|\^/| Maple 12 (IBM INTEL LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 1
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 1;
> ret;;
> end;
check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
> # End Function number 3
> # Begin Function number 4
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_value3,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> 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_const_3D0,
array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> 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_const_3D0,
array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> 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_const_3D0,
array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> 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_const_3D0,
array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> 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_const_3D0,
array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> 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_const_3D0,
array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> 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_const_3D0,
array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> 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_const_3D0,
array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_real_pole,
> array_complex_pole,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_1D0[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_const_3D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] + array_const_2D0[1];
> #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := expt(array_tmp2[1] , array_tmp4[1] ) ;
> array_tmp5_a1[1] := ln(array_tmp2[1] ) ;
> array_tmp5_a1[2] := array_tmp2[2] / array_tmp2[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp6[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp6[1] + array_const_1D0[1];
> #emit pre ln 1 LINEAR $eq_no = 1
> array_tmp8[1] := ln(array_tmp7[1]);
> #emit pre mult CONST FULL $eq_no = 1 i = 1
> array_tmp9[1] := array_const_3D0[1] * array_tmp8[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp10[1] := array_const_3D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp11[1] := array_tmp10[1] + array_const_2D0[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp12[1] := array_const_2D0[1] * array_tmp11[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp13[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp14[1] := array_tmp13[1] + array_const_1D0[1];
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp15[1] := array_tmp12[1] / array_tmp14[1];
> #emit pre add FULL FULL $eq_no = 1 i = 1
> array_tmp16[1] := array_tmp9[1] + array_tmp15[1];
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp17[1] := (array_tmp5[1] * (array_tmp16[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp18[1] := array_const_0D0[1] + array_tmp17[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_tmp18[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := array_const_3D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp5_a2[1] := (array_tmp5_a1[1] * array_tmp4[2] + array_tmp5_a1[2] * array_tmp4[1]) / glob_h;
> array_tmp5[2] := array_tmp5[1] * array_tmp5_a2[1] * glob_h;
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp6[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp7[2] := array_tmp6[2];
> #emit pre ln 2 LINEAR $eq_no = 1
> array_tmp8[2] := array_tmp7[2] / array_tmp7[1];
> #emit pre mult CONST FULL $eq_no = 1 i = 2
> array_tmp9[2] := array_const_3D0[1] * array_tmp8[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp10[2] := array_const_3D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp11[2] := array_tmp10[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp12[2] := array_const_2D0[1] * array_tmp11[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp13[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp14[2] := array_tmp13[2];
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp15[2] := (array_tmp12[2] - array_tmp15[1] * array_tmp14[2]) / array_tmp14[1];
> #emit pre add FULL FULL $eq_no = 1 i = 2
> array_tmp16[2] := array_tmp9[2] + array_tmp15[2];
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp17[2] := ats(2,array_tmp5,array_tmp16,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp18[2] := array_tmp17[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_tmp18[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 expt LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp5_a1[3] := -array_tmp5_a1[2] * array_tmp2[2] * 1 / array_tmp2[1] / 2;
> array_tmp5_a2[2] := (array_tmp5_a1[2] * array_tmp4[2] + array_tmp5_a1[3] * array_tmp4[1]) * 2 / glob_h;
> array_tmp5[3] := ats(2,array_tmp5,array_tmp5_a2,1)*glob_h/2;
> #emit pre ln ID_LINEAR iii = 3 $eq_no = 1
> array_tmp8[3] := - array_tmp7[2] * array_tmp8[2] * 1 / array_tmp7[1] / 2;
> #emit pre mult CONST FULL $eq_no = 1 i = 3
> array_tmp9[3] := array_const_3D0[1] * array_tmp8[3];
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp15[3] := - array_tmp15[2] * array_tmp14[2] / array_tmp14[1];
> #emit pre add FULL FULL $eq_no = 1 i = 3
> array_tmp16[3] := array_tmp9[3] + array_tmp15[3];
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp17[3] := ats(3,array_tmp5,array_tmp16,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp18[3] := array_tmp17[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_tmp18[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 expt LINEAR - LINEAR $eq_no = 1 i = 4
> array_tmp5_a1[4] := -array_tmp5_a1[3] * array_tmp2[2] * 2 / array_tmp2[1] / 3;
> array_tmp5_a2[3] := (array_tmp5_a1[3] * array_tmp4[2] + array_tmp5_a1[4] * array_tmp4[1]) * 3 / glob_h;
> array_tmp5[4] := ats(3,array_tmp5,array_tmp5_a2,1)*glob_h/3;
> #emit pre ln ID_LINEAR iii = 4 $eq_no = 1
> array_tmp8[4] := - array_tmp7[2] * array_tmp8[3] * 2 / array_tmp7[1] / 3;
> #emit pre mult CONST FULL $eq_no = 1 i = 4
> array_tmp9[4] := array_const_3D0[1] * array_tmp8[4];
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 4
> array_tmp15[4] := - array_tmp15[3] * array_tmp14[2] / array_tmp14[1];
> #emit pre add FULL FULL $eq_no = 1 i = 4
> array_tmp16[4] := array_tmp9[4] + array_tmp15[4];
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp17[4] := ats(4,array_tmp5,array_tmp16,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp18[4] := array_tmp17[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_tmp18[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 expt LINEAR - LINEAR $eq_no = 1 i = 5
> array_tmp5_a1[5] := -array_tmp5_a1[4] * array_tmp2[2] * 3 / array_tmp2[1] / 4;
> array_tmp5_a2[4] := (array_tmp5_a1[4] * array_tmp4[2] + array_tmp5_a1[5] * array_tmp4[1]) * 4 / glob_h;
> array_tmp5[5] := ats(4,array_tmp5,array_tmp5_a2,1)*glob_h/4;
> #emit pre ln ID_LINEAR iii = 5 $eq_no = 1
> array_tmp8[5] := - array_tmp7[2] * array_tmp8[4] * 3 / array_tmp7[1] / 4;
> #emit pre mult CONST FULL $eq_no = 1 i = 5
> array_tmp9[5] := array_const_3D0[1] * array_tmp8[5];
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 5
> array_tmp15[5] := - array_tmp15[4] * array_tmp14[2] / array_tmp14[1];
> #emit pre add FULL FULL $eq_no = 1 i = 5
> array_tmp16[5] := array_tmp9[5] + array_tmp15[5];
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp17[5] := ats(5,array_tmp5,array_tmp16,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp18[5] := array_tmp17[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_tmp18[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 expt LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp5_a1[kkk] := -array_tmp5_a1[kkk-1] * array_tmp4[2] * (kkk-2) / array_tmp2[1] / (kkk - 1);
> array_tmp5_a2[kkk-1] := (array_tmp5_a1[kkk-1] * array_tmp4[2] + array_tmp5_a1[kkk] * array_tmp4[1]) * (kkk-1) / glob_h;
> array_tmp5[kkk] := ats(kkk-1,array_tmp5,array_tmp5_a2,1)*glob_h/(kkk-1);
> #emit ln LINEAR $eq_no = 1
> array_tmp8[kkk] := - array_tmp7[2] * array_tmp8[kkk - 1] * (kkk - 2)/ array_tmp7[1] / (kkk - 1);
> #emit mult CONST FULL $eq_no = 1 i = 1
> array_tmp9[kkk] := array_const_3D0[1] * array_tmp8[kkk];
> #emit div LINEAR - LINEAR (NOP) $eq_no = 1 i = 1
> array_tmp15[kkk] := - array_tmp15[kkk-1] * array_tmp14[2] / array_tmp14[1];
> #emit FULL - FULL add $eq_no = 1
> array_tmp16[kkk] := array_tmp9[kkk] + array_tmp15[kkk];
> #emit mult FULL FULL $eq_no = 1
> array_tmp17[kkk] := ats(kkk,array_tmp5,array_tmp16,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp18[kkk] := array_tmp17[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_tmp18[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_const_3D0,
array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_real_pole, array_complex_pole,
array_fact_2, glob_last;
array_tmp1[1] := array_const_2D0[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_1D0[1];
array_tmp3[1] := array_const_3D0[1]*array_x[1];
array_tmp4[1] := array_tmp3[1] + array_const_2D0[1];
array_tmp5[1] := expt(array_tmp2[1], array_tmp4[1]);
array_tmp5_a1[1] := ln(array_tmp2[1]);
array_tmp5_a1[2] := array_tmp2[2]/array_tmp2[1];
array_tmp6[1] := array_const_2D0[1]*array_x[1];
array_tmp7[1] := array_tmp6[1] + array_const_1D0[1];
array_tmp8[1] := ln(array_tmp7[1]);
array_tmp9[1] := array_const_3D0[1]*array_tmp8[1];
array_tmp10[1] := array_const_3D0[1]*array_x[1];
array_tmp11[1] := array_tmp10[1] + array_const_2D0[1];
array_tmp12[1] := array_const_2D0[1]*array_tmp11[1];
array_tmp13[1] := array_const_2D0[1]*array_x[1];
array_tmp14[1] := array_tmp13[1] + array_const_1D0[1];
array_tmp15[1] := array_tmp12[1]/array_tmp14[1];
array_tmp16[1] := array_tmp9[1] + array_tmp15[1];
array_tmp17[1] := array_tmp5[1]*array_tmp16[1];
array_tmp18[1] := array_const_0D0[1] + array_tmp17[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp18[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_2D0[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_const_3D0[1]*array_x[2];
array_tmp4[2] := array_tmp3[2];
array_tmp5_a2[1] := (
array_tmp5_a1[1]*array_tmp4[2] + array_tmp5_a1[2]*array_tmp4[1])/
glob_h;
array_tmp5[2] := array_tmp5[1]*array_tmp5_a2[1]*glob_h;
array_tmp6[2] := array_const_2D0[1]*array_x[2];
array_tmp7[2] := array_tmp6[2];
array_tmp8[2] := array_tmp7[2]/array_tmp7[1];
array_tmp9[2] := array_const_3D0[1]*array_tmp8[2];
array_tmp10[2] := array_const_3D0[1]*array_x[2];
array_tmp11[2] := array_tmp10[2];
array_tmp12[2] := array_const_2D0[1]*array_tmp11[2];
array_tmp13[2] := array_const_2D0[1]*array_x[2];
array_tmp14[2] := array_tmp13[2];
array_tmp15[2] :=
(array_tmp12[2] - array_tmp15[1]*array_tmp14[2])/array_tmp14[1];
array_tmp16[2] := array_tmp9[2] + array_tmp15[2];
array_tmp17[2] := ats(2, array_tmp5, array_tmp16, 1);
array_tmp18[2] := array_tmp17[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp18[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_tmp5_a1[3] := -1/2*array_tmp5_a1[2]*array_tmp2[2]/array_tmp2[1];
array_tmp5_a2[2] := 2*
(array_tmp5_a1[2]*array_tmp4[2] + array_tmp5_a1[3]*array_tmp4[1])/
glob_h;
array_tmp5[3] := 1/2*ats(2, array_tmp5, array_tmp5_a2, 1)*glob_h;
array_tmp8[3] := -1/2*array_tmp7[2]*array_tmp8[2]/array_tmp7[1];
array_tmp9[3] := array_const_3D0[1]*array_tmp8[3];
array_tmp15[3] := -array_tmp15[2]*array_tmp14[2]/array_tmp14[1];
array_tmp16[3] := array_tmp9[3] + array_tmp15[3];
array_tmp17[3] := ats(3, array_tmp5, array_tmp16, 1);
array_tmp18[3] := array_tmp17[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp18[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_tmp5_a1[4] := -2/3*array_tmp5_a1[3]*array_tmp2[2]/array_tmp2[1];
array_tmp5_a2[3] := 3*
(array_tmp5_a1[3]*array_tmp4[2] + array_tmp5_a1[4]*array_tmp4[1])/
glob_h;
array_tmp5[4] := 1/3*ats(3, array_tmp5, array_tmp5_a2, 1)*glob_h;
array_tmp8[4] := -2/3*array_tmp7[2]*array_tmp8[3]/array_tmp7[1];
array_tmp9[4] := array_const_3D0[1]*array_tmp8[4];
array_tmp15[4] := -array_tmp15[3]*array_tmp14[2]/array_tmp14[1];
array_tmp16[4] := array_tmp9[4] + array_tmp15[4];
array_tmp17[4] := ats(4, array_tmp5, array_tmp16, 1);
array_tmp18[4] := array_tmp17[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp18[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_tmp5_a1[5] := -3/4*array_tmp5_a1[4]*array_tmp2[2]/array_tmp2[1];
array_tmp5_a2[4] := 4*
(array_tmp5_a1[4]*array_tmp4[2] + array_tmp5_a1[5]*array_tmp4[1])/
glob_h;
array_tmp5[5] := 1/4*ats(4, array_tmp5, array_tmp5_a2, 1)*glob_h;
array_tmp8[5] := -3/4*array_tmp7[2]*array_tmp8[4]/array_tmp7[1];
array_tmp9[5] := array_const_3D0[1]*array_tmp8[5];
array_tmp15[5] := -array_tmp15[4]*array_tmp14[2]/array_tmp14[1];
array_tmp16[5] := array_tmp9[5] + array_tmp15[5];
array_tmp17[5] := ats(5, array_tmp5, array_tmp16, 1);
array_tmp18[5] := array_tmp17[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp18[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_tmp5_a1[kkk] := -array_tmp5_a1[kkk - 1]*array_tmp4[2]*
(kkk - 2)/(array_tmp2[1]*(kkk - 1));
array_tmp5_a2[kkk - 1] := (array_tmp5_a1[kkk - 1]*array_tmp4[2]
+ array_tmp5_a1[kkk]*array_tmp4[1])*(kkk - 1)/glob_h;
array_tmp5[kkk] :=
ats(kkk - 1, array_tmp5, array_tmp5_a2, 1)*glob_h/(kkk - 1);
array_tmp8[kkk] := -array_tmp7[2]*array_tmp8[kkk - 1]*(kkk - 2)/(
array_tmp7[1]*(kkk - 1));
array_tmp9[kkk] := array_const_3D0[1]*array_tmp8[kkk];
array_tmp15[kkk] :=
-array_tmp15[kkk - 1]*array_tmp14[2]/array_tmp14[1];
array_tmp16[kkk] := array_tmp9[kkk] + array_tmp15[kkk];
array_tmp17[kkk] := ats(kkk, array_tmp5, array_tmp16, 1);
array_tmp18[kkk] := array_tmp17[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_tmp18[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(expt(2.0*x+1.0,3.0*x+2.0));
> end;
exact_soln_y := proc(x) return expt(2.0*x + 1.0, 3.0*x + 2.0) 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,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_tmp18,
> 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/expt_lin_lin_newpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 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(expt(2.0*x+1.0,3.0*x+2.0));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 1.0e-200;
> glob_smallish_float := 1.0e-64;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(max_terms + 1),[]);
> array_1st_rel_error:= Array(0..(max_terms + 1),[]);
> array_last_rel_error:= Array(0..(max_terms + 1),[]);
> array_type_pole:= Array(0..(max_terms + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5_c1:= Array(0..(max_terms + 1),[]);
> array_tmp5_a1:= Array(0..(max_terms + 1),[]);
> array_tmp5_a2:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_tmp6:= Array(0..(max_terms + 1),[]);
> array_tmp7:= Array(0..(max_terms + 1),[]);
> array_tmp8:= Array(0..(max_terms + 1),[]);
> array_tmp9:= Array(0..(max_terms + 1),[]);
> array_tmp10:= Array(0..(max_terms + 1),[]);
> array_tmp11:= Array(0..(max_terms + 1),[]);
> array_tmp12:= Array(0..(max_terms + 1),[]);
> array_tmp13:= Array(0..(max_terms + 1),[]);
> array_tmp14:= Array(0..(max_terms + 1),[]);
> array_tmp15:= Array(0..(max_terms + 1),[]);
> array_tmp16:= Array(0..(max_terms + 1),[]);
> array_tmp17:= Array(0..(max_terms + 1),[]);
> array_tmp18:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp5_c1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp5_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp5_a2[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[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_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_tmp18[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> term := 1;
> while (term <= max_terms) do # do number 2
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=2) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_real_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=1) do # do number 2
> term := 1;
> while (term <= 3) do # do number 3
> array_complex_pole[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> ord := 1;
> while (ord <=max_terms) do # do number 2
> term := 1;
> while (term <= max_terms) do # do number 3
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 3;
> ord := ord + 1;
> od;# end do number 2;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp5_c1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp5_c1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp5_a1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp5_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp5_a2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp5_a2[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 := 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_tmp15 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp16 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp17 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_tmp18 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_tmp18[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_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 2
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> array_const_3D0[1] := 3.0;
> 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 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 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,"2013-01-28T14:02:49-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"expt_lin_lin_new")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 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,"expt_lin_lin_new diffeq.mxt")
> ;
> logitem_str(html_log_file,"expt_lin_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_const_3D0,
array_y_init, array_norms, array_fact_1, array_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1,
array_tmp5_a1, array_tmp5_a2, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_tmp18, 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/expt_lin_lin_newpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 *\
x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.\
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(expt(2.0*x+1.0,3.0*x+2.0));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.10*10^(-199);
glob_smallish_float := 0.10*10^(-63);
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. max_terms + 1, []);
array_1st_rel_error := Array(0 .. max_terms + 1, []);
array_last_rel_error := Array(0 .. max_terms + 1, []);
array_type_pole := Array(0 .. max_terms + 1, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5_c1 := Array(0 .. max_terms + 1, []);
array_tmp5_a1 := Array(0 .. max_terms + 1, []);
array_tmp5_a2 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_tmp6 := Array(0 .. max_terms + 1, []);
array_tmp7 := Array(0 .. max_terms + 1, []);
array_tmp8 := Array(0 .. max_terms + 1, []);
array_tmp9 := Array(0 .. max_terms + 1, []);
array_tmp10 := Array(0 .. max_terms + 1, []);
array_tmp11 := Array(0 .. max_terms + 1, []);
array_tmp12 := Array(0 .. max_terms + 1, []);
array_tmp13 := Array(0 .. max_terms + 1, []);
array_tmp14 := Array(0 .. max_terms + 1, []);
array_tmp15 := Array(0 .. max_terms + 1, []);
array_tmp16 := Array(0 .. max_terms + 1, []);
array_tmp17 := Array(0 .. max_terms + 1, []);
array_tmp18 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 2, 0 .. 4, []);
array_real_pole := Array(0 .. 2, 0 .. 4, []);
array_complex_pole := Array(0 .. 2, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do
array_type_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5_c1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5_a1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5_a2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp8[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp9[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp10[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp11[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp12[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp13[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp14[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp15[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp16[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp17[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp18[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_real_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 1 do
term := 1;
while term <= 3 do
array_complex_pole[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5_c1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp5_c1[term] := 0.; term := term + 1
end do;
array_tmp5_a1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp5_a1[term] := 0.; term := term + 1
end do;
array_tmp5_a2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp5_a2[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_tmp7 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp7[term] := 0.; term := term + 1
end do;
array_tmp8 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp8[term] := 0.; term := term + 1
end do;
array_tmp9 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp9[term] := 0.; term := term + 1
end do;
array_tmp10 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp10[term] := 0.; term := term + 1
end do;
array_tmp11 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp11[term] := 0.; term := term + 1
end do;
array_tmp12 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp12[term] := 0.; term := term + 1
end do;
array_tmp13 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp13[term] := 0.; term := term + 1
end do;
array_tmp14 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp14[term] := 0.; term := term + 1
end do;
array_tmp15 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp15[term] := 0.; term := term + 1
end do;
array_tmp16 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp16[term] := 0.; term := term + 1
end do;
array_tmp17 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp17[term] := 0.; term := term + 1
end do;
array_tmp18 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp18[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_const_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
array_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 ) = expt( 2.0 * x + 1.0 , 3.0\
* x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * \
x + 2.0 ) ) / ( 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, "2013-01-28T14:02:49-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"expt_lin_lin_new")
;
logitem_str(html_log_file, "diff ( y , x , 1 ) = expt( 2.0 * \
x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+\
( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 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, "expt_lin_lin_new diffeq.mxt");
logitem_str(html_log_file, "expt_lin_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/expt_lin_lin_newpostode.ode#################
diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 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(expt(2.0*x+1.0,3.0*x+2.0));
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 = 1.0586729919606403141380028720834e-74
max_value3 = 1.0586729919606403141380028720834e-74
value3 = 1.0586729919606403141380028720834e-74
best_h = 0.001
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 1.5209567545525317650119915799094
y[1] (numeric) = 1.5209567545525317650119915799094
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.101
y[1] (analytic) = 1.5276363683101829670359254771936
y[1] (numeric) = 1.5276363683101829703287798191519
absolute error = 3.2928543419583e-18
relative error = 2.1555223548394166539400198179444e-16 %
Correct digits = 17
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.102
y[1] (analytic) = 1.5343508520732434848867475809715
y[1] (numeric) = 1.5343508520732434914664954046983
absolute error = 6.5797478237268e-18
relative error = 4.2882941765477706987254931273335e-16 %
Correct digits = 17
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=2.8MB, time=0.13
x[1] = 0.103
y[1] (analytic) = 1.5411004019605970489461918588459
y[1] (numeric) = 1.5411004019605970588069297506913
absolute error = 9.8607378918454e-18
relative error = 6.3985045226777638336665893307962e-16 %
Correct digits = 17
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.104
y[1] (analytic) = 1.5478852152658195991410237999714
y[1] (numeric) = 1.5478852152658196122769053878717
absolute error = 1.31358815879003e-17
relative error = 8.4863408851957179962618824847640e-16 %
Correct digits = 17
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.105
y[1] (analytic) = 1.5547054904645634687731639708319
y[1] (numeric) = 1.5547054904645634851783995238914
absolute error = 1.64052355530595e-17
relative error = 1.0551989205465165812370110137540e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.106
y[1] (analytic) = 1.561561427221989677900433082215
y[1] (numeric) = 1.561561427221989697569289114769
absolute error = 1.96688560325540e-17
relative error = 1.2595633889052191150222055789323e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.107
y[1] (analytic) = 1.5684532264002486629301074533598
y[1] (numeric) = 1.5684532264002486858569063334649
absolute error = 2.29267988801051e-17
relative error = 1.4617457820354843053487226679170e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.108
y[1] (analytic) = 1.575381090066009771335297153818
y[1] (numeric) = 1.5753810900660097975144167161179
absolute error = 2.61791195622999e-17
relative error = 1.6617642377059999638918177936477e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.109
y[1] (analytic) = 1.5823452214980398526683739612408
y[1] (numeric) = 1.5823452214980398820942471241562
absolute error = 2.94258731629154e-17
relative error = 1.8596367444429920579138385350406e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 1.5893458251948312793263967179729
y[1] (numeric) = 1.5893458251948313119935111051637
absolute error = 3.26671143871908e-17
relative error = 2.0553811429420198479567873725276e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=7.6MB, alloc=3.9MB, time=0.27
x[1] = 0.111
y[1] (analytic) = 1.5963831068822797328208227710936
y[1] (numeric) = 1.5963831068822797687237203371434
absolute error = 3.59028975660498e-17
relative error = 2.2490151274632190540306071267061e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.112
y[1] (analytic) = 1.6034572735214120936178719611691
y[1] (numeric) = 1.603457273521412132751148621443
absolute error = 3.91332766602739e-17
relative error = 2.4405562472102457185648557621601e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.113
y[1] (analytic) = 1.610568533316164774946841063385
y[1] (numeric) = 1.6105685333161648173051463280108
absolute error = 4.23583052646258e-17
relative error = 2.6300219076930517153280087729412e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.114
y[1] (analytic) = 1.6177170957212128433215696226135
y[1] (numeric) = 1.6177170957212128888996062345391
absolute error = 4.55780366119256e-17
relative error = 2.8174293720748458504162595348702e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.115
y[1] (analytic) = 1.6249031714498502708852516714628
y[1] (numeric) = 1.6249031714498503196777752485419
absolute error = 4.87925235770791e-17
relative error = 3.0027957625033778168587066197291e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.116
y[1] (analytic) = 1.6321269724819216670709917617522
y[1] (numeric) = 1.6321269724819217190728104428112
absolute error = 5.20018186810590e-17
relative error = 3.1861380614267742362380805060754e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.117
y[1] (analytic) = 1.6393887120718058394700389394548
y[1] (numeric) = 1.6393887120718058946760130342954
absolute error = 5.52059740948406e-17
relative error = 3.3674731128942016078953254648752e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.118
y[1] (analytic) = 1.6466886047564515362166206011529
y[1] (numeric) = 1.6466886047564515946216622444444
absolute error = 5.84050416432915e-17
relative error = 3.5468176238414985470834742217362e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=11.4MB, alloc=4.1MB, time=0.42
x[1] = 0.119
y[1] (analytic) = 1.6540268663634657246328624285044
y[1] (numeric) = 1.6540268663634657862319352375211
absolute error = 6.15990728090167e-17
relative error = 3.7241881653620342402633971099061e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 1.6614037140192547633295446461219
y[1] (numeric) = 1.6614037140192548281176633822807
absolute error = 6.47881187361588e-17
relative error = 3.8996011739629433032047074544003e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.121
y[1] (analytic) = 1.6688193661572188274285335316242
y[1] (numeric) = 1.6688193661572188954007637657799
absolute error = 6.79722302341557e-17
relative error = 4.0730729528070482892087921597195e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.122
y[1] (analytic) = 1.6762740425259999490607662787227
y[1] (numeric) = 1.6762740425260000202122240601771
absolute error = 7.11514577814544e-17
relative error = 4.2446196729405479084850884888827e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.123
y[1] (analytic) = 1.6837679641977840377997838458307
y[1] (numeric) = 1.6837679641977841121256353750131
absolute error = 7.43258515291824e-17
relative error = 4.4142573745067229183739165844434e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.124
y[1] (analytic) = 1.6913013535766572482151282075134
y[1] (numeric) = 1.6913013535766573257105895122913
absolute error = 7.74954613047779e-17
relative error = 4.5820019679458893886712460650585e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.125
y[1] (analytic) = 1.6988744344070170642725763871133
y[1] (numeric) = 1.6988744344070171449329130026913
absolute error = 8.06603366155780e-17
relative error = 4.7478692351817074918358909552900e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.126
y[1] (analytic) = 1.706487431782038472869303744879
y[1] (numeric) = 1.7064874317820385566898303972456
absolute error = 8.38205266523666e-17
relative error = 4.9118748307941008845324519784642e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=15.2MB, alloc=4.2MB, time=0.58
x[1] = 0.127
y[1] (analytic) = 1.7141405721521956013717842280948
y[1] (numeric) = 1.7141405721521956883478645209772
absolute error = 8.69760802928824e-17
relative error = 5.0740342831789610664967843201081e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.128
y[1] (analytic) = 1.7218340833338391966226777083048
y[1] (numeric) = 1.7218340833338392867497238135914
absolute error = 9.01270461052866e-17
relative error = 5.2343629956947625729428587729049e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.129
y[1] (analytic) = 1.7295681945178303255002572417872
y[1] (numeric) = 1.7295681945178304187737295933798
absolute error = 9.32734723515926e-17
relative error = 5.3928762477963705761930769488278e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 1.7373431362782306797502262616139
y[1] (numeric) = 1.7373431362782307761656332526701
absolute error = 9.64154069910562e-17
relative error = 5.5495891961560977586980129954489e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.131
y[1] (analytic) = 1.7451591405810498704652025810616
y[1] (numeric) = 1.7451591405810499700181002645902
absolute error = 9.95528976835286e-17
relative error = 5.7045168757722869951367016979061e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.132
y[1] (analytic) = 1.7530164407930501002618389734241
y[1] (numeric) = 1.7530164407930502029478307661955
absolute error = 1.026859917927714e-16
relative error = 5.8576742010655136169423527597224e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.133
y[1] (analytic) = 1.7609152716906086038996463905022
y[1] (numeric) = 1.7609152716906087097143827802374
absolute error = 1.058147363897352e-16
relative error = 6.0090759669626378268423881669421e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.134
y[1] (analytic) = 1.7688558694686382507992240799348
y[1] (numeric) = 1.7688558694686383597384023357362
absolute error = 1.089391782558014e-16
relative error = 6.1587368499688203456999065909479e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=19.0MB, alloc=4.3MB, time=0.73
x[1] = 0.135
y[1] (analytic) = 1.7768384717495667056509205466049
y[1] (numeric) = 1.7768384717495668177102844325933
absolute error = 1.120593638859884e-16
relative error = 6.3066714092277041249194909081959e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.136
y[1] (analytic) = 1.7848633175923745460580911672256
y[1] (numeric) = 1.7848633175923746612334306593475
absolute error = 1.151753394921219e-16
