690425431674963477817439
y[1] (numeric) = 0.268990816904254443685151236206
absolute error = 1.2693551645803161e-16
relative error = 4.7189535285590642665641982157537e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.70764915008583083820018354369442
y[1] (analytic) = 0.26913825778333167069801999274061
y[1] (numeric) = 0.26913825778333179763935306117341
absolute error = 1.2694133306843280e-16
relative error = 4.7165844838984670850396991336112e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.5MB, time=9.22
x[1] = 0.70844965546125848695921028516236
y[1] (analytic) = 0.26921157327321157621535410635835
y[1] (numeric) = 0.26921157327321170315957591776715
absolute error = 1.2694422181140880e-16
relative error = 4.7154073009550155513139532478724e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7092501608366861357182370266303
y[1] (analytic) = 0.26928461929664353926505041392958
y[1] (numeric) = 0.26928461929664366621214801879187
absolute error = 1.2694709760486229e-16
relative error = 4.7142349955389600101748245534713e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71005066621211378447726376809824
y[1] (analytic) = 0.26935739622751858616496091570178
y[1] (numeric) = 0.26935739622751871311492143295256
absolute error = 1.2694996051725078e-16
relative error = 4.7130675561631778364897997957564e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71165167696296908199531725103412
y[1] (analytic) = 0.26950214430277354051925238330394
y[1] (numeric) = 0.26950214430277366747490035393384
absolute error = 1.2695564797062990e-16
relative error = 4.7107472298254123823760733599169e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71245218233839673075434399250206
y[1] (analytic) = 0.26957411619055600510906090741968
y[1] (numeric) = 0.26957411619055613206753355393042
absolute error = 1.2695847264651074e-16
relative error = 4.7095943201300006142715251347237e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71325268771382437951337073397
y[1] (analytic) = 0.26964582047259264045245616940776
y[1] (numeric) = 0.26964582047259276741374088052009
absolute error = 1.2696128471111233e-16
relative error = 4.7084462310075723156387738323452e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71405319308925202827239747543794
y[1] (analytic) = 0.26971725751841289537472938319868
y[1] (numeric) = 0.26971725751841302233881361408198
absolute error = 1.2696408423088330e-16
relative error = 4.7073029512105206069812044923817e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71565420384010732579045095837382
y[1] (analytic) = 0.2698593313752080140022401897358
y[1] (numeric) = 0.26985933137520814097188608949712
absolute error = 1.2696964589976132e-16
relative error = 4.7050307748381987471596382008837e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71645470921553497454947769984176
y[1] (analytic) = 0.26992996892093655321458434813382
y[1] (numeric) = 0.26992996892093668018699252794055
absolute error = 1.2697240817980673e-16
relative error = 4.7039018560031546333261103539373e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7172552145909626233085044413097
y[1] (analytic) = 0.27000034069996191785136354762134
y[1] (numeric) = 0.27000034069996204482652172452469
absolute error = 1.2697515817690335e-16
relative error = 4.7027777019735167759343895872820e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71805571996639027206753118277764
y[1] (analytic) = 0.27007044707752589919571848577923
y[1] (numeric) = 0.27007044707752602617361444133547
absolute error = 1.2697789595555624e-16
relative error = 4.7016583017358508406027611735885e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.4274
Order of pole = 3.821e-27
TOP MAIN SOLVE Loop
x[1] = 0.71965673071724556958558466571352
y[1] (analytic) = 0.27020986508499581509661572633116
y[1] (numeric) = 0.27020986508499594207995083997922
absolute error = 1.2698333511364806e-16
relative error = 4.6994337188135170437871507161983e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.5MB, time=9.43
x[1] = 0.72045723609267321834461140718146
y[1] (analytic) = 0.27027917744115291968033353006557
y[1] (numeric) = 0.27027917744115304666637015026719
absolute error = 1.2698603662020162e-16
relative error = 4.6983285143321820100295560211538e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7212577414681008671036381486494
y[1] (analytic) = 0.27034822584835672073865305541455
y[1] (numeric) = 0.27034822584835684772737921796017
absolute error = 1.2698872616254562e-16
relative error = 4.6972280200490727851068840714503e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72205824684352851586266489011734
y[1] (analytic) = 0.2704170106676338162581414681794
y[1] (numeric) = 0.27041701066763394324954527148381
absolute error = 1.2699140380330441e-16
relative error = 4.6961322251797230538508792193282e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72365925759438381338071837305322
y[1] (analytic) = 0.27055379098234476940335388579398
y[1] (numeric) = 0.27055379098234489640007751451638
absolute error = 1.2699672362872240e-16
relative error = 4.6939546907701502230133441590881e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 4.262
Order of pole = 1.241e-25
TOP MAIN SOLVE Loop
x[1] = 0.72445976296981146213974511452116
y[1] (analytic) = 0.27062178719567078961868148180844
y[1] (numeric) = 0.27062178719567091661804741860447
absolute error = 1.2699936593679603e-16
relative error = 4.6928729298861002208556531017639e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7252602683452391108987718559891
y[1] (analytic) = 0.27068952125686005668123894883806
y[1] (numeric) = 0.27068952125686018368323553895617
absolute error = 1.2700199659011811e-16
relative error = 4.6917958257277575154701607652567e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72606077372066675965779859745704
y[1] (analytic) = 0.27075699352279501691642662537182
y[1] (numeric) = 0.27075699352279514392104227486484
absolute error = 1.2700461564949302e-16
relative error = 4.6907233677345626216750444706064e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72766178447152205717585208039292
y[1] (analytic) = 0.27089115409233243595185329458195
y[1] (numeric) = 0.27089115409233256296167252241851
absolute error = 1.2700981922783656e-16
relative error = 4.6885923482221071246329175250398e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72846228984694970593487882186086
y[1] (analytic) = 0.27095784310560873516570438727417
y[1] (numeric) = 0.27095784310560886217810825391283
absolute error = 1.2701240386663866e-16
relative error = 4.6875337658018708391738018432346e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7292627952223773546939055633288
y[1] (analytic) = 0.27102427174298392562566227843211
y[1] (numeric) = 0.27102427174298405264063942959724
absolute error = 1.2701497715116513e-16
relative error = 4.6864797877444420833302929617173e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73006330059780500345293230479674
y[1] (analytic) = 0.27109044035726595325787201544128
y[1] (numeric) = 0.27109044035726608027541115590013
absolute error = 1.2701753914045885e-16
relative error = 4.6854304037082375180613540180368e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73166431134866030097098578773262
y[1] (analytic) = 0.27122199892375171430762944672945
y[1] (numeric) = 0.27122199892375184133025891452405
absolute error = 1.2702262946779460e-16
relative error = 4.6833453765490573508646519152321e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73246481672408794973001252920056
y[1] (analytic) = 0.27128738957754890207801981411801
y[1] (numeric) = 0.27128738957754902910317773632213
memory used=179.2MB, alloc=4.5MB, time=9.62
absolute error = 1.2702515792220412e-16
relative error = 4.6823097129582325188426827442162e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7332653220995155984890392706685
y[1] (analytic) = 0.27135252161144524549155331204832
y[1] (numeric) = 0.27135252161144537251922862616862
absolute error = 1.2702767531412030e-16
relative error = 4.6812786024525545340669312977752e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73406582747494324724806601213644
y[1] (analytic) = 0.27141739537424248236717110768544
y[1] (numeric) = 0.27141739537424260939735280856645
absolute error = 1.2703018170088101e-16
relative error = 4.6802520349046197291566045551034e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73566683822579854476611949507232
y[1] (analytic) = 0.27154636947778343589455288538185
y[1] (numeric) = 0.27154636947778356292971457199965
absolute error = 1.2703516168661780e-16
relative error = 4.6782124883835421988474650929849e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73646734360122619352514623654026
y[1] (analytic) = 0.27161047051217546979992785495199
y[1] (numeric) = 0.27161047051217559683756325355831
absolute error = 1.2703763539860632e-16
relative error = 4.6771994893662101986932927291810e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7372678489766538422841729780082
y[1] (analytic) = 0.27167431466277033637455885045997
y[1] (numeric) = 0.27167431466277046341465718192848
absolute error = 1.2704009833146851e-16
relative error = 4.6761909932178734514934951428541e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73806835435208149104319971947614
y[1] (analytic) = 0.27173790227443052924711384657682
y[1] (numeric) = 0.27173790227443065628966438746857
absolute error = 1.2704255054089175e-16
relative error = 4.6751869900206392997006902463501e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.9873
Order of pole = 9.40e-28
TOP MAIN SOLVE Loop
x[1] = 0.73966936510293678856125320241202
y[1] (analytic) = 0.27186430925649984488512211554331
y[1] (numeric) = 0.27186430925649997193254512609762
absolute error = 1.2704742301055431e-16
relative error = 4.6731924230144898070399354663179e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74046987047836443732027994387996
y[1] (analytic) = 0.27192712931274477001124294402559
y[1] (numeric) = 0.27192712931274489706108632458365
absolute error = 1.2704984338055806e-16
relative error = 4.6722018395758295607046657809549e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7412703758537920860793066853479
y[1] (analytic) = 0.27198969420173182814518123480653
y[1] (numeric) = 0.27198969420173195519743448146235
absolute error = 1.2705225324665582e-16
relative error = 4.6712157098284220842419933079881e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74207088122921973483833342681584
y[1] (analytic) = 0.27205200426444993407635489529038
y[1] (numeric) = 0.27205200426445006113100755822741
absolute error = 1.2705465266293703e-16
relative error = 4.6702340240593383764096746899397e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74367189198007503235638690975172
y[1] (analytic) = 0.27217586127120277348063827376383
