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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> display_poles := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ;
> local rad_given;
> if (glob_type_given_pole = 4) then # if number 1
> rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 2;
> if (array_poles[1,1] <> glob_large_float) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 2;
> if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 2;
> if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 2
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_large_float, array_pole,
glob_type_given_pole, array_given_rad_poles, array_given_ord_poles,
array_complex_poles, array_poles, array_real_poles, array_x;
if glob_type_given_pole = 4 then
rad_given := sqrt(
expt(array_x[1] - array_given_rad_poles[1, 1], 2.0)
+ expt(array_given_rad_poles[1, 2], 2.0));
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ")
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_poles[1, 1], 4, " ");
omniout_str(ALWAYS, "Order of pole (ratio test) \
Not computed")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if 0. < array_real_poles[1, 1] and
array_real_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_real_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_real_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if 0. < array_complex_poles[1, 1] and
array_complex_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_complex_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
> # End Function number 3
> # Begin Function number 4
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 2
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 2;
> 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 4
> # Begin Function number 5
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 2
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> if (min_size < 1.0) then # if number 2
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 5
> # Begin Function number 6
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := 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,"");
> est_tmp := 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 (est_tmp >= max_estimated_step_error) then # if number 2
> max_estimated_step_error := est_tmp;
> fi;# end if 2;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
max_estimated_step_error := 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, "");
est_tmp := 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_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
> # End Function number 6
> # Begin Function number 7
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2
> ret := true;
> else
> ret := false;
> fi;# end if 2;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 7
> # Begin Function number 8
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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 2
> if (iter >= 0) then # if number 3
> 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 4
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 5
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 5;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 4;
> if (glob_iter = 1) then # if number 4
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 4;
> 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 3;
> #BOTTOM DISPLAY ALOT
> fi;# end if 2;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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)) + 3
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 8
> # Begin Function number 9
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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 2
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 3
> glob_normmax := tmp;
> fi;# end if 3
> fi;# end if 2;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 3
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 3
> fi;# end if 2;
> if ( not glob_reached_optimal_h) then # if number 2
> 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 2;
> 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, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 9
> # Begin Function number 10
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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 2
> 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 2;
> 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, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 10
> # Begin Function number 11
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad;
> #TOP CHECK FOR POLE
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> #TOP radius ratio test in Henrici1
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3
> if (tmp_rad < rad_c) then # if number 4
> rad_c := tmp_rad;
> fi;# end if 4;
> elif
> (cnt = 0) then # if number 4
> if (tmp_rad < rad_c) then # if number 5
> rad_c := tmp_rad;
> fi;# end if 5;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5
> fi;# end if 4;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 4
> if (rad_c < array_pole[1]) then # if number 5
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 5;
> fi;# end if 4;
> #BOTTOM radius ratio test in Henrici1
> #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]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 4
> 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) > 0.0) then # if number 5
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[1,1] := rcs;
> array_real_poles[1,2] := ord_no;
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 5
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 4;
> #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 1
> if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 4;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 4
> 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) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6
> 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) <> 0.0) then # if number 7
> if (rcs > 0.0) then # if number 8
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 8
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> fi;# end if 5;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 4;
> #BOTTOM RADII COMPLEX EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> 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 1;
> glob_h := h_new;
> fi;# end if 4;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 4
> display_poles();
> fi;# end if 4
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test,
tmp_rad, tmp_ratio, prev_tmp_rad;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_y_higher[1, n]) = 0. or
omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[1, 1] := rad_c
end if
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or
omniabs(array_y_higher[1, m - 1]) = 0. or
omniabs(array_y_higher[1, m - 2]) = 0.) 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 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[1, 1] := rcs;
array_real_poles[1, 2] := ord_no
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y_higher[1, n]) <> 0. 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
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) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. 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 omniabs(rcs) <> 0. 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_poles[1, 1] := rad_c;
array_complex_poles[1, 2] := ord_no
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_poles() end if
end proc
> # End Function number 11
> # Begin Function number 12
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 4
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 1;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 5;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 4;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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 12
> # Begin Function number 13