relative error = 6.4528940875698773712401045997887e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.137
y[1] (analytic) = 1.7929306475016927389322241139297
y[1] (numeric) = 1.7929306475016928572193751199008
absolute error = 1.182871510059711e-16
relative error = 6.5974192125498497797565890025545e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.138
y[1] (analytic) = 1.8010407034369598801504189961729
y[1] (numeric) = 1.801040703436960001545263078522
absolute error = 1.213948440823491e-16
relative error = 6.7402609974715748344540756687956e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.139
y[1] (analytic) = 1.809193728821639604799166341796
y[1] (numeric) = 1.809193728821639729297630443977
absolute error = 1.244984641021810e-16
relative error = 6.8814335424028408215708796600997e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 1.8173899685524985781622358939287
y[1] (numeric) = 1.8173899685524987057602920694654
absolute error = 1.275980561755367e-16
relative error = 7.0209508351784874858607797998456e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.141
y[1] (analytic) = 1.8256296690089454804648840293993
y[1] (numeric) = 1.8256296690089456111585491740315
absolute error = 1.306936651446322e-16
relative error = 7.1588267523927827090626566628765e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.142
y[1] (analytic) = 1.8339130780624314012616828856774
y[1] (numeric) = 1.8339130780624315350470184724747
absolute error = 1.337853355867973e-16
relative error = 7.2950750603809632910373195860798e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.143
y[1] (analytic) = 1.842240445085912062251204654496
y[1] (numeric) = 1.8422404450859121991243164719071
absolute error = 1.368731118174111e-16
relative error = 7.4297094161901370817683418910841e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=22.8MB, alloc=4.3MB, time=0.88
x[1] = 0.144
y[1] (analytic) = 1.8506120209633722902177137646538
y[1] (numeric) = 1.8506120209633724301747516574602
absolute error = 1.399570378928064e-16
relative error = 7.5627433685397237399987594670193e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.145
y[1] (analytic) = 1.8590280580994131647380783116048
y[1] (numeric) = 1.8590280580994133077752359247469
absolute error = 1.430371576131421e-16
relative error = 7.6941903587715006861597970215212e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.146
y[1] (analytic) = 1.8674888104289022682514622569256
y[1] (numeric) = 1.8674888104289024143649767821709
absolute error = 1.461135145252453e-16
relative error = 7.8240637217894608550722842076635e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.147
y[1] (analytic) = 1.875994533426687469070154966487
y[1] (numeric) = 1.8759945334266876182563068919092
absolute error = 1.491861519254222e-16
relative error = 7.9523766869895459968997290618203e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.148
y[1] (analytic) = 1.884545484117374670912289130475
y[1] (numeric) = 1.8845454841173748231674019927145
absolute error = 1.522551128622395e-16
relative error = 8.0791423791794580650144087807831e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.149
y[1] (analytic) = 1.8931419210851699655613477664013
y[1] (numeric) = 1.8931419210851701208817879056774
absolute error = 1.553204401392761e-16
relative error = 8.2043738194886466540517374810622e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 1.9017841044837866283034228181341
y[1] (numeric) = 1.9017841044837867866855991359792
absolute error = 1.583821763178451e-16
relative error = 8.3280839262685804618979989862330e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.151
y[1] (analytic) = 1.9104722960464173988613200235854
y[1] (numeric) = 1.9104722960464175603016837432726
absolute error = 1.614403637196872e-16
relative error = 8.4502855159834674340195508968348e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=26.7MB, alloc=4.3MB, time=1.04
x[1] = 0.152
y[1] (analytic) = 1.9192067590957724936349666569604
y[1] (numeric) = 1.9192067590957726581300110865961
absolute error = 1.644950444296357e-16
relative error = 8.5709913040915383676405333955633e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.153
y[1] (analytic) = 1.9279877585541837981703311251027
y[1] (numeric) = 1.9279877585541839657165914233559
absolute error = 1.675462602982532e-16
relative error = 8.6902139059170023270999872529351e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.154
y[1] (analytic) = 1.9368155609537756919143681276147
y[1] (numeric) = 1.9368155609537758625084210720552
absolute error = 1.705940529444405e-16
relative error = 8.8079658375128018328023503072394e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.155
y[1] (analytic) = 1.9456904344467029604715233514832
y[1] (numeric) = 1.9456904344467031341099871095017
absolute error = 1.736384637580185e-16
relative error = 8.9242595165143094155526347954405e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.156
y[1] (analytic) = 1.9546126488154562537582319044033
y[1] (numeric) = 1.9546126488154564304377658066857
absolute error = 1.766795339022824e-16
relative error = 9.0391072629840280528094788891855e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.157
y[1] (analytic) = 1.9635824754832355516557906144141
y[1] (numeric) = 1.9635824754832357313730949309445
absolute error = 1.797173043165304e-16
relative error = 9.1525213002475061916783110127121e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.158
y[1] (analytic) = 1.9726001875243921019891429394989
y[1] (numeric) = 1.9726001875243922847409586580633
absolute error = 1.827518157185644e-16
relative error = 9.2645137557204348768169472027689e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.159
y[1] (analytic) = 1.9816660596749392989096548362974
y[1] (numeric) = 1.9816660596749394846927634434639
absolute error = 1.857831086071665e-16
relative error = 9.3750966617272162867091761361487e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 1.9907803683431329730340501323101
y[1] (numeric) = 1.9907803683431331618452733968592
absolute error = 1.888112232645491e-16
relative error = 9.4842819563109837414459649628031e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
memory used=30.5MB, alloc=4.3MB, time=1.20
TOP MAIN SOLVE Loop
x[1] = 0.161
y[1] (analytic) = 1.9999433916201215679894856438878
y[1] (numeric) = 1.999943391620121759825685402667
absolute error = 1.918361997587792e-16
relative error = 9.5920814840351965691398819682577e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.162
y[1] (analytic) = 2.0091554092906666813364517179271
y[1] (numeric) = 2.009155409290666876194529664106
absolute error = 1.948580779461789e-16
relative error = 9.6985069967770010156185345029539e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.163
y[1] (analytic) = 2.0184167028439344511869566150803
y[1] (numeric) = 2.0184167028439346490638540887806
absolute error = 1.978768974737003e-16
relative error = 9.8035701545123556959046544945158e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.164
y[1] (analytic) = 2.0277275554843582732054681040421
y[1] (numeric) = 2.0277275554843584740981658853191
absolute error = 2.008926977812770e-16
relative error = 9.9072825260931199129968071301932e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.165
y[1] (analytic) = 2.0370882521425733360745190584071
y[1] (numeric) = 2.0370882521425735399800371625581
absolute error = 2.039055181041510e-16
relative error = 1.0009655590016131519850540930739e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.166
y[1] (analytic) = 2.046499079486423466925913358404
y[1] (numeric) = 2.0464990794864236738413108335801
absolute error = 2.069153974751761e-16
relative error = 1.0110700735184414854721376546318e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.167
y[1] (analytic) = 2.055960325932040781682272988432
y[1] (numeric) = 2.0559603259320409916046477155297
absolute error = 2.099223747270977e-16
relative error = 1.0210429261660598207142106501769e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.168
y[1] (analytic) = 2.0654722816549986387224272567623
y[1] (numeric) = 2.0654722816549988516489157515732
absolute error = 2.129264884948109e-16
relative error = 1.0308852381412716583139765784101e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=34.3MB, alloc=4.4MB, time=1.35
x[1] = 0.169
y[1] (analytic) = 2.0750352386015383977780423051321
y[1] (numeric) = 2.0750352386015386137058195227259
absolute error = 2.159277772175938e-16
relative error = 1.0405981219052330488752336862170e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 2.0846494904998704894881066824681
y[1] (numeric) = 2.084649490499870708414385823788
absolute error = 2.189262791413199e-16
relative error = 1.0501826812565232100809280048338e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.171
y[1] (analytic) = 2.0943153328715503045826112981872
y[1] (numeric) = 2.0943153328715505265046436188353
absolute error = 2.219220323206481e-16
relative error = 1.0596400114034744722545822027126e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.172
y[1] (analytic) = 2.1040330630429294152371755365002
y[1] (numeric) = 2.1040330630429296401522501576906
absolute error = 2.249150746211904e-16
relative error = 1.0689711990357699486018067456563e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.173
y[1] (analytic) = 2.113802980156682644736663124845
y[1] (numeric) = 2.1138029801566828726421068465033
absolute error = 2.279054437216583e-16
relative error = 1.0781773223953215004134430440780e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.174
y[1] (analytic) = 2.1236253851834115052081903692641
y[1] (numeric) = 2.1236253851834117361013674852525
absolute error = 2.308931771159884e-16
relative error = 1.0872594513464379723812345501957e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.175
y[1] (analytic) = 2.1335005809333245268325459112896
y[1] (numeric) = 2.1335005809333247607108580267354
absolute error = 2.338783121154458e-16
relative error = 1.0962186474452846174375618265288e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.176
y[1] (analytic) = 2.1434288720679950056181070012066
y[1] (numeric) = 2.1434288720679952424789928519148
absolute error = 2.368608858507082e-16
relative error = 1.1050559640086548733952618250266e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.177
y[1] (analytic) = 2.153410565112196700523045671075
y[1] (numeric) = 2.1534105651121969403639809450037
absolute error = 2.398409352739287e-16
memory used=38.1MB, alloc=4.4MB, time=1.51
relative error = 1.1137724461820523326005379157768e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.178
y[1] (analytic) = 2.1634459684658180144401638611363
y[1] (numeric) = 2.1634459684658182572586610219146
absolute error = 2.428184971607783e-16
relative error = 1.1223691310070948995964677143424e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.179
y[1] (analytic) = 2.1735353924158551973142757335809
y[1] (numeric) = 2.17353539241585544310788384605
absolute error = 2.457936081124691e-16
relative error = 1.1308470474882528979470634037512e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 2.183679149148485113444865832242
y[1] (numeric) = 2.1836791491484853622111703899993
absolute error = 2.487663045577573e-16
relative error = 1.1392072166589239558641725288645e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.181
y[1] (analytic) = 2.193877552761218118836992666608
y[1] (numeric) = 2.1938775527612183705736154215352
absolute error = 2.517366227549272e-16
relative error = 1.1474506516468571685787037966815e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.182
y[1] (analytic) = 2.204130919275131598301279492648
y[1] (numeric) = 2.2041309192751318530058782864035
absolute error = 2.547045987937555e-16
relative error = 1.1555783577389301526661812682244e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.183
y[1] (analytic) = 2.2144395666471847158695398496278
y[1] (numeric) = 2.2144395666471849735398084470852
absolute error = 2.576702685974574e-16
relative error = 1.1635913324452926046224437900705e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.184
y[1] (analytic) = 2.2248038147826149359863286603556
y[1] (numeric) = 2.2248038147826151966199965849689
absolute error = 2.606336679246133e-16
relative error = 1.1714905655628775302087919933473e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.185
y[1] (analytic) = 2.2352239855474168768586958432004
y[1] (numeric) = 2.2352239855474171404535282142781
absolute error = 2.635948323710777e-16
relative error = 1.1792770392382939852128525703296e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=41.9MB, alloc=4.4MB, time=1.66
x[1] = 0.186
y[1] (analytic) = 2.2457004027809040612968554225478
y[1] (numeric) = 2.2457004027809043278506527944173
absolute error = 2.665537973718695e-16
relative error = 1.1869517280301041576862892133203e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.187
y[1] (analytic) = 2.2562333923083541343575776501515
y[1] (numeric) = 2.2562333923083544038681758531958
absolute error = 2.695105982030443e-16
relative error = 1.1945155989704939073531937066095e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.188
y[1] (analytic) = 2.2668232819537381211100748502604
y[1] (numeric) = 2.26682328195373839357534483381
absolute error = 2.724652699835496e-16
relative error = 1.2019696116263470478165083692310e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.189
y[1] (analytic) = 2.2774704015525343018811953725122
y[1] (numeric) = 2.2774704015525345772990430495741
absolute error = 2.754178476770619e-16
relative error = 1.2093147181597251135677709053438e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 2.2881750829646272864030775953138
y[1] (numeric) = 2.2881750829646275647714436891202
absolute error = 2.783683660938064e-16
relative error = 1.2165518633877618973440318565981e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.191
y[1] (analytic) = 2.2989376600872928723822624186474
y[1] (numeric) = 2.2989376600872931536991223110079
absolute error = 2.813168598923605e-16
relative error = 1.2236819848419840513033811933824e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.192
y[1] (analytic) = 2.3097584688682692781348348138751
y[1] (numeric) = 2.3097584688682695623981983953144
absolute error = 2.842633635814393e-16
relative error = 1.2307060128270558108617145228117e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.193
y[1] (analytic) = 2.3206378473189153430876811114287
y[1] (numeric) = 2.3206378473189156302955926330946
absolute error = 2.872079115216659e-16
relative error = 1.2376248704789659667294711970884e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=45.7MB, alloc=4.4MB, time=1.82
x[1] = 0.194
y[1] (analytic) = 2.3315761355274562941316288272182
y[1] (numeric) = 2.3315761355274565842821667545422
absolute error = 2.901505379273240e-16
relative error = 1.2444394738226519748051846772030e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.195
y[1] (analytic) = 2.3425736756723176800283016592621
y[1] (numeric) = 2.3425736756723179731195785273569
absolute error = 2.930912768680948e-16
relative error = 1.2511507318290756608160740359545e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.196
y[1] (analytic) = 2.3536308120355480803191972262439
y[1] (numeric) = 2.3536308120355483763493594970224
absolute error = 2.960301622707785e-16
relative error = 1.2577595464717573822362862966803e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.197
y[1] (analytic) = 2.3647478910163311994630042756132
y[1] (numeric) = 2.3647478910163314984302321966121
absolute error = 2.989672279209989e-16
relative error = 1.2642668127827678043612590477967e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.198
y[1] (analytic) = 2.3759252611445879612357462868095
y[1] (numeric) = 2.3759252611445882631382537517031
absolute error = 3.019025074648936e-16
relative error = 1.2706734189081934766144181834042e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.199
y[1] (analytic) = 2.3871632730946692227681981945627
y[1] (numeric) = 2.3871632730946695276042326053504
absolute error = 3.048360344107877e-16
relative error = 1.2769802461630726808712088896895e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 2.3984622796991397319664026633917
y[1] (numeric) = 2.3984622796991400397342447942452
absolute error = 3.077678421308535e-16
relative error = 1.2831881690858174915674304748126e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.201
y[1] (analytic) = 2.4098226359626539564642440218923
y[1] (numeric) = 2.4098226359626542671622078846464
absolute error = 3.106979638627541e-16
relative error = 1.2892980554921184586760492953189e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.202
y[1] (analytic) = 2.4212446990759244166921554509675
y[1] (numeric) = 2.4212446990759247303185881622407
absolute error = 3.136264327112732e-16
relative error = 1.2953107665283467846701381730847e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=49.5MB, alloc=4.4MB, time=1.98
x[1] = 0.203
y[1] (analytic) = 2.4327288284297831601133739362683
y[1] (numeric) = 2.4327288284297834766666555861978
absolute error = 3.165532816499295e-16
relative error = 1.3012271567244524306502871516711e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.204
y[1] (analytic) = 2.444275385629337018178955263241
y[1] (numeric) = 2.4442753856293373376574987858181
absolute error = 3.194785435225771e-16
relative error = 1.3070480740463690683785664210744e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.205
y[1] (analytic) = 2.4558847345082172920852571873983
y[1] (numeric) = 2.45588473450821761448750823239
absolute error = 3.224022510449917e-16
relative error = 1.3127743599479300194502965198576e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.206
y[1] (analytic) = 2.467557241142924517983033913016
y[1] (numeric) = 2.4675572411429248433074707194588
absolute error = 3.253244368064428e-16
relative error = 1.3184068494223009339870415050066e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.207
y[1] (analytic) = 2.4792932738672689668859020606744
y[1] (numeric) = 2.4792932738672692951310353319259
absolute error = 3.282451332712515e-16
relative error = 1.3239463710529324695040158355511e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.208
y[1] (analytic) = 2.4910932032869075391579821520057
y[1] (numeric) = 2.4910932032869078703223549323411
absolute error = 3.311643727803354e-16
relative error = 1.3293937470640438785131421718241e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.209
y[1] (analytic) = 2.5029574022939777181262369106179
y[1] (numeric) = 2.5029574022939780522084244633573
absolute error = 3.340821875527394e-16
relative error = 1.3347497933706373567261508717043e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 2.5148862460818292520626668752815
y[1] (numeric) = 2.514886246081829589061276562435
absolute error = 3.369986096871535e-16
relative error = 1.3400153196280522934802837160601e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.211
y[1] (analytic) = 2.5268801121598542385153353450758
y[1] (numeric) = 2.526880112159854578429006508493
memory used=53.4MB, alloc=4.4MB, time=2.14
absolute error = 3.399136711634172e-16
relative error = 1.3451911292810624235785634073832e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.212
y[1] (analytic) = 2.538939380368416289735430836742
y[1] (numeric) = 2.5389393803684166325628346807529
absolute error = 3.428274038440109e-16
relative error = 1.3502780196125220531665664713286e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.213
y[1] (analytic) = 2.5510644328938794627504902673244
y[1] (numeric) = 2.5510644328938798084903297428593
absolute error = 3.457398394755349e-16
relative error = 1.3552767817915682179892270047149e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.214
y[1] (analytic) = 2.5632556542837376424717561551192
y[1] (numeric) = 2.5632556542837379911227658452942
absolute error = 3.486510096901750e-16
relative error = 1.3601882009213792634640838149076e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.215
y[1] (analytic) = 2.5755134314618450710966843879497
y[1] (numeric) = 2.5755134314618454226576303951061
absolute error = 3.515609460071564e-16
relative error = 1.3650130560865009319626520491887e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.216
y[1] (analytic) = 2.587838153743748721976115637764
y[1] (numeric) = 2.5878381537437490764457954719483
absolute error = 3.544696798341843e-16
relative error = 1.3697521203997380013233850750009e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.217
y[1] (analytic) = 2.6002302128521232210598353862779
y[1] (numeric) = 2.6002302128521235784370778551512
absolute error = 3.573772424688733e-16
relative error = 1.3744061610486239496869455260471e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.218
y[1] (analytic) = 2.6126900029323090240144388485611
y[1] (numeric) = 2.6126900029323093842981039487254
absolute error = 3.602836651001643e-16
relative error = 1.3789759393414677627924578258427e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.219
y[1] (analytic) = 2.6252179205679545621238539348431
y[1] (numeric) = 2.6252179205679549253128327445723
absolute error = 3.631889788097292e-16
relative error = 1.3834622107529832517206382884081e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=57.2MB, alloc=4.4MB, time=2.30
x[1] = 0.22
y[1] (analytic) = 2.6378143647967630751358258995295
y[1] (numeric) = 2.6378143647967634412290404728939
absolute error = 3.660932145733644e-16
relative error = 1.3878657249695088236685641756912e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.221
y[1] (analytic) = 2.650479737126344854307401659366
y[1] (numeric) = 2.6504797371263452233038049217386
absolute error = 3.689964032623726e-16
relative error = 1.3921872259338198093799522071658e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.222
y[1] (analytic) = 2.663214441550175624029242149073
y[1] (numeric) = 2.6632144415501759959278177940057
absolute error = 3.718985756449327e-16
relative error = 1.3964274518895366170196843240017e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.223
y[1] (analytic) = 2.6760188845636617955727118277761
y[1] (numeric) = 2.6760188845636621703724742152356
absolute error = 3.747997623874595e-16
relative error = 1.4005871354251390777518239669570e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.224
y[1] (analytic) = 2.6888934751803133317054219501174
y[1] (numeric) = 2.688893475180313709405416006068
absolute error = 3.776999940559506e-16
relative error = 1.4046670035175810795773801718165e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.225
y[1] (analytic) = 2.7018386249480249661605169766501
y[1] (numeric) = 2.7018386249480253467598180939742
absolute error = 3.805993011173241e-16
relative error = 1.4086677775755228739496153831839e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.226
y[1] (analytic) = 2.7148547479654665272227721473389
y[1] (numeric) = 2.7148547479654669107204860880833
absolute error = 3.834977139407444e-16
relative error = 1.4125901734821746877123631106702e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.227
y[1] (analytic) = 2.7279422608985831200107975479228
y[1] (numeric) = 2.7279422608985835064060603468596
absolute error = 3.863952627989368e-16
relative error = 1.4164349016377580905228383395046e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.228
y[1] (analytic) = 2.7411015829972059273896048859688
y[1] (numeric) = 2.7411015829972063166815827554619
absolute error = 3.892919778694931e-16
relative error = 1.4202026670015969084838835229512e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
memory used=61.0MB, alloc=4.4MB, time=2.45
TOP MAIN SOLVE Loop
x[1] = 0.229
y[1] (analytic) = 2.7543331361117743948417747587194
y[1] (numeric) = 2.7543331361117747870296639948848
absolute error = 3.921878892361654e-16
relative error = 1.4238941691338309814845630083875e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 2.7676373447101705700587537245564
y[1] (numeric) = 2.7676373447101709651417806147063
absolute error = 3.950830268901499e-16
relative error = 1.4275101022367630464123005333412e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.231
y[1] (analytic) = 2.7810146358946663734867034762434
y[1] (numeric) = 2.7810146358946667714641242076043
absolute error = 3.979774207313609e-16
relative error = 1.4310511551958429922850720537466e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.232
y[1] (analytic) = 2.7944654394189845815741125719687
y[1] (numeric) = 2.7944654394189849824452131416628
absolute error = 4.008711005696941e-16
relative error = 1.4345180116202897405526814056150e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.233
y[1] (analytic) = 2.8079901877054743100213604642017
y[1] (numeric) = 2.8079901877054747137854565904828
absolute error = 4.037640961262811e-16
relative error = 1.4379113498833610712219888587112e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.234
y[1] (analytic) = 2.8215893158624017899258921879473
y[1] (numeric) = 2.8215893158624021965823292226797
absolute error = 4.066564370347324e-16
relative error = 1.4412318431622651217612332917046e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.235
y[1] (analytic) = 2.8352632617013572353509205146238
y[1] (numeric) = 2.8352632617013576448990733569963
absolute error = 4.095481528423725e-16
relative error = 1.4444801594777298490975800176434e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.236
y[1] (analytic) = 2.849012465754778606520923422476
y[1] (numeric) = 2.84901246575477901896019643394
absolute error = 4.124392730114640e-16
relative error = 1.4476569617332227065923645941484e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=64.8MB, alloc=4.4MB, time=2.61
x[1] = 0.237
y[1] (analytic) = 2.8628373712935930785639534650796
y[1] (numeric) = 2.8628373712935934938937803855031
absolute error = 4.153298269204235e-16
relative error = 1.4507629077538337931827141505910e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.238
y[1] (analytic) = 2.8767384243449770314792294486864
y[1] (numeric) = 2.8767384243449774496990733137136
absolute error = 4.182198438650272e-16
relative error = 1.4537986503248182905497402550130e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.239
y[1] (analytic) = 2.8907160737102353828089495139062
y[1] (numeric) = 2.890716073710235803918302573514
absolute error = 4.211093530596078e-16
relative error = 1.4567648372298070617769284298506e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 2.9047707709828010903360603769508
y[1] (numeric) = 2.9047707709828015143344440151929
absolute error = 4.239983836382421e-16
relative error = 1.4596621112886864685378402629383e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.241
y[1] (analytic) = 2.9189029705663556580151546202718
y[1] (numeric) = 2.9189029705663560849021192762022
absolute error = 4.268869646559304e-16
relative error = 1.4624911103951543428080578590588e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.242
y[1] (analytic) = 2.9331131296930714842720634305512
y[1] (numeric) = 2.9331131296930719140471885203171
absolute error = 4.297751250897659e-16
relative error = 1.4652524675539489896978607505675e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.243
y[1] (analytic) = 2.9474017084419768977793853793861
y[1] (numeric) = 2.947401708441977330442279219482
absolute error = 4.326628938400959e-16
relative error = 1.4679468109177605261825498671737e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.244
y[1] (analytic) = 2.9617691697574447318304644800421
y[1] (numeric) = 2.9617691697574451673807642117171
absolute error = 4.355502997316750e-16
relative error = 1.4705747638238281939448508776226e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.245
y[1] (analytic) = 2.9762159794678052944935270380462
y[1] (numeric) = 2.9762159794678057329308985528549
absolute error = 4.384373715148087e-16
relative error = 1.4731369448302211866104639594418e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=68.6MB, alloc=4.4MB, time=2.77
x[1] = 0.246
y[1] (analytic) = 2.9907426063040845978311334230035
y[1] (numeric) = 2.9907426063040850391552712894928
absolute error = 4.413241378664893e-16
relative error = 1.4756339677518124200522491949650e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.247
y[1] (analytic) = 3.0053495219188687156181269948611
y[1] (numeric) = 3.0053495219188691598287543863848
absolute error = 4.442106273915237e-16
relative error = 1.4780664416959467481255369840994e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.248
y[1] (analytic) = 3.0200372009052951451841997021604
y[1] (numeric) = 3.0200372009052955922810683258127
absolute error = 4.470968686236523e-16
relative error = 1.4804349710978038309939517271160e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.249
y[1] (analytic) = 3.034806120816172055245376545423
y[1] (numeric) = 3.0348061208161725052282665720832
absolute error = 4.499828900266602e-16
relative error = 1.4827401557554625333634869595854e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 3.0496567621832263078724859285086
y[1] (numeric) = 3.0496567621832267607412059239896
absolute error = 4.528687199954810e-16
relative error = 1.4849825908646706001404587099416e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.251
y[1] (analytic) = 3.064589608536481149074369236938
y[1] (numeric) = 3.0645896085364816048287560942296
absolute error = 4.557543868572916e-16
relative error = 1.4871628670533170966174284018913e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.252
y[1] (analytic) = 3.0796051464237644688495327065002
y[1] (numeric) = 3.0796051464237649274894515791005
absolute error = 4.586399188726003e-16
relative error = 1.4892815704156179463487062632731e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.253
y[1] (analytic) = 3.0947038654303485379825023089187
y[1] (numeric) = 3.0947038654303489995078465452453
absolute error = 4.615253442363266e-16
relative error = 1.4913392825460119817055419032819e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=72.4MB, alloc=4.4MB, time=2.93
x[1] = 0.254
y[1] (analytic) = 3.1098862581987221353306551441827
y[1] (numeric) = 3.1098862581987225997413462230563
absolute error = 4.644106910788736e-16
relative error = 1.4933365805727731428630273640757e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.255
y[1] (analytic) = 3.1251528204484959858641185011632
y[1] (numeric) = 3.1251528204484964531601059683566
absolute error = 4.672959874671934e-16
relative error = 1.4952740371913427249784374228593e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.256
y[1] (analytic) = 3.1405040509964424362858028090399
y[1] (numeric) = 3.140504050996442906467064214884
absolute error = 4.701812614058441e-16
relative error = 1.4971522206973797705236530334698e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.257
y[1] (analytic) = 3.1559404517766703016711223220572
y[1] (numeric) = 3.1559404517766707747376631600979
absolute error = 4.730665408380407e-16
relative error = 1.4989716950195395817475456628960e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.258
y[1] (analytic) = 3.1714625278609358232278154405984
y[1] (numeric) = 3.1714625278609362991796690872968
absolute error = 4.759518536466984e-16
relative error = 1.5007330197519780381736370356022e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.259
y[1] (analytic) = 3.187070787479090683985865685965
y[1] (numeric) = 3.187070787479091162823093341433
absolute error = 4.788372276554680e-16
relative error = 1.5024367501865833360630683019553e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 3.2027657420396680359862078811511
y[1] (numeric) = 3.202765742039668517708898510917
absolute error = 4.817226906297659e-16
relative error = 1.5040834373449455249234839149300e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.261
y[1] (analytic) = 3.2185479061506074993450481862288
y[1] (numeric) = 3.2185479061506079839533184640246
absolute error = 4.846082702777958e-16
relative error = 1.5056736280100571105358650508580e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.262
y[1] (analytic) = 3.2344177976401201004286002313232
y[1] (numeric) = 3.2344177976401205879225944828877
absolute error = 4.874939942515645e-16
relative error = 1.5072078647577547169440367555976e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=76.2MB, alloc=4.4MB, time=3.08
x[1] = 0.263
y[1] (analytic) = 3.2503759375776941232812144364713
y[1] (numeric) = 3.2503759375776946136611045843619
absolute error = 4.903798901478906e-16