y[1] (numeric) = 0.27217586127120290054005863460617
absolute error = 1.2705942036084234e-16
relative error = 4.6682839458065380989173364234957e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74447239735550268111541365121966
y[1] (analytic) = 0.27223740889339084872269114886275
y[1] (numeric) = 0.27223740889339097578447989794891
absolute error = 1.2706178874908616e-16
relative error = 4.6673155340985490639666122252039e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=183.1MB, alloc=4.5MB, time=9.83
TOP MAIN SOLVE Loop
x[1] = 0.7452729027309303298744403926876
y[1] (analytic) = 0.27229870304562175687075241492198
y[1] (numeric) = 0.27229870304562188393489931567882
absolute error = 1.2706414690075684e-16
relative error = 4.6663515279199888260935646852568e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74607340810635797863346713415554
y[1] (analytic) = 0.27235974406507522970641404260437
y[1] (numeric) = 0.27235974406507535677290891100097
absolute error = 1.2706649486839660e-16
relative error = 4.6653919177584648826862620568230e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74767441885721327615152061709142
y[1] (analytic) = 0.2724810680506002187741445047032
y[1] (numeric) = 0.27248106805060034584530496493991
absolute error = 1.2707116046023671e-16
relative error = 4.6634858476347196931111428903094e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74847492423264092491054735855936
y[1] (analytic) = 0.27254135168727015992602321652381
y[1] (numeric) = 0.27254135168727028699950140453557
absolute error = 1.2707347818801176e-16
relative error = 4.6625393688449626211493432771122e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7492754296080685736695741000273
y[1] (analytic) = 0.27260138353236451899363560809601
y[1] (numeric) = 0.27260138353236464606942154700515
absolute error = 1.2707578593890914e-16
relative error = 4.6615972484168300169794773502431e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75007593498349622242860084149524
y[1] (analytic) = 0.27266116391931699936787695640986
y[1] (numeric) = 0.2726611639193171264459607203827
absolute error = 1.2707808376397284e-16
relative error = 4.6606594770341565457838986792543e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75167694573435151994665432443112
y[1] (analytic) = 0.27277997164882493356978926851678
y[1] (numeric) = 0.27277997164882506065243910782432
absolute error = 1.2708264983930754e-16
relative error = 4.6587969443340536980895872909903e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.6562
Order of pole = 7.378e-27
TOP MAIN SOLVE Loop
x[1] = 0.75247745110977916870568106589906
y[1] (analytic) = 0.27283899965454898453790042132147
y[1] (numeric) = 0.27283899965454911162281861152593
absolute error = 1.2708491819020446e-16
relative error = 4.6578721645773194783219511307226e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.753277956485206817464707807367
y[1] (analytic) = 0.2728977775284732584782076151174
y[1] (numeric) = 0.27289777752847338556538443164065
absolute error = 1.2708717681652325e-16
relative error = 4.6569516969871032042800664547690e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75407846186063446622373454883494
y[1] (analytic) = 0.27295630560034737137924728485821
y[1] (numeric) = 0.27295630560034749846867305271517
absolute error = 1.2708942576785696e-16
relative error = 4.6560355324392704797630885149745e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75567947261148976374178803177082
y[1] (analytic) = 0.27307261365329855143330567211265
y[1] (numeric) = 0.27307261365329867852720051463251
absolute error = 1.2709389484251986e-16
relative error = 4.6542160761636172551097424891841e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75647997798691741250081477323876
y[1] (analytic) = 0.27313039429023707681122039815318
y[1] (numeric) = 0.27313039429023720390733546177227
absolute error = 1.2709611506361909e-16
relative error = 4.6533127663764399841878041175772e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.5MB, time=10.02
x[1] = 0.7572804833623450612598415147067
y[1] (analytic) = 0.27318792643685317110392977441246
y[1] (numeric) = 0.27318792643685329820225557968935
absolute error = 1.2709832580527689e-16
relative error = 4.6524137235126094540359554278461e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75808098873777271001886825617464
y[1] (analytic) = 0.27324521041927311714339257888874
y[1] (numeric) = 0.27324521041927324424391969456974
absolute error = 1.2710052711568100e-16
relative error = 4.6515189386359349360473200419265e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75968199948862800753692173911052
y[1] (analytic) = 0.27335903519244467678313501460964
y[1] (numeric) = 0.27335903519244480388803664871189
absolute error = 1.2710490163410225e-16
relative error = 4.6497421072846719079128598101613e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76048250486405565629594848057846
y[1] (analytic) = 0.2734155766318709514390419266585
y[1] (numeric) = 0.27341557663187107854611686378173
absolute error = 1.2710707493712323e-16
relative error = 4.6488600431226079140610930580042e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7612830102394833050549752220464
y[1] (analytic) = 0.27347187120445512164665002100332
y[1] (numeric) = 0.27347187120445524875588901990498
absolute error = 1.2710923899890166e-16
relative error = 4.6479822015724346054078947820446e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76208351561491095381400196351434
y[1] (analytic) = 0.2735279192327597307914140752352
y[1] (numeric) = 0.27352791923275985790280794149923
absolute error = 1.2711139386626403e-16
relative error = 4.6471085738819244970191546248597e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76368452636576625133205544645022
y[1] (analytic) = 0.27363927694325428391694010335267
y[1] (numeric) = 0.27363927694325441103261630706542
absolute error = 1.2711567620371275e-16
relative error = 4.6453739252524503997356529223952e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76448503174119390009108218791816
y[1] (analytic) = 0.27369458726705013816180753421922
y[1] (numeric) = 0.27369458726705026527961130034257
absolute error = 1.2711780376612335e-16
relative error = 4.6445128869900364227335456612108e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7652855371166215488501089293861
y[1] (analytic) = 0.2737496523297828837729429652376
y[1] (numeric) = 0.27374965232978301089286528400734
absolute error = 1.2711992231876974e-16
relative error = 4.6436560279400798064076102292665e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76608604249204919760913567085404
y[1] (analytic) = 0.27380447245050978341038385220477
y[1] (numeric) = 0.27380447245050991053241575936448
absolute error = 1.2712203190715971e-16
relative error = 4.6428033395304397113394655009294e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76768705324290449512718915378992
y[1] (analytic) = 0.27391337913870668442332788302539
y[1] (numeric) = 0.2739133791387068115495522549347
absolute error = 1.2712622437190931e-16
relative error = 4.6411104405211987062260797347961e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76848755861833214388621589525786
y[1] (analytic) = 0.27396746634082964672819234685868
y[1] (numeric) = 0.27396746634082977385649968485592
absolute error = 1.2712830733799724e-16
relative error = 4.6402702129545219160999080993312e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=190.7MB, alloc=4.5MB, time=10.23
x[1] = 0.7692880639937597926452426367258
y[1] (analytic) = 0.27402130987025722899339269817588
y[1] (numeric) = 0.27402130987025735612377421746442
absolute error = 1.2713038151928854e-16
relative error = 4.6394341220937102990385836685705e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77008856936918744140426937819374
y[1] (analytic) = 0.27407491004259876179089317376761
y[1] (numeric) = 0.274074910042598888923340133781
absolute error = 1.2713244696001339e-16
relative error = 4.6386021595429336875925925317177e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77168958012004273892232286112962
y[1] (analytic) = 0.27418138157504924037579476072311
y[1] (numeric) = 0.27418138157504936751234655615557
absolute error = 1.2713655179543246e-16
relative error = 4.6369505859621069159411448629795e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77249008549547038768134960259756
y[1] (analytic) = 0.27423425356297180347643491174985
y[1] (numeric) = 0.27423425356297193061502618908963
absolute error = 1.2713859127733978e-16
relative error = 4.6361309583139010473833501878628e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7732905908708980364403763440655
y[1] (analytic) = 0.2742868834494400099036029197324
y[1] (numeric) = 0.27428688344944013704422511284234
absolute error = 1.2714062219310994e-16
relative error = 4.6353154257391272667949026821711e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77409109624632568519940308553344
y[1] (analytic) = 0.27433927154667152097662827375607
y[1] (numeric) = 0.27433927154667164811927285949128
absolute error = 1.2714264458573521e-16
relative error = 4.6345039800145884337251435542517e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77569210699718098271745656846932
y[1] (analytic) = 0.27444332361893892097016785598089
y[1] (numeric) = 0.27444332361893904811683182828782
absolute error = 1.2714666397230693e-16
relative error = 4.6328933163937506680800155265405e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77649261237260863147648330993726
y[1] (analytic) = 0.27449498821506054152190126163529
y[1] (numeric) = 0.27449498821506066867056231266459
absolute error = 1.2714866105102930e-16
relative error = 4.6320940822209560281558473101269e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7772931177480362802355100514052
y[1] (analytic) = 0.27454641226412130411237186308125
y[1] (numeric) = 0.27454641226412143126302163924284
absolute error = 1.2715064977616159e-16
relative error = 4.6312989023451204096537617589501e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77809362312346392899453679287314
y[1] (analytic) = 0.27459759607500240151774170367718
y[1] (numeric) = 0.27459759607500252867037189317367
absolute error = 1.2715263018949649e-16
relative error = 4.6305077687120964347409403707506e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77969463387431922651259027580902
y[1] (analytic) = 0.27469924421444872277566962904897
y[1] (numeric) = 0.27469924421444884993223587581811
absolute error = 1.2715656624676914e-16
relative error = 4.6289376081246937910371398127541e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78049513924974687527161701727696
y[1] (analytic) = 0.2747497091574811494859303852168
y[1] (numeric) = 0.27474970915748127664445235833778
absolute error = 1.2715852197312098e-16