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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_3D0[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> array_tmp4_g[1] := sin(array_tmp3[1]);
> array_tmp4[1] := cos(array_tmp3[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0;
> #emit pre cos FULL $eq_no = 1
> array_tmp4_g[2] := (att(1,array_tmp4,array_tmp3,1));
> array_tmp4[2] := (-att(1,array_tmp4_g,array_tmp3,1));
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0.0;
> array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre cos FULL $eq_no = 1
> array_tmp4_g[3] := (att(2,array_tmp4,array_tmp3,1));
> array_tmp4[3] := (-att(2,array_tmp4_g,array_tmp3,1));
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0.0;
> array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre cos FULL $eq_no = 1
> array_tmp4_g[4] := (att(3,array_tmp4,array_tmp3,1));
> array_tmp4[4] := (-att(3,array_tmp4_g,array_tmp3,1));
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0.0;
> array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre cos FULL $eq_no = 1
> array_tmp4_g[5] := (att(4,array_tmp4,array_tmp3,1));
> array_tmp4[5] := (-att(4,array_tmp4_g,array_tmp3,1));
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0.0;
> array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0;
> #emit cos FULL $eq_no = 1
> array_tmp4[kkk] := -att(kkk-1,array_tmp4_g,array_tmp3,1);
> array_tmp4_g[kkk] := att(kkk-1,array_tmp4,array_tmp3,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> 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 1
> 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, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2,
glob_last;
array_tmp1[1] := array_const_2D0[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4_g[1] := sin(array_tmp3[1]);
array_tmp4[1] := cos(array_tmp3[1]);
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_2D0[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0);
array_tmp4_g[2] := att(1, array_tmp4, array_tmp3, 1);
array_tmp4[2] := -att(1, array_tmp4_g, array_tmp3, 1);
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp3[3] := 0.;
array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4_g[3] := att(2, array_tmp4, array_tmp3, 1);
array_tmp4[3] := -att(2, array_tmp4_g, array_tmp3, 1);
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp3[4] := 0.;
array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4_g[4] := att(3, array_tmp4, array_tmp3, 1);
array_tmp4[4] := -att(3, array_tmp4_g, array_tmp3, 1);
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp3[5] := 0.;
array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4_g[5] := att(4, array_tmp4, array_tmp3, 1);
array_tmp4[5] := -att(4, array_tmp4_g, array_tmp3, 1);
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp3[kkk] := 0.;
array_tmp3[kkk] :=
-ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0);
array_tmp4[kkk] := -att(kkk - 1, array_tmp4_g, array_tmp3, 1);
array_tmp4_g[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1);
array_tmp5[kkk] := array_tmp4[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp5[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 13
> #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
", 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
", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s
", 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
", prelabel, value, postlabel)
else printf("%-30s = %-32d %s
", 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, " |
")
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 Mi\
nutes %d Seconds
", years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\
Seconds
", days_int, hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\
s
", hours_int, minutes_int, sec_int)
elif 0 < minutes_int then printf(" = %d Minutes %d Seconds
", minutes_int, sec_int)
else printf(" = %d Seconds
", sec_int)
end if
else printf(" Unknown
")
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,m,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_int(ALWAYS,"m",4, m ,4," ");
> 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, m, 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_int(ALWAYS, "m", 4, m, 4, " ");
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
> 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 16
> # Begin Function number 17
> 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 17
> # Begin Function number 18
> 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 18
> # Begin Function number 19
> 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 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> 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 21
> # Begin Function number 22
> 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");
> elif
> (pole = 4) then # if number 9
> fprintf(file,"Yes");
> else
> fprintf(file,"No");
> fi;# end if 9
> 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")
elif pole = 4 then fprintf(file, "Yes")
else fprintf(file, "No")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file)
fprintf(file, "
")
end proc
> # End Function number 24
> # Begin Function number 25
> 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 9
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 9;
> if (glob_max_iter < 2) then # if number 9
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 9;
> if (errflag) then # if number 9
> quit;
> fi;# end if 9
> 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 25
> # Begin Function number 26
> 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 9
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 10
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 10
> fi;# end if 9;
> 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 26
> # Begin Function number 27
> 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 9
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 9;
> 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 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 9
> if (array_fact_1[nnn] = 0) then # if number 10
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 10;
> else
> ret := factorial_2(nnn);
> fi;# end if 9;
> 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 29
> # Begin Function number 30
> 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 9
> if (array_fact_2[mmm,nnn] = 0) then # if number 10
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 10;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 9;
> 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 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> 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 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0)));
> end;
exact_soln_y := proc(x)
return
cos(sqrt(2.0*x + 3.0)) + sqrt(2.0*x + 3.0)*sin(sqrt(2.0*x + 3.0))
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,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> 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_min_h,
> glob_type_given_pole,
> 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_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> 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;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_estimated_step_error := 0.0;
> glob_ratio_of_radius := 0.1;
> 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_min_h := 0.000001;
> glob_type_given_pole := 0;
> 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 := 0.0;
> glob_smallish_float := 0.0;
> 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/cos_sqrt_linpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));");
> 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 := -1.0;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> 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,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"glob_max_minutes := 10;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=10;");
> omniout_str(ALWAYS,"glob_display_interval:=0.01;");