relative error = 1.5086866859879004105586261013165e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.264
y[1] (analytic) = 3.2664228502952428554086282988144
y[1] (numeric) = 3.266422850295243348674613808221
absolute error = 4.932659855094066e-16
relative error = 1.5101106259553066213732996126327e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.265
y[1] (analytic) = 3.2825590634083952160277694173757
y[1] (numeric) = 3.2825590634083957121800772429303
absolute error = 4.961523078255546e-16
relative error = 1.5114802148004076023398846046641e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.266
y[1] (analytic) = 3.2987851078379302619555806508852
y[1] (numeric) = 3.2987851078379307609944651844606
absolute error = 4.990388845335754e-16
relative error = 1.5127959785796791125695416527903e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.267
y[1] (analytic) = 3.3151015178313565734220913067313
y[1] (numeric) = 3.3151015178313570753478343262226
absolute error = 5.019257430194913e-16
relative error = 1.5140584392958095237559014262789e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.268
y[1] (analytic) = 3.3315088309846375292578158087715
y[1] (numeric) = 3.3315088309846380340707264278541
absolute error = 5.048129106190826e-16
relative error = 1.5152681149276245943957217820068e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.269
y[1] (analytic) = 3.348007588264063488122911008325
y[1] (numeric) = 3.3480075882640639958233256271835
absolute error = 5.077004146188585e-16
relative error = 1.5164255194597702291267494606322e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 3.3645983340282718997157572791211
y[1] (numeric) = 3.3645983340282724103040395361416
absolute error = 5.105882822570205e-16
relative error = 1.5175311629121497125328515309509e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.271
y[1] (analytic) = 3.3812816160504163772221418622236
y[1] (numeric) = 3.381281616050416890698682586645
absolute error = 5.134765407244214e-16
relative error = 1.5185855513691269003126061445768e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
memory used=80.1MB, alloc=4.4MB, time=3.24
TOP MAIN SOLVE Loop
x[1] = 0.272
y[1] (analytic) = 3.3980579855404857696434137090895
y[1] (numeric) = 3.3980579855404862860086308746066
absolute error = 5.163652171655171e-16
relative error = 1.5195891870084891057907911012363e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.273
y[1] (analytic) = 3.4149279971677742800732484605165
y[1] (numeric) = 3.4149279971677747993275871398296
absolute error = 5.192543386793131e-16
relative error = 1.5205425681301774941380209494307e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.274
y[1] (analytic) = 3.4318922090835036834784144128829
y[1] (numeric) = 3.4318922090835042056223467331887
absolute error = 5.221439323203058e-16
relative error = 1.5214461891847873124703007554470e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.275
y[1] (analytic) = 3.448951182943598705079572667076
y[1] (numeric) = 3.4489511829435992301135977664923
absolute error = 5.250340250994163e-16
relative error = 1.5223005408018332980154825874378e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.276
y[1] (analytic) = 3.4661054839316166280240875497472
y[1] (numeric) = 3.4661054839316171559487315346679
absolute error = 5.279246439849207e-16
relative error = 1.5231061098177940310100658111568e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.277
y[1] (analytic) = 3.4833556807818322066944803986334
y[1] (numeric) = 3.483355680781832737510296302007
absolute error = 5.308158159033736e-16
relative error = 1.5238633793039275654612170755728e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.278
y[1] (analytic) = 3.5007023458024789697039476331994
y[1] (numeric) = 3.5007023458024795034115153737257
absolute error = 5.337075677405263e-16
relative error = 1.5245728285938647455247619074443e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.279
y[1] (analytic) = 3.5181460548991480043947025948103
y[1] (numeric) = 3.5181460548991485409946289370498
absolute error = 5.365999263422395e-16
relative error = 1.5252349333109815950467483353833e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=83.9MB, alloc=4.4MB, time=3.40
x[1] = 0.28
y[1] (analytic) = 3.5356873875983453224762130541403
y[1] (numeric) = 3.5356873875983458619691315695319
absolute error = 5.394929185153916e-16
relative error = 1.5258501653955558517074329538619e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.281
y[1] (analytic) = 3.5533269270712089143191189006542
y[1] (numeric) = 3.5533269270712094567056899294346
absolute error = 5.423865710287804e-16
relative error = 1.5264189931317032908362638816272e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.282
y[1] (analytic) = 3.5710652601573866073571569638526
y[1] (numeric) = 3.571065260157387152638067577873
absolute error = 5.452809106140204e-16
relative error = 1.5269418811741020374661125565070e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.283
y[1] (analytic) = 3.5889029773890758520442250689476
y[1] (numeric) = 3.5889029773890764002201890353826
absolute error = 5.481759639664350e-16
relative error = 1.5274192905745047222799132199174e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.284
y[1] (analytic) = 3.6068406730152265668672215128454
y[1] (numeric) = 3.6068406730152271179389792587891
absolute error = 5.510717577459437e-16
relative error = 1.5278516788080406190565969377056e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.285
y[1] (analytic) = 3.6248789450259081820279387092898
y[1] (numeric) = 3.6248789450259087359962572872332
absolute error = 5.539683185779434e-16
relative error = 1.5282394997993071166841168950090e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.286
y[1] (analytic) = 3.643018395176842029579513707539
y[1] (numeric) = 3.6430183951768425864451867617258
absolute error = 5.568656730541868e-16
relative error = 1.5285832039482606685637210054627e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.287
y[1] (analytic) = 3.6612596290141002360351899391551
y[1] (numeric) = 3.6612596290141007957990376728086
absolute error = 5.597638477336535e-16
relative error = 1.5288832381558968063752564710872e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.288
y[1] (analytic) = 3.6796032558989722817598736100876
y[1] (numeric) = 3.6796032558989728444227427535062
absolute error = 5.626628691434186e-16
relative error = 1.5291400458497342762710613558927e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=87.7MB, alloc=4.4MB, time=3.55
x[1] = 0.289
y[1] (analytic) = 3.698049889033000399808627790097
y[1] (numeric) = 3.698049889033000965371391569612
absolute error = 5.655627637795150e-16
relative error = 1.5293540670090945612820933318046e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 3.7166001454831849952912940872986
y[1] (numeric) = 3.7166001454831855637548521950904
absolute error = 5.684635581077918e-16
relative error = 1.5295257381901851358278581464647e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.291
y[1] (analytic) = 3.7352546462073612748193259565698
y[1] (numeric) = 3.7352546462073618461846045213379
absolute error = 5.713652785647681e-16
relative error = 1.5296554925509862245226542814050e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.292
y[1] (analytic) = 3.7540140160797482841301228239146
y[1] (numeric) = 3.7540140160797488583980743823973
absolute error = 5.742679515584827e-16
relative error = 1.5297437598759440966325712374519e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.293
y[1] (analytic) = 3.7728788839166715605861375119604
y[1] (numeric) = 3.7728788839166721377577409812982
absolute error = 5.771716034693378e-16
relative error = 1.5297909666004674996283928389767e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.294
y[1] (analytic) = 3.7918498825024606159112616996332
y[1] (numeric) = 3.7918498825024611959875223505741
absolute error = 5.800762606509409e-16
relative error = 1.5297975358352401114187080078989e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.295
y[1] (analytic) = 3.8109276486155224732559497222935
y[1] (numeric) = 3.8109276486155230562378991532332
absolute error = 5.829819494309397e-16
relative error = 1.5297638873903367657259348093258e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.296
y[1] (analytic) = 3.8301128230545924914756979312576
y[1] (numeric) = 3.8301128230545930773643940431123
absolute error = 5.858886961118547e-16
relative error = 1.5296904377991575909809675214054e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=91.5MB, alloc=4.4MB, time=3.71
x[1] = 0.297
y[1] (analytic) = 3.8494060506651637183653367594756
y[1] (numeric) = 3.8494060506651643071618637313829
absolute error = 5.887965269719073e-16
relative error = 1.5295776003421757691236728246231e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.298
y[1] (analytic) = 3.868807980366096023514600949108
y[1] (numeric) = 3.8688079803660966152200692149502
absolute error = 5.917054682658422e-16
relative error = 1.5294257850704974253658859950331e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.299
y[1] (analytic) = 3.8883192651764062704391091715984
y[1] (numeric) = 3.8883192651764068650546553973469
absolute error = 5.946155462257485e-16
relative error = 1.5292353988292466736702159508060e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 3.9079405622422407966957003440841
y[1] (numeric) = 3.9079405622422413942224874059583
absolute error = 5.975267870618742e-16
relative error = 1.5290068452807635521161768389452e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.301
y[1] (analytic) = 3.9276725328640314798125369269298
y[1] (numeric) = 3.9276725328640320802517538903684
absolute error = 6.004392169634386e-16
relative error = 1.5287405249276280709028791868075e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.302
y[1] (analytic) = 3.9475158425238366760529957913868
y[1] (numeric) = 3.9475158425238372794058578908268
absolute error = 6.033528620994400e-16
relative error = 1.5284368351355051328824170079030e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.303
y[1] (analytic) = 3.9674711609128683282886291251979
y[1] (numeric) = 3.9674711609128689345563777446569
absolute error = 6.062677486194590e-16
relative error = 1.5280961701558126521291730685093e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.304
y[1] (analytic) = 3.9875391619592065485808994143748
y[1] (numeric) = 3.9875391619592071577648020688348
absolute error = 6.091839026544600e-16
relative error = 1.5277189211482209206179830638078e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.305
y[1] (analytic) = 4.0077205238557029904644858140394
y[1] (numeric) = 4.0077205238557036025658361316261
absolute error = 6.121013503175867e-16
relative error = 1.5273054762029740307468863760380e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=95.3MB, alloc=4.4MB, time=3.87
x[1] = 0.306
y[1] (analytic) = 4.0280159290880743353872401387929
y[1] (numeric) = 4.0280159290880749504073578437484
absolute error = 6.150201177049555e-16
relative error = 1.5268562203630446847618837621841e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.307
y[1] (analytic) = 4.0484260644631872272938591587806
y[1] (numeric) = 4.0484260644631878452340900552256
absolute error = 6.179402308964450e-16
relative error = 1.5263715356461192372621292662762e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.308
y[1] (analytic) = 4.0689516211375359989425597639655
y[1] (numeric) = 4.068951621137536619804275720447
absolute error = 6.208617159564815e-16
relative error = 1.5258518010664141657294054000687e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.309
y[1] (analytic) = 4.089593294645914543217022757007
y[1] (numeric) = 4.0895932946459151670016216918284
absolute error = 6.237845989348214e-16
relative error = 1.5252973926563276077575337377221e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 4.1103517849302836924401415050797
y[1] (numeric) = 4.11035178493028431914904737241
absolute error = 6.267089058673303e-16
relative error = 1.5247086834879268270507000524768e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.311
y[1] (analytic) = 4.1312277963688354785122094546477
y[1] (numeric) = 4.1312277963688361081468722314063
absolute error = 6.296346627767586e-16
relative error = 1.5240860436942724798563111823992e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.312
y[1] (analytic) = 4.1522220378052556565846457352548
y[1] (numeric) = 4.1522220378052562891465414087682
absolute error = 6.325618956735134e-16
relative error = 1.5234298404905805627405361771425e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.313
y[1] (analytic) = 4.1733352225781858849417350383951
y[1] (numeric) = 4.1733352225781865204323655948232
absolute error = 6.354906305564281e-16
relative error = 1.5227404381952267653723426253567e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.314
y[1] (analytic) = 4.1945680685508869637976951223487
y[1] (numeric) = 4.1945680685508876022185885358762
absolute error = 6.384208934135275e-16
relative error = 1.5220181982505892227473311555400e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
memory used=99.1MB, alloc=4.4MB, time=4.03
TOP MAIN SOLVE Loop
x[1] = 0.315
y[1] (analytic) = 4.21592129814110454582523534014
y[1] (numeric) = 4.2159212981411051871779455629312
absolute error = 6.413527102227912e-16
relative error = 1.5212634792437377249352995534708e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.316
y[1] (analytic) = 4.2373956383511387414151894347649
y[1] (numeric) = 4.2373956383511393857012963876777
absolute error = 6.442861069529128e-16
relative error = 1.5204766369269646535087752613476e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.317
y[1] (analytic) = 4.2589918207981190519253566884245
y[1] (numeric) = 4.2589918207981196991464662524807
absolute error = 6.472211095640562e-16
relative error = 1.5196580242381620677647315546252e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.318
y[1] (analytic) = 4.2807105817444860745109328546043
y[1] (numeric) = 4.280710581744486724668676863214
absolute error = 6.501577440086097e-16
relative error = 1.5188079913210478268971200338166e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.319
y[1] (analytic) = 4.3025526621286814325394259899033
y[1] (numeric) = 4.3025526621286820856354622218392
absolute error = 6.530960362319359e-16
relative error = 1.5179268855452372831126382975096e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 4.3245188075960473960803065594379
y[1] (numeric) = 4.324518807596048052116318732558
absolute error = 6.560360121731201e-16
relative error = 1.5170150515261681295130497512349e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.321
y[1] (analytic) = 4.3466097685299376675244146488818
y[1] (numeric) = 4.3466097685299383265021124145961
absolute error = 6.589776977657143e-16
relative error = 1.5160728311448728378383265870119e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.322
y[1] (analytic) = 4.3688263000830408180309228561425
y[1] (numeric) = 4.3688263000830414799520417946228
absolute error = 6.619211189384803e-16
relative error = 1.5151005635676080346344357050158e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=103.0MB, alloc=4.4MB, time=4.19
x[1] = 0.323
y[1] (analytic) = 4.3911691622089178712210190143605
y[1] (numeric) = 4.3911691622089185360873206304883
absolute error = 6.648663016161278e-16
relative error = 1.5140985852653325193732561977273e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.324
y[1] (analytic) = 4.4136391196937555413380203879289
y[1] (numeric) = 4.413639119693756209151292107981
absolute error = 6.678132717200521e-16
relative error = 1.5130672300330457137104247582116e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.325
y[1] (analytic) = 4.4362369421883366439739570069851
y[1] (numeric) = 4.4362369421883373147360121760523
absolute error = 6.707620551690672e-16
relative error = 1.5120068290089780574571357983329e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.326
y[1] (analytic) = 4.458963404240229208423367570995
y[1] (numeric) = 4.4589634042402298821360454511325
absolute error = 6.737126778801375e-16
relative error = 1.5109177106936418432124050077133e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.327
y[1] (analytic) = 4.481819285326195831766742687438
y[1] (numeric) = 4.4818192853261965084319084565446
absolute error = 6.766651657691066e-16
relative error = 1.5098002009687401904343866298868e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.328
y[1] (analytic) = 4.5048053698848248259093376031438
y[1] (numeric) = 4.5048053698848255055288823545672
absolute error = 6.796195447514234e-16
relative error = 1.5086546231159357632492034984111e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.329
y[1] (analytic) = 4.5279224473493847200065752129988
y[1] (numeric) = 4.5279224473493854025824159558648
absolute error = 6.825758407428660e-16
relative error = 1.5074812978354814717171328993202e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 4.551171312180903691995589903174
y[1] (numeric) = 4.5511713121809043775296695634371
absolute error = 6.855340796602631e-16
relative error = 1.5062805432647135846909843639500e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.331
y[1] (analytic) = 4.5745527639014755143242483804697
y[1] (numeric) = 4.5745527639014762028185358026825
absolute error = 6.884942874222128e-16
relative error = 1.5050526749964081386468264750607e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=106.8MB, alloc=4.5MB, time=4.35
x[1] = 0.332
y[1] (analytic) = 4.5980676071277936104248545369243
y[1] (numeric) = 4.598067607127794301881344486724
absolute error = 6.914564899497997e-16
relative error = 1.5037980060970037023318536171292e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.333
y[1] (analytic) = 4.621716651604914830020335922467
y[1] (numeric) = 4.6217166516049155244410490897756
absolute error = 6.944207131673086e-16
relative error = 1.5025168471246878429239470047698e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.334
y[1] (analytic) = 4.6455007122402545629766587507778
y[1] (numeric) = 4.6455007122402552603636417537151
absolute error = 6.973869830029373e-16
relative error = 1.5012095061473538239690537364476e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.335
y[1] (analytic) = 4.6694206091378148231271706651824
y[1] (numeric) = 4.6694206091378155234824960546885
absolute error = 7.003553253895061e-16
relative error = 1.4998762887604233415400692386946e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.336
y[1] (analytic) = 4.6934771676326469452931748191256
y[1] (numeric) = 4.6934771676326476486189410842915
absolute error = 7.033257662651659e-16
relative error = 1.4985174981045404715731072786461e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.337
y[1] (analytic) = 4.7176712183255505506109492513519
y[1] (numeric) = 4.7176712183255512569092808254552
absolute error = 7.062983315741033e-16
relative error = 1.4971334348831344070861306589749e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.338
y[1] (analytic) = 4.7420035971180104472493011652255
y[1] (numeric) = 4.7420035971180111565223484324705
absolute error = 7.092730472672450e-16
relative error = 1.4957243973798569210371502847321e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.339
y[1] (analytic) = 4.7664751452473731456642507339451
y[1] (numeric) = 4.7664751452473738579141900369039
absolute error = 7.122499393029588e-16
relative error = 1.4942906814758897926837993022646e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
memory used=110.6MB, alloc=4.5MB, time=4.51
y[1] (analytic) = 4.7910867093222646796892427411163
y[1] (numeric) = 4.7910867093222653949182763888697
absolute error = 7.152290336477534e-16
relative error = 1.4928325806671278899122179098885e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.341
y[1] (analytic) = 4.8158391413582514370010611747214
y[1] (numeric) = 4.8158391413582521552114174516972
absolute error = 7.182103562769758e-16
relative error = 1.4913503860812363419250488828647e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.342
y[1] (analytic) = 4.8407332988137457148340514608234
y[1] (numeric) = 4.8407332988137464360279846363311
absolute error = 7.211939331755077e-16
relative error = 1.4898443864945857041348747555187e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.343
y[1] (analytic) = 4.8657700446261577292390222242516
y[1] (numeric) = 4.8657700446261584534188125627099
absolute error = 7.241797903384583e-16
relative error = 1.4883148683490606695925225400202e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.344
y[1] (analytic) = 4.890950247248295818698993444892
y[1] (numeric) = 4.8909502472482965458669472167494
absolute error = 7.271679537718574e-16
relative error = 1.4867621157687513853899463318114e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.345
y[1] (analytic) = 4.9162747806850165955224761041834
y[1] (numeric) = 4.9162747806850173256809255975283
absolute error = 7.301584494933449e-16
relative error = 1.4851864105765202288612976421331e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.346
y[1] (analytic) = 4.9417445245301268111369107089568
y[1] (numeric) = 4.9417445245301275442882142418167
absolute error = 7.331513035328599e-16
relative error = 1.4835880323104515888952854835815e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.347
y[1] (analytic) = 4.9673603640035387142009646606619
y[1] (numeric) = 4.9673603640035394503475065939891
absolute error = 7.361465419333272e-16
relative error = 1.4819672582401810502947236563307e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.348
y[1] (analytic) = 4.993123189988680693345302971145
y[1] (numeric) = 4.9931231899886814324894937224878
absolute error = 7.391441907513428e-16
relative error = 1.4803243633831081674989782415177e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=114.4MB, alloc=4.5MB, time=4.66
x[1] = 0.349
y[1] (analytic) = 5.0190338990701650093379204600422
y[1] (numeric) = 5.0190338990701657514821965178989
absolute error = 7.421442760578567e-16
relative error = 1.4786596205204902988280402276451e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = 5.0450933935717144345528789797121
y[1] (numeric) = 5.0450933935717151796997029185679
absolute error = 7.451468239388558e-16
relative error = 1.4769733002134240262653513800548e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.351
y[1] (analytic) = 5.071302581594349630801058648592
y[1] (numeric) = 5.0713025815943503789529191446357
absolute error = 7.481518604960437e-16
relative error = 1.4752656708187086171452060733865e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.352
y[1] (analytic) = 5.097662377054839109859041394595
y[1] (numeric) = 5.0976623770548398610184532421149
absolute error = 7.511594118475199e-16
relative error = 1.4735369985045974225879267693916e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.353
y[1] (analytic) = 5.1241736997244136344082378369467
y[1] (numeric) = 5.1241736997244143885777419654037
absolute error = 7.541695041284570e-16
relative error = 1.4717875472664352851805883881875e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.354
y[1] (analytic) = 5.1508374752677469305715898908164
y[1] (numeric) = 5.1508374752677476877537533825934
absolute error = 7.571821634917770e-16
relative error = 1.4700175789421849900926936418169e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.355
y[1] (analytic) = 5.1776546352822045968103824349657
y[1] (numeric) = 5.1776546352822053570077985437914
absolute error = 7.601974161088257e-16
relative error = 1.4682273532278416425811610734657e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.356
y[1] (analytic) = 5.2046261173373631076196347017778
y[1] (numeric) = 5.2046261173373638708349228718238
absolute error = 7.632152881700460e-16
relative error = 1.4664171276927373879861194713084e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.357
y[1] (analytic) = 5.23175286501480082423797833283
y[1] (numeric) = 5.2317528650148015904737842184798
absolute error = 7.662358058856498e-16
relative error = 1.4645871577947367173461240821864e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=118.2MB, alloc=4.5MB, time=4.82
x[1] = 0.358
y[1] (analytic) = 5.2590358279481629384676327768427
y[1] (numeric) = 5.2590358279481637077266282631317
absolute error = 7.692589954862890e-16
relative error = 1.4627376968953241411535171678666e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.359
y[1] (analytic) = 5.2864759618635022896828343055084
y[1] (numeric) = 5.2864759618635030619677175292326
absolute error = 7.722848832237242e-16
relative error = 1.4608689962745823742506249487522e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 5.3140742286198980091916427779536
y[1] (numeric) = 5.3140742286198987845051381494473
absolute error = 7.753134953714937e-16
relative error = 1.4589813051460668067830625910470e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.361
y[1] (analytic) = 5.3418315962503539603072268113113
y[1] (numeric) = 5.341831596250354738652085036891
absolute error = 7.783448582255797e-16
relative error = 1.4570748706715711551726034299196e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.362
y[1] (analytic) = 5.3697490390029789567813056985162
y[1] (numeric) = 5.3697490390029797381603038035912
absolute error = 7.813789981050750e-16
relative error = 1.4551499379757913433511674491846e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.363
y[1] (analytic) = 5.3978275373824507566552038586201
y[1] (numeric) = 5.3978275373824515410711452114674
absolute error = 7.844159413528473e-16
relative error = 1.4532067501608829150008689018721e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.364
y[1] (analytic) = 5.4260680781917658430937555794661
y[1] (numeric) = 5.4260680781917666305494699156689
absolute error = 7.874557143362028e-16
relative error = 1.4512455483209159754095845949895e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.365
y[1] (analytic) = 5.4544716545742770183848953018442
y[1] (numeric) = 5.4544716545742778088832387493934
absolute error = 7.904983434475492e-16
relative error = 1.4492665715562285905761147679375e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=122.0MB, alloc=4.5MB, time=4.98
x[1] = 0.366
y[1] (analytic) = 5.4830392660560208520139989460098
y[1] (numeric) = 5.4830392660560216455578540510671
absolute error = 7.935438551050573e-16
relative error = 1.4472700569876779172263548539370e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.367
y[1] (analytic) = 5.5117719185883370385577283559124
y[1] (numeric) = 5.5117719185883378351500041092339
absolute error = 7.965922757533215e-16
relative error = 1.4452562397707903892143918348929e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.368
y[1] (analytic) = 5.5406706245907817360881037559509
y[1] (numeric) = 5.5406706245907825357317356199706
absolute error = 7.996436318640197e-16
relative error = 1.4432253531098126182935176636187e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.369
y[1] (analytic) = 5.5697364029943369708346245138573
y[1] (numeric) = 5.5697364029943377735325744504295
absolute error = 8.026979499365722e-16
relative error = 1.4411776282716630083474686653655e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 5.5989702792849182090213192780774
y[1] (numeric) = 5.5989702792849190147765757768773
absolute error = 8.057552564987999e-16
relative error = 1.4391132945997853576968164019769e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.371
y[1] (analytic) = 5.6283732855471822120774820185481
y[1] (numeric) = 5.6283732855471830208930601261292
absolute error = 8.088155781075811e-16
relative error = 1.4370325795279039198101999079568e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.372
y[1] (analytic) = 5.6579464605086373068163965201148
y[1] (numeric) = 5.6579464605086381186953378696227
absolute error = 8.118789413495079e-16
relative error = 1.4349357085936824445889563602693e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.373
y[1] (analytic) = 5.6876908495840582176864309478788
y[1] (numeric) = 5.6876908495840590326318037894211
absolute error = 8.149453728415423e-16
relative error = 1.4328229054522880604584074980384e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.374
y[1] (analytic) = 5.7176075049202076238243653812027
y[1] (numeric) = 5.7176075049202084418392646128733
absolute error = 8.180148992316706e-16
relative error = 1.4306943918898582222827914071716e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=125.8MB, alloc=4.5MB, time=5.14
x[1] = 0.375
y[1] (analytic) = 5.7476974854408666193825745758359
y[1] (numeric) = 5.7476974854408674404701217753938
absolute error = 8.210875471995579e-16
relative error = 1.4285503878368746158700611060235e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.376
y[1] (analytic) = 5.777961856892176271460608312566
y[1] (numeric) = 5.7779618568921770956239517697672
absolute error = 8.241633434572012e-16
relative error = 1.4263911113814420613238385075717e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.377
y[1] (analytic) = 5.8084016918882924859486820031168
y[1] (numeric) = 5.8084016918882933131909967526998
absolute error = 8.272423147495830e-16
relative error = 1.4242167787824764162037514845198e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.378
y[1] (analytic) = 5.8390180699573564076865071067744
y[1] (numeric) = 5.8390180699573572380109949620973
absolute error = 8.303244878553229e-16
relative error = 1.4220276044827978012104520423978e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.379
y[1] (analytic) = 5.8698120775877825975566576554848
y[1] (numeric) = 5.8698120775877834309665472428145
absolute error = 8.334098895873297e-16
relative error = 1.4198238011221341657448882375084e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 5.9007848082748672454681960705165
y[1] (numeric) = 5.9007848082748680819667428639692
absolute error = 8.364985467934527e-16
relative error = 1.4176055795500335858356447569535e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.381
y[1] (analytic) = 5.9319373625677186946444858032608
y[1] (numeric) = 5.9319373625677195342349721603925
absolute error = 8.395904863571317e-16
relative error = 1.4153731488386851249267197106078e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.382
y[1] (analytic) = 5.9632708481165125692099245682624
y[1] (numeric) = 5.9632708481165134118956597663106
absolute error = 8.426857351980482e-16
relative error = 1.4131267162956531495222149051375e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.383
y[1] (analytic) = 5.9947863797200738137746716347544
y[1] (numeric) = 5.9947863797200746595589919075287
absolute error = 8.457843202727743e-16
relative error = 1.4108664874765198013798828961369e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=129.7MB, alloc=4.5MB, time=5.30
x[1] = 0.384
y[1] (analytic) = 6.0264850793737879705452545914004
y[1] (numeric) = 6.0264850793737888194315231668231
absolute error = 8.488862685754227e-16
relative error = 1.4085926661974420207433038115080e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.385
y[1] (analytic) = 6.0583680763178440364431712529629
y[1] (numeric) = 6.0583680763178448884347783912582
absolute error = 8.519916071382953e-16
relative error = 1.4063054545476195325598331809311e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.386
y[1] (analytic) = 6.0904365070858112597942043174318
y[1] (numeric) = 6.0904365070858121148945673499634
absolute error = 8.551003630325316e-16
relative error = 1.4040050529016764541164403383462e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.387
y[1] (analytic) = 6.1226915155535522533591007705599
y[1] (numeric) = 6.1226915155535531115716641393177
absolute error = 8.582125633687578e-16
relative error = 1.4016916599319586041776932367277e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.388
y[1] (analytic) = 6.1551342529884748178125030752062
y[1] (numeric) = 6.1551342529884756791407383729402
absolute error = 8.613282352977340e-16
relative error = 1.3993654726207428414996177015154e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.389
y[1] (analytic) = 6.187765878099124887242530578057
y[1] (numeric) = 6.1877658780991257516899365890595
absolute error = 8.644474060110025e-16
relative error = 1.3970266862723639860455052884077e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 6.2205875570851230258391805771457
y[1] (numeric) = 6.2205875570851238934092833186806