relative error = 4.6281585652284060076827098660394e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.5MB, time=10.43
x[1] = 0.7812956446251745240306437587449
y[1] (analytic) = 0.27479993509127260864342934028329
y[1] (numeric) = 0.27479993509127273580389889278979
absolute error = 1.2716046955250650e-16
relative error = 4.6273835366908352194936634303346e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78209615000060217278967050021284
y[1] (analytic) = 0.27484992232142198615164975044626
y[1] (numeric) = 0.27484992232142211331405877600208
absolute error = 1.2716240902555582e-16
relative error = 4.6266125146233922394770430063143e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78369716075145747030772398314872
y[1] (analytic) = 0.27494918188994189845319592084381
y[1] (numeric) = 0.27494918188994202561945973487075
absolute error = 1.2716626381402694e-16
relative error = 4.6250824585079041802015806044799e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78449766612688511906675072461666
y[1] (analytic) = 0.27499845483626840881120735996003
y[1] (numeric) = 0.27499845483626853597938656953384
absolute error = 1.2716817920957381e-16
relative error = 4.6243234088456458051805392356088e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7852981715023127678257774660846
y[1] (analytic) = 0.27504749029486900013138210732129
y[1] (numeric) = 0.2750474902948691273014687663587
absolute error = 1.2717008665903741e-16
relative error = 4.6235683344248192491741474233942e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78609867687774041658480420755254
y[1] (analytic) = 0.27509628856811339659051992093319
y[1] (numeric) = 0.27509628856811352376250612285431
absolute error = 1.2717198620192112e-16
relative error = 4.6228172275189943786410298104867e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78769968762859571410285769048842
y[1] (analytic) = 0.27519317476481686558487524558012
y[1] (numeric) = 0.27519317476481699276063697043794
absolute error = 1.2717576172485782e-16
relative error = 4.6213268855066494366742205027298e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78850019300402336286188443195636
y[1] (analytic) = 0.27524126328982597691288435134165
y[1] (numeric) = 0.27524126328982610409052213415887
absolute error = 1.2717763778281722e-16
relative error = 4.6205876351068984694476901185692e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7893006983794510116209111734243
y[1] (analytic) = 0.27528911583258310374739055380704
y[1] (numeric) = 0.27528911583258323092689664381922
absolute error = 1.2717950609001218e-16
relative error = 4.6198523216354225091616568545847e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 4.519
Order of pole = 6.441e-26
TOP MAIN SOLVE Loop
x[1] = 0.79010120375487866037993791489224
y[1] (analytic) = 0.2753367326922809591179167554886
y[1] (numeric) = 0.27533673269228108629928344034251
absolute error = 1.2718136668485391e-16
relative error = 4.6191209375246366586816091564527e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79170221450573395789799139782812
y[1] (analytic) = 0.2754312605561255960911810008937
y[1] (numeric) = 0.27543126055612572327624589094537
absolute error = 1.2718506489005167e-16
relative error = 4.6176699272715531967714451106037e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79250271988116160665701813929606
y[1] (analytic) = 0.27547817215551980264758069754987
y[1] (numeric) = 0.27547817215551992983448327371325
absolute error = 1.2718690257616338e-16
relative error = 4.6169502861504635026552618731637e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.157
Order of pole = 8.274e-27
TOP MAIN SOLVE Loop
x[1] = 0.793303225256589255416044880764
y[1] (analytic) = 0.27552484926235364342121271134912
y[1] (numeric) = 0.27552484926235377060994541278494
absolute error = 1.2718873270143582e-16
relative error = 4.6162345444322237824049911934115e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
memory used=198.3MB, alloc=4.5MB, time=10.64
Complex estimate of poles used for equation 1
Radius of convergence = 1.963
Order of pole = 6.013e-27
TOP MAIN SOLVE Loop
x[1] = 0.79410373063201690417507162223194
y[1] (analytic) = 0.27557129217269399772390119575572
y[1] (numeric) = 0.27557129217269412491445649897711
absolute error = 1.2719055530322139e-16
relative error = 4.6155226947048636483731547896068e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79570474138287220169312510516782
y[1] (analytic) = 0.27566347658506821752272740264329
y[1] (numeric) = 0.2756634765850683447169054873468
absolute error = 1.2719417808470351e-16
relative error = 4.6141106417284878588386723349002e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79650524675829985045215184663576
y[1] (analytic) = 0.27570921867614829178160444116466
y[1] (numeric) = 0.27570921867614841897758277923538
absolute error = 1.2719597833807072e-16
relative error = 4.6134104238087448445567365336826e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7973057521337274992111785881037
y[1] (analytic) = 0.27575472774883127751139431058325
y[1] (numeric) = 0.27575472774883140470916552587818
absolute error = 1.2719777121529493e-16
relative error = 4.6127140685381786084913585483218e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79810625750915514797020532957164
y[1] (analytic) = 0.27580000409610844547654923834572
y[1] (numeric) = 0.27580000409610857267610599104775
absolute error = 1.2719955675270203e-16
relative error = 4.6120215686572871715115422052348e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79970726826001044548825881250752
y[1] (analytic) = 0.27588985978336649024246024388721
y[1] (numeric) = 0.27588985978336661744556619624932
absolute error = 1.2720310595236211e-16
relative error = 4.6106481061770156449319330409053e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.80050777363543809424728555397546
y[1] (analytic) = 0.2759344397062918732447325288599
y[1] (numeric) = 0.27593443970629200044960221512415
absolute error = 1.2720486968626425e-16
relative error = 4.6099671292087617258768549696236e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 2.241
Order of pole = 3.053e-26
TOP MAIN SOLVE Loop
x[1] = 0.8013082790108657430063122954434
y[1] (analytic) = 0.27597878806970435755445432519047
y[1] (numeric) = 0.27597878806970448476108054884048
absolute error = 1.2720662622365001e-16
relative error = 4.6092899788921911753563302008082e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.80210878438629339176533903691134
y[1] (analytic) = 0.27602290516356889867867941864697
y[1] (numeric) = 0.27602290516356902588705501849699
absolute error = 1.2720837559985002e-16
relative error = 4.6086166481172055284152655714086e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.276
Order of pole = 4.964e-27
TOP MAIN SOLVE Loop
x[1] = 0.80370979513714868928339251984722
y[1] (analytic) = 0.27611044669951875910137866770107
y[1] (numeric) = 0.27611044669951888631323167674045
absolute error = 1.2721185300903938e-16
relative error = 4.6072814168990695137261167356720e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.80451030051257633804241926131516
y[1] (analytic) = 0.27615387171854455190819152044309
y[1] (numeric) = 0.27615387171854467912177263216083
absolute error = 1.2721358111171774e-16
relative error = 4.6066195023828438524723170147063e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8053108058880039868014460027831
y[1] (analytic) = 0.27619706662190718303883956305216
y[1] (numeric) = 0.27619706662190731025414175564286
absolute error = 1.2721530219259070e-16
relative error = 4.6059613792618149442528709597036e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=202.1MB, alloc=4.5MB, time=10.83
TOP MAIN SOLVE Loop
x[1] = 0.80611131126343163556047274425104
y[1] (analytic) = 0.27624003169659367403387765257296
y[1] (numeric) = 0.27624003169659380125089393859672
absolute error = 1.2721701628602376e-16
relative error = 4.6053070405722979684782141644153e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 3.052
Order of pole = 2.946e-26
TOP MAIN SOLVE Loop
x[1] = 0.80771232201428693307852622718692
y[1] (analytic) = 0.27632527350493891460029991551355
y[1] (numeric) = 0.27632527350493904182072356259942
absolute error = 1.2722042364708587e-16
relative error = 4.6040096887775988732647505977831e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.80851282738971458183755296865486
y[1] (analytic) = 0.27636755080962997036858855722337
y[1] (numeric) = 0.27636755080963009759070553972646
absolute error = 1.2722211698250309e-16
relative error = 4.6033666618892387544734076327591e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8093133327651422305965797101228
y[1] (analytic) = 0.27640959942771326224407769179707
y[1] (numeric) = 0.27640959942771338946788115785612
absolute error = 1.2722380346605905e-16
relative error = 4.6027273918658047472689300761685e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81011383814056987935560645159074
y[1] (analytic) = 0.27645141964324536648994231797913
y[1] (numeric) = 0.27645141964324549371542544916242
absolute error = 1.2722548313118329e-16
relative error = 4.6020918718871131106315256685412e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81171484889142517687365993452662
y[1] (analytic) = 0.27653437599998183666652100410284
y[1] (numeric) = 0.27653437599998196389534314303991
absolute error = 1.2722882213893707e-16
relative error = 4.6008320549248975340660520805621e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81251535426685282563268667599456
y[1] (analytic) = 0.27657551270640444069884255000416
y[1] (numeric) = 0.27657551270640456792932409751549
absolute error = 1.2723048154751133e-16
relative error = 4.6002077444423428245835545774460e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8133158596422804743917134174625
y[1] (analytic) = 0.27661642214071602800570534150531
y[1] (numeric) = 0.27661642214071615523783961105081
absolute error = 1.2723213426954550e-16
relative error = 4.5995871570062437030583339675743e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81411636501770812315074015893044
y[1] (analytic) = 0.27665710458408934458676987126353
y[1] (numeric) = 0.27665710458408947182055020882491
absolute error = 1.2723378033756138e-16
relative error = 4.5989702859370792080328498540198e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81571737576856342066879364186632
y[1] (analytic) = 0.27673778961985773400439497457368
y[1] (numeric) = 0.27673778961985786124144761530905
absolute error = 1.2723705264073537e-16
relative error = 4.5977476663203529823340132929971e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81651788114399106942782038333426
y[1] (analytic) = 0.27677779277174934728987340503456
y[1] (numeric) = 0.27677779277174947452855234508474
absolute error = 1.2723867894005018e-16