> 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(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0)));");
> 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 := 0.0;
> glob_smallish_float := 0.0;
> 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..(4 + 1),[]);
> array_real_pole:= Array(0..(4 + 1),[]);
> array_complex_pole:= Array(0..(4 + 1),[]);
> array_1st_rel_error:= Array(0..(2 + 1),[]);
> array_last_rel_error:= Array(0..(2 + 1),[]);
> array_type_pole:= Array(0..(2 + 1),[]);
> array_type_real_pole:= Array(0..(2 + 1),[]);
> array_type_complex_pole:= Array(0..(2 + 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_g:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> 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 1
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_2D0[1] := 2.0;
> array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_3D0[1] := 3.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := -1.0;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> glob_display_interval := 0.1;
> glob_max_minutes := 10;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> 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);
> found_h := false;
> glob_h := glob_min_h;
> if (glob_max_h < glob_h) then # if number 4
> glob_h := glob_max_h;
> fi;# end if 4;
> if (glob_display_interval < glob_h) then # if number 4
> glob_h := glob_display_interval;
> fi;# end if 4;
> best_h := glob_h;
> min_value := glob_large_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> 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,"");
> estimated_step_error := 0.0;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> 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 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
> ;
> atomall();
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4
> found_h := true;
> glob_h := glob_max_h;
> best_h := glob_h;
> elif
> ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5
> glob_h := glob_h/2.0;
> best_h := glob_h;
> found_h := true;
> else
> glob_h := glob_h*2.0;
> best_h := glob_h;
> fi;# end if 5;
> omniout_float(ALWAYS,"best_h",32,best_h,32,"");
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 5
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 5;
> if (opt_iter > 100) then # if number 5
> glob_h := glob_max_h;
> found_h := false;
> fi;# end if 5;
> if (glob_display_interval < glob_h) then # if number 5
> glob_h := glob_display_interval;
> fi;# end if 5;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 5
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 5;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 5
> 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 1
> 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 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> 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 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> 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 1
> #left paren 0001C
> if (reached_interval()) then # if number 6
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 6;
> 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 6
> #left paren 0004C
> check_for_pole();
> fi;# end if 6;#was right paren 0004C
> if (reached_interval()) then # if number 6
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 6;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_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 2
> 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 2;
> #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 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> 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 2
> 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 2;
> #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 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> 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 2
> 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 2;
> #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 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> 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 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 6
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 6;
> if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 6;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 6
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-05-26T00:14:26-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"cos_sqrt_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));")
> ;
> 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_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 7
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 7;
> log_revs(html_log_file," 189 | ")
> ;
> logitem_str(html_log_file,"cos_sqrt_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"cos_sqrt_lin maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
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_min_h, glob_type_given_pole, 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_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1,
array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_poles, array_given_rad_poles,
array_given_ord_poles, array_real_poles, array_complex_poles, 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;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_estimated_step_error := 0.;
glob_ratio_of_radius := 0.1;
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_min_h := 0.1*10^(-5);
glob_type_given_pole := 0;
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.;
glob_smallish_float := 0.;
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/cos_sqrt_linpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));");
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 := -1.0;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
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, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "glob_max_minutes := 10;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=10;");
omniout_str(ALWAYS, "glob_display_interval:=0.01;");
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(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(\
sqrt(2.0*x+3.0)));");
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.;
glob_smallish_float := 0.;
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 .. 5, []);
array_real_pole := Array(0 .. 5, []);
array_complex_pole := Array(0 .. 5, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
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_g := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_real_poles := Array(0 .. 3, 0 .. 4, []);
array_complex_poles := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_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 <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do
array_type_complex_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_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_poles[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_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_g[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_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_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 := -1.0;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
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);
found_h := false;
glob_h := glob_min_h;
if glob_max_h < glob_h then glob_h := glob_max_h end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
best_h := glob_h;
min_value := glob_large_float;
est_answer := est_size_answer();
opt_iter := 1;
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, "");
estimated_step_error := 0.;
while opt_iter <= 100 and not found_h 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();
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if est_needed_step_err < estimated_step_error and opt_iter = 1 or
glob_max_h <= glob_h then
found_h := true; glob