absolute error = 8.675701027415349e-16
relative error = 1.3946754945252561456458339939344e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.391
y[1] (analytic) = 6.253600463687446922666739998854
y[1] (numeric) = 6.2536004636874477933630927632338
absolute error = 8.706963527643798e-16
relative error = 1.3923120893639119808244583101433e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=133.5MB, alloc=4.5MB, time=5.46
x[1] = 0.392
y[1] (analytic) = 6.2868057792390623492746691892765
y[1] (numeric) = 6.2868057792390632231008525865863
absolute error = 8.738261833973098e-16
relative error = 1.3899366611307583829284208477482e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.393
y[1] (analytic) = 6.3202046927159050628939452267215
y[1] (numeric) = 6.32020469271590593985356722819
absolute error = 8.769596220014685e-16
relative error = 1.3875493985379502896282513039354e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.394
y[1] (analytic) = 6.3537984007882161560926475036702
y[1] (numeric) = 6.3537984007882170361893434856876
absolute error = 8.800966959820174e-16
relative error = 1.3851504886790830515182101000472e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.395
y[1] (analytic) = 6.387588107872233372026655062317
y[1] (numeric) = 6.3875881078722342552640878510998
absolute error = 8.832374327887828e-16
relative error = 1.3827401170408240797165962797892e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.396
y[1] (analytic) = 6.4215750261822409228197331750477
y[1] (numeric) = 6.4215750261822418092015930919504
absolute error = 8.863818599169027e-16
relative error = 1.3803184675144643383155956808869e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.397
y[1] (analytic) = 6.455760375782980367143053802043
y[1] (numeric) = 6.4557603757829812566730587095162
absolute error = 8.895300049074732e-16
relative error = 1.3778857224073894674549921286211e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.398
y[1] (analytic) = 6.4901453846424251217383667427354
y[1] (numeric) = 6.4901453846424260144202620909309
absolute error = 8.926818953481955e-16
relative error = 1.3754420624544728173355222743122e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.399
y[1] (analytic) = 6.524731288684921200442669547566
y[1] (numeric) = 6.5247312886849220962802284215889
absolute error = 8.958375588740229e-16
relative error = 1.3729876668293899920437971271887e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 6.5595193318446967932263767681539
y[1] (numeric) = 6.5595193318446976922233999359612
absolute error = 8.989970231678073e-16
relative error = 1.3705227131558546906511641365185e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=137.3MB, alloc=4.5MB, time=5.62
x[1] = 0.401
y[1] (analytic) = 6.5945107661197433168527333341424
y[1] (numeric) = 6.5945107661197442190130492950888
absolute error = 9.021603159609464e-16
relative error = 1.3680473775187782397812857008843e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.402
y[1] (analytic) = 6.6297068516260705880046314948791
y[1] (numeric) = 6.6297068516260714933320965289098
absolute error = 9.053274650340307e-16
relative error = 1.3655618344753519629390523005513e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.403
y[1] (analytic) = 6.6651088566523387891071629652036
y[1] (numeric) = 6.6651088566523396976056611826943
absolute error = 9.084984982174907e-16
relative error = 1.3630662570660535372946499586167e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.404
y[1] (analytic) = 6.7007180577148699166012632146622
y[1] (numeric) = 6.7007180577148708282747066069067
absolute error = 9.116734433922445e-16
relative error = 1.3605608168255781609205158627052e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.405
y[1] (analytic) = 6.7365357396130414210967872889414
y[1] (numeric) = 6.7365357396130423359491157792865
absolute error = 9.148523284903451e-16
relative error = 1.3580456837936940015234669563257e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.406
y[1] (analytic) = 6.7725631954850647686534087715427
y[1] (numeric) = 6.7725631954850656866885902671712
absolute error = 9.180351814956285e-16
relative error = 1.3555210265260240966807727139766e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.407
y[1] (analytic) = 6.8088017268641516724059767405344
y[1] (numeric) = 6.8088017268641525936280071848964
absolute error = 9.212220304443620e-16
relative error = 1.3529870121047543058894635038542e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.408
y[1] (analytic) = 6.8452526437350707638685298130423
y[1] (numeric) = 6.8452526437350716882814332389343
absolute error = 9.244129034258920e-16
relative error = 1.3504438061492668035996014372831e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.409
y[1] (analytic) = 6.8819172645910974935191903367525
y[1] (numeric) = 6.8819172645910984211270189200461
absolute error = 9.276078285832936e-16
relative error = 1.3478915728267030020148316407385e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=141.1MB, alloc=4.5MB, time=5.78
x[1] = 0.41
y[1] (analytic) = 6.9187969164913600706877930644552
y[1] (numeric) = 6.918796916491361001494627178474
absolute error = 9.308068341140188e-16
relative error = 1.3453304748624516966199595160897e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.411
y[1] (analytic) = 6.9558929351185842733404977292942
y[1] (numeric) = 6.9558929351185852073504459998406
absolute error = 9.340099482705464e-16
relative error = 1.3427606735505674802708573699870e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.412
y[1] (analytic) = 6.9932066648372399790819593034294
y[1] (numeric) = 6.9932066648372409162991586644614
absolute error = 9.372171993610320e-16
relative error = 1.3401823287641175557713388793852e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.413
y[1] (analytic) = 7.0307394587520922895770579044691
y[1] (numeric) = 7.030739458752093230005673654427
absolute error = 9.404286157499579e-16
relative error = 1.3375955989654571642136753997276e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.414
y[1] (analytic) = 7.0684926787671601416319059716995
y[1] (numeric) = 7.0684926787671610852761318304837
absolute error = 9.436442258587842e-16
relative error = 1.3350006412164359773289863039606e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.415
y[1] (analytic) = 7.1064676956450853193690463255224
y[1] (numeric) = 7.1064676956450862662331044921223
absolute error = 9.468640581665999e-16
relative error = 1.3323976111885342020765901761504e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.416
y[1] (analytic) = 7.1446658890669148032856331772247
y[1] (numeric) = 7.1446658890669157533737743879989
absolute error = 9.500881412107742e-16
relative error = 1.3297866631729291753060343700655e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.417
y[1] (analytic) = 7.1830886476922994134971605450432
y[1] (numeric) = 7.1830886476923003668136641326527
absolute error = 9.533165035876095e-16
relative error = 1.3271679500904950208030088172721e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=144.9MB, alloc=4.5MB, time=5.94
x[1] = 0.418
y[1] (analytic) = 7.2217373692201117261441897472428
y[1] (numeric) = 7.2217373692201126826933637002367
absolute error = 9.565491739529939e-16
relative error = 1.3245416235017327250717979029830e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.419
y[1] (analytic) = 7.2606134604494862637767600667961
y[1] (numeric) = 7.2606134604494872235629410898506
absolute error = 9.597861810230545e-16
relative error = 1.3219078336166329376265168465648e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 7.2997183373412849825319842658789
y[1] (numeric) = 7.2997183373412859455595378406904
absolute error = 9.630275535748115e-16
relative error = 1.3192667293044719401115565644204e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.421
y[1] (analytic) = 7.3390534250799911010859829654533
y[1] (numeric) = 7.3390534250799920673593034122866
absolute error = 9.662733204468333e-16
relative error = 1.3166184581035414985858572877374e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.422
y[1] (analytic) = 7.3786201581360343386930583086672
y[1] (numeric) = 7.3786201581360353082165688485583
absolute error = 9.695235105398911e-16
relative error = 1.3139631662308109951653042635767e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.423
y[1] (analytic) = 7.4184199803285506521241169057028
y[1] (numeric) = 7.4184199803285516249022697233183
absolute error = 9.727781528176155e-16
relative error = 1.3113009985915257121613851421775e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.424
y[1] (analytic) = 7.4584543448885795839841037947111
y[1] (numeric) = 7.4584543448885805600213801018645
absolute error = 9.760372763071534e-16
relative error = 1.3086320987887393621712645504353e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.425
y[1] (analytic) = 7.4987247145227023577258919828258
y[1] (numeric) = 7.4987247145227033370268020826509
absolute error = 9.793009100998251e-16
relative error = 1.3059566091327811879078115087914e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.426
y[1] (analytic) = 7.5392325614771238776869850175835
y[1] (numeric) = 7.5392325614771248602560683693661
absolute error = 9.825690833517826e-16
relative error = 1.3032746706506594173555072926808e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=148.7MB, alloc=4.5MB, time=6.10
x[1] = 0.427
y[1] (analytic) = 7.5799793676022018156568420566794
y[1] (numeric) = 7.5799793676022028014986673413488
absolute error = 9.858418252846694e-16
relative error = 1.3005864230954018762559662269499e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.428
y[1] (analytic) = 7.6209666244174259888379453168047
y[1] (numeric) = 7.6209666244174269779571105030842
absolute error = 9.891191651862795e-16
relative error = 1.2978920049553311291901883390613e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.429
y[1] (analytic) = 7.6621958331768512575942281245489
y[1] (numeric) = 7.662195833176852249995360535768
absolute error = 9.924011324112191e-16
relative error = 1.2951915534632792182961942731067e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 7.7036685049349871950875079497673
y[1] (numeric) = 7.7036685049349881907752643313347
absolute error = 9.956877563815674e-16
relative error = 1.2924852046057376515397342104950e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.431
y[1] (analytic) = 7.7453861606131478047874730935766
y[1] (numeric) = 7.7453861606131488037665396811166
absolute error = 9.989790665875400e-16
relative error = 1.2897730931319476599565950114480e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.432
y[1] (analytic) = 7.7873503310662645859049149644853
y[1] (numeric) = 7.787350331066265588180007552637
absolute error = 1.0022750925881517e-15
relative error = 1.2870553525629269407047193124711e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.433
y[1] (analytic) = 7.8295625571501662710426515415373
y[1] (numeric) = 7.829562557150167276618515553419
absolute error = 1.0055758640118817e-15
relative error = 1.2843321152004371979986249420611e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.434
y[1] (analytic) = 7.8720243897893285847853338104049
y[1] (numeric) = 7.8720243897893295936667443677434
absolute error = 1.0088814105573385e-15
relative error = 1.2816035121358893840578858307304e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.435
y[1] (analytic) = 7.9147373900450973965594585524779
y[1] (numeric) = 7.9147373900450984087512205464045
absolute error = 1.0121917619939266e-15
relative error = 1.2788696732591897540137039382951e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=152.5MB, alloc=4.5MB, time=6.26
x[1] = 0.436
y[1] (analytic) = 7.9577031291843886658898316065734
y[1] (numeric) = 7.9577031291843896813967797690874
absolute error = 1.0155069481625140e-15
relative error = 1.2761307272675258350540712107758e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.437
y[1] (analytic) = 8.0009231887488686031598502852809
y[1] (numeric) = 8.0009231887488696219868492613818
absolute error = 1.0188269989761009e-15
relative error = 1.2733868016740932127229081593548e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.438
y[1] (analytic) = 8.0443991606246174941517277161228
y[1] (numeric) = 8.0443991606246185163036721366117
absolute error = 1.0221519444204889e-15
relative error = 1.2706380228167626458523830746527e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.439
y[1] (analytic) = 8.0881326471122806620006023075349
y[1] (numeric) = 8.0881326471122816874824168624875
absolute error = 1.0254818145549526e-15
relative error = 1.2678845158666902718043633559285e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 8.1321252609977100657448103280285
y[1] (numeric) = 8.1321252609977110945614498409392
absolute error = 1.0288166395129107e-15
relative error = 1.2651264048368676568386642439783e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.441
y[1] (analytic) = 8.1763786256231000603949080403563
y[1] (numeric) = 8.1763786256231010925513575429559
absolute error = 1.0321564495025996e-15
relative error = 1.2623638125906158158293997680756e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.442
y[1] (analytic) = 8.2208943749586208693777826368448
y[1] (numeric) = 8.2208943749586219048790574445923
absolute error = 1.0355012748077475e-15
relative error = 1.2595968608500210809528188312489e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.443
y[1] (analytic) = 8.2656741536745533463408705323985
y[1] (numeric) = 8.2656741536745543851920163206483
absolute error = 1.0388511457882498e-15
relative error = 1.2568256702043141910915554238434e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=156.4MB, alloc=4.5MB, time=6.42
x[1] = 0.444
y[1] (analytic) = 8.3107196172139286296266011034202
y[1] (numeric) = 8.3107196172139296718326939842662
absolute error = 1.0422060928808460e-15
relative error = 1.2540503601181932071162507743461e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.445
y[1] (analytic) = 8.3560324318656763192502090813378
y[1] (numeric) = 8.3560324318656773648163556811354
absolute error = 1.0455661465997976e-15
relative error = 1.2512710489400900081271111871988e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.446
y[1] (analytic) = 8.4016142748382848329365266301577
y[1] (numeric) = 8.4016142748382858818678641677253
absolute error = 1.0489313375375676e-15
relative error = 1.2484878539103814572434455962556e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.447
y[1] (analytic) = 8.4474668343339776246948056074799
y[1] (numeric) = 8.4474668343339786769965019729806
absolute error = 1.0523016963655007e-15
relative error = 1.2457008911695445166499475808110e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.448
y[1] (analytic) = 8.493591809623408976536572507961
y[1] (numeric) = 8.4935918096234100322138263424666
absolute error = 1.0556772538345056e-15
relative error = 1.2429102757662573441734570187747e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.449
y[1] (analytic) = 8.5399909111208831012715360234688
y[1] (numeric) = 8.5399909111208841603295767992072
absolute error = 1.0590580407757384e-15
relative error = 1.2401161216654455192635334949677e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 8.586665860460100321852215052577
y[1] (numeric) = 8.5866658604601013842963031538638
absolute error = 1.0624440881012868e-15
relative error = 1.2373185417562734111915501057624e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.451
y[1] (analytic) = 8.6336183905704341204808105984849
y[1] (numeric) = 8.6336183905704351863162374033417
absolute error = 1.0658354268048568e-15
relative error = 1.2345176478600830319215550229399e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.452
y[1] (analytic) = 8.6808502457537428786434978681838
y[1] (numeric) = 8.6808502457537439478755858306438
absolute error = 1.0692320879624600e-15
relative error = 1.2317135507382784809925408301820e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=160.2MB, alloc=4.5MB, time=6.58
x[1] = 0.453
y[1] (analytic) = 8.7283631817617201573993669980552
y[1] (numeric) = 8.7283631817617212300334697311581
absolute error = 1.0726341027331029e-15
relative error = 1.2289063601001579649960517030477e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.454
y[1] (analytic) = 8.7761589658737873956253066640122
y[1] (numeric) = 8.776158965873788471666809023489
absolute error = 1.0760415023594768e-15
relative error = 1.2260961846106921113709450835934e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.455
y[1] (analytic) = 8.8242393769755329325058314795638
y[1] (numeric) = 8.8242393769755340119601496482147
absolute error = 1.0794543181686509e-15
relative error = 1.2232831318982518974510625837165e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.456
y[1] (analytic) = 8.8726062056377012893598413445712
y[1] (numeric) = 8.8726062056377023722324229173359
absolute error = 1.0828725815727647e-15
relative error = 1.2204673085622820587818815967630e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.457
y[1] (analytic) = 8.9212612541957366749162213935732
y[1] (numeric) = 8.9212612541957377612125454632976
absolute error = 1.0862963240697244e-15
relative error = 1.2176488201809256721406317905131e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.458
y[1] (analytic) = 8.9702063368298847073887104306123
y[1] (numeric) = 8.9702063368298857971142876745109
absolute error = 1.0897255772438986e-15
relative error = 1.2148277713185948959727015854672e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.459
y[1] (analytic) = 9.019443279645856376159262267775
y[1] (numeric) = 9.0194432796458574693196350345924
absolute error = 1.0931603727668174e-15
relative error = 1.2120042655334928369000689473548e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 9.068973920756058295559889865965
y[1] (numeric) = 9.0689739207560593921606322638373
absolute error = 1.0966007423978723e-15
relative error = 1.2091784053850839209157994686351e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.461
y[1] (analytic) = 9.1188001103613933331474214901753
y[1] (numeric) = 9.1188001103613944331941394751929
absolute error = 1.1000467179850176e-15
relative error = 1.2063502924415138919928791628290e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=164.0MB, alloc=4.5MB, time=6.74
x[1] = 0.462
y[1] (analytic) = 9.1689237108336357249954294468464
y[1] (numeric) = 9.1689237108336368284937609123205
absolute error = 1.1034983314654741e-15
relative error = 1.2035200272869806340122878902610e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.463
y[1] (analytic) = 9.2193465967983848208845470104866
y[1] (numeric) = 9.219346596798385927840161876921
absolute error = 1.1069556148664344e-15
relative error = 1.2006877095290553450073771518302e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.464
y[1] (analytic) = 9.2700706552186016328582130535889
y[1] (numeric) = 9.2700706552186027432768133593581
absolute error = 1.1104186003057692e-15
relative error = 1.1978534378059537327842292004716e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.465
y[1] (analytic) = 9.3210977854787323914273354988976
y[1] (numeric) = 9.3210977854787335053146554916341
absolute error = 1.1138873199927365e-15
relative error = 1.1950173097937596097738365724979e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.466
y[1] (analytic) = 9.3724298994694233447562166035295
y[1] (numeric) = 9.3724298994694244621180228322211
absolute error = 1.1173618062286916e-15
relative error = 1.1921794222135989056891807269363e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.467
y[1] (analytic) = 9.424068921672831067445121713281
y[1] (numeric) = 9.4240689216728321882872131210809
absolute error = 1.1208420914077999e-15
relative error = 1.1893398708387665647833295919369e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.468
y[1] (analytic) = 9.4760167892485325770438989215457
y[1] (numeric) = 9.4760167892485337013721069392961
absolute error = 1.1243282080177504e-15
relative error = 1.1864987505018043724234710724940e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.469
y[1] (analytic) = 9.5282754521200395881878845465155
y[1] (numeric) = 9.5282754521200407160080731869876
absolute error = 1.1278201886404721e-15
relative error = 1.1836561551015323651650407027701e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=167.8MB, alloc=4.5MB, time=6.90
x[1] = 0.47
y[1] (analytic) = 9.5808468730619212662437872176946
y[1] (numeric) = 9.5808468730619223975618531705465
absolute error = 1.1313180659528519e-15
relative error = 1.1808121776100326172874324583349e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.471
y[1] (analytic) = 9.6337330277875398745911746650889
y[1] (numeric) = 9.6337330277875410094130473925428
absolute error = 1.1348218727274539e-15
relative error = 1.1779669100795856097750018774060e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.472
y[1] (analytic) = 9.6869359050374037421464494843962
y[1] (numeric) = 9.6869359050374048804780913176381
absolute error = 1.1383316418332419e-15
relative error = 1.1751204436495613519737344112944e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.473
y[1] (analytic) = 9.7404575066681420104626652022739
y[1] (numeric) = 9.7404575066681431523100714385763
absolute error = 1.1418474062363024e-15
relative error = 1.1722728685532627227698915632948e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.474
y[1] (analytic) = 9.7942998477421056527120885366127
y[1] (numeric) = 9.7942998477421067980812875371836
absolute error = 1.1453691990005709e-15
relative error = 1.1694242741247242352017111133962e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.475
y[1] (analytic) = 9.8484649566175992900809592598211
y[1] (numeric) = 9.8484649566176004389780125483801
absolute error = 1.1488970532885590e-15
relative error = 1.1665747488054639185651555368731e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.476
y[1] (analytic) = 9.9029548750397483645793518408212
y[1] (numeric) = 9.9029548750397495170103542029062
absolute error = 1.1524310023620850e-15
relative error = 1.1637243801511913744904214973881e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.477
y[1] (analytic) = 9.9577716582320062609953343850303
y[1] (numeric) = 9.9577716582320074169664139680354
absolute error = 1.1559710795830051e-15
relative error = 1.1608732548384693173746044099486e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.478
y[1] (analytic) = 10.012917374988306004703696760514
y[1] (numeric) = 10.012917374988307164221015174462
absolute error = 1.159517318413948e-15
relative error = 1.1580214586713317303780029214010e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=171.6MB, alloc=4.5MB, time=7.06
x[1] = 0.479
y[1] (analytic) = 10.068394107765861196277342890946
y[1] (numeric) = 10.068394107765862359347095309995
absolute error = 1.163069752419049e-15
relative error = 1.1551690765878549880151043086867e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 10.124203952778620878345989080179
y[1] (numeric) = 10.124203952778622044974404344871
absolute error = 1.166628415264692e-15
relative error = 1.1523161926666906160656882203027e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.481
y[1] (analytic) = 10.180349020091383064904073469849
y[1] (numeric) = 10.180349020091384235097414190095
absolute error = 1.170193340720246e-15
relative error = 1.1494628901335465763929282496365e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.482
y[1] (analytic) = 10.236831433714571698289769496854
y[1] (numeric) = 10.236831433714572872054332155666
absolute error = 1.173764562658812e-15
relative error = 1.1466092513676331706355517905851e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.483
y[1] (analytic) = 10.29365333169968183434173242846
y[1] (numeric) = 10.293653331699683011683847486421
absolute error = 1.177342115057961e-15
relative error = 1.1437553579080547678821677174873e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.484
y[1] (analytic) = 10.3508168662353978917917324912
y[1] (numeric) = 10.350816866235399072717764491688
absolute error = 1.180926032000488e-15
relative error = 1.1409012904601720968640706745929e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.485
y[1] (analytic) = 10.408324203744389837771696549683
y[1] (numeric) = 10.408324203744391022288044224843
absolute error = 1.184516347675160e-15
relative error = 1.1380471289019137101469627830313e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.486
y[1] (analytic) = 10.466177524980792217404964626131
y[1] (numeric) = 10.466177524980793405518061003594
absolute error = 1.188113096377463e-15
relative error = 1.1351929522900419692079514473642e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.487
y[1] (analytic) = 10.524379025128370971815855921806
y[1] (numeric) = 10.524379025128372163532168432167
absolute error = 1.191716312510361e-15
relative error = 1.1323388388663862819051107014412e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=175.4MB, alloc=4.5MB, time=7.22
x[1] = 0.488
y[1] (analytic) = 10.58293091389938302553103592572
y[1] (numeric) = 10.582930913899384220857066510772
absolute error = 1.195326030585052e-15
relative error = 1.1294848660640293158330491719426e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.489
y[1] (analytic) = 10.64183541563413366116280269973
y[1] (numeric) = 10.641835415634134860105087921453
absolute error = 1.198942285221723e-15
relative error = 1.1266311105134485195484666978541e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 10.701094769401236736460404177439
y[1] (numeric) = 10.701094769401237939025515327753
absolute error = 1.202565111150314e-15
relative error = 1.1237776480486226711585738640845e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.491
y[1] (analytic) = 10.760711229098582836293013744125
y[1] (numeric) = 10.760711229098584042487556955409
absolute error = 1.206194543211284e-15
relative error = 1.1209245537130969578056021515408e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.492
y[1] (analytic) = 10.820687063555020489889199818605
y[1] (numeric) = 10.820687063555021699719816174974
absolute error = 1.209830616356369e-15
relative error = 1.1180719017659976094024933277029e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.493
y[1] (analytic) = 10.881024556632755621704815018344
y[1] (numeric) = 10.881024556632756835178180667704
absolute error = 1.213473365649360e-15
relative error = 1.1152197656880224417558586040925e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.494
y[1] (analytic) = 10.941726007330474442626407315382
y[1] (numeric) = 10.941726007330475659749233582248
absolute error = 1.217122826266866e-15
relative error = 1.1123682181873749357082760871044e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.495
y[1] (analytic) = 11.002793729887195026842742254846
y[1] (numeric) = 11.002793729887196247621775753941
absolute error = 1.220779033499095e-15
relative error = 1.1095173312056727135212929381718e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.496
y[1] (analytic) = 11.06423005388685285863506213376
y[1] (numeric) = 11.064230053886854083077084884382
absolute error = 1.224442022750622e-15
relative error = 1.1066671759238020836075239291504e-14 %
Correct digits = 15
h = 0.001
memory used=179.2MB, alloc=4.5MB, time=7.38
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.497
y[1] (analytic) = 11.12603732436362567254955293937
y[1] (numeric) = 11.126037324363626900661382480545
absolute error = 1.228111829541175e-15
relative error = 1.1038178227677473052690520218467e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.498
y[1] (analytic) = 11.188217901908002949925418468408
y[1] (numeric) = 11.188217901908004181713907974818
absolute error = 1.231788489506410e-15
relative error = 1.1009693414143683462586065652753e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.499
y[1] (analytic) = 11.250774162773605474561266908609
y[1] (numeric) = 11.250774162773606710033305307311
absolute error = 1.235472038398702e-15
relative error = 1.0981218007971518434224745521925e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 11.313708498984760390413509793678
y[1] (numeric) = 11.3137084989847616295760218816
absolute error = 1.239162512087922e-15
relative error = 1.0952752691119085166992690326340e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.501
y[1] (analytic) = 11.377023318444837244635486333378
y[1] (numeric) = 11.377023318444838487495432895617
absolute error = 1.242859946562239e-15
relative error = 1.0924298138224521244372791989372e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.502
y[1] (analytic) = 11.440721045045350539987405666088
y[1] (numeric) = 11.440721045045351786551783594986
absolute error = 1.246564377928898e-15
relative error = 1.0895855016662165902094144435554e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.503
y[1] (analytic) = 11.50480411877583436167731202591
y[1] (numeric) = 11.504804118775835611953154440935
absolute error = 1.250275842415025e-15
relative error = 1.0867423986598567748711720453681e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.504
y[1] (analytic) = 11.569274995834494685034508201615
y[1] (numeric) = 11.569274995834495939028884570036
absolute error = 1.253994376368421e-15
relative error = 1.0839005701047994438429088020583e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=183.1MB, alloc=4.5MB, time=7.54
x[1] = 0.505
y[1] (analytic) = 11.634136148739645012071624776717
y[1] (numeric) = 11.634136148739646269791641035079
absolute error = 1.257720016258362e-15
relative error = 1.0810600805927597353092121104490e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.506
y[1] (analytic) = 11.699390066441931026962219160755
y[1] (numeric) = 11.699390066441932288415017837155
absolute error = 1.261452798676400e-15
relative error = 1.0782209940112189681756010652118e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.507
y[1] (analytic) = 11.765039254437350002749871079162
y[1] (numeric) = 11.765039254437351267942631416336
absolute error = 1.265192760337174e-15
relative error = 1.0753833735488717204598997349952e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.508
y[1] (analytic) = 11.831086234881070734214670909037
y[1] (numeric) = 11.831086234881072003154608988253
absolute error = 1.268939938079216e-15
relative error = 1.0725472817010294795415083852187e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.509
y[1] (analytic) = 11.897533546702059814756254308227
y[1] (numeric) = 11.897533546702061087450623173989
absolute error = 1.272694368865762e-15
relative error = 1.0697127802749897490087516437678e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = 11.964383745718520118411620769194
y[1] (numeric) = 11.964383745718521394867710554761
absolute error = 1.276456089785567e-15
relative error = 1.0668799303953699210005853151547e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.511
y[1] (analytic) = 12.03163940475414739171340448286
y[1] (numeric) = 12.031639404754148671938542536583
absolute error = 1.280225138053723e-15
relative error = 1.0640487925094052609684772847370e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.512
y[1] (analytic) = 12.099303113755210904012582485896
y[1] (numeric) = 12.099303113755212188014133498378
absolute error = 1.284001551012482e-15
relative error = 1.0612194263922128684039542238904e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.513
y[1] (analytic) = 12.167377479908464149141366730096
y[1] (numeric) = 12.16737747990846543692673286217
absolute error = 1.287785366132074e-15
relative error = 1.0583918911520135399217085462633e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=186.9MB, alloc=4.5MB, time=7.70
x[1] = 0.514
y[1] (analytic) = 12.235865127759891635879812834056
y[1] (numeric) = 12.235865127759892927456433845594
absolute error = 1.291576621011538e-15
relative error = 1.0555662452353267132517499425975e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.515
y[1] (analytic) = 12.304768699334297849616088533139
y[1] (numeric) = 12.304768699334299144991441912691
absolute error = 1.295375353379552e-15
relative error = 1.0527425464321269994258812608008e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.516
y[1] (analytic) = 12.374090854255744512857999371683
y[1] (numeric) = 12.374090854255745812039600466944
absolute error = 1.299181601095261e-15
relative error = 1.0499208518809618320906703521227e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.517