relative error = 4.5971419045523006981818701391001e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8173183865194187181868471248022
y[1] (analytic) = 0.27681757005169939775975916744967
y[1] (numeric) = 0.27681757005169952500005788111194
absolute error = 1.2724029871366227e-16
relative error = 4.5965398327099842646192929920984e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=205.9MB, alloc=4.5MB, time=11.03
x[1] = 0.81811889189484636694587386627014
y[1] (analytic) = 0.27685712173804256095738889909891
y[1] (numeric) = 0.27685712173804268819930089231187
absolute error = 1.2724191199321296e-16
relative error = 4.5959414442517778203516654111316e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81971990264570166446392734920602
y[1] (analytic) = 0.27693554944043773345145320298775
y[1] (numeric) = 0.27693554944043786069657239881971
absolute error = 1.2724511919583196e-16
relative error = 4.5947556914573499463998395870996e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82052040802112931322295409067396
y[1] (analytic) = 0.27697442601035526370189786313683
y[1] (numeric) = 0.27697442601035539094861104445946
absolute error = 1.2724671318132263e-16
relative error = 4.5941683141737153581674996491177e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8213209133965569619819808321419
y[1] (analytic) = 0.27701307809440050933621247285664
y[1] (numeric) = 0.27701307809440063658451327045528
absolute error = 1.2724830079759864e-16
relative error = 4.5935845943791494010677334223180e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82212141877198461074100757360984
y[1] (analytic) = 0.27705150596811499806498950193483
y[1] (numeric) = 0.27705150596811512531487157738204
absolute error = 1.2724988207544721e-16
relative error = 4.5930045256672239788814265149439e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82372242952283990825906105654572
y[1] (analytic) = 0.27712769018395301683710636927343
y[1] (numeric) = 0.27712769018395314409013210744668
absolute error = 1.2725302573817325e-16
relative error = 4.5918553159990864202074634546743e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82452293489826755701808779801366
y[1] (analytic) = 0.27716544707440006982232552077979
y[1] (numeric) = 0.27716544707440019707691370457036
absolute error = 1.2725458818379057e-16
relative error = 4.5912861623632100466906330678021e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8253234402736952057771145394816
y[1] (analytic) = 0.27720298085116690765972130456638
y[1] (numeric) = 0.27720298085116703491586571702849
absolute error = 1.2725614441246211e-16
relative error = 4.5907206344504363324129785916449e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82612394564912285453614128094954
y[1] (analytic) = 0.27724029178704601325671776171461
y[1] (numeric) = 0.27724029178704614051441221586111
absolute error = 1.2725769445414650e-16
relative error = 4.5901587259869052528749201769735e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 7.636
Order of pole = 1.833e-25
TOP MAIN SOLVE Loop
x[1] = 0.82772495639997815205419476388542
y[1] (analytic) = 0.27731424622458974745112898984897
y[1] (numeric) = 0.27731424622458987471190508542458
absolute error = 1.2726077609557561e-16
relative error = 4.5890457424430459142839621230369e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82852546177540580081322150535336
y[1] (analytic) = 0.27735089026912330054075393782714
y[1] (numeric) = 0.27735089026912342780306169225498
absolute error = 1.2726230775442784e-16
relative error = 4.5884946549456090584293052613784e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8293259671508334495722482468213
y[1] (analytic) = 0.27738731255851040273103775672803
y[1] (numeric) = 0.27738731255851052999487110123787
absolute error = 1.2726383334450984e-16
relative error = 4.5879471620629936484170395896042e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.5MB, time=11.23
x[1] = 0.83012647252626109833127498828924
y[1] (analytic) = 0.2774235133628377927296551445779
y[1] (numeric) = 0.27742351336283791999500803955421
absolute error = 1.2726535289497631e-16
relative error = 4.5874032576513434448253023580132e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83172748327711639584932847122512
y[1] (analytic) = 0.27749525159398197433764731302662
y[1] (numeric) = 0.27749525159398210160602130591948
absolute error = 1.2726837399289286e-16
relative error = 4.5863261897939057516690852983503e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83252798865254404460835521269306
y[1] (analytic) = 0.27753078955829890355430936429729
y[1] (numeric) = 0.27753078955829903082418496216394
absolute error = 1.2726987559786665e-16
relative error = 4.5857930141885024808960839988429e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.833328494027971693367381954161
y[1] (analytic) = 0.27756610711255976595764479988629
y[1] (numeric) = 0.27756610711255989322901607816043
absolute error = 1.2727137127827414e-16
relative error = 4.5852634027346329591099380985431e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83412899940339934212640869562894
y[1] (analytic) = 0.27760120452418807099027633509958
y[1] (numeric) = 0.27760120452418819826313739758956
absolute error = 1.2727286106248998e-16
relative error = 4.5847373494159455187830633166496e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83573001015425463964446217856482
y[1] (analytic) = 0.27767073998660465019230959802393
y[1] (numeric) = 0.27767073998660477746813265310391
absolute error = 1.2727582305507998e-16
relative error = 4.5836958932446393519968501724379e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.9725
Order of pole = 7.28e-28
TOP MAIN SOLVE Loop
x[1] = 0.83653051552968228840348892003276
y[1] (analytic) = 0.27770517856960853176397070006685
y[1] (numeric) = 0.27770517856960865904126601950782
absolute error = 1.2727729531944097e-16
relative error = 4.5831804784849600349939791550898e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8373310209051099371625156615007
y[1] (analytic) = 0.27773939807441438003326469937915
y[1] (numeric) = 0.27773939807441450731202649896492
absolute error = 1.2727876179958577e-16
relative error = 4.5826685980461484883699703114563e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83813152628053758592154240296864
y[1] (analytic) = 0.27777339876582422080176967841532
y[1] (numeric) = 0.27777339876582434808199220154733
absolute error = 1.2728022252313201e-16
relative error = 4.5821602460369181932602915651777e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83973253703139288343959588590452
y[1] (analytic) = 0.27784074476506884761229858745908
y[1] (numeric) = 0.2778407447650689748954253976159
absolute error = 1.2728312681015682e-16
relative error = 4.5811541038655939858165567666775e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84053304240682053219862262737246
y[1] (analytic) = 0.27787409059991744497141478017713
y[1] (numeric) = 0.27787409059991757225598520830791
absolute error = 1.2728457042813078e-16
relative error = 4.5806563020441818630353236854125e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8413335477822481809576493688404
y[1] (analytic) = 0.27790721867540090709004455224335
y[1] (numeric) = 0.27790721867540103437605295074204
absolute error = 1.2728600839849869e-16
relative error = 4.5801620053335258351525766288580e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.5MB, time=11.43
x[1] = 0.84213405315767582971667611030834
y[1] (analytic) = 0.27794012925374076841134920966576
y[1] (numeric) = 0.27794012925374089569878995780933
absolute error = 1.2728744074814357e-16
relative error = 4.5796712079650305142501438079324e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84373506390853112723472959324422
y[1] (analytic) = 0.27800529896532120878884833462831
y[1] (numeric) = 0.27800529896532133607913702670384
absolute error = 1.2729028869207553e-16
relative error = 4.5787000883013351640490985607341e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84453556928395877599375633471216
y[1] (analytic) = 0.27803755862045504619460935241816
y[1] (numeric) = 0.27803755862045517348631369182866
absolute error = 1.2729170433941050e-16
relative error = 4.5782197545898653399799749632392e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8453360746593864247527830761801
y[1] (analytic) = 0.27806960182223499072298244504155
y[1] (numeric) = 0.27806960182223511801609691716145
absolute error = 1.2729311447211990e-16
relative error = 4.5777428973878328082116265276095e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 6.377
Order of pole = 1.204e-25
TOP MAIN SOLVE Loop
x[1] = 0.84613658003481407351180981764804
y[1] (analytic) = 0.27810142883034233999091536059602
y[1] (numeric) = 0.27810142883034246728543447696972
absolute error = 1.2729451911637370e-16
relative error = 4.5772695110470138378007520438580e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84773759078566937102986330058392
y[1] (analytic) = 0.2781644353017496153993235078411
y[1] (numeric) = 0.27816443530174974269663555133602
absolute error = 1.2729731204349492e-16
relative error = 4.5763331284750418885989978377153e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84853809616109701978889004205186
y[1] (analytic) = 0.27819561528190202984849672951547
y[1] (numeric) = 0.27819561528190215714719710752073
absolute error = 1.2729870037800526e-16
relative error = 4.5758701210660905799984754971372e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8493386015365246685479167835198
y[1] (analytic) = 0.27822658010208995967343332709117
y[1] (numeric) = 0.27822658010209008697351665443866
absolute error = 1.2730008332734749e-16
relative error = 4.5754105621625777818187662919718e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85013910691195231730694352498774
y[1] (analytic) = 0.278257330019493997669304606827
y[1] (numeric) = 0.27825733001949412497076552382647
absolute error = 1.2730146091699947e-16
relative error = 4.5749544462343922752652446165598e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85174011766280761482499700792362
y[1] (analytic) = 0.27831818617219701841140421186686
y[1] (numeric) = 0.27831818617219714571560433033199
absolute error = 1.2730420011846513e-16
relative error = 4.5740525213002541406867687825776e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85254062303823526358402374939156
y[1] (analytic) = 0.2783482929193860722456103785775
y[1] (numeric) = 0.27834829291938619955117215913544
absolute error = 1.2730556178055794e-16
relative error = 4.5736067013505119652365261709919e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8533411284136629123430504908595
y[1] (analytic) = 0.27837818578757445441853634293443
y[1] (numeric) = 0.27837818578757458172545452645473
absolute error = 1.2730691818352030e-16
relative error = 4.5731643024883419636542919978012e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85414163378909056110207723232744
y[1] (analytic) = 0.2784078650314808772443732641876
y[1] (numeric) = 0.27840786503148100455264261634584
absolute error = 1.2730826935215824e-16
relative error = 4.5727253192995427609449666792852e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
memory used=217.4MB, alloc=4.5MB, time=11.64
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85574264453994585862013071526332
y[1] (analytic) = 0.27846658366288532171746500746744
y[1] (numeric) = 0.27846658366288544902842109249309
absolute error = 1.2731095608502565e-16
relative error = 4.5718575783997723644134219087330e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85654314991537350737915745673126
y[1] (analytic) = 0.27849562355738794932257023910825
y[1] (numeric) = 0.27849562355738807663486193731851
absolute error = 1.2731229169821026e-16
relative error = 4.5714288099746661732421668811542e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8573436552908011561381841981992
y[1] (analytic) = 0.27852445084162085260860468621585
y[1] (numeric) = 0.27852445084162097992222686119809
absolute error = 1.2731362217498224e-16
relative error = 4.5710034357944898233881444383122e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85814416066622880489721093966714
y[1] (analytic) = 0.27855306576787899460100322289591
y[1] (numeric) = 0.27855306576787912191595076239127
absolute error = 1.2731494753949536e-16
relative error = 4.5705814505588014657204098987846e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85974517141708410241526442260302
y[1] (analytic) = 0.27860965955325116893604627250035
y[1] (numeric) = 0.27860965955325129625362930022025
absolute error = 1.2731758302771990e-16
relative error = 4.5697476258315250451025697072076e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86054567679251175117429116407096
y[1] (analytic) = 0.27863763891455992215555444492494
y[1] (numeric) = 0.278637638914560049474447644026
absolute error = 1.2731889319910106e-16
relative error = 4.5693357758512122778435457642006e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8613461821679393999333179055389
y[1] (analytic) = 0.27866540692228632518859841910127
y[1] (numeric) = 0.27866540692228645250879677266554
absolute error = 1.2732019835356427e-16
relative error = 4.5689272938377702186416181642874e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86214668754336704869234464700684
y[1] (analytic) = 0.27869296382633904399071859885964
y[1] (numeric) = 0.27869296382633917131221711348963
absolute error = 1.2732149851462999e-16
relative error = 4.5685221746024195587193130121556e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86374769829422234621039812994272
y[1] (analytic) = 0.2787474453206954393137803960083
y[1] (numeric) = 0.27874744532069556663786434603757
absolute error = 1.2732408395002927e-16
relative error = 4.5677220038212191875743751334143e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86454820366964999496942487141066
y[1] (analytic) = 0.27877437040845818765566896403048
y[1] (numeric) = 0.27877437040845831498103823481496
absolute error = 1.2732536927078448e-16
relative error = 4.5673269420079138366864172275235e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8653487090450776437284516128786
y[1] (analytic) = 0.2788010853874683120976146261302
y[1] (numeric) = 0.2788010853874684394242643171171
absolute error = 1.2732664969098690e-16
relative error = 4.5669352224376254414610655859167e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86614921442050529248747835434654
y[1] (analytic) = 0.27882759050528496861504579811044
y[1] (numeric) = 0.2788275905052850959429710316525
absolute error = 1.2732792523354206e-16
relative error = 4.5665468400311931945317964476309e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=221.2MB, alloc=4.5MB, time=11.84
TOP MAIN SOLVE Loop
x[1] = 0.86775022517136059000553183728242
y[1] (analytic) = 0.27887997214524821640079184233372
y[1] (numeric) = 0.27887997214524834373125361906289
absolute error = 1.2733046177672917e-16
relative error = 4.5657800665015854521900050511842e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86855073054678823876455857875036
y[1] (analytic) = 0.278905849160191149799394160205
y[1] (numeric) = 0.27890584916019127713111698277583
absolute error = 1.2733172282257083e-16
relative error = 4.5654016653281852039431740990201e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8693512359222158875235853202183
y[1] (analytic) = 0.27893151729953616462786222649875
y[1] (numeric) = 0.27893151729953629196084130768475
absolute error = 1.2733297908118600e-16
relative error = 4.5650265812180322614375212947744e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 3.692
Order of pole = 3.846e-26
TOP MAIN SOLVE Loop
x[1] = 0.87015174129764353628261206168624
y[1] (analytic) = 0.27895697680852904236424103159033
y[1] (numeric) = 0.27895697680852916969847160647337
absolute error = 1.2733423057488304e-16
relative error = 4.5646548091995893244646037464236e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87175275204849883380066554462212
y[1] (analytic) = 0.27900727091415095202208229177821
y[1] (numeric) = 0.27900727091415107935880164794839
absolute error = 1.2733671935617018e-16
relative error = 4.5639211816580582535843573890683e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87255325742392648255969228609006
y[1] (analytic) = 0.27903210599898522581683838828081
y[1] (numeric) = 0.27903210599898535315479507607383
absolute error = 1.2733795668779302e-16
relative error = 4.5635593162980362631729049237087e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.873353762799354131318719027558
y[1] (analytic) = 0.2790567334298806608089157303935
y[1] (numeric) = 0.27905673342988078814810507295806
absolute error = 1.2733918934256456e-16
relative error = 4.5632007433557026880355366715333e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87415426817478178007774576902594
y[1] (analytic) = 0.27908115344980516106283734714967
y[1] (numeric) = 0.27908115344980528840325468936291
absolute error = 1.2734041734221324e-16
relative error = 4.5628454579651996918442124831712e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87575527892563707759579925196182
y[1] (analytic) = 0.27912937222635750799445078112054
y[1] (numeric) = 0.2791293722263576353373102436071
absolute error = 1.2734285946248656e-16
relative error = 4.5621447304807101693990525069278e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87655578430106472635482599342976
y[1] (analytic) = 0.27915317146666986189929337987757
y[1] (numeric) = 0.27915317146666998924336700587844
absolute error = 1.2734407362600087e-16
relative error = 4.5617992787592388143394218449625e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8773562896764923751138527348977
y[1] (analytic) = 0.27917676426338306053229063107562
y[1] (numeric) = 0.27917676426338318787757385124859
absolute error = 1.2734528322017297e-16
relative error = 4.5614570953344783727920583203345e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87815679505192002387287947636564
y[1] (analytic) = 0.27920015085722200213196125785251
y[1] (numeric) = 0.27920015085722212947844952402055
absolute error = 1.2734648826616804e-16
relative error = 4.5611181754443525395137287169748e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=225.0MB, alloc=4.5MB, time=12.04
TOP MAIN SOLVE Loop
x[1] = 0.87975780580277532139093295930152
y[1] (analytic) = 0.27924630639695571901182529184039
y[1] (numeric) = 0.27924630639695584636071008957527
absolute error = 1.2734888479773488e-16
relative error = 4.5604501073222864714648220111212e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88055831117820297014995970076946
y[1] (analytic) = 0.27926907582208339416650735035674
y[1] (numeric) = 0.27926907582208352151658367544282
absolute error = 1.2735007632508608e-16
relative error = 4.5601209496685628077031839465420e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 0.7859
Order of pole = 6.929e-27
TOP MAIN SOLVE Loop
x[1] = 0.8813588165536306189089864422374
y[1] (analytic) = 0.27929164000280532851469628020088
y[1] (numeric) = 0.27929164000280545586595966802122
absolute error = 1.2735126338782034e-16
relative error = 4.5597950367057591733227631237331e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88215932192905826766801318370534
y[1] (analytic) = 0.27931399917763767316487924983874
y[1] (numeric) = 0.27931399917763780051732525639447
absolute error = 1.2735244600655573e-16
relative error = 4.5594723637737299319525432499286e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88376033267991356518606666664122
y[1] (analytic) = 0.27935810346151108211123240057757
y[1] (numeric) = 0.27935810346151120946603039454264
absolute error = 1.2735479799396507e-16
relative error = 4.5588367194621773059240373683387e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88456083805534121394509340810916
y[1] (analytic) = 0.27937984904540135282310003751746
y[1] (numeric) = 0.27937984904540148017906744085745
absolute error = 1.2735596740333999e-16
relative error = 4.5585237388629154688225478802211e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8853613434307688627041201495771
y[1] (analytic) = 0.27940139057310311558582395192011
y[1] (numeric) = 0.27940139057310324294295640203926
absolute error = 1.2735713245011915e-16
relative error = 4.5582139798548062579014097191828e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88616184880619651146314689104504
y[1] (analytic) = 0.27942272828095743249707282171355
y[1] (numeric) = 0.27942272828095755985536597610268
absolute error = 1.2735829315438913e-16
relative error = 4.5579074378778283515095232531263e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88776285955705180898120037398092
y[1] (analytic) = 0.27946479318033414110770140148482
y[1] (numeric) = 0.27946479318033426846830301671104
absolute error = 1.2736060161522622e-16
relative error = 4.5573039868761740580323541917473e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.88856336493247945774022711544886
y[1] (analytic) = 0.27948552084238877060352326829455
y[1] (numeric) = 0.27948552084238889796527267974113
absolute error = 1.2736174941144658e-16
relative error = 4.5570070688302357047210624939287e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8893638703079071064992538569168
y[1] (analytic) = 0.27950604562566305214928906052954
y[1] (numeric) = 0.27950604562566317951218200499503
absolute error = 1.2736289294446549e-16
relative error = 4.5567133497727668745474170896596e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89016437568333475525828059838474
y[1] (analytic) = 0.2795263677643560284065633330774