y[1] (analytic) = 12.443834269868842317864908743739
y[1] (numeric) = 12.443834269868843620860310892857
absolute error = 1.302995402149118e-15
relative error = 1.0471012180740426534725475862337e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.518
y[1] (analytic) = 12.514001641360903350627275536454
y[1] (numeric) = 12.514001641360904657444070200175
absolute error = 1.306816794663721e-15
relative error = 1.0442837008622959404127942840299e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.519
y[1] (analytic) = 12.584595681884960471728347869684
y[1] (numeric) = 12.58459568188496178237416476434
absolute error = 1.310645816894656e-15
relative error = 1.0414683554603824441184788884891e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = 12.655619122683659966281799385696
y[1] (numeric) = 12.655619122683661280764306617034
absolute error = 1.314482507231338e-15
relative error = 1.0386552364516784322413832481319e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.521
y[1] (analytic) = 12.727074713214033822153000144632
y[1] (numeric) = 12.7270747132140351404799043425
absolute error = 1.318326904197868e-15
relative error = 1.0358443977932334358870783458801e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.522
y[1] (analytic) = 12.798965221273158043042923807821
y[1] (numeric) = 12.798965221273159365221970261697
absolute error = 1.322179046453876e-15
relative error = 1.0330358928206808615972879696743e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
memory used=190.7MB, alloc=4.5MB, time=7.86
TOP MAIN SOLVE Loop
x[1] = 0.523
y[1] (analytic) = 12.871293433124703450745174458612
y[1] (numeric) = 12.871293433124704776784147253995
absolute error = 1.326038972795383e-15
relative error = 1.0302297742531278357571271191231e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.524
y[1] (analytic) = 12.944062153626385478981059943123
y[1] (numeric) = 12.944062153626386808887782098778
absolute error = 1.329906722155655e-15
relative error = 1.0274260941980031308235131429932e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.525
y[1] (analytic) = 13.017274206358319509677855816047
y[1] (numeric) = 13.017274206358320843460189422112
absolute error = 1.333782333606065e-15
relative error = 1.0246249041558760037338608476055e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.526
y[1] (analytic) = 13.090932433752288351384228812268
y[1] (numeric) = 13.090932433752289689050075169232
absolute error = 1.337665846356964e-15
relative error = 1.0218262550252467574710563449702e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.527
y[1] (analytic) = 13.165039697221928508717077530726
y[1] (numeric) = 13.165039697221929850274377289266
absolute error = 1.341557299758540e-15
relative error = 1.0190301971072930937944826821663e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.528
y[1] (analytic) = 13.23959887729384194130867952367
y[1] (numeric) = 13.239598877293843286765412825366
absolute error = 1.345456733301696e-15
relative error = 1.0162367801105963228422830937862e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.529
y[1] (analytic) = 13.314612873739640060674909737053
y[1] (numeric) = 13.314612873739641410039096355979
absolute error = 1.349364186618926e-15
relative error = 1.0134460531558313749369702071126e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = 13.390084605708926763757339626584
y[1] (numeric) = 13.390084605708928117037039111775
absolute error = 1.353279699485191e-15
relative error = 1.0106580647804224571492137633357e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=194.5MB, alloc=4.5MB, time=8.02
x[1] = 0.531
y[1] (analytic) = 13.466017011863227352607186718074
y[1] (numeric) = 13.466017011863228709810498536875
absolute error = 1.357203311818801e-15
relative error = 1.0078728629431690962800716900597e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.532
y[1] (analytic) = 13.542413050510870240780331572773
y[1] (numeric) = 13.542413050510871601915395255077
absolute error = 1.361135063682304e-15
relative error = 1.0050904950288434140471436965496e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.533
y[1] (analytic) = 13.619275699742828398502947170663
y[1] (numeric) = 13.619275699742829763577942454037
absolute error = 1.365074995283374e-15
relative error = 1.0023110078527528396453283886718e-14 %
Correct digits = 15
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.534
y[1] (analytic) = 13.696607957569527540549712366793
y[1] (numeric) = 13.696607957569528909572859342494
absolute error = 1.369023146975701e-15
relative error = 9.9953444766527076294606124076186e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.535
y[1] (analytic) = 13.774412842058628113054147843878
y[1] (numeric) = 13.774412842058629486033707103771
absolute error = 1.372979559259893e-15
relative error = 9.9676086015634261120999761423325e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.536
y[1] (analytic) = 13.852693391473788188146385412282
y[1] (numeric) = 13.852693391473789565090658196654
absolute error = 1.376944272784372e-15
relative error = 9.9399029045995428985582453594732e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.537
y[1] (analytic) = 13.931452664414414428390749319257
y[1] (numeric) = 13.931452664414415809308077665537
absolute error = 1.380917328346280e-15
relative error = 9.9122278315857492525658496622829e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.538
y[1] (analytic) = 14.010693739956408336477005529993
y[1] (numeric) = 14.010693739956409721375772422379
absolute error = 1.384898766892386e-15
relative error = 9.8845838228756747809742382380870e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.539
y[1] (analytic) = 14.090419717793915059508160419392
y[1] (numeric) = 14.09041971779391644839678993939
absolute error = 1.388888629519998e-15
relative error = 9.8569713133957031603131215767306e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=198.3MB, alloc=4.5MB, time=8.18
x[1] = 0.54
y[1] (analytic) = 14.170633718382082071527427427623
y[1] (numeric) = 14.170633718382083464414384905499
absolute error = 1.392886957477876e-15
relative error = 9.8293907326884705825547816543141e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.541
y[1] (analytic) = 14.251338883080835112640617421165
y[1] (numeric) = 14.251338883080836509534409588319
absolute error = 1.396893792167154e-15
relative error = 9.8018425049561055306375512273443e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.542
y[1] (analytic) = 14.332538374299678818220959375963
y[1] (numeric) = 14.332538374299680219130134518225
absolute error = 1.400909175142262e-15
relative error = 9.7743270491031473181122920917707e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.543
y[1] (analytic) = 14.414235375643529527234461549244
y[1] (numeric) = 14.414235375643530932167609661092
absolute error = 1.404933148111848e-15
relative error = 9.7468447787791461388901161967256e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.544
y[1] (analytic) = 14.496433092059587814698644100579
y[1] (numeric) = 14.496433092059589223664397040296
absolute error = 1.408965752939717e-15
relative error = 9.7193961024210646166079797130689e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.545
y[1] (analytic) = 14.579134749985258349689102515855
y[1] (numeric) = 14.579134749985259762696134161613
absolute error = 1.413007031645758e-15
relative error = 9.6919814232952799754431197300603e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.546
y[1] (analytic) = 14.662343597497124737140213527188
y[1] (numeric) = 14.662343597497126154197239934074
absolute error = 1.417057026406886e-15
relative error = 9.6646011395393769872886903333295e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.547
y[1] (analytic) = 14.746062904460987058951714056055
y[1] (numeric) = 14.746062904460988480067493614037
absolute error = 1.421115779557982e-15
relative error = 9.6372556442036150061043283005778e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.548
y[1] (analytic) = 14.830295962682969887615237995771
y[1] (numeric) = 14.830295962682971312798571588612
absolute error = 1.425183333592841e-15
relative error = 9.6099453252921397578509529657754e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=202.1MB, alloc=4.5MB, time=8.34
x[1] = 0.549
y[1] (analytic) = 14.915046086061708603717580976068
y[1] (numeric) = 14.915046086061710032977312141191
absolute error = 1.429259731165123e-15
relative error = 9.5826705658039068817060763613949e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = 15.000316610741621907263902037024
y[1] (numeric) = 15.000316610741623340608917126328
absolute error = 1.433345015089304e-15
relative error = 9.5554317437732990947484282898643e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.551
y[1] (analytic) = 15.08611089526727847179771285454
y[1] (numeric) = 15.086110895267279909236941196178
absolute error = 1.437439228341638e-15
relative error = 9.5282292323105125531990033451187e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.552
y[1] (analytic) = 15.172432320738865749778826547133
y[1] (numeric) = 15.172432320738867191321240608251
absolute error = 1.441542414061118e-15
relative error = 9.5010633996416330475038571841287e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.553
y[1] (analytic) = 15.259284290968768997618943384718
y[1] (numeric) = 15.259284290968770443273558935159
absolute error = 1.445654615550441e-15
relative error = 9.4739346091484377125519726338037e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.554
y[1] (analytic) = 15.3466702326392686491707718544
y[1] (numeric) = 15.346670232639270098946648131383
absolute error = 1.449775876276983e-15
relative error = 9.4468432194079629257391738568906e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.555
y[1] (analytic) = 15.434593595461364227324080387967
y[1] (numeric) = 15.434593595461365681230320261737
absolute error = 1.453906239873770e-15
relative error = 9.4197895842317477007022872162758e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.556
y[1] (analytic) = 15.523057852334733044684435648822
y[1] (numeric) = 15.523057852334734502730185789281
absolute error = 1.458045750140459e-15
relative error = 9.3927740527048464254673539123939e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=206.0MB, alloc=4.5MB, time=8.49
x[1] = 0.557
y[1] (analytic) = 15.612066499508832006101224023079
y[1] (numeric) = 15.612066499508833468295675067403
absolute error = 1.462194451044324e-15
relative error = 9.3657969692245789312156255881035e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.558
y[1] (analytic) = 15.701623056745150888074518881265
y[1] (numeric) = 15.701623056745152354426905602504
absolute error = 1.466352386721239e-15
relative error = 9.3388586735389682612827853378610e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.559
y[1] (analytic) = 15.791731067480625532809121134663
y[1] (numeric) = 15.791731067480627003328722611335
absolute error = 1.470519601476672e-15
relative error = 9.3119595007849581499866022151246e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = 15.882394098992219457902367537025
y[1] (numeric) = 15.882394098992220932598507323709
absolute error = 1.474696139786684e-15
relative error = 9.2850997815263722042546001378933e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.561
y[1] (analytic) = 15.973615742562682446353802316956
y[1] (numeric) = 15.973615742562683925235848615886
absolute error = 1.478882046298930e-15
relative error = 9.2582798417915973209713266519452e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.562
y[1] (analytic) = 16.065399613647494745773304848826
y[1] (numeric) = 16.065399613647496228850670682485
absolute error = 1.483077365833659e-15
relative error = 9.2315000031109747318041640857493e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.563
y[1] (analytic) = 16.157749352043005570343550739285
y[1] (numeric) = 16.157749352043007057625694124013
absolute error = 1.487282143384728e-15
relative error = 9.2047605825539943071442337049051e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.564
y[1] (analytic) = 16.250668622055774664266577499293
y[1] (numeric) = 16.250668622055776155763001619912
absolute error = 1.491496424120619e-15
relative error = 9.1780618927662234794730955573573e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.565
y[1] (analytic) = 16.344161112673125751096580724215
y[1] (numeric) = 16.344161112673127246816834109666
absolute error = 1.495720253385451e-15
relative error = 9.1514042420059236470656327466422e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=209.8MB, alloc=4.5MB, time=8.65
x[1] = 0.566
y[1] (analytic) = 16.438230537734920759535764756037
y[1] (numeric) = 16.438230537734922259489441456047
absolute error = 1.499953676700010e-15
relative error = 9.1247879341804977339945969624340e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.567
y[1] (analytic) = 16.53288063610656378295102623945
y[1] (numeric) = 16.532880636106565287147766002223
absolute error = 1.504196739762773e-15
relative error = 9.0982132688826218400318126721780e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.568
y[1] (analytic) = 16.628115171853243797060403889717
y[1] (numeric) = 16.628115171853245305509892340659
absolute error = 1.508449488450942e-15
relative error = 9.0716805414261611893615721481271e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.569
y[1] (analytic) = 16.72393793441542522794355849246
y[1] (numeric) = 16.72393793441542674065552731394
absolute error = 1.512711968821480e-15
relative error = 9.0451900428818226122844575025940e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (analytic) = 16.820352738785595530754060476938
y[1] (numeric) = 16.820352738785597047738287589094
absolute error = 1.516984227112156e-15
relative error = 9.0187420601125871908900917406475e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.571
y[1] (analytic) = 16.917363425686279008256996918125
y[1] (numeric) = 16.917363425686280529523306660715
absolute error = 1.521266309742590e-15
relative error = 8.9923368758088701973343737219825e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.572
y[1] (analytic) = 17.014973861749326167587436106705
y[1] (numeric) = 17.014973861749327693145699422007
absolute error = 1.525558263315302e-15
relative error = 8.9659747685234343180761872227670e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.573
y[1] (analytic) = 17.113187939696487983427708720569
y[1] (numeric) = 17.113187939696489513287843337342
absolute error = 1.529860134616773e-15
relative error = 8.9396560127061044257940311352044e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.574
y[1] (analytic) = 17.212009578521284506138415499212
y[1] (numeric) = 17.212009578521286040310386117713
absolute error = 1.534171970618501e-15
relative error = 8.9133808787381847604153924082736e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=213.6MB, alloc=4.5MB, time=8.81
x[1] = 0.575
y[1] (analytic) = 17.31144272367217732425372031036
y[1] (numeric) = 17.311442723672178862747538788432
absolute error = 1.538493818478072e-15
relative error = 8.8871496329666976849500802063175e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.576
y[1] (analytic) = 17.411491347237055462170035800992
y[1] (numeric) = 17.411491347237057004995761341218
absolute error = 1.542825725540226e-15
relative error = 8.8609625377383280866150533163548e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.577
y[1] (analytic) = 17.512159448129044365822890951408
y[1] (numeric) = 17.512159448129045912990630289345
absolute error = 1.547167739337937e-15
relative error = 8.8348198514331855274409740470643e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.578
y[1] (analytic) = 17.613451052273647701663853892366
y[1] (numeric) = 17.613451052273649253183761485856
absolute error = 1.551519907593490e-15
relative error = 8.8087218284982868169970955023875e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.579
y[1] (analytic) = 17.715370212797231767322171245344
y[1] (numeric) = 17.715370212797233323204449464913
absolute error = 1.555882278219569e-15
relative error = 8.7826687194808411546033085162189e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = 17.817921010216862385968613074175
y[1] (numeric) = 17.817921010216863946223512394522
absolute error = 1.560254899320347e-15
relative error = 8.7566607710612872254544748462858e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.581
y[1] (analytic) = 17.921107552631504230596250762194
y[1] (numeric) = 17.921107552631505795234069954775
absolute error = 1.564637819192581e-15
relative error = 8.7306982260861009498263539819298e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.582
y[1] (analytic) = 18.024933975914592599198948899835
y[1] (numeric) = 18.02493397591459416823003522655
absolute error = 1.569031086326715e-15
relative error = 8.7047813236003917969297222328046e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=217.4MB, alloc=4.5MB, time=8.97
x[1] = 0.583
y[1] (analytic) = 18.129404443907987737167661687323
y[1] (numeric) = 18.129404443907989310602411095306
absolute error = 1.573434749407983e-15
relative error = 8.6789102988802441311744425046854e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.584
y[1] (analytic) = 18.234523148617321879141664768199
y[1] (numeric) = 18.23452314861732345699052208572
absolute error = 1.577848857317521e-15
relative error = 8.6530853834648553361065498063551e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.585
y[1] (analytic) = 18.340294310408749259051135677058
y[1] (numeric) = 18.340294310408750841324594810542
absolute error = 1.582273459133484e-15
relative error = 8.6273068051884492760777512751034e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.586
y[1] (analytic) = 18.446722178207109414173566882915
y[1] (numeric) = 18.446722178207111000882171015084
absolute error = 1.586708604132169e-15
relative error = 8.6015747882119717846299368650767e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.587
y[1] (analytic) = 18.553811029695514186703937509486
y[1] (numeric) = 18.553811029695515777858279298624
absolute error = 1.591154341789138e-15
relative error = 8.5758895530545368880637465734257e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.588
y[1] (analytic) = 18.66156517151636890461200237525
y[1] (numeric) = 18.661565171516370500222724155603
absolute error = 1.595610721780353e-15
relative error = 8.5502513166246904239089870020693e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.589
y[1] (analytic) = 18.769988939473838302434135861291
y[1] (numeric) = 18.769988939473839902511929844603
absolute error = 1.600077793983312e-15
relative error = 8.5246602922514321806810467444489e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 18.879086698737767822126586102977
y[1] (numeric) = 18.87908669873776942668219458117
absolute error = 1.604555608478193e-15
relative error = 8.4991166897150357686137057539477e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.591
y[1] (analytic) = 18.988862844049071014196482207939
y[1] (numeric) = 18.988862844049072623240697756941
absolute error = 1.609044215549002e-15
relative error = 8.4736207152776457664104346049240e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=221.2MB, alloc=4.5MB, time=9.13
x[1] = 0.592
y[1] (analytic) = 19.099321799926593840031261299416
y[1] (numeric) = 19.09932179992659545357492698414
absolute error = 1.613543665684724e-15
relative error = 8.4481725717136483823861600517699e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.593
y[1] (analytic) = 19.210468020875466757671148722269
y[1] (numeric) = 19.210468020875468375725158302755
absolute error = 1.618054009580486e-15
relative error = 8.4227724583398641583587690513791e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.594
y[1] (analytic) = 19.322305991596955555217777465697
y[1] (numeric) = 19.322305991596957177793075604418
absolute error = 1.622575298138721e-15
relative error = 8.3974205710455055561186068751424e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.595
y[1] (analytic) = 19.434840227199821978649853981791
y[1] (numeric) = 19.434840227199823605757436452125
absolute error = 1.627107582470334e-15
relative error = 8.3721171023219066772894934476092e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.596
y[1] (analytic) = 19.548075273413205284028888146573
y[1] (numeric) = 19.548075273413206915679802042456
absolute error = 1.631650913895883e-15
relative error = 8.3468622412920934948374903672114e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.597
y[1] (analytic) = 19.662015706801035927929365271077
y[1] (numeric) = 19.662015706801037564134709217836
absolute error = 1.636205343946759e-15
relative error = 8.3216561737401123824002583560423e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.598
y[1] (analytic) = 19.776666134977992694423347408108
y[1] (numeric) = 19.776666134977994335194271774477
absolute error = 1.640770924366369e-15
relative error = 8.2964990821401396727637621013956e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.599
y[1] (analytic) = 19.892031196827014642094389050383
y[1] (numeric) = 19.89203119682701628744209616172
absolute error = 1.645347707111337e-15
relative error = 8.2713911456854493066937300383986e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 20.008115562718379340354918084786
y[1] (numeric) = 20.008115562718380990290662437479
absolute error = 1.649935744352693e-15
relative error = 8.2463325403170872124203955028067e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=225.0MB, alloc=4.5MB, time=9.29
x[1] = 0.601
y[1] (analytic) = 20.124923934730358950799986357594
y[1] (numeric) = 20.12492393473036060533507483468
absolute error = 1.654535088477086e-15
relative error = 8.2213234387524360239445481882853e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.602
y[1] (analytic) = 20.242461046871465796453695941016
y[1] (numeric) = 20.242461046871467455599488029002
absolute error = 1.659145792087986e-15
relative error = 8.1963640105134946104593061034805e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.603
y[1] (analytic) = 20.360731665304299149557858746609
y[1] (numeric) = 20.360731665304300813325766753515
absolute error = 1.663767908006906e-15
relative error = 8.1714544219550291572858504340671e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.604
y[1] (analytic) = 20.479740588571005057020791462938
y[1] (numeric) = 20.479740588571006725422280737561
absolute error = 1.668401489274623e-15
relative error = 8.1465948362924914774793299061792e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.605
y[1] (analytic) = 20.599492647820361111792869576087
y[1] (numeric) = 20.599492647820362784839458728491
absolute error = 1.673046589152404e-15
relative error = 8.1217854136297361347499404053592e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.606
y[1] (analytic) = 20.719992707036498168269890188812
y[1] (numeric) = 20.71999270703649984597315131205
absolute error = 1.677703261123238e-15
relative error = 8.0970263109865424418952661057193e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.607
y[1] (analytic) = 20.841245663269271090350792606605
y[1] (numeric) = 20.841245663269272772722351499687
absolute error = 1.682371558893082e-15
relative error = 8.0723176823259807575745526619467e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.608
y[1] (analytic) = 20.963256446866290711998270061986
y[1] (numeric) = 20.963256446866292399049806454087
absolute error = 1.687051536392101e-15
relative error = 8.0476596785815271501602962190582e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=228.8MB, alloc=4.5MB, time=9.45
x[1] = 0.609
y[1] (analytic) = 21.086030021706629282074730437902
y[1] (numeric) = 21.086030021706630973817978213822
absolute error = 1.691743247775920e-15
relative error = 8.0230524476840151895582438505625e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 21.209571385436211757857426792734
y[1] (numeric) = 21.209571385436213454304174219622
absolute error = 1.696446747426888e-15
relative error = 7.9984961345884247316634470446449e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.611
y[1] (analytic) = 21.333885569704905404980922028494
y[1] (numeric) = 21.33388556970490710614301198383
absolute error = 1.701162089955336e-15
relative error = 7.9739908813004232125823279660569e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.612
y[1] (analytic) = 21.458977640405320255617962460073
y[1] (numeric) = 21.45897764040532196150729266092
absolute error = 1.705889330200847e-15
relative error = 7.9495368269027466912107455141989e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.613
y[1] (analytic) = 21.584852697913333071496943107564
y[1] (numeric) = 21.584852697913334782125466341104
absolute error = 1.710628523233540e-15
relative error = 7.9251341075814297887815447980103e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.614
y[1] (analytic) = 21.711515877330347553871128867096
y[1] (numeric) = 21.711515877330349269250853222441
absolute error = 1.715379724355345e-15
relative error = 7.9007828566517781198607616367642e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.615
y[1] (analytic) = 21.8389723487273036388073711529
y[1] (numeric) = 21.838972348727305358950360254195
absolute error = 1.720142989101295e-15
relative error = 7.8764832045842061571852842046950e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.616
y[1] (analytic) = 21.967227317390448813155995558475
y[1] (numeric) = 21.967227317390450538074368799299
absolute error = 1.724918373240824e-15
relative error = 7.8522352790298894167300313760434e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.617
y[1] (analytic) = 22.096286024068884484304644919133
y[1] (numeric) = 22.096286024068886214010577698198
absolute error = 1.729705932779065e-15
relative error = 7.8280392048462048617558946252808e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=232.7MB, alloc=4.5MB, time=9.61
x[1] = 0.618
y[1] (analytic) = 22.2261537452239005353130025528
y[1] (numeric) = 22.226153745223902269818726510961
absolute error = 1.734505723958161e-15
relative error = 7.8038951041220201776598733721918e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.619
y[1] (analytic) = 22.356835793280111296278397785962
y[1] (numeric) = 22.356835793280113035596201044544
absolute error = 1.739317803258582e-15
relative error = 7.7798030962028003508149191404539e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = 22.488337516878406262800262583988
y[1] (numeric) = 22.488337516878408006942489984426
absolute error = 1.744142227400438e-15
relative error = 7.7557632977154881361524606952803e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.621
y[1] (analytic) = 22.620664301130728993200264099714
y[1] (numeric) = 22.620664301130730742179317444533
absolute error = 1.748979053344819e-15
relative error = 7.7317758225932983280455179209162e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.622
y[1] (analytic) = 22.753821567876697717720730968107
y[1] (numeric) = 22.753821567876699471549069263227
absolute error = 1.753828338295120e-15
relative error = 7.7078407821002384666268903295323e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.623
y[1] (analytic) = 22.887814775942081295272817168791
y[1] (numeric) = 22.887814775942083053962956867179
absolute error = 1.758690139698388e-15
relative error = 7.6839582848555225004515973819301e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.624
y[1] (analytic) = 23.022649421399144256443850827919
y[1] (numeric) = 23.022649421399146020008366074586
absolute error = 1.763564515246667e-15
relative error = 7.6601284368577713109244850861606e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.625
y[1] (analytic) = 23.158331037828874775406690019612
y[1] (numeric) = 23.158331037828876543858212897968
absolute error = 1.768451522878356e-15
relative error = 7.6363513415090673572739159630201e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.626
y[1] (analytic) = 23.294865196585109518108896443508
y[1] (numeric) = 23.294865196585111291460117223072
absolute error = 1.773351220779564e-15
relative error = 7.6126270996387945539492882381363e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=236.5MB, alloc=4.5MB, time=9.77
x[1] = 0.627
y[1] (analytic) = 23.432257507060569419662433592018
y[1] (numeric) = 23.432257507060571197926100977505
absolute error = 1.778263667385487e-15
relative error = 7.5889558095273727119156771015453e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.628
y[1] (analytic) = 23.570513616954820550211741680426
y[1] (numeric) = 23.570513616954822333400663062204
absolute error = 1.783188921381778e-15
relative error = 7.5653375669297617320876019472391e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.629
y[1] (analytic) = 23.709639212544174335735830811347
y[1] (numeric) = 23.709639212544176123862872517277
absolute error = 1.788127041705930e-15
relative error = 7.5417724650988232413654017014723e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 23.849640018953541508244911223882
y[1] (numeric) = 23.84964001895354330132299877255
absolute error = 1.793078087548668e-15
relative error = 7.5182605948085227175963489996553e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.631
y[1] (analytic) = 23.990521800430254268670541116784
y[1] (numeric) = 23.990521800430256066712659472122
absolute error = 1.798042118355338e-15
relative error = 7.4948020443769226156459060724140e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.632
y[1] (analytic) = 24.132290360619871255426866368926
y[1] (numeric) = 24.132290360619873058446060196246
absolute error = 1.803019193827320e-15
relative error = 7.4713968996890809755695866822192e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.633
y[1] (analytic) = 24.274951542843980022145852719573
y[1] (numeric) = 24.274951542843981830155226643003
absolute error = 1.808009373923430e-15
relative error = 7.4480452442197092897430648443202e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.634
y[1] (analytic) = 24.418511230380011839468122524274
y[1] (numeric) = 24.418511230380013652480841385616
absolute error = 1.813012718861342e-15
relative error = 7.4247471590557205388848564439018e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.635
y[1] (analytic) = 24.562975346743083748009811104899
y[1] (numeric) = 24.562975346743085566039100223911
absolute error = 1.818029289119012e-15
relative error = 7.4015027229185927798206743214414e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
memory used=240.3MB, alloc=4.5MB, time=9.93
TOP MAIN SOLVE Loop
x[1] = 0.636
y[1] (analytic) = 24.708349855969882902731511556019
y[1] (numeric) = 24.708349855969884725790656992129
absolute error = 1.823059145436110e-15
relative error = 7.3783120121865742995956823864570e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.637
y[1] (analytic) = 24.854640762904608362914695237213
y[1] (numeric) = 24.854640762904610191017044052668
absolute error = 1.828102348815455e-15
relative error = 7.3551751009167109318209829530531e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.638
y[1] (analytic) = 25.001854113486985596810846083093
y[1] (numeric) = 25.00185411348698742996980660756
absolute error = 1.833158960524467e-15
relative error = 7.3320920608667530773487294225142e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.639
y[1] (analytic) = 25.149995995042369085775853181072
y[1] (numeric) = 25.149995995042370924004895277693
absolute error = 1.838229042096621e-15
relative error = 7.3090629615168820103202716135391e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = 25.29907253657394852934394599718
y[1] (numeric) = 25.299072536573950372656601330084
absolute error = 1.843312655332904e-15
relative error = 7.2860878700912611424393109939389e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.641
y[1] (analytic) = 25.449089909057074270238664132123
y[1] (numeric) = 25.449089909057076118648526435407
absolute error = 1.848409862303284e-15
relative error = 7.2631668515794491491072694445451e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.642
y[1] (analytic) = 25.600054325735717676770118738808
y[1] (numeric) = 25.600054325735719530290844086999
absolute error = 1.853520725348191e-15
relative error = 7.2402999687576750221551274010824e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.643
y[1] (analytic) = 25.751972042421082339435272576031
y[1] (numeric) = 25.751972042421084198080579656027
absolute error = 1.858645307079996e-15
relative error = 7.2174872822099207671376020047238e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=244.1MB, alloc=4.5MB, time=10.10
x[1] = 0.644
y[1] (analytic) = 25.904849357792382058828344089975
y[1] (numeric) = 25.904849357792383922612014474481
absolute error = 1.863783670384506e-15
relative error = 7.1947288503488835764415160150872e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.645
y[1] (analytic) = 26.058692613699801723188989480002
y[1] (numeric) = 26.05869261369980359212486790246
absolute error = 1.868935878422458e-15
relative error = 7.1720247294367516831181447394608e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.646
y[1] (analytic) = 26.213508195469657296073955054842
y[1] (numeric) = 26.213508195469659170175949685874
absolute error = 1.874101994631032e-15
relative error = 7.1493749736058723627578709213716e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.647
y[1] (analytic) = 26.369302532211771257740798490662
y[1] (numeric) = 26.369302532211773137022881216023
absolute error = 1.879282082725361e-15
relative error = 7.1267796348792276396747632157948e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.648
y[1] (analytic) = 26.526082097129079967887489043448
y[1] (numeric) = 26.526082097129081852363695743501
absolute error = 1.884476206700053e-15
relative error = 7.1042387631907767253029277865777e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.649
y[1] (analytic) = 26.683853407829489542406710012661
y[1] (numeric) = 26.683853407829491432091140843387
absolute error = 1.889684430830726e-15
relative error = 7.0817524064056690399945481948637e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 26.842623026639996962796058440144
y[1] (numeric) = 26.842623026639998857702878115684
absolute error = 1.894906819675540e-15
relative error = 7.0593206103402681765165661432487e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.651
y[1] (analytic) = 27.002397560923093263822684254602
y[1] (numeric) = 27.002397560923095163966122331349
absolute error = 1.900143438076747e-15
relative error = 7.0369434187820670296145696667015e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.652
y[1] (analytic) = 27.163183663395465772980911883527
y[1] (numeric) = 27.163183663395467678375263045771
absolute error = 1.905394351162244e-15
relative error = 7.0146208735094380653891745087422e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=247.9MB, alloc=4.5MB, time=10.26
x[1] = 0.653
y[1] (analytic) = 27.324988032449016504211781240756
y[1] (numeric) = 27.324988032449018414871405587887
absolute error = 1.910659624347131e-15
relative error = 6.9923530143112275707253733896556e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.654
y[1] (analytic) = 27.487817412474213938282033391611
y[1] (numeric) = 27.487817412474215854221356726901
absolute error = 1.915939323335290e-15
relative error = 6.9701398790062532927596044564899e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.655
y[1] (analytic) = 27.65167859418579555315471297762
y[1] (numeric) = 27.651678594185797474388227098573
absolute error = 1.921233514120953e-15
relative error = 6.9479815034625885227101903744832e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.656
y[1] (analytic) = 27.816578414950838599632191481197
y[1] (numeric) = 27.816578414950840526174454471492
absolute error = 1.926542262990295e-15
relative error = 6.9258779216167656706890910171492e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.657
y[1] (analytic) = 27.98252375911921675052302292484
y[1] (numeric) = 27.982523759119218682388659447866
absolute error = 1.931865636523026e-15
relative error = 6.9038291654928046092085826704783e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.658
y[1] (analytic) = 28.149521558356460385584680907044
y[1] (numeric) = 28.149521558356462322788382501039
absolute error = 1.937203701593995e-15
relative error = 6.8818352652211140770191923302805e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.659
y[1] (analytic) = 28.317578791979038409533011756939
y[1] (numeric) = 28.317578791979040352089537131741
absolute error = 1.942556525374802e-15
relative error = 6.8598962490572521803409543031407e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = 28.486702487292079636494356845036
y[1] (numeric) = 28.486702487292081584418532180449
absolute error = 1.947924175335413e-15
relative error = 6.8380121434005292035123565166646e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.661
y[1] (analytic) = 28.656899719929551911415997075318
y[1] (numeric) = 28.656899719929553864722716321113
absolute error = 1.953306719245795e-15
relative error = 6.8161829728125135464539870453618e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=251.7MB, alloc=4.5MB, time=10.42
x[1] = 0.662
y[1] (analytic) = 28.828177614196917277153169747686
y[1] (numeric) = 28.828177614196919235857394925233
absolute error = 1.958704225177547e-15
relative error = 6.7944087600353565494411690316815e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.663
y[1] (analytic) = 29.000543343416281635224784386382
y[1] (numeric) = 29.000543343416283599341545891931
absolute error = 1.964116761505549e-15
relative error = 6.7726895260100145817203415713358e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.664
y[1] (analytic) = 29.174004130274057488583569012184
y[1] (numeric) = 29.174004130274059458127965921796
absolute error = 1.969544396909612e-15
relative error = 6.7510252898943094433464524435443e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.665
y[1] (analytic) = 29.348567247171158496188228637955
y[1] (numeric) = 29.348567247171160471175429014099
absolute error = 1.974987200376144e-15
relative error = 6.7294160690808799694517917418784e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.666
y[1] (analytic) = 29.524240016575744711703878695384
y[1] (numeric) = 29.5242400165757466921491198952
absolute error = 1.980445241199816e-15
relative error = 6.7078618792149702728592646110204e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.667
y[1] (analytic) = 29.701029811378537522301181679584
y[1] (numeric) = 29.701029811378539508219770664835
absolute error = 1.985918588985251e-15
relative error = 6.6863627342121339759421712202199e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.668
y[1] (analytic) = 29.87894405525072344828298892971
y[1] (numeric) = 29.878944055250725439690302578412
absolute error = 1.991407313648702e-15
relative error = 6.6649186462757392988625867986661e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.669
y[1] (analytic) = 30.057990223004466110148664491463
y[1] (numeric) = 30.057990223004468107060149911221
absolute error = 1.996911485419758e-15
relative error = 6.6435296259144082051395226594626e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=255.5MB, alloc=4.5MB, time=10.58
x[1] = 0.67
y[1] (analytic) = 30.238175840956045816719508286455
y[1] (numeric) = 30.238175840956047819150683129499
absolute error = 2.002431174843044e-15
relative error = 6.6221956819592751439190269504223e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.671
y[1] (analytic) = 30.419508487291646376102736283448
y[1] (numeric) = 30.419508487291648384069189063388
absolute error = 2.007966452779940e-15
relative error = 6.6009168215811503072308094410988e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.672
y[1] (analytic) = 30.601995792435808880575322630923
y[1] (numeric) = 30.60199579243581089409271304123
absolute error = 2.013517390410307e-15
relative error = 6.5796930503075474489045128672821e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.673
y[1] (analytic) = 30.785645439422572366931741619123
y[1] (numeric) = 30.78564543942257438601580085334
absolute error = 2.019084059234217e-15
relative error = 6.5585243720395674512311700641182e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.674
y[1] (analytic) = 30.970465164269321405470417577618
y[1] (numeric) = 30.970465164269323430136948651316
absolute error = 2.024666531073698e-15
relative error = 6.5374107890686744913545191011847e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.675
y[1] (analytic) = 31.156462756353360823601723494309
y[1] (numeric) = 31.156462756353362853866601568793
absolute error = 2.030264878074484e-15
relative error = 6.5163523020933325485125334973851e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.676
y[1] (analytic) = 31.343646058791237924054963402108
y[1] (numeric) = 31.343646058791239959934136109887
absolute error = 2.035879172707779e-15
relative error = 6.4953489102355321655493334471187e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.677
y[1] (analytic) = 31.532022968820832712852303187436
y[1] (numeric) = 31.53202296882083475436179095946
absolute error = 2.041509487772024e-15
relative error = 6.4744006110571725682225607205524e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.678
y[1] (analytic) = 31.721601438186236808613528433553
y[1] (numeric) = 31.721601438186238855769424828234
absolute error = 2.047155896394681e-15
relative error = 6.4535074005763447413929037559789e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=259.4MB, alloc=4.5MB, time=10.74
x[1] = 0.679
y[1] (analytic) = 31.912389473525441862366331074238
y[1] (numeric) = 31.912389473525443915184803108257
absolute error = 2.052818472034019e-15
relative error = 6.4326692732834680604444521045785e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = 32.10439513676085847587216031908
y[1] (numeric) = 32.104395136760860534369448799994
absolute error = 2.058497288480914e-15
relative error = 6.4118862221573194513756833789151e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.681
y[1] (analytic) = 32.297626545492686766547195930286
y[1] (numeric) = 32.297626545492688830739615790944
absolute error = 2.064192419860658e-15
relative error = 6.3911582386809396093626425941449e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.682
y[1] (analytic) = 32.492091873395159888371469610282
y[1] (numeric) = 32.492091873395161958275410245057
absolute error = 2.069903940634775e-15
relative error = 6.3704853128574107960727905729992e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.683
y[1] (analytic) = 32.687799350615681980746407478617
y[1] (numeric) = 32.687799350615684056378333081467
absolute error = 2.075631925602850e-15
relative error = 6.3498674332255255060856399355464e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.684
y[1] (analytic) = 32.884757264176882181092006845073
y[1] (numeric) = 32.884757264176884262468456749443
absolute error = 2.081376449904370e-15
relative error = 6.3293045868753431221884127569846e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.685
y[1] (analytic) = 33.082973958381606502079486826312
y[1] (numeric) = 33.082973958381608589217075846875
absolute error = 2.087137589020563e-15
relative error = 6.3087967594635925426100320851090e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.686
y[1] (analytic) = 33.282457835220869540783638191785
y[1] (numeric) = 33.282457835220871633699056968045
absolute error = 2.092915418776260e-15
relative error = 6.2883439352289979807236911940224e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.687
y[1] (analytic) = 33.483217354784788154721397484341
y[1] (numeric) = 33.483217354784790253431412826106
absolute error = 2.098710015341765e-15
relative error = 6.2679460970074820411667036093140e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=263.2MB, alloc=4.5MB, time=10.89
x[1] = 0.688
y[1] (analytic) = 33.685261035676519408729619862538
y[1] (numeric) = 33.685261035676521513251075097262
absolute error = 2.104521455234724e-15
relative error = 6.2476032262472201786042049335717e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.689
y[1] (analytic) = 33.88859745542922526693594243844
y[1] (numeric) = 33.888597455429227377285757760459
absolute error = 2.110349815322019e-15
relative error = 6.2273153030236252049919899878446e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = 34.093235250926086675702416253551
y[1] (numeric) = 34.093235250926088791897589075212
absolute error = 2.116195172821661e-15
relative error = 6.2070823060541842763770854693161e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.691
y[1] (analytic) = 34.299183118823389856382725173191
y[1] (numeric) = 34.299183118823391978440330477888
absolute error = 2.122057605304697e-15
relative error = 6.1869042127131940352247897464842e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.692
y[1] (analytic) = 34.50644981597670780104087290492
y[1] (numeric) = 34.506449815976709928978063602052
absolute error = 2.127937190697132e-15
relative error = 6.1667809990463968827423330901202e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.693
y[1] (analytic) = 34.715044159870200139942859057796
y[1] (numeric) = 34.715044159870202273776866339646
absolute error = 2.133834007281850e-15
relative error = 6.1467126397854722602333458671051e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.694
y[1] (analytic) = 34.924975029049054726663821327559
y[1] (numeric) = 34.924975029049056866411955028116
absolute error = 2.139748133700557e-15
relative error = 6.1266991083624507192167419240336e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.695
y[1] (analytic) = 35.136251363555094465062219561524
y[1] (numeric) = 35.13625136355509661074186851725
absolute error = 2.145679648955726e-15
relative error = 6.1067403769239929835937267756879e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.696
y[1] (analytic) = 35.348882165365573082170791745973
y[1] (numeric) = 35.348882165365575233799424158532
absolute error = 2.151628632412559e-15
relative error = 6.0868364163455779946190875667379e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
memory used=267.0MB, alloc=4.5MB, time=11.05
TOP MAIN SOLVE Loop
x[1] = 0.697
y[1] (analytic) = 35.562876498835183732252222775677
y[1] (numeric) = 35.562876498835185889847386576631
absolute error = 2.157595163800954e-15
relative error = 6.0669871962455659452183040195082e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.698
y[1] (analytic) = 35.778243491141304499876823621402
y[1] (numeric) = 35.778243491141306663456146838888
absolute error = 2.163579323217486e-15
relative error = 6.0471926849991626510949278708063e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.699
y[1] (analytic) = 35.994992332732505053911199844822
y[1] (numeric) = 35.994992332732507223492390972218
absolute error = 2.169581191127396e-15
relative error = 6.0274528497522687102581322275181e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 36.213132277780338889772162914236
y[1] (numeric) = 36.213132277780341065373011280831
absolute error = 2.175600848366595e-15
relative error = 6.0077676564352336170317582251485e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.701
y[1] (analytic) = 36.432672644634445784210364731288
y[1] (numeric) = 36.432672644634447965848740874962
absolute error = 2.181638376143674e-15
relative error = 5.9881370697764901444710628449255e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.702
y[1] (analytic) = 36.653622816280989275254765900991
y[1] (numeric) = 36.653622816280991462948621942918
absolute error = 2.187693856041927e-15
relative error = 5.9685610533160891671056718369198e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.703
y[1] (analytic) = 36.875992240804454169783624453964
y[1] (numeric) = 36.875992240804456363550994475351
absolute error = 2.193767370021387e-15
relative error = 5.9490395694191351829011285991513e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.704
y[1] (analytic) = 37.099790431852829272501849779692
y[1] (numeric) = 37.099790431852831472360850200558
absolute error = 2.199859000420866e-15
relative error = 5.9295725792890985436132250026652e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=270.8MB, alloc=4.5MB, time=11.21
x[1] = 0.705
y[1] (analytic) = 37.325026969106200722910035960279
y[1] (numeric) = 37.325026969106202928878865920297
absolute error = 2.205968829960018e-15
relative error = 5.9101600429810565994589677636382e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.706
y[1] (analytic) = 37.551711498748781521159093467234
y[1] (numeric) = 37.551711498748783733256035208635
absolute error = 2.212096941741401e-15
relative error = 5.8908019194147989823782939227863e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.707
y[1] (analytic) = 37.779853733944403019508057486665
y[1] (numeric) = 37.77985373394440523775147673922
absolute error = 2.218243419252555e-15
relative error = 5.8714981663878438976545970233384e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.708
y[1] (analytic) = 38.00946345531549435345338016229
y[1] (numeric) = 38.009463455315496577861726530383
absolute error = 2.224408346368093e-15
relative error = 5.8522487405883574729702723670284e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.709
y[1] (analytic) = 38.240550511425575985487924770859
y[1] (numeric) = 38.240550511425578216079732122663
absolute error = 2.230591807351804e-15
relative error = 5.8330535976079738416188958705150e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = 38.473124819265293734889181830354
y[1] (numeric) = 38.473124819265295971683068689116
absolute error = 2.236793886858762e-15
relative error = 5.8139126919545007750578205822322e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.711
y[1] (analytic) = 38.707196364742019868941228324517
y[1] (numeric) = 38.707196364742022111955898261964
absolute error = 2.243014669937447e-15
relative error = 5.7948259770645274417830050300180e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.712
y[1] (analytic) = 38.942775203173048034576058726021
y[1] (numeric) = 38.942775203173050283830300757908
absolute error = 2.249254242031887e-15
relative error = 5.7757934053159578130719568933438e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.713
y[1] (analytic) = 39.179871459782409014589637425529
y[1] (numeric) = 39.17987145978241127010232640933
absolute error = 2.255512688983801e-15
relative error = 5.7568149280404181048586166058308e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=274.6MB, alloc=4.5MB, time=11.37
x[1] = 0.714
y[1] (analytic) = 39.41849533020133449935896444544
y[1] (numeric) = 39.418495330201336761149061480197
absolute error = 2.261790097034757e-15
relative error = 5.7378904955355753983749228134418e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.715
y[1] (analytic) = 39.658657080972396273371319490256
y[1] (numeric) = 39.6586570809723985414578723186
absolute error = 2.268086552828344e-15
relative error = 5.7190200570773650162428076693006e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.716
y[1] (analytic) = 39.900367050057348425888465480657
y[1] (numeric) = 39.900367050057350700290608893009
absolute error = 2.274402143412352e-15
relative error = 5.7002035609321118337565949222967e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.717
y[1] (analytic) = 40.143635647348700406719867059673
y[1] (numeric) = 40.143635647348702687456823300639
absolute error = 2.280736956240966e-15
relative error = 5.6814409543685613361121280753322e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.718
y[1] (analytic) = 40.388473355185048961382931619791
y[1] (numeric) = 40.388473355185051248474010796765
absolute error = 2.287091079176974e-15
relative error = 5.6627321836698206463026188159523e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.719
y[1] (analytic) = 40.634890728870197194898034653144
y[1] (numeric) = 40.634890728870199488362635147128
absolute error = 2.293464600493984e-15
relative error = 5.6440771941451974527349067132132e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 40.882898397196089230114878006848
y[1] (numeric) = 40.882898397196091529972486885501
absolute error = 2.299857608878653e-15
relative error = 5.6254759301419449396536553676100e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.721
y[1] (analytic) = 41.132507062969589144807885992065
y[1] (numeric) = 41.132507062969591451078079424993
absolute error = 2.306270193432928e-15
relative error = 5.6069283350569131703322738618118e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.722
y[1] (analytic) = 41.383727503543133091825314908095
y[1] (numeric) = 41.383727503543135404527758584398
absolute error = 2.312702443676303e-15
relative error = 5.5884343513481170423385652697349e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=278.4MB, alloc=4.5MB, time=11.53
x[1] = 0.723
y[1] (analytic) = 41.636570571349283728343089541802
y[1] (numeric) = 41.636570571349286047497539089887
absolute error = 2.319154449548085e-15
relative error = 5.5699939205462040491015654592693e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.724
y[1] (analytic) = 41.89104719443921630377374809626
y[1] (numeric) = 41.891047194439218629400049505934
absolute error = 2.325626301409674e-15
relative error = 5.5516069832658345576140302191012e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.725
y[1] (analytic) = 42.147168377025165981127047562874
y[1] (numeric) = 42.147168377025168313245137609724
absolute error = 2.332118090046850e-15
relative error = 5.5332734792169582563473296848901e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.726
y[1] (analytic) = 42.404945200026866193625638716935
y[1] (numeric) = 42.40494520002686853225554538902
absolute error = 2.338629906672085e-15
relative error = 5.5149933472160301983102099317968e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.727
y[1] (analytic) = 42.664388821622008067160759703149
y[1] (numeric) = 42.664388821622010412322602629999
absolute error = 2.345161842926850e-15
relative error = 5.4967665251970952845078420164438e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.728
y[1] (analytic) = 42.925510477800751169743228595092
y[1] (numeric) = 42.925510477800753521457219479047
absolute error = 2.351713990883955e-15
relative error = 5.4785929502228319018288016713210e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.729
y[1] (analytic) = 43.188321482924316081478361291188
y[1] (numeric) = 43.18832148292431843976480434107
absolute error = 2.358286443049882e-15
relative error = 5.4604725584954604789313157870933e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = 43.452833230287689512784139432896
y[1] (numeric) = 43.452833230287691877663431800042
absolute error = 2.364879292367146e-15
relative error = 5.4424052853675998856169123923945e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.731
y[1] (analytic) = 43.719057192686472934594457276125
y[1] (numeric) = 43.719057192686475306087089492787
absolute error = 2.371492632216662e-15
relative error = 5.4243910653530202584012566439177e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
memory used=282.2MB, alloc=4.5MB, time=11.69
TOP MAIN SOLVE Loop
x[1] = 0.732
y[1] (analytic) = 43.987004922987905922158156934723
y[1] (numeric) = 43.987004922987908300284713354846
absolute error = 2.378126556420123e-15
relative error = 5.4064298321373047075564429444933e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.733
y[1] (analytic) = 44.256688054706095653774506165111
y[1] (numeric) = 44.256688054706098038555665407509
absolute error = 2.384781159242398e-15
relative error = 5.3885215185884408334324180582409e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.734
y[1] (analytic) = 44.528118302581484247411588557482
y[1] (numeric) = 44.528118302581486638868123951418
absolute error = 2.391456535393936e-15
relative error = 5.3706660567673103351494436702983e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.735
y[1] (analytic) = 44.801307463164585861650688961631
y[1] (numeric) = 44.801307463164588259803468994821
absolute error = 2.398152780033190e-15
relative error = 5.3528633779381090463119558177694e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.736
y[1] (analytic) = 45.076267415404025732802214141736
y[1] (numeric) = 45.076267415404028137672202910785
absolute error = 2.404869988769049e-15
relative error = 5.3351134125786705157672377166135e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.737
y[1] (analytic) = 45.353010121238913567362158567328
y[1] (numeric) = 45.353010121238915978970416230613
absolute error = 2.411608257663285e-15
relative error = 5.3174160903907094637251191988015e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.738
y[1] (analytic) = 45.631547626195583958237899053123
y[1] (numeric) = 45.631547626195586376605582286135
absolute error = 2.418367683233012e-15
relative error = 5.2997713403099787677472273778558e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.739
y[1] (analytic) = 45.911892059988736744383594412302
y[1] (numeric) = 45.91189205998873916953195686547
absolute error = 2.425148362453168e-15
relative error = 5.2821790905163644552554325420922e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=286.1MB, alloc=4.5MB, time=11.85
x[1] = 0.74
y[1] (analytic) = 46.194055637127010486664216761738
y[1] (numeric) = 46.194055637127012918614609520731
absolute error = 2.431950392758993e-15
relative error = 5.2646392684438597478758844588587e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.741
y[1] (analytic) = 46.478050657523022487928914632736
y[1] (numeric) = 46.478050657523024926702786681273
absolute error = 2.438773872048537e-15
relative error = 5.2471518007904933294588683060165e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.742
y[1] (analytic) = 46.763889507107909042434796290664
y[1] (numeric) = 46.763889507107911488053694975839
absolute error = 2.445618898685175e-15
relative error = 5.2297166135281615100329004903755e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.743
y[1] (analytic) = 47.051584658450399858937244057885
y[1] (numeric) = 47.051584658450402311422815558019
absolute error = 2.452485571500134e-15
relative error = 5.2123336319123759121288979923757e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.744
y[1] (analytic) = 47.341148671380460862968575134537
y[1] (numeric) = 47.341148671380463322342564929576
absolute error = 2.459373989795039e-15
relative error = 5.1950027804919420004119208551731e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.745
y[1] (analytic) = 47.632594193617539847079429405992
y[1] (numeric) = 47.632594193617542313363682750463
absolute error = 2.466284253344471e-15
relative error = 5.1777239831185536605746186688534e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.746
y[1] (analytic) = 47.925933961403449703132998882112
y[1] (numeric) = 47.925933961403452176349461280648
absolute error = 2.473216462398536e-15
relative error = 5.1604971629563022873353367738740e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.747
y[1] (analytic) = 48.221180800139924238137557556257
y[1] (numeric) = 48.221180800139926718308275241709
absolute error = 2.480170717685452e-15
relative error = 5.1433222424911155338967451539144e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.748
y[1] (analytic) = 48.51834762503088184459427846568
y[1] (numeric) = 48.518347625030884331741398879832
absolute error = 2.487147120414152e-15
relative error = 5.1261991435401216121834048258118e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=289.9MB, alloc=4.5MB, time=12.01
x[1] = 0.749
y[1] (analytic) = 48.817447441729432567941744575599
y[1] (numeric) = 48.817447441729435062087516852494
absolute error = 2.494145772276895e-15
relative error = 5.1091277872609229568299365947407e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = 49.118493346989664387412715025737
y[1] (numeric) = 49.118493346989666888579490477635
absolute error = 2.501166775451898e-15
relative error = 5.0921080941608066310730242304386e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.751
y[1] (analytic) = 49.421498529323244802499577842683
y[1] (numeric) = 49.421498529323247310709810448661
absolute error = 2.508210232605978e-15
relative error = 5.0751399841058689841043526272194e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.752
y[1] (analytic) = 49.726476269660874095269621468647
y[1] (numeric) = 49.726476269660876610545868365858
absolute error = 2.515276246897211e-15
relative error = 5.0582233763300693773214002308156e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.753
y[1] (analytic) = 50.033439942018626918997046013363
y[1] (numeric) = 50.033439942018629441361967990971
absolute error = 2.522364921977608e-15
relative error = 5.0413581894442131106143109190118e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.754
y[1] (analytic) = 50.342403014169219146002906356813
y[1] (numeric) = 50.342403014169221675479268352612
absolute error = 2.529476361995799e-15
relative error = 5.0245443414448458115370282643336e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.755
y[1] (analytic) = 50.653379048318237192234469349277
y[1] (numeric) = 50.653379048318239728845140949014
absolute error = 2.536610671599737e-15
relative error = 5.0077817497230838955469699403285e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.756
y[1] (analytic) = 50.966381701785367322989454639768
y[1] (numeric) = 50.96638170178536986675741057919
absolute error = 2.543767955939422e-15
relative error = 4.9910703310733809876120640265929e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.757
y[1] (analytic) = 51.28142472769066273331613458335
y[1] (numeric) = 51.281424727690665284264455252974
absolute error = 2.550948320669624e-15
relative error = 4.9744100017021892596839287553775e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=293.7MB, alloc=4.5MB, time=12.17
x[1] = 0.758
y[1] (analytic) = 51.598521975645886488015259079318
y[1] (numeric) = 51.59852197564588904616713103196
absolute error = 2.558151871952642e-15
relative error = 4.9578006772365890725167421128457e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.759
y[1] (analytic) = 51.917687392450968699852357487503
y[1] (numeric) = 51.917687392450971265231073948562
absolute error = 2.565378716461059e-15
relative error = 4.9412422727328084451325666118405e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 52.238935022795616620577410131111
y[1] (numeric) = 52.23893502279561919320637151164
absolute error = 2.572628961380529e-15
relative error = 4.9247347026847031961801332567562e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.761
y[1] (analytic) = 52.56227900996611661766158246083
y[1] (numeric) = 52.562279009966119197564296873396
absolute error = 2.579902714412566e-15
relative error = 4.9082778810321396118639531163435e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.762
y[1] (analytic) = 52.88773359655736731031623104854
y[1] (numeric) = 52.887733596557369897516314825898
absolute error = 2.587200083777358e-15
relative error = 4.8918717211693245539460424148507e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.763
y[1] (analytic) = 53.215313125190183441376427931741
y[1] (numeric) = 53.215313125190186035897606148332
absolute error = 2.594521178216591e-15
relative error = 4.8755161359530543505146037577493e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.764
y[1] (analytic) = 53.545032039233910367028665819578
y[1] (numeric) = 53.545032039233912968894772815871
absolute error = 2.601866106996293e-15
relative error = 4.8592110377109019132152937029020e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.765
y[1] (analytic) = 53.876904883534389354159211569146
y[1] (numeric) = 53.876904883534391963394191478836
absolute error = 2.609234979909690e-15
relative error = 4.8429563382493271888085064085495e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.766
y[1] (analytic) = 54.210946305147314185314933567796
y[1] (numeric) = 54.210946305147316801942840847874
absolute error = 2.616627907280078e-15
relative error = 4.8267519488617189334071368777872e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
memory used=297.5MB, alloc=4.5MB, time=12.33
TOP MAIN SOLVE Loop
x[1] = 0.767
y[1] (analytic) = 54.547171054077019883921660052926
y[1] (numeric) = 54.547171054077022507966660016645
absolute error = 2.624044999963719e-15
relative error = 4.8105977803363827645470381407766e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.768
y[1] (analytic) = 54.885593984020744687515706501119
y[1] (numeric) = 54.885593984020747319002075853861
absolute error = 2.631486369352742e-15
relative error = 4.7944937429644405344859206805330e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.769
y[1] (analytic) = 55.226230053118406714331775544733
y[1] (numeric) = 55.226230053118409353283902922798
absolute error = 2.638952127378065e-15
relative error = 4.7784397465476711715239725013200e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 55.569094324707937088674776232824
y[1] (numeric) = 55.569094324707939735117162745159