y[1] (numeric) = 0.27952636776435615577059556693062
absolute error = 1.2736403223385322e-16
relative error = 4.5564228252421101496909166243462e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=228.8MB, alloc=4.5MB, time=12.24
TOP MAIN SOLVE Loop
x[1] = 0.89176538643419005277633408132062
y[1] (analytic) = 0.2795664050426730983208117367102
y[1] (numeric) = 0.27956640504267322568710989621942
absolute error = 1.2736629815950922e-16
relative error = 4.5558513420118554936789561397124e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89256589180961770153536082278856
y[1] (analytic) = 0.27958612064857802072772568114275
y[1] (numeric) = 0.27958612064857814809515051555566
absolute error = 1.2736742483441291e-16
relative error = 4.5555703744859948098639854321866e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8933663971850453502943875642565
y[1] (analytic) = 0.27960563454246587197535196704741
y[1] (numeric) = 0.27960563454246599934389931000476
absolute error = 1.2736854734295735e-16
relative error = 4.5552925838342825967787251002211e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89416690256047299905341430572444
y[1] (analytic) = 0.27962494695642616807637864646046
y[1] (numeric) = 0.27962494695642629544604435067162
absolute error = 1.2736966570421116e-16
relative error = 4.5550179656917062812930137684453e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89576791331132829657146778866032
y[1] (analytic) = 0.27966296827083315078086574904722
y[1] (numeric) = 0.27966296827083327815275580967602
absolute error = 1.2737189006062880e-16
relative error = 4.5544782295694734632253502503815e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89656841868675594533049453012826
y[1] (analytic) = 0.27968167763337367463790432923316
y[1] (numeric) = 0.27968167763337380201090042267223
absolute error = 1.2737299609343907e-16
relative error = 4.5542131029551571656844706137025e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.293
Order of pole = 2.784e-27
TOP MAIN SOLVE Loop
x[1] = 0.8973689240621835940895212715962
y[1] (analytic) = 0.27970018644017684971415899381658
y[1] (numeric) = 0.27970018644017697708825704806925
absolute error = 1.2737409805425267e-16
relative error = 4.5539511315805232862757399526956e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89816942943761124284854801306414
y[1] (analytic) = 0.27971849492125459286201270773903
y[1] (numeric) = 0.27971849492125472023720866938979
absolute error = 1.2737519596165076e-16
relative error = 4.5536923111755265057630141866175e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89977044018846654036660149600002
y[1] (analytic) = 0.27975451182422401387218522222998
y[1] (numeric) = 0.27975451182422414124956491227661
absolute error = 1.2737737969004663e-16
relative error = 4.5531841062881828562046511563999e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.90057094556389418912562823746796
y[1] (analytic) = 0.27977222070408583573397087128489
y[1] (numeric) = 0.27977222070408596311243641901472
absolute error = 1.2737846554772983e-16
relative error = 4.5529347133594659873739189568502e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9013714509393218378846549789359
y[1] (analytic) = 0.27978973017416500164219410313747
y[1] (numeric) = 0.27978973017416512902174152850698
absolute error = 1.2737954742536951e-16
relative error = 4.5526884545075192997409153214678e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.90217195631474948664368172040384
y[1] (analytic) = 0.27980704046242720270636372180353
y[1] (numeric) = 0.27980704046242733008698906287672
absolute error = 1.2738062534107319e-16
relative error = 4.5524453255556305610811237659603e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 5.466
Order of pole = 1.748e-25
memory used=232.7MB, alloc=4.5MB, time=12.44
TOP MAIN SOLVE Loop
x[1] = 0.90377296706560478416173520333972
y[1] (analytic) = 0.27984106440333706201900724879754
y[1] (numeric) = 0.27984106440333718940177660743509
absolute error = 1.2738276935863755e-16
relative error = 4.5519684407374820541337795883177e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.90457347244103243292076194480766
y[1] (analytic) = 0.27985777850989337214600678546452
y[1] (numeric) = 0.27985777850989349952984228171435
absolute error = 1.2738383549624983e-16
relative error = 4.5517346766099134705109305322711e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9053739778164600816797886862756
y[1] (analytic) = 0.27987429434245246614695543133577
y[1] (numeric) = 0.27987429434245259353185317476608
absolute error = 1.2738489774343031e-16
relative error = 4.5515040258596572705121834463710e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.90617448319188773043881542774354
y[1] (analytic) = 0.27989061212696463970765094862033
y[1] (numeric) = 0.27989061212696476709360706644656
absolute error = 1.2738595611782623e-16
relative error = 4.5512764844017387798202712966576e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.90777549394274302795686891067942
y[1] (analytic) = 0.27992265445365348352091635671697
y[1] (numeric) = 0.2799226544536536109089776751182
absolute error = 1.2738806131840123e-16
relative error = 4.5508307131137449635711644366995e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.90857599931817067671589565214736
y[1] (analytic) = 0.27993837944573843925121215522209
y[1] (numeric) = 0.27993837944573856664032033464641
absolute error = 1.2738910817942432e-16
relative error = 4.5506124752042673565147510370197e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9093765046935983254749223936153
y[1] (analytic) = 0.27995390728959544829090799660153
y[1] (numeric) = 0.27995390728959557568105923395341
absolute error = 1.2739015123735188e-16
relative error = 4.5503973304281995435516266976619e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91017701006902597423394913508324
y[1] (analytic) = 0.279969238209189708847698637192
y[1] (numeric) = 0.27996923820918983623888914657574
absolute error = 1.2739119050938374e-16
relative error = 4.5501852747907449287819201437924e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91177802081988127175200261801912
y[1] (analytic) = 0.27999931016948481497549813951693
y[1] (numeric) = 0.27999931016948494236875590363739
absolute error = 1.2739325776412046e-16
relative error = 4.5497704150416927921203210100054e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91257852619530892051102935948706
y[1] (analytic) = 0.28001405165615365113662125951017
y[1] (numeric) = 0.28001405165615377853090704029741
absolute error = 1.2739428578078724e-16
relative error = 4.5495676030295244226129610658584e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.913379031570736569270056100955
y[1] (analytic) = 0.28002859711049808145162113356686
y[1] (numeric) = 0.28002859711049820884693121304997
absolute error = 1.2739531007948311e-16
relative error = 4.5493678643547061701385662156794e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.036
Order of pole = 4.643e-27
TOP MAIN SOLVE Loop
x[1] = 0.91417953694616421802908284242294
y[1] (analytic) = 0.28004294675452798270499543711488
y[1] (numeric) = 0.28004294675452811010132611408798
absolute error = 1.2739633067697310e-16
relative error = 4.5491711951111028348242929034098e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=236.5MB, alloc=4.5MB, time=12.64
TOP MAIN SOLVE Loop
x[1] = 0.91578054769701951554713632535882
y[1] (analytic) = 0.28007105949774718986248996313465
y[1] (numeric) = 0.28007105949774731726085079810313
absolute error = 1.2739836083496848e-16
relative error = 4.5487870493807031625065824294655e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91658105307244716430616306682676
y[1] (analytic) = 0.28008482303902322950386795852266
y[1] (numeric) = 0.28008482303902335690323838710103
absolute error = 1.2739937042857837e-16
relative error = 4.5485995651691653968955313867157e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9173815584478748130651898082947
y[1] (analytic) = 0.28009839165416052848752545670644
y[1] (numeric) = 0.28009839165416065588790184389873
absolute error = 1.2740037638719229e-16
relative error = 4.5484151349392408739237876451889e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.91818206382330246182421654976264
y[1] (analytic) = 0.28011176556324290658608308500091
y[1] (numeric) = 0.28011176556324303398746181215351
absolute error = 1.2740137872715260e-16
relative error = 4.5482337548719726216175733007396e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 3.709
Order of pole = 4.141e-26
TOP MAIN SOLVE Loop
x[1] = 0.91978307457415775934227003269852
y[1] (analytic) = 0.28013793014167060578341878959049
y[1] (numeric) = 0.28013793014167073318679140565714
absolute error = 1.2740337261606665e-16
relative error = 4.5478801300358204508309599431398e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92058357994958540810129677416646
y[1] (analytic) = 0.28015072124927942858595925744057
y[1] (numeric) = 0.28015072124927955599032345473196
absolute error = 1.2740436419729139e-16
relative error = 4.5477078777150956497710226431194e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9213840853250130568603235156344
y[1] (analytic) = 0.28016331852736261510548543612202
y[1] (numeric) = 0.28016331852736274251083766052747
absolute error = 1.2740535222440545e-16
relative error = 4.5475386604532311390247307195471e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92218459070044070561935025710234
y[1] (analytic) = 0.28017572219410669088780576772689
y[1] (numeric) = 0.28017572219410681829414248106715
absolute error = 1.2740633671334026e-16
relative error = 4.5473724745170003585721542310866e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92378560145129600313740374003822
y[1] (analytic) = 0.28019994956444448553153939168945
y[1] (numeric) = 0.28019994956444461293983453168386
absolute error = 1.2740829513999441e-16
relative error = 4.5470491817733602225149889175077e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92458610682672365189643048150616
y[1] (analytic) = 0.28021177370253550547647872060685
y[1] (numeric) = 0.28021177370253563288574782978131
absolute error = 1.2740926910917446e-16
relative error = 4.5468920675841535143235229653155e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9253866122021513006554572229741
y[1] (analytic) = 0.28022340509828425908563894805044
y[1] (numeric) = 0.28022340509828438649587855114804
absolute error = 1.2741023960309760e-16
relative error = 4.5467379699568750417769223015303e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92618711757757894941448396444204
y[1] (analytic) = 0.28023484396800824863015604899304
y[1] (numeric) = 0.28023484396800837604136268628883
absolute error = 1.2741120663729579e-16
relative error = 4.5465868852426187844580636516952e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=240.3MB, alloc=4.5MB, time=12.85
x[1] = 0.92778812832843424693253744737792
y[1] (analytic) = 0.28025714499280077858748173603337
y[1] (numeric) = 0.28025714499280090600061212428625
absolute error = 1.2741313038825288e-16
relative error = 4.5462937400409847721844907809814e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 1.16
Order of pole = 1.277e-26
TOP MAIN SOLVE Loop
x[1] = 0.92858863370386189569156418884586
y[1] (analytic) = 0.28026800757865647683768911384731
y[1] (numeric) = 0.28026800757865660425177624953202
absolute error = 1.2741408713568471e-16
relative error = 4.5461516723390657647003846630595e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9293891390792895444505909303138
y[1] (analytic) = 0.28027867850006393072963306612896
y[1] (numeric) = 0.28027867850006405814467355086726
absolute error = 1.2741504048473830e-16
relative error = 4.5460126031209768605261971851107e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93018964445471719320961767178174
y[1] (analytic) = 0.28028915797149940795394445100312
y[1] (numeric) = 0.28028915797149953536993490156034
absolute error = 1.2741599045055722e-16
relative error = 4.5458765288207557869208035546689e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93179065520557249072767115471762
y[1] (analytic) = 0.28030954342053582177570368541998
y[1] (numeric) = 0.28030954342053594919358397810382
absolute error = 1.2741788029268384e-16
relative error = 4.5456133507921460742063099208434e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93259116058100013948669789618556
y[1] (analytic) = 0.28031944982526887523508393540968
y[1] (numeric) = 0.28031944982526900265390413430814
absolute error = 1.2741882019889846e-16
relative error = 4.5454862400137504669085639291145e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9333916659564277882457246376535
y[1] (analytic) = 0.28032916563429635232006173918218
y[1] (numeric) = 0.2803291656342964797398185208753
absolute error = 1.2741975678169312e-16
relative error = 4.5453621100531034422319113965801e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93419217133185543700475137912144
y[1] (analytic) = 0.28033869106028060193900038438957
y[1] (numeric) = 0.28033869106028072935969044022329
absolute error = 1.2742069005583372e-16
relative error = 4.5452409574258422257117973470770e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93579318208271073452280486205732
y[1] (analytic) = 0.2803571716119721506555781698745
y[1] (numeric) = 0.28035717161197227807812490671986
absolute error = 1.2742254673684536e-16
relative error = 4.5450075703147808637596062524595e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93659368745813838328183160352526
y[1] (analytic) = 0.2803661271612106913221283768673
y[1] (numeric) = 0.28036612716121081874559854974578
absolute error = 1.2742347017287848e-16
relative error = 4.5448953289428543628396678365861e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 2.834
Order of pole = 2.255e-26
TOP MAIN SOLVE Loop
x[1] = 0.9373941928335660320408583449932
y[1] (analytic) = 0.28037489317447061749178730481571
y[1] (numeric) = 0.28037489317447074491617766339823
absolute error = 1.2742439035858252e-16
relative error = 4.5447860511279573499173610105024e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93819469820899368079988508646114
y[1] (analytic) = 0.28038346986262721134740615789741
y[1] (numeric) = 0.28038346986262733877271346625353
absolute error = 1.2742530730835612e-16
relative error = 4.5446797334660154128171444946381e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.5MB, time=13.04
x[1] = 0.93979570895984897831793856939702
y[1] (analytic) = 0.28040005610536142673928934898672
y[1] (numeric) = 0.28040005610536155416642090633255
absolute error = 1.2742713155734583e-16
relative error = 4.5444759650641647109315511222982e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94059621433527662707696531086496
y[1] (analytic) = 0.28040806607992266175091861369872
y[1] (numeric) = 0.28040806607992278917895749869841
absolute error = 1.2742803888499969e-16
relative error = 4.5443785075954201462568016907628e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9413967197107042758359920523329
y[1] (analytic) = 0.28041588756934988520071021362924
y[1] (numeric) = 0.28041588756935001262965324722863
absolute error = 1.2742894303359939e-16
relative error = 4.5442839968218574152685254360657e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94219722508613192459501879380084
y[1] (analytic) = 0.28042352078275770981329798813454
y[1] (numeric) = 0.28042352078275783724314200532094
absolute error = 1.2742984401718640e-16
relative error = 4.5441924294184109128846179195940e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94379823583698722211307227673672
y[1] (analytic) = 0.28043822321622961980782939264666
y[1] (numeric) = 0.28043822321622974723946593778414
absolute error = 1.2743163654513748e-16
relative error = 4.5440181114998132453239245928474e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94459874121241487087209901820466
y[1] (analytic) = 0.2804452928527820369935496557321
y[1] (numeric) = 0.28044529285278216442607777296692
absolute error = 1.2743252811723482e-16
relative error = 4.5439353544125880797350883903897e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9453992465878425196311257596726
y[1] (analytic) = 0.28045217504629377741383073934285
y[1] (numeric) = 0.28045217504629390484724731912968
absolute error = 1.2743341657978683e-16
relative error = 4.5438555275512342295328560531564e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94619975196327016839015250114054
y[1] (analytic) = 0.28045887000414473556754370528292
y[1] (numeric) = 0.28045887000414486300184565177054
absolute error = 1.2743430194648762e-16
relative error = 4.5437786276684472097846563388124e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94700025733869781714917924260848
y[1] (analytic) = 0.28046537793337093781013876987878
y[1] (numeric) = 0.28046537793337106524532300084174
absolute error = 1.2743518423096296e-16
relative error = 4.5437046515323270303948502590573e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94860126808955311466723272554436
y[1] (analytic) = 0.28047783353237993820696088378488
y[1] (numeric) = 0.28047783353238006564390049118603
absolute error = 1.2743693960740115e-16
relative error = 4.5435654576492267836988839559984e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9494017734649807634262594670123
y[1] (analytic) = 0.28048378161452458471807895894234
y[1] (numeric) = 0.28048378161452471215589168521967
absolute error = 1.2743781272627733e-16
relative error = 4.5435002335150377405696647290111e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95020227884040841218528620848024
y[1] (analytic) = 0.28048954349277018898419313910546
y[1] (numeric) = 0.28048954349277031642287595586097
absolute error = 1.2743868281675551e-16
relative error = 4.5434379203530034535002291785653e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95100278421583606094431294994818
y[1] (analytic) = 0.28049511937244862389012400775608
y[1] (numeric) = 0.28049511937244875132967389988155
absolute error = 1.2743954989212547e-16
relative error = 4.5433785150075271872145888283906e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=247.9MB, alloc=4.5MB, time=13.24
TOP MAIN SOLVE Loop
x[1] = 0.95260379496669135846236643288406
y[1] (analytic) = 0.28050571395574338784331973587047
y[1] (numeric) = 0.28050571395574351528459478624022
absolute error = 1.2744127505036975e-16
relative error = 4.5432684152194032246204457663615e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.953404300342119007221393174352
y[1] (analytic) = 0.2805107330683383597368776372093
y[1] (numeric) = 0.28051073306833848717901079670393
absolute error = 1.2744213315949463e-16
relative error = 4.5432177145409628709670250809968e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95420480571754665598041991581994
y[1] (analytic) = 0.28051556700032543104860384140719
y[1] (numeric) = 0.28051556700032555849159214742031
absolute error = 1.2744298830601312e-16
relative error = 4.5431699092074013541375449456496e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95500531109297430473944665728788
y[1] (analytic) = 0.28052021595535732102307544960702
y[1] (numeric) = 0.28052021595535744846691595249519
absolute error = 1.2744384050288817e-16
relative error = 4.5431249961382425669978849247565e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95660632184382960225750014022376
y[1] (analytic) = 0.28052895974750307488153479615008
y[1] (numeric) = 0.28052895974750320232707089538857
absolute error = 1.2744553609923849e-16
relative error = 4.5430438345456009208502595195534e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9574068272192572510165268816917
y[1] (analytic) = 0.28053305499026195453577816081961
y[1] (numeric) = 0.28053305499026208198215768513921
absolute error = 1.2744637952431960e-16
relative error = 4.5430075799354055241643998432043e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95820733259468489977555362315964
y[1] (analytic) = 0.28053696606735763425770678785666
y[1] (numeric) = 0.28053696606735776170492683882622
absolute error = 1.2744722005096956e-16
relative error = 4.5429742054160933822510459261724e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95900783797011254853458036462758
y[1] (analytic) = 0.28054069318078826019153132546919
y[1] (numeric) = 0.28054069318078838763958901730253
absolute error = 1.2744805769183334e-16
relative error = 4.5429437079811537746719085290172e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
Complex estimate of poles used for equation 1
Radius of convergence = 2.525
Order of pole = 1.316e-26
TOP MAIN SOLVE Loop
x[1] = 0.96060884872096784605263384756346
y[1] (analytic) = 0.28054759632300789231670143222597
y[1] (numeric) = 0.28054759632300801976642579869581
absolute error = 1.2744972436646984e-16
relative error = 4.5428913324115906724573060647471e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9614093540963954948116605890314
y[1] (analytic) = 0.28055077275415703507531487130445
y[1] (numeric) = 0.28055077275415716252586829652557
absolute error = 1.2745055342522112e-16
relative error = 4.5428694483370526818863896797095e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96220985947182314357068733049934
y[1] (analytic) = 0.28055376602636331445463674921819
y[1] (numeric) = 0.2805537660263634419060163973622
absolute error = 1.2745137964814401e-16
relative error = 4.5428504294669689288989287495855e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96301036484725079232971407196728
y[1] (analytic) = 0.28055657633999447272525294456849
y[1] (numeric) = 0.28055657633999460017745599214262