absolute error = 2.646442386512335e-15
relative error = 4.7624357004062874986519737828925e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.771
y[1] (analytic) = 55.914201968086211613104185246825
y[1] (numeric) = 55.914201968086214267061445019713
absolute error = 2.653957259772888e-15
relative error = 4.7464815133866527613241199541241e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.772
y[1] (analytic) = 56.261568259275623400597497229375
y[1] (numeric) = 56.261568259275626062094357954086
absolute error = 2.661496860724711e-15
relative error = 4.7305770938689048791273087675415e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.773
y[1] (analytic) = 56.611208581796339207554364256391
y[1] (numeric) = 56.61120858179634187661566773983
absolute error = 2.669061303483439e-15
relative error = 4.7147223497745481163576165089241e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.774
y[1] (analytic) = 56.963138427444282538775649840917
y[1] (numeric) = 56.963138427444285215426352559273
absolute error = 2.676650702718356e-15
relative error = 4.6989171885739566106924156955826e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=301.3MB, alloc=4.5MB, time=12.49
x[1] = 0.775
y[1] (analytic) = 57.31737339707488692842243081336
y[1] (numeric) = 57.317373397074889612687604468775
absolute error = 2.684265173655415e-15
relative error = 4.6831615172938171826719677803129e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.776
y[1] (analytic) = 57.673929201392663136449748402085
y[1] (numeric) = 57.673929201392665828354580482369
absolute error = 2.691904832080284e-15
relative error = 4.6674552425245236654121872414077e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.777
y[1] (analytic) = 58.032821661746624338139583958417
y[1] (numeric) = 58.032821661746627037709378299813
absolute error = 2.699569794341396e-15
relative error = 4.6517982704274844306227334597781e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.778
y[1] (analytic) = 58.394066710931613725148231229218
y[1] (numeric) = 58.394066710931616432408408582244
absolute error = 2.707260177353026e-15
relative error = 4.6361905067423837467393416628958e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.779
y[1] (analytic) = 58.757680393995579279956243558483
y[1] (numeric) = 58.75768039399558199493234215686
absolute error = 2.714976098598377e-15
relative error = 4.6206318567943658589461667304064e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = 59.123678869052840831785911470559
y[1] (numeric) = 59.123678869052843554503587603253
absolute error = 2.722717676132694e-15
relative error = 4.6051222255011748009081543973382e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.781
y[1] (analytic) = 59.492078408103394850953408643623
y[1] (numeric) = 59.492078408103397581438437230008
absolute error = 2.730485028586385e-15
relative error = 4.5896615173802141108662655920949e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.782
y[1] (analytic) = 59.862895397858302790272142968503
y[1] (numeric) = 59.862895397858305528550418136671
absolute error = 2.738278275168168e-15
relative error = 4.5742496365555592167900670121917e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.783
y[1] (analytic) = 60.236146340571209136542452052664
y[1] (numeric) = 60.23614634057121188263998772089
absolute error = 2.746097535668226e-15
relative error = 4.5588864867648922440395939368378e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=305.1MB, alloc=4.5MB, time=12.65
x[1] = 0.784
y[1] (analytic) = 60.611847854876035692372755681547
y[1] (numeric) = 60.611847854876038446315686142938
absolute error = 2.753942930461391e-15
relative error = 4.5435719713663948441517942347918e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.785
y[1] (analytic) = 60.990016676630898968600968033372
y[1] (numeric) = 60.990016676630901730415548543711
absolute error = 2.761814580510339e-15
relative error = 4.5283059933455689684961564171368e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.786
y[1] (analytic) = 61.370669659768297930444908121198
y[1] (numeric) = 61.370669659768300700157515490004
absolute error = 2.769712607368806e-15
relative error = 4.5130884553220026234790037782186e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.787
y[1] (analytic) = 61.753823777151619706229339385641
y[1] (numeric) = 61.753823777151622483866472570456
absolute error = 2.777637133184815e-15
relative error = 4.4979192595560644420048415519372e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.788
y[1] (analytic) = 62.139496121438011236138014586024
y[1] (numeric) = 62.139496121438014021726295289959
absolute error = 2.785588280703935e-15
relative error = 4.4827983079555616078564916220713e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.789
y[1] (analytic) = 62.527703905947665209944782287086
y[1] (numeric) = 62.527703905947668003510955559631
absolute error = 2.793566173272545e-15
relative error = 4.4677255020823172184910809895827e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 62.918464465539569017111696144321
y[1] (numeric) = 62.918464465539571818682630985445
absolute error = 2.801570934841124e-15
relative error = 4.4527007431587016343521208719525e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.791
y[1] (analytic) = 63.311795257493765810027616914856
y[1] (numeric) = 63.311795257493768619630306882414
absolute error = 2.809602689967558e-15
relative error = 4.4377239320741033026303541130490e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.792
y[1] (analytic) = 63.70771386240017716152165951336
y[1] (numeric) = 63.707713862400179979183223333823
absolute error = 2.817661563820463e-15
relative error = 4.4227949693913378251048423951329e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=309.0MB, alloc=4.5MB, time=12.82
x[1] = 0.793
y[1] (analytic) = 64.10623798505403718114585570809
y[1] (numeric) = 64.106237985054040006893537890621
absolute error = 2.825747682182531e-15
relative error = 4.4079137553530065997044122208054e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.794
y[1] (analytic) = 64.507385455357988341104613375155
y[1] (numeric) = 64.507385455357991174965784829046
absolute error = 2.833861171453891e-15
relative error = 4.3930801898877925699753122821048e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.795
y[1] (analytic) = 64.911174229230889652139187313543
y[1] (numeric) = 64.911174229230892494141345969037
absolute error = 2.842002158655494e-15
relative error = 4.3782941726167074354916996996457e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.796
y[1] (analytic) = 65.317622389523388222177863346956
y[1] (numeric) = 65.317622389523391072348634779468
absolute error = 2.850170771432512e-15
relative error = 4.3635556028592748964190290743377e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.797
y[1] (analytic) = 65.726748146940305626161524468401
y[1] (numeric) = 65.72674814694030848452866252616
absolute error = 2.858367138057759e-15
relative error = 4.3488643796396626671537229855008e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.798
y[1] (analytic) = 66.138569840969890914174543217738
y[1] (numeric) = 66.138569840969893780765930652868
absolute error = 2.866591387435130e-15
relative error = 4.3342204016927572410956180989739e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.799
y[1] (analytic) = 66.553105940819992486877558503289
y[1] (numeric) = 66.553105940819995361721207606352
absolute error = 2.874843649103063e-15
relative error = 4.3196235674701892226749952402863e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 66.970375046361201472276881621063
y[1] (numeric) = 66.970375046361204355400934859076
absolute error = 2.883124053238013e-15
relative error = 4.3050737751462927803140881073505e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.801
y[1] (analytic) = 67.39039588907701964610047465809
y[1] (numeric) = 67.390395889077022537533205316048
absolute error = 2.891432730657958e-15
relative error = 4.2905709226240296044148159671351e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
memory used=312.8MB, alloc=4.5MB, time=12.98
TOP MAIN SOLVE Loop
x[1] = 0.802
y[1] (analytic) = 67.813187333021105349508301289362
y[1] (numeric) = 67.813187333021108249278114115272
absolute error = 2.899769812825910e-15
relative error = 4.2761149075408369597677216612839e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.803
y[1] (analytic) = 68.238768375781651272571220530391
y[1] (numeric) = 68.238768375781654180706652383851
absolute error = 2.908135431853460e-15
relative error = 4.2617056272744434973562343342692e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.804
y[1] (analytic) = 68.667158149452948389933544194189
y[1] (numeric) = 68.66715814945295130646326469852
absolute error = 2.916529720504331e-15
relative error = 4.2473429789486142556365323549659e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.805
y[1] (analytic) = 69.098375921614190756356186830481
y[1] (numeric) = 69.098375921614193681308999028446
absolute error = 2.924952812197965e-15
relative error = 4.2330268594388634535664832865395e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.806
y[1] (analytic) = 69.532441096315576294446495061581
y[1] (numeric) = 69.532441096315579227851336074693
absolute error = 2.933404841013112e-15
relative error = 4.2187571653780883713011585466663e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.807
y[1] (analytic) = 69.969373215071759134844059563722
y[1] (numeric) = 69.969373215071762076730001255181
absolute error = 2.941885941691459e-15
relative error = 4.2045337931621799835581115385831e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.808
y[1] (analytic) = 70.409191957862709500476013173246
y[1] (numeric) = 70.40919195786271245087226281451
absolute error = 2.950396249641264e-15
relative error = 4.1903566389555595950068474906533e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.809
y[1] (analytic) = 70.851917144142037561247647827803
y[1] (numeric) = 70.851917144142040520183548768826
absolute error = 2.958935900941023e-15
relative error = 4.1762255986966821644136868394552e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=316.6MB, alloc=4.5MB, time=13.14
x[1] = 0.81
y[1] (analytic) = 71.297568733852838123722007606463
y[1] (numeric) = 71.297568733852841091227039949611
absolute error = 2.967505032343148e-15
relative error = 4.1621405681034748818835488644154e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.811
y[1] (analytic) = 71.746166828451113461993024378492
y[1] (numeric) = 71.746166828451116438096805656161
absolute error = 2.976103781277669e-15
relative error = 4.1481014426787299137281645212035e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.812
y[1] (analytic) = 72.197731671936832041098570767886
y[1] (numeric) = 72.197731671936835025830856623848
absolute error = 2.984732285855962e-15
relative error = 4.1341081177154540780081963288247e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.813
y[1] (analytic) = 72.652283651892681332980553297312
y[1] (numeric) = 72.652283651892684326371238171807
absolute error = 2.993390684874495e-15
relative error = 4.1201604883021643209546442421053e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.814
y[1] (analytic) = 73.109843300530573377207126321789
y[1] (numeric) = 73.109843300530576379286244140379
absolute error = 3.002079117818590e-15
relative error = 4.1062584493281266352660159273125e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.815
y[1] (analytic) = 73.570431295745962194455774842963
y[1] (numeric) = 73.570431295745965205253499709177
absolute error = 3.010797724866214e-15
relative error = 4.0924018954885565877998212405969e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.816
y[1] (analytic) = 74.034068462180032620144124071868
y[1] (numeric) = 74.034068462180035639690770963657
absolute error = 3.019546646891789e-15
relative error = 4.0785907212897676700688394790507e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.817
y[1] (analytic) = 74.500775772289820588616852584651
y[1] (numeric) = 74.500775772289823616942878054676
absolute error = 3.028326025470025e-15
relative error = 4.0648248210542731699615040362019e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.818
y[1] (analytic) = 74.970574347426325364981217273574
y[1] (numeric) = 74.970574347426328402117220153347
absolute error = 3.037136002879773e-15
relative error = 4.0511040889258376588319321520376e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=320.4MB, alloc=4.6MB, time=13.30
x[1] = 0.819
y[1] (analytic) = 75.44348545892067469205988344884
y[1] (numeric) = 75.443485458920677738036605556736
absolute error = 3.045976722107896e-15
relative error = 4.0374284188744757216508362441642e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = 75.919530529178404294027674012685
y[1] (numeric) = 75.91953052917840734887600086586
absolute error = 3.054848326853175e-15
relative error = 4.0237977047014207203881663498380e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.821
y[1] (analytic) = 76.39873113278191365614843141315
y[1] (numeric) = 76.398731132781916719899392943374
absolute error = 3.063750961530224e-15
relative error = 4.0102118400440289736279732208500e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.822
y[1] (analytic) = 76.881108997601160481659593091912
y[1] (numeric) = 76.881108997601163554344364365344
absolute error = 3.072684771273432e-15
relative error = 3.9966707183806436983244535584380e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.823
y[1] (analytic) = 77.366686005912656712295729583942
y[1] (numeric) = 77.366686005912659793945631524875
absolute error = 3.081649901940933e-15
relative error = 3.9831742330354198981044597147024e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.824
y[1] (analytic) = 77.855484195526829488228846773233
y[1] (numeric) = 77.855484195526832578875346891821
absolute error = 3.090646500118588e-15
relative error = 3.9697222771830894942943072495485e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.825
y[1] (analytic) = 78.3475257609238109163636228312
y[1] (numeric) = 78.347525760923814016038335955199
absolute error = 3.099674713123999e-15
relative error = 3.9563147438536929905858664366851e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.826
y[1] (analytic) = 78.842833054397721012991101213183
y[1] (numeric) = 78.842833054397724121725790223727
absolute error = 3.108734689010544e-15
relative error = 3.9429515259372633518168633328056e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.827
y[1] (analytic) = 79.34142858720950868780611338087
y[1] (numeric) = 79.3414285872095118056326899523
absolute error = 3.117826576571430e-15
relative error = 3.9296325161884585798650855397305e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=324.2MB, alloc=4.6MB, time=13.46
x[1] = 0.828
y[1] (analytic) = 79.843335030748416141263534844968
y[1] (numeric) = 79.843335030748419268214060188746
absolute error = 3.126950525343778e-15
relative error = 3.9163576072311609545725154828690e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.829
y[1] (analytic) = 80.348575217702132556218320571127
y[1] (numeric) = 80.348575217702135692325006183849
absolute error = 3.136106685612722e-15
relative error = 3.9031266915630201980512226528929e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 80.857172143235703477796316490481
y[1] (numeric) = 80.85717214323570662309152490602
absolute error = 3.145295208415539e-15
relative error = 3.8899396615599622515894803812399e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.831
y[1] (analytic) = 81.369148966179262792509561531484
y[1] (numeric) = 81.369148966179265947025807077284
absolute error = 3.154516245545800e-15
relative error = 3.8767964094806511073624180897747e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.832
y[1] (analytic) = 81.884529010224654738793903146736
y[1] (numeric) = 81.884529010224657902563852704278
absolute error = 3.163769949557542e-15
relative error = 3.8636968274709039838738847964159e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.833
y[1] (analytic) = 82.403335765131013906441240026256
y[1] (numeric) = 82.403335765131017079497713795726
absolute error = 3.173056473769470e-15
relative error = 3.8506408075680710582396221736102e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.834
y[1] (analytic) = 82.925592887939371711856839435031
y[1] (numeric) = 82.925592887939374894232811704208
absolute error = 3.182375972269177e-15
relative error = 3.8376282417053650964163178707937e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.835
y[1] (analytic) = 83.451324204196358369727486077852
y[1] (numeric) = 83.451324204196361561456085995246
absolute error = 3.191728599917394e-15
relative error = 3.8246590217161558246773473077109e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.836
y[1] (analytic) = 83.980553709187069919572511343211
y[1] (numeric) = 83.98055370918707312068702369547
absolute error = 3.201114512352259e-15
relative error = 3.8117330393382157714072701311216e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
memory used=328.0MB, alloc=4.6MB, time=13.62
TOP MAIN SOLVE Loop
x[1] = 0.837
y[1] (analytic) = 84.513305569177170407801109320537
y[1] (numeric) = 84.513305569177173618334975314152
absolute error = 3.210533865993615e-15
relative error = 3.7988501862179298301649707809430e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.838
y[1] (analytic) = 85.049604122664299872350130867327
y[1] (numeric) = 85.049604122664303092336948914658
absolute error = 3.219986818047331e-15
relative error = 3.7860103539144613845305389146980e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.839
y[1] (analytic) = 85.589473881638859327761401915586
y[1] (numeric) = 85.589473881638862557234928425233
absolute error = 3.229473526509647e-15
relative error = 3.7732134339038763813021817144340e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (analytic) = 86.132939532854244503711463115081
y[1] (numeric) = 86.132939532854247742705613286623
absolute error = 3.238994150171542e-15
relative error = 3.7604593175832243613822188395163e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.841
y[1] (analytic) = 86.680025939106600649564686400894
y[1] (numeric) = 86.680025939106603898113535024031
absolute error = 3.248548848623137e-15
relative error = 3.7477478962745905188422816502946e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.842
y[1] (analytic) = 87.230758140524171281518489721201
y[1] (numeric) = 87.230758140524174539656271979313
absolute error = 3.258137782258112e-15
relative error = 3.7350790612290943321830295408265e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.843
y[1] (analytic) = 87.785161355866314317382633922578
y[1] (numeric) = 87.785161355866317585143746200729
absolute error = 3.267761112278151e-15
relative error = 3.7224527036308514161990617765681e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.844
y[1] (analytic) = 88.343260983832259617019428404743
y[1] (numeric) = 88.343260983832262894438429102161
absolute error = 3.277419000697418e-15
relative error = 3.7098687146009019774876685591074e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=331.8MB, alloc=4.6MB, time=13.78
x[1] = 0.845
y[1] (analytic) = 88.905082604379682524004472578726
y[1] (numeric) = 88.905082604379685811116082925781
absolute error = 3.287111610347055e-15
relative error = 3.6973269852010955965006281699842e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.846
y[1] (analytic) = 89.470651980053168586184994008717
y[1] (numeric) = 89.470651980053171883024098888424
absolute error = 3.296839104879707e-15
relative error = 3.6848274064379382310215280554185e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.847
y[1] (analytic) = 90.039995057322645219551887136718
y[1] (numeric) = 90.039995057322648526153535910786
absolute error = 3.306601648774068e-15
relative error = 3.6723698692663948378614448303554e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.848
y[1] (analytic) = 90.613137967931856671239487050429
y[1] (numeric) = 90.613137967931859987638894389894
absolute error = 3.316399407339465e-15
relative error = 3.6599542645936667366458270455757e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.849
y[1] (analytic) = 91.190107030256959233561514360822
y[1] (numeric) = 91.190107030256962559794061081276
absolute error = 3.326232546720454e-15
relative error = 3.6475804832829147356541016232636e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 91.770928750675314261820391072801
y[1] (numeric) = 91.770928750675317597921624974256
absolute error = 3.336101233901455e-15
relative error = 3.6352484161569582556862727394761e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.851
y[1] (analytic) = 92.355629824944557154228454744085
y[1] (numeric) = 92.355629824944560500234091455491
absolute error = 3.346005636711406e-15
relative error = 3.6229579540019282966227177917688e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.852
y[1] (analytic) = 92.944237139592021062692003409544
y[1] (numeric) = 92.944237139592024418637927237995
absolute error = 3.355945923828451e-15
relative error = 3.6107089875708908660550183770649e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.853
y[1] (analytic) = 93.536777773314594718471416264677
y[1] (numeric) = 93.536777773314598084393681049319
absolute error = 3.365922264784642e-15
relative error = 3.5985014075874192500526927541875e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=335.7MB, alloc=4.6MB, time=13.94
x[1] = 0.854
y[1] (analytic) = 94.13327899838909437688196252292
y[1] (numeric) = 94.133278998389097752816792493607
absolute error = 3.375934829970687e-15
relative error = 3.5863351047491498451533386129868e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.855
y[1] (analytic) = 94.733768282093230510279801403872
y[1] (numeric) = 94.733768282093233896263592044579
absolute error = 3.385983790640707e-15
relative error = 3.5742099697312817021745969089232e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.856
y[1] (analytic) = 95.338273288137250508625881398599
y[1] (numeric) = 95.338273288137253904695200315634
absolute error = 3.396069318917035e-15
relative error = 3.5621258931900553639212061038218e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.857
y[1] (analytic) = 95.946821878106339281977084313009
y[1] (numeric) = 95.946821878106342688168672108045
absolute error = 3.406191587795036e-15
relative error = 3.5500827657661885265069457136529e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.858
y[1] (analytic) = 96.559442112913860299359475330412
y[1] (numeric) = 96.559442112913863715710246478364
absolute error = 3.416350771147952e-15
relative error = 3.5380804780882730781444423675869e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.859
y[1] (analytic) = 97.176162254265520243673692110152
y[1] (numeric) = 97.176162254265523670220735841936
absolute error = 3.426547043731784e-15
relative error = 3.5261189207761460899000311888281e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 97.797010766134541112608445584922
y[1] (numeric) = 97.797010766134544549389026775113
absolute error = 3.436780581190191e-15
relative error = 3.5141979844442139878200632496818e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.861
y[1] (analytic) = 98.422016316247924251036261428907
y[1] (numeric) = 98.42201631624792769808782148834
absolute error = 3.447051560059433e-15
relative error = 3.5023175597047579443548031026939e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.862
y[1] (analytic) = 99.051207777583891461077752696072
y[1] (numeric) = 99.051207777583894918437910469395
absolute error = 3.457360157773323e-15
relative error = 3.4904775371711845327533632100779e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=339.5MB, alloc=4.6MB, time=14.10
x[1] = 0.863
y[1] (analytic) = 99.684614229880589001989012008526
y[1] (numeric) = 99.68461422988059246969556467675
absolute error = 3.467706552668224e-15
relative error = 3.4786778074612587321916912476538e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.864
y[1] (analytic) = 100.32226496115614096329362247468
y[1] (numeric) = 100.32226496115614444138454646275
absolute error = 3.47809092398807e-15
relative error = 3.4669182612002977029062047719393e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.865
y[1] (analytic) = 100.96418946924013917118913510132
y[1] (numeric) = 100.96418946924014265970258699074
absolute error = 3.48851345188942e-15
relative error = 3.4551987890243345526610141723680e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.866
y[1] (analytic) = 101.61041746331665747025082289371
y[1] (numeric) = 101.61041746331666096922514034021
absolute error = 3.49897431744650e-15
relative error = 3.4435192815832077189734272667514e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.867
y[1] (analytic) = 102.26097886547887890987662828829
y[1] (numeric) = 102.26097886547888241935033094468
absolute error = 3.50947370265639e-15
relative error = 3.4318796295437313895907453474883e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.868
y[1] (analytic) = 102.91590381229542505781035826794
y[1] (numeric) = 102.91590381229542857782214871201
absolute error = 3.52001179044407e-15
relative error = 3.4202797235926640813488932508419e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.869
y[1] (analytic) = 103.57522265638847736148959772915
y[1] (numeric) = 103.57522265638848089207836239681
absolute error = 3.53058876466766e-15
relative error = 3.4087194544398063423679459012040e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 104.23896596802378118193511668763
y[1] (numeric) = 104.23896596802378472313992681121
absolute error = 3.54120481012358e-15
relative error = 3.3971987128209576580950669218728e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.871
y[1] (analytic) = 104.90716453671262383447471704216
y[1] (numeric) = 104.90716453671262738633482959393
memory used=343.3MB, alloc=4.6MB, time=14.26
absolute error = 3.55186011255177e-15
relative error = 3.3857173895008708491917614430754e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.872
y[1] (analytic) = 105.57984937282587868582184527335
y[1] (numeric) = 105.57984937282588224837670391436
absolute error = 3.56255485864101e-15
relative error = 3.3742753752762406231960450406146e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.873
y[1] (analytic) = 106.25705170922020807795360619187
y[1] (numeric) = 106.25705170922021165124284222598
absolute error = 3.57328923603411e-15
relative error = 3.3628725609785069469242335389205e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.874
y[1] (analytic) = 106.93880300287651857590014247869
y[1] (numeric) = 106.93880300287652215996357581201
absolute error = 3.58406343333332e-15
relative error = 3.3515088374768073902202222325045e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.875
y[1] (analytic) = 107.62513493655076276901416645891
y[1] (numeric) = 107.62513493655076636389180656456
absolute error = 3.59487764010565e-15
relative error = 3.3401840956807824964123469158188e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.876
y[1] (analytic) = 108.31607942043718259358259702012
y[1] (numeric) = 108.31607942043718619931464390835
absolute error = 3.60573204688823e-15
relative error = 3.3288982265433593519512125131949e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.877
y[1] (analytic) = 109.01166859384408988881900322162
y[1] (numeric) = 109.01166859384409350544584841539
absolute error = 3.61662684519377e-15
relative error = 3.3176511210635680709278326552123e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.878
y[1] (analytic) = 109.71193482688228064838351223265
y[1] (numeric) = 109.71193482688228427594573974859
absolute error = 3.62756222751594e-15
relative error = 3.3064426702892243605706102103879e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.879
y[1] (analytic) = 110.41691072216618018566401920171
y[1] (numeric) = 110.41691072216618382420240653663
absolute error = 3.63853838733492e-15
relative error = 3.2952727653197092220676663240570e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=347.1MB, alloc=4.6MB, time=14.42
x[1] = 0.88
y[1] (analytic) = 111.1266291165278171931673512911
y[1] (numeric) = 111.12662911652782084272287041396
absolute error = 3.64955551912286e-15
relative error = 3.2841412973086062321812287204762e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.881
y[1] (analytic) = 111.84112308274372544456029586926
y[1] (numeric) = 111.84112308274372910517411421869
absolute error = 3.66061381834943e-15
relative error = 3.2730481574663623673716094414241e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.882
y[1] (analytic) = 112.56042593127487266221731317262
y[1] (numeric) = 112.56042593127487633393079466004
absolute error = 3.67171348148742e-15
relative error = 3.2619932370629345396412778613453e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.883
y[1] (analytic) = 113.28457121201971685362393037402
y[1] (numeric) = 113.28457121201972053647863639233
absolute error = 3.68285470601831e-15
relative error = 3.2509764274303505846211942112734e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.884
y[1] (analytic) = 114.01359271608049120670227835208
y[1] (numeric) = 114.01359271608049490073996879002
absolute error = 3.69403769043794e-15
relative error = 3.2399976199653012667709019818060e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.885
y[1] (analytic) = 114.74752447754281942711841704677
y[1] (numeric) = 114.74752447754282313238105130891
absolute error = 3.70526263426214e-15
relative error = 3.2290567061316386788777515698036e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.886
y[1] (analytic) = 115.48640077526876419995084710979
y[1] (numeric) = 115.48640077526876791648058514228
absolute error = 3.71652973803249e-15
relative error = 3.2181535774629311589473961491799e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.887
y[1] (analytic) = 116.23025613470341226379718956654
y[1] (numeric) = 116.23025613470341599163639288857
absolute error = 3.72783920332203e-15
relative error = 3.2072881255649161210937002267354e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.888
y[1] (analytic) = 116.97912532969510039752311778378
y[1] (numeric) = 116.9791253296951041367143505248
absolute error = 3.73919123274102e-15
relative error = 3.1964602421179395858725636315297e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
memory used=350.9MB, alloc=4.6MB, time=14.58
x[1] = 0.889
y[1] (analytic) = 117.73304338432938743846635851382
y[1] (numeric) = 117.73304338432939118905238845659
absolute error = 3.75058602994277e-15
relative error = 3.1856698188793987931567401174375e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 118.4920455747768782760514809779
y[1] (numeric) = 118.49204557477688203807528060736
absolute error = 3.76202379962946e-15
relative error = 3.1749167476861190384436212993600e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.891
y[1] (analytic) = 119.25616743115500659650123673026
y[1] (numeric) = 119.25616743115501037000598428828
absolute error = 3.77350474755802e-15
relative error = 3.1642009204567251542456951602795e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.892
y[1] (analytic) = 120.02544473940388399270080593991
y[1] (numeric) = 120.02544473940388777772988648599
absolute error = 3.78502908054608e-15
relative error = 3.1535222291940150246528167139381e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.893
y[1] (analytic) = 120.79991354317632389833629455785
y[1] (numeric) = 120.79991354317632769493330103569
absolute error = 3.79659700647784e-15
relative error = 3.1428805659872096738641268924890e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.894
y[1] (analytic) = 121.57961014574214965724250137165
y[1] (numeric) = 121.57961014574215346545123568175
absolute error = 3.80820873431010e-15
relative error = 3.1322758230142816565581197108470e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.895
y[1] (analytic) = 122.36457111190689689751207060054
y[1] (numeric) = 122.3645711119069007173765446788
absolute error = 3.81986447407826e-15
relative error = 3.1217078925442018402933502280484e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.896
y[1] (analytic) = 123.15483326994502124539385123141
y[1] (numeric) = 123.15483326994502507695828813375
absolute error = 3.83156443690234e-15
relative error = 3.1111766669391476382005906412324e-15 %
Correct digits = 16
h = 0.001
NO POLE for equation 1
TOP MAIN SOLVE Loop
x[1] = 0.897
y[1] (analytic) = 123.95043371354772328639823964273
y[1] (numeric) = 123.95043371354772712970707463587
absolute error = 3.84330883499314e-15
relative error = 3.1006820386567700871317960480982e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 8055
Order of pole = 2.371e+06
TOP MAIN SOLVE Loop
memory used=354.7MB, alloc=4.6MB, time=14.74
x[1] = 0.898
y[1] (analytic) = 124.7514098037855035603875860235
y[1] (numeric) = 124.75140980378550741548546768177
absolute error = 3.85509788165827e-15
relative error = 3.0902239002522995649801474829133e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 200
Order of pole = 5.882e+04
TOP MAIN SOLVE Loop
x[1] = 0.899
y[1] (analytic) = 125.55779917108556126381695820879
y[1] (numeric) = 125.55779917108556513074874951716
absolute error = 3.86693179130837e-15
relative error = 3.0798021443807510638754680067311e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 102.4
Order of pole = 3.012e+04
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = 126.36963971722415122576170494765
y[1] (numeric) = 126.36963971722415510457248441092
absolute error = 3.87881077946327e-15
relative error = 3.0694166637990256389711983132883e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 69.38
Order of pole = 2.039e+04
TOP MAIN SOLVE Loop
x[1] = 0.901
y[1] (analytic) = 127.18696961733401462498083987988
y[1] (numeric) = 127.18696961733401851571590263811
absolute error = 3.89073506275823e-15
relative error = 3.0590673513680216011105064642325e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 52.75
Order of pole = 1.550e+04
TOP MAIN SOLVE Loop
x[1] = 0.902
y[1] (analytic) = 128.00982732192699982307724659562
y[1] (numeric) = 128.00982732192700372578210554581
absolute error = 3.90270485895019e-15
relative error = 3.0487541000546992331384434244100e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 42.75
Order of pole = 1.256e+04
TOP MAIN SOLVE Loop
x[1] = 0.903
y[1] (analytic) = 128.83825155893199060388553038692
y[1] (numeric) = 128.83825155893199451860591731104
absolute error = 3.91472038692412e-15
relative error = 3.0384768029341698540464852225566e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 36.07
Order of pole = 1.059e+04
TOP MAIN SOLVE Loop
x[1] = 0.904
y[1] (analytic) = 129.67228133574826003160494128902
y[1] (numeric) = 129.6722813357482639583868079883
absolute error = 3.92678186669928e-15
relative error = 3.0282353531916605153240678701586e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 31.3
Order of pole = 9186
TOP MAIN SOLVE Loop
x[1] = 0.905
y[1] (analytic) = 130.51195594131436906995757869757
y[1] (numeric) = 130.51195594131437300884709813324
absolute error = 3.93888951943567e-15
relative error = 3.0180296441245733366452800885641e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 27.72
Order of pole = 8132
TOP MAIN SOLVE Loop
memory used=358.5MB, alloc=4.6MB, time=14.90
x[1] = 0.906
y[1] (analytic) = 131.35731494819273004185096256645
y[1] (numeric) = 131.35731494819273399289453000686
absolute error = 3.95104356744041e-15
relative error = 3.0078595691444362477633442755149e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 24.93
Order of pole = 7312
TOP MAIN SOLVE Loop
x[1] = 0.907
y[1] (analytic) = 132.20839821466995595371941573501
y[1] (numeric) = 132.2083982146699599169636499092
absolute error = 3.96324423417419e-15
relative error = 2.9977250217788547866177961455979e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 22.7
Order of pole = 6656
TOP MAIN SOLVE Loop
x[1] = 0.908
y[1] (analytic) = 133.06524588687311766097143968725
y[1] (numeric) = 133.06524588687312163646318394502
absolute error = 3.97549174425777e-15
relative error = 2.9876258956734488220379126010633e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 20.88
Order of pole = 6119
TOP MAIN SOLVE Loop
x[1] = 0.909
y[1] (analytic) = 133.92789840090203181084177713359
y[1] (numeric) = 133.92789840090203579862810061208
absolute error = 3.98778632347849e-15
relative error = 2.9775620845937439445472556475087e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 19.36
Order of pole = 5673
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = 134.79639648497770346649904028311
y[1] (numeric) = 134.79639648497770746662723907998
absolute error = 4.00012819879687e-15
relative error = 2.9675334824270778480796578469050e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 18.08
Order of pole = 5295
TOP MAIN SOLVE Loop
x[1] = 0.911
y[1] (analytic) = 135.67078116160704829155505475297
y[1] (numeric) = 135.67078116160705230407265310615
absolute error = 4.01251759835318e-15
relative error = 2.9575399831844315329275553346599e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 16.98
Order of pole = 4971
TOP MAIN SOLVE Loop
x[1] = 0.912
y[1] (analytic) = 136.5510937497640201572233513683
y[1] (numeric) = 136.55109374976402418217810284241
absolute error = 4.02495475147411e-15
relative error = 2.9475814810022828529299735457690e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 16.03
Order of pole = 4691
TOP MAIN SOLVE Loop
x[1] = 0.913
y[1] (analytic) = 137.43737586708727102534497598221
y[1] (numeric) = 137.43737586708727506278486466164
absolute error = 4.03743988867943e-15
relative error = 2.9376578701444003435773177564932e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 15.2
Order of pole = 4447
TOP MAIN SOLVE Loop
x[1] = 0.914
y[1] (analytic) = 138.3296694320944709594039482776
y[1] (numeric) = 138.32966943209447500937718996635
absolute error = 4.04997324168875e-15
relative error = 2.9277690450036584950393024731632e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 14.47
Order of pole = 4231
TOP MAIN SOLVE Loop
memory used=362.4MB, alloc=4.6MB, time=15.07
x[1] = 0.915
y[1] (analytic) = 139.22801666641341712255677910338
y[1] (numeric) = 139.22801666641342118511182253161
absolute error = 4.06255504342823e-15
relative error = 2.9179149001037647519808529428000e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 13.82
Order of pole = 4040
TOP MAIN SOLVE Loop
x[1] = 0.916
y[1] (analytic) = 140.13246009703006163666547887206
y[1] (numeric) = 140.13246009703006571185100690947
absolute error = 4.07518552803741e-15
relative error = 2.9080953301010224959655938753214e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 13.24
Order of pole = 3869
TOP MAIN SOLVE Loop
x[1] = 0.917
y[1] (analytic) = 141.04304255855358919941701979543
y[1] (numeric) = 141.04304255855359328728195067151
absolute error = 4.08786493087608e-15
relative error = 2.8983102297860706842922682326599e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 12.72
Order of pole = 3715
TOP MAIN SOLVE Loop
x[1] = 0.918
y[1] (analytic) = 141.9598071954986763879003558993
y[1] (numeric) = 141.95980719549868048849384443041
absolute error = 4.10059348853111e-15
relative error = 2.8885594940855438204320262042444e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 12.25
Order of pole = 3576
TOP MAIN SOLVE Loop
x[1] = 0.919
y[1] (analytic) = 142.882797464585065616561505743
y[1] (numeric) = 142.88279746458506972993294456641
absolute error = 4.11337143882341e-15
relative error = 2.8788430180637738184328914026153e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 11.82
Order of pole = 3450
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 143.81205713705458776533506230756
y[1] (numeric) = 143.81205713705459189153408312244
absolute error = 4.12619902081488e-15
relative error = 2.8691606969244335574069447308551e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 11.43
Order of pole = 3336
TOP MAIN SOLVE Loop
x[1] = 0.921
y[1] (analytic) = 144.7476303010057685500245657593
y[1] (numeric) = 144.74763030100577268910104057472
absolute error = 4.13907647481542e-15
relative error = 2.8595124260121721131452091846608e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 11.07
Order of pole = 3231
TOP MAIN SOLVE Loop
x[1] = 0.922
y[1] (analytic) = 145.68956136374615477174276995373
y[1] (numeric) = 145.68956136374615892374681234371
absolute error = 4.15200404238998e-15
relative error = 2.8498981008142273442469380537175e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 10.75
Order of pole = 3134
TOP MAIN SOLVE Loop
x[1] = 0.923
y[1] (analytic) = 146.63789505416249765549482855693
y[1] (numeric) = 146.63789505416250182047679492256
absolute error = 4.16498196636563e-15
relative error = 2.8403176169620022418518411975565e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 10.45
Order of pole = 3046
TOP MAIN SOLVE Loop
memory used=366.2MB, alloc=4.6MB, time=15.23
x[1] = 0.924
y[1] (analytic) = 147.59267642510893156986226591348
y[1] (numeric) = 147.59267642510893574787275675223
absolute error = 4.17801049083875e-15
relative error = 2.8307708702326734684063791768437e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 10.17
Order of pole = 2964
TOP MAIN SOLVE Loop
x[1] = 0.925
y[1] (analytic) = 148.5539508558132875102932988647
y[1] (numeric) = 148.5539508558132917013831600468
absolute error = 4.19108986118210e-15
relative error = 2.8212577565506681205882307817154e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 9.913
Order of pole = 2888
TOP MAIN SOLVE Loop
x[1] = 0.926
y[1] (analytic) = 149.52176405430168182779623419358
y[1] (numeric) = 149.52176405430168603201655824573
absolute error = 4.20422032405215e-15
relative error = 2.8117781719892678388565310146450e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 9.674
Order of pole = 2817
TOP MAIN SOLVE Loop
x[1] = 0.927
y[1] (analytic) = 150.49616205984152179293846064869
y[1] (numeric) = 150.49616205984152601034058804494
absolute error = 4.21740212739625e-15
relative error = 2.8023320127720545311092517969293e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 9.452
Order of pole = 2752
TOP MAIN SOLVE Loop
x[1] = 0.928
y[1] (analytic) = 151.47719124540307070204575068249
y[1] (numeric) = 151.47719124540307493268127114246
absolute error = 4.23063552045997e-15
relative error = 2.7929191752744217323453784894036e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 9.245
Order of pole = 2691
TOP MAIN SOLVE Loop
x[1] = 0.929
y[1] (analytic) = 152.46489832013971635844754385873
y[1] (numeric) = 152.46489832013972060236829765319
absolute error = 4.24392075379446e-15
relative error = 2.7835395560250493596343841192211e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 9.051
Order of pole = 2634
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = 153.45933033188708789659655764281
y[1] (numeric) = 153.45933033188709215385463690659
absolute error = 4.25725807926378e-15
relative error = 2.7741930517073099876422539522232e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 8.87
Order of pole = 2580
TOP MAIN SOLVE Loop
x[1] = 0.931
y[1] (analytic) = 154.46053466968116706097902087237
y[1] (numeric) = 154.46053466968117133162677092479
absolute error = 4.27064775005242e-15
relative error = 2.7648795591607512507899455625773e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 8.7
Order of pole = 2530
TOP MAIN SOLVE Loop
memory used=370.0MB, alloc=4.6MB, time=15.39
x[1] = 0.932
y[1] (analytic) = 155.46855906629554120499921712101
y[1] (numeric) = 155.4685590662955454890892377937
absolute error = 4.28409002067269e-15
relative error = 2.7555989753824442058608103958646e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 8.54
Order of pole = 2483
TOP MAIN SOLVE Loop
x[1] = 0.933
y[1] (analytic) = 156.48345160079794643754363862818
y[1] (numeric) = 156.48345160079795073512878560046
absolute error = 4.29758514697228e-15
relative error = 2.7463511975283944902816069518026e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 8.39
Order of pole = 2438
TOP MAIN SOLVE Loop
x[1] = 0.934
y[1] (analytic) = 157.50526070112625051678128352624
y[1] (numeric) = 157.50526070112625482791466966808
absolute error = 4.31113338614184e-15
relative error = 2.7371361229149173366440220467099e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 8.249
Order of pole = 2396
TOP MAIN SOLVE Loop
x[1] = 0.935
y[1] (analytic) = 158.5340351466840262720134998101
y[1] (numeric) = 158.53403514668403059674849653265
absolute error = 4.32473499672255e-15
relative error = 2.7279536490199582397453099055520e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 8.115
Order of pole = 2357
TOP MAIN SOLVE Loop
x[1] = 0.936
y[1] (analytic) = 159.56982407095586752512593715148
y[1] (numeric) = 159.5698240709558718635161757653
absolute error = 4.33839023861382e-15
relative error = 2.7188036734844485804371866261428e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 7.989
Order of pole = 2319
TOP MAIN SOLVE Loop
x[1] = 0.937
y[1] (analytic) = 160.61267696414260068349389402928
y[1] (numeric) = 160.61267696414260503559326711024
absolute error = 4.35209937308096e-15
relative error = 2.7096860941135941361528697408798e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 7.869
Order of pole = 2284
TOP MAIN SOLVE Loop
x[1] = 0.938
y[1] (analytic) = 161.66264367581654638612856328996
y[1] (numeric) = 161.66264367581655075199122605287
absolute error = 4.36586266276291e-15
relative error = 2.7006008088781542942878925938843e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 7.756
Order of pole = 2251
TOP MAIN SOLVE Loop
x[1] = 0.939
y[1] (analytic) = 162.71977441759698680450394886863
y[1] (numeric) = 162.71977441759699118418432054873
absolute error = 4.37968037168010e-15
relative error = 2.6915477159157545535494407858470e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 7.649
Order of pole = 2219
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 163.7841197658459954289517642289
y[1] (numeric) = 163.78411976584599982250452947112
absolute error = 4.39355276524222e-15
relative error = 2.6825267135320956167322773315268e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 7.547
Order of pole = 2189
TOP MAIN SOLVE Loop
memory used=373.8MB, alloc=4.6MB, time=15.55
x[1] = 0.941
y[1] (analytic) = 164.85573066438478741083429832915
y[1] (numeric) = 164.85573066438479181831440858529
absolute error = 4.40748011025614e-15
relative error = 2.6735377002022084607935974668696e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 7.451
Order of pole = 2160
TOP MAIN SOLVE Loop
x[1] = 0.942
y[1] (analytic) = 165.93465842723074977998357727189
y[1] (numeric) = 165.93465842723075420144625220573
absolute error = 4.42146267493384e-15
relative error = 2.6645805745716681036975819324874e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 7.359
Order of pole = 2133
TOP MAIN SOLVE Loop
x[1] = 0.943
y[1] (analytic) = 167.02095474135531211621035491353
y[1] (numeric) = 167.02095474135531655171108381389
absolute error = 4.43550072890036e-15
relative error = 2.6556552354577730650739460455745e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 7.271
Order of pole = 2107
TOP MAIN SOLVE Loop
x[1] = 0.944
y[1] (analytic) = 168.11467166946281952312040085471
y[1] (numeric) = 168.1146716694628239727149440566
absolute error = 4.44959454320189e-15
relative error = 2.6467615818507626190977362115790e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 7.188
Order of pole = 2082
TOP MAIN SOLVE Loop
x[1] = 0.945
y[1] (analytic) = 169.21586165279057103211076385402
y[1] (numeric) = 169.21586165279057549585515416779
absolute error = 4.46374439031377e-15
relative error = 2.6378995129149333739993427686437e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 7.109
Order of pole = 2058
TOP MAIN SOLVE Loop
x[1] = 0.946
y[1] (analytic) = 170.32457751393018785433840014616
y[1] (numeric) = 170.32457751393019233228894429484
absolute error = 4.47795054414868e-15
relative error = 2.6290689279898232887211928394677e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 7.033
Order of pole = 2036
TOP MAIN SOLVE Loop
x[1] = 0.947
y[1] (analytic) = 171.44087245967047719874168534424
y[1] (numeric) = 171.440872459670481690954965409
absolute error = 4.49221328006476e-15
relative error = 2.6202697265913076106399950243145e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.96
Order of pole = 2014
TOP MAIN SOLVE Loop
x[1] = 0.948
y[1] (analytic) = 172.56480008386195868493648588359
y[1] (numeric) = 172.56480008386196319146936075745
absolute error = 4.50653287487386e-15
relative error = 2.6115018084127257890210232427630e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.891
Order of pole = 1994
TOP MAIN SOLVE Loop
x[1] = 0.949
y[1] (analytic) = 173.69641437030322170108796184201
y[1] (numeric) = 173.69641437030322622199756869181
absolute error = 4.52090960684980e-15
relative error = 2.6027650733259680767866950771421e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.825
Order of pole = 1974
TOP MAIN SOLVE Loop
memory used=377.6MB, alloc=4.6MB, time=15.71
x[1] = 0.95
y[1] (analytic) = 174.83576969564928338876312403636
y[1] (numeric) = 174.83576969564928792410687977304
absolute error = 4.53534375573668e-15
relative error = 2.5940594213825457103538267577558e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.762
Order of pole = 1955
TOP MAIN SOLVE Loop
x[1] = 0.951
y[1] (analytic) = 175.9829208323421182793841031284
y[1] (numeric) = 175.98292083234212282921970588569
absolute error = 4.54983560275729e-15
relative error = 2.5853847528146730277859532627837e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.702
Order of pole = 1937
TOP MAIN SOLVE Loop
x[1] = 0.952
y[1] (analytic) = 177.13792295156353196031555361385
y[1] (numeric) = 177.13792295156353652470098423531
absolute error = 4.56438543062146e-15
relative error = 2.5767409680362698593052507828978e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.644
Order of pole = 1920
TOP MAIN SOLVE Loop
x[1] = 0.953
y[1] (analytic) = 178.30083162621055251291978154109
y[1] (numeric) = 178.30083162621055709191330507566
absolute error = 4.57899352353457e-15
relative error = 2.5681279676440103998043759645250e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.588
Order of pole = 1903
TOP MAIN SOLVE Loop
x[1] = 0.954
y[1] (analytic) = 179.471702833893514840188952189
y[1] (numeric) = 179.4717028338935194338491193951
absolute error = 4.59366016720610e-15
relative error = 2.5595456524183488242115100748040e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.535
Order of pole = 1887
TOP MAIN SOLVE Loop
x[1] = 0.955
y[1] (analytic) = 180.65059295995701438790473948596
y[1] (numeric) = 180.65059295995701899629038834407
absolute error = 4.60838564885811e-15
relative error = 2.5509939233244610105886772951092e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.484
Order of pole = 1872
TOP MAIN SOLVE Loop
x[1] = 0.956
y[1] (analytic) = 181.83755880052390816077240178764
y[1] (numeric) = 181.8375588005239127839426590216
absolute error = 4.62317025723396e-15
relative error = 2.5424726815132758910180348459899e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.435
Order of pole = 1858
TOP MAIN SOLVE Loop
x[1] = 0.957
y[1] (analytic) = 183.03265756556254234371963645133
y[1] (numeric) = 183.03265756556254698173391905824
absolute error = 4.63801428260691e-15
relative error = 2.5339818283223949206026082021573e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.388
Order of pole = 1843
TOP MAIN SOLVE Loop
memory used=381.4MB, alloc=4.6MB, time=15.87
x[1] = 0.958
y[1] (analytic) = 184.23594688197738725863256101274
y[1] (numeric) = 184.23594688197739191155057780162
absolute error = 4.65291801678888e-15
relative error = 2.5255212652770559388276288889316e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.343
Order of pole = 1830
TOP MAIN SOLVE Loop
x[1] = 0.959
y[1] (analytic) = 185.44748479672326181831443545647
y[1] (numeric) = 185.44748479672326648619618859569
absolute error = 4.66788175313922e-15
relative error = 2.5170908940910577819788323416221e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.3
Order of pole = 1817
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = 186.66732977994333108249068943009
y[1] (numeric) = 186.66732977994333576539647600363
absolute error = 4.68290578657354e-15
relative error = 2.5086906166676734512059527562558e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.258
Order of pole = 1804
TOP MAIN SOLVE Loop
x[1] = 0.961
y[1] (analytic) = 187.8955407281310619753406356747
y[1] (numeric) = 187.89554072813106667333104924727
absolute error = 4.69799041357257e-15
relative error = 2.5003203351005356440323565679902e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.218
Order of pole = 1792
TOP MAIN SOLVE Loop
x[1] = 0.962
y[1] (analytic) = 189.13217696731632369040690235385
y[1] (numeric) = 189.13217696731632840354283454498
absolute error = 4.71313593219113e-15
relative error = 2.4919799516745374644026121078669e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.179
Order of pole = 1781
TOP MAIN SOLVE Loop
x[1] = 0.963
y[1] (analytic) = 190.37729825627582078691385536333
y[1] (numeric) = 190.37729825627582551525649743044
absolute error = 4.72834264206711e-15
relative error = 2.4836693688666943572776812621670e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.142
Order of pole = 1770
TOP MAIN SOLVE Loop
x[1] = 0.964
y[1] (analytic) = 191.63096478976804847161265379503
y[1] (numeric) = 191.63096478976805321522349822554
absolute error = 4.74361084443051e-15
relative error = 2.4753884893469943800905312939631e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.107
Order of pole = 1759
TOP MAIN SOLVE Loop
x[1] = 0.965
y[1] (analytic) = 192.89323720179296106236043456559
y[1] (numeric) = 192.89323720179296582130127667808
absolute error = 4.75894084211249e-15
relative error = 2.4671372159792106959167615104447e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.072
Order of pole = 1749
TOP MAIN SOLVE Loop
x[1] = 0.966
y[1] (analytic) = 194.16417656887654614383260993978
y[1] (numeric) = 194.16417656887655091816554949439
absolute error = 4.77433293955461e-15
relative error = 2.4589154518217699979213974513984e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.039
Order of pole = 1739
TOP MAIN SOLVE Loop
memory used=385.2MB, alloc=4.6MB, time=16.03
x[1] = 0.967
y[1] (analytic) = 195.44384441338049845215935227419
y[1] (numeric) = 195.44384441338050324194679509217
absolute error = 4.78978744281798e-15
relative error = 2.4507231001285303378531937561186e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 6.008
Order of pole = 1729
TOP MAIN SOLVE Loop
x[1] = 0.968
y[1] (analytic) = 196.73230270683718906396982246526
y[1] (numeric) = 196.73230270683719386927448205776
absolute error = 4.80530465959250e-15
relative error = 2.4425600643495632455683127646603e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.977
Order of pole = 1720
TOP MAIN SOLVE Loop
x[1] = 0.969
y[1] (analytic) = 198.02961387331012701642118858507
y[1] (numeric) = 198.0296138733101318373060877913
absolute error = 4.82088489920623e-15
relative error = 2.4344262481319594561434041790484e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.947
Order of pole = 1711
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 199.3358407927801120483854298465
y[1] (numeric) = 199.33584079278011688491390248125
absolute error = 4.83652847263475e-15
relative error = 2.4263215553205862302912152728985e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.919
Order of pole = 1702
TOP MAIN SOLVE Loop
x[1] = 0.971
y[1] (analytic) = 200.65104680455727872916762072877
y[1] (numeric) = 200.65104680455728358140331323933
absolute error = 4.85223569251056e-15
relative error = 2.4182458899588226790342049418131e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.892
Order of pole = 1694
TOP MAIN SOLVE Loop
x[1] = 0.972
y[1] (analytic) = 201.97529571071923383003798181412
y[1] (numeric) = 201.9752957107192386980448549467
absolute error = 4.86800687313258e-15
relative error = 2.4101991562893031163255016887296e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.865
Order of pole = 1686
TOP MAIN SOLVE Loop
x[1] = 0.973
y[1] (analytic) = 203.30865177957549039558046439224
y[1] (numeric) = 203.30865177957549527942279486795
absolute error = 4.88384233047571e-15
relative error = 2.4021812587546477163299496727869e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.84
Order of pole = 1678
TOP MAIN SOLVE Loop
x[1] = 0.974
y[1] (analytic) = 204.65117974915840358649786488908
y[1] (numeric) = 204.65117974915840848624024708948
absolute error = 4.89974238220040e-15
relative error = 2.3941921019981559304266692656599e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.815
Order of pole = 1671
TOP MAIN SOLVE Loop
x[1] = 0.975
y[1] (analytic) = 206.00294483074081499317317258078
y[1] (numeric) = 206.00294483074081990888052024311
absolute error = 4.91570734766233e-15
relative error = 2.3862315908645122248483931909493e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.791
Order of pole = 1663
memory used=389.1MB, alloc=4.6MB, time=16.19
TOP MAIN SOLVE Loop
x[1] = 0.976
y[1] (analytic) = 207.36401271238061376007564729528
y[1] (numeric) = 207.3640127123806186918131952174
absolute error = 4.93173754792212e-15
relative error = 2.3782996304004643273875129110267e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.769
Order of pole = 1656
TOP MAIN SOLVE Loop
x[1] = 0.977
y[1] (analytic) = 208.73444956249242451512549521112
y[1] (numeric) = 208.7344495624924294629588009662
absolute error = 4.94783330575508e-15
relative error = 2.3703961258554793516919234908227e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.747
Order of pole = 1650
TOP MAIN SOLVE Loop
x[1] = 0.978
y[1] (analytic) = 210.11432203344663376550134510464
y[1] (numeric) = 210.11432203344663872949629076574
absolute error = 4.96399494566110e-15
relative error = 2.3625209826824257412062970205467e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.725
Order of pole = 1643
TOP MAIN SOLVE Loop
x[1] = 0.979
y[1] (analytic) = 211.50369726519596810219930898282
y[1] (numeric) = 211.5036972651959730824221028573
absolute error = 4.98022279387448e-15
relative error = 2.3546741065381846292333364353428e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.705
Order of pole = 1637
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 212.90264288892983925004143189001
y[1] (numeric) = 212.90264288892984424655861026392
absolute error = 4.99651717837391e-15
relative error = 2.3468554032842918107864688871853e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.685
Order of pole = 1631
TOP MAIN SOLVE Loop
x[1] = 0.981
y[1] (analytic) = 214.31122703075667270789590275685
y[1] (numeric) = 214.31122703075667772077433164932
absolute error = 5.01287842889247e-15
relative error = 2.3390647789875476292714853065256e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.666
Order of pole = 1625
TOP MAIN SOLVE Loop
x[1] = 0.982
y[1] (analytic) = 215.72951831541443844572354117091
y[1] (numeric) = 215.72951831541444347503041809861
absolute error = 5.02930687692770e-15
relative error = 2.3313021399206187661793432547722e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.648
Order of pole = 1619
TOP MAIN SOLVE Loop
x[1] = 0.983
y[1] (analytic) = 217.15758587000960386081775409691
y[1] (numeric) = 217.15758587000960890662060984868
absolute error = 5.04580285575177e-15
relative error = 2.3235673925626454781796343449878e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.63
Order of pole = 1614
TOP MAIN SOLVE Loop
memory used=392.9MB, alloc=4.6MB, time=16.35
x[1] = 0.984
y[1] (analytic) = 218.59549932778473094537227039684
y[1] (numeric) = 218.59549932778473600773897081845
absolute error = 5.06236670042161e-15
relative error = 2.3158604435997893423579255713319e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.613
Order of pole = 1608
TOP MAIN SOLVE Loop
x[1] = 0.985
y[1] (analytic) = 220.04332883191494138140735425999
y[1] (numeric) = 220.0433288319149464604061020492
absolute error = 5.07899874778921e-15
relative error = 2.3081811999258190294506260745227e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.596
Order of pole = 1603
TOP MAIN SOLVE Loop
x[1] = 0.986
y[1] (analytic) = 221.50114503933347505722667030418
y[1] (numeric) = 221.50114503933348015292600681611
absolute error = 5.09569933651193e-15
relative error = 2.3005295686426595112787408888106e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.58
Order of pole = 1598
TOP MAIN SOLVE Loop
x[1] = 0.987
y[1] (analytic) = 222.96901912458656929208028432495
y[1] (numeric) = 222.9690191245865744045490913878
absolute error = 5.11246880706285e-15
relative error = 2.2929054570609191916195800103569e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.565
Order of pole = 1594
TOP MAIN SOLVE Loop
x[1] = 0.988
y[1] (analytic) = 224.44702278371788786269216594266
y[1] (numeric) = 224.4470227837178929919996676839
absolute error = 5.12930750174124e-15
relative error = 2.2853087727004309976772022376952e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.55
Order of pole = 1589
TOP MAIN SOLVE Loop
x[1] = 0.989
y[1] (analytic) = 225.93522823818273074689172270829
y[1] (numeric) = 225.93522823818273589310748739134
absolute error = 5.14621576468305e-15
relative error = 2.2777394232907619179721544833864e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.535
Order of pole = 1584
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 227.43370823879225733588803628182
y[1] (numeric) = 227.43370823879226249908197815329
absolute error = 5.16319394187147e-15
relative error = 2.2701973167717137959611791151103e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.522
Order of pole = 1580
TOP MAIN SOLVE Loop
x[1] = 0.991
y[1] (analytic) = 228.94253606968795771786328183024
y[1] (numeric) = 228.94253606968796289810566297783
absolute error = 5.18024238114759e-15
relative error = 2.2626823612938282787135748550013e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.508
Order of pole = 1576
TOP MAIN SOLVE Loop
x[1] = 0.992
y[1] (analytic) = 230.46178555234660850165998695391
y[1] (numeric) = 230.46178555234661369902141917499
absolute error = 5.19736143222108e-15
relative error = 2.2551944652188604094368515336364e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.495
Order of pole = 1572
TOP MAIN SOLVE Loop
memory used=396.7MB, alloc=4.6MB, time=16.51
x[1] = 0.993
y[1] (analytic) = 231.99153104961595153051803324988
y[1] (numeric) = 231.99153104961595674506947993079
absolute error = 5.21455144668091e-15
relative error = 2.2477335371202303146519723438382e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.483
Order of pole = 1568
TOP MAIN SOLVE Loop
x[1] = 0.994
y[1] (analytic) = 233.53184746978133573220534945161
y[1] (numeric) = 233.53184746978134096401812745785
absolute error = 5.23181277800624e-15
relative error = 2.2402994857835090694437505155677e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.471
Order of pole = 1564
TOP MAIN SOLVE Loop
x[1] = 0.995
y[1] (analytic) = 235.0828102706635642636058463175
y[1] (numeric) = 235.08281027066356951275162789476
absolute error = 5.24914578157726e-15
relative error = 2.2328922202068429974200989586880e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.459
Order of pole = 1560
TOP MAIN SOLVE Loop
x[1] = 0.996
y[1] (analytic) = 236.64449546374819103500509409106
y[1] (numeric) = 236.64449546374819630155590877725
absolute error = 5.26655081468619e-15
relative error = 2.2255116496014073700299566081159e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.448
Order of pole = 1557
TOP MAIN SOLVE Loop
x[1] = 0.997
y[1] (analytic) = 238.21697961834651264207538382811
y[1] (numeric) = 238.21697961834651792610362037635
absolute error = 5.28402823654824e-15
relative error = 2.2181576833918036211199431571015e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.437
Order of pole = 1553
TOP MAIN SOLVE Loop
x[1] = 0.998
y[1] (analytic) = 239.80033986578850369203503978781
y[1] (numeric) = 239.80033986578850899361344810056
absolute error = 5.30157840831275e-15
relative error = 2.2108302312164938273834381579292e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.427
Order of pole = 1550
TOP MAIN SOLVE Loop
x[1] = 0.999
y[1] (analytic) = 241.39465390364794548477112111843
y[1] (numeric) = 241.39465390364795080397281419276
absolute error = 5.31920169307433e-15
relative error = 2.2035292029281956090313265274360e-15 %
Correct digits = 16
h = 0.001
Real estimate of pole used for equation 1
Radius of convergence = 5.417
Order of pole = 1547
Finished!
diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ;
Iterations = 900
Total Elapsed Time = 16 Seconds
Elapsed Time(since restart) = 16 Seconds
Time to Timeout = 2 Minutes 43 Seconds
Percent Done = 100.1 %
> quit
memory used=399.7MB, alloc=4.6MB, time=16.63