absolute error = 1.2745220304757413e-16
relative error = 4.5428342728676684331867138701596e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
memory used=251.7MB, alloc=4.5MB, time=13.44
TOP MAIN SOLVE Loop
x[1] = 0.96461137559810608984776755490316
y[1] (analytic) = 0.28056164889138726187711553223951
y[1] (numeric) = 0.28056164889138738933095695723411
absolute error = 1.2745384142499460e-16
relative error = 4.5428105348188664622518036142192e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9654118809735337386067942963711
y[1] (analytic) = 0.28056391152827208321449503439574
y[1] (numeric) = 0.28056391152827221066915146174898
absolute error = 1.2745465642735324e-16
relative error = 4.5428029475740250258064064712520e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96621238634896138736582103783904
y[1] (analytic) = 0.28056599200483004965704405398653
y[1] (numeric) = 0.28056599200483017711251270894287
absolute error = 1.2745546865495634e-16
relative error = 4.5427982110091997859059649416778e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96701289172438903612484777930698
y[1] (analytic) = 0.28056789051982226531930039968224
y[1] (numeric) = 0.28056789051982239277557851952077
absolute error = 1.2745627811983853e-16
relative error = 4.5427963222624607002509840771467e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96861390247524433364290126224286
y[1] (analytic) = 0.28057114245856223882736470535785
y[1] (numeric) = 0.28057114245856236628525351464084
absolute error = 1.2745788880928299e-16
relative error = 4.5428010768465734357451203168602e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9694144078506719824019280037108
y[1] (analytic) = 0.28057249627824337476659554234257
y[1] (numeric) = 0.28057249627824350222528559996231
absolute error = 1.2745869005761974e-16
relative error = 4.5428077145244887103794425805914e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97021491322609963116095474517874
y[1] (analytic) = 0.28057366892822737004543753819758
y[1] (numeric) = 0.28057366892822749750492612898279
absolute error = 1.2745948859078521e-16
relative error = 4.5428171887145334262882450088029e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97101541860152727991998148664668
y[1] (analytic) = 0.28057466060569206046559197684529
y[1] (numeric) = 0.28057466060569218792587639736644
absolute error = 1.2746028442052115e-16
relative error = 4.5428294966254462959879036073991e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97261642935238257743803496958256
y[1] (analytic) = 0.28057610183020636814580819853338
y[1] (numeric) = 0.28057610183020649560767621491709
absolute error = 1.2746186801638371e-16
relative error = 4.5428626025148294358140972801384e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9734169347278102261970617110505
y[1] (analytic) = 0.2805765517700459006451512668486
y[1] (numeric) = 0.28057655177004602810780707255562
absolute error = 1.2746265580570702e-16
relative error = 4.5428833949806499139203652732656e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97421744010323787495608845251844
y[1] (analytic) = 0.28057682152294778191995130358266
y[1] (numeric) = 0.28057682152294790938339224157744
absolute error = 1.2746344093799478e-16
relative error = 4.5429070101419555807771683605935e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97501794547866552371511519398638
y[1] (analytic) = 0.28057691128452956089766714547862
y[1] (numeric) = 0.28057691128452968836189057018238
absolute error = 1.2746422342470376e-16
relative error = 4.5429334452771088552898710949563e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.5MB, time=13.65
x[1] = 0.97661895622952082123316867692226
y[1] (analytic) = 0.28057655161465724232082404748716
y[1] (numeric) = 0.28057655161465736978660455441954
absolute error = 1.2746578050693238e-16
relative error = 4.5429947646513737567522011027040e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9774194616049484699921954183902
y[1] (analytic) = 0.28057610257289517719761941661841
y[1] (numeric) = 0.28057610257289530466417454170482
absolute error = 1.2746655512508641e-16
relative error = 4.5430296435160551462926511709508e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97821996698037611875122215985814
y[1] (analytic) = 0.28057547431919886759649390970835
y[1] (numeric) = 0.28057547431919899506382105263939
absolute error = 1.2746732714293104e-16
relative error = 4.5430673316056429520167307432295e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.97902047235580376751024890132608
y[1] (analytic) = 0.28057466704764817591334337049872
y[1] (numeric) = 0.28057466704764830338143994214439
absolute error = 1.2746809657164567e-16
relative error = 4.5431078262671016521271969616371e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98062148310665906502830238426196
y[1] (analytic) = 0.28057251622577969047830792890783
y[1] (numeric) = 0.28057251622577981794793563503787
absolute error = 1.2746962770613004e-16
relative error = 4.5431972247614543144042350382929e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9814219884820867137873291257299
y[1] (analytic) = 0.28057117306210087139304810650722
y[1] (numeric) = 0.28057117306210099886343754049416
absolute error = 1.2747038943398694e-16
relative error = 4.5432461233561220374785156282214e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98222249385751436254635586719784
y[1] (analytic) = 0.28056965165384738288227154371801
y[1] (numeric) = 0.28056965165384751035342016060674
absolute error = 1.2747114861688873e-16
relative error = 4.5432978180461289878277099420718e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98302299923294201130538260866578
y[1] (analytic) = 0.28056795219358362720863341925316
y[1] (numeric) = 0.28056795219358375468053868499804
absolute error = 1.2747190526574488e-16
relative error = 4.5433523062460468787617637964347e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98462400998379730882343609160166
y[1] (analytic) = 0.28056401988578150851924802598353
y[1] (numeric) = 0.28056401988578163599265903067647
absolute error = 1.2747341100469294e-16
relative error = 4.5434696529008874689025169505872e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9854245153592249575824628330696
y[1] (analytic) = 0.28056178742187314659444355887167
y[1] (numeric) = 0.28056178742187327406860367521105
absolute error = 1.2747416011633938e-16
relative error = 4.5435325062518205479401446938588e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98622502073465260634148957453754
y[1] (analytic) = 0.28055937767321625393253667791598
y[1] (numeric) = 0.2805593776732163814074434149658
absolute error = 1.2747490673704982e-16
relative error = 4.5435981429046090263414316638113e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98702552611008025510051631600548
y[1] (analytic) = 0.28055679083088163211511412182524
y[1] (numeric) = 0.28055679083088175959076499929624
absolute error = 1.2747565087747100e-16
relative error = 4.5436665603404605269309343601762e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.5MB, time=13.85
x[1] = 0.98862653686093555261856979894136
y[1] (analytic) = 0.28055108662798262039737746395499
y[1] (numeric) = 0.28055108662798274787450922372935
absolute error = 1.2747713175977436e-16
relative error = 4.5438117275522105971795390640826e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9894270422363632013775965404093
y[1] (analytic) = 0.28054796964808261519310250208325
y[1] (numeric) = 0.2805479696480827426709710247759
absolute error = 1.2747786852269265e-16
relative error = 4.5438884723564381807713179293079e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99022754761179085013662328187724
y[1] (analytic) = 0.28054467633583535593186385592081
y[1] (numeric) = 0.28054467633583548341046670331524
absolute error = 1.2747860284739443e-16
relative error = 4.5439679880003111996569138873056e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99102805298721849889565002334518
y[1] (analytic) = 0.28054120688083954286875182553946
y[1] (numeric) = 0.28054120688083967034808656981016
absolute error = 1.2747933474427070e-16
relative error = 4.5440502720307256239991648936561e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99262906373807379641370350628106
y[1] (analytic) = 0.28053374029953854158991917286507
y[1] (numeric) = 0.28053374029953866907071046872446
absolute error = 1.2748079129585939e-16
relative error = 4.5442231355038575015326315854494e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.993429569113501445172730247749
y[1] (analytic) = 0.28052974355097476539803055731034
y[1] (numeric) = 0.28052974355097489287954652841359
absolute error = 1.2748151597110325e-16
relative error = 4.5443137101053499331785684368517e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99423007448892909393175698921694
y[1] (analytic) = 0.2805255714151469371514476843991
y[1] (numeric) = 0.28052557141514706463368594398414
absolute error = 1.2748223825958504e-16
relative error = 4.5444070434108615886518054899484e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99503057986435674269078373068488
y[1] (analytic) = 0.28052122408020280173822369615165
y[1] (numeric) = 0.28052122408020292922118186759844
absolute error = 1.2748295817144679e-16
relative error = 4.5445031330320518501041971740603e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99663159061521204020883721362076
y[1] (analytic) = 0.28051200456411899719666851931103
y[1] (numeric) = 0.28051200456411912468105942494468
absolute error = 1.2748439090563365e-16
relative error = 4.5447035717322916368251462321112e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9974320959906396889678639550887
y[1] (analytic) = 0.28050713275783971094615985240173
y[1] (numeric) = 0.28050713275783983843126360040065
absolute error = 1.2748510374799892e-16
relative error = 4.5448079160987367784927272413542e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99823260136606733772689069655664
y[1] (analytic) = 0.28050208650216653349638551467698
y[1] (numeric) = 0.28050208650216666098219976850199
absolute error = 1.2748581425382501e-16
relative error = 4.5449150073555812548237102521086e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99903310674149498648591743802458
y[1] (analytic) = 0.28049686598381705349263226705973
y[1] (numeric) = 0.2804968659838171809791547000713
absolute error = 1.2748652243301157e-16
relative error = 4.5450248431783462204950717563318e-14 %
Correct digits = 15
h = 0.00080050537542764875902674146794202
NO POLE for equation 1
Finished!
diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ;
Iterations = 1072
Total Elapsed Time = 13 Seconds
Elapsed Time(since restart) = 13 Seconds
Time to Timeout = 2 Minutes 46 Seconds
Percent Done = 100.2 %
> quit
memory used=263.0MB, alloc=4.5MB, time=14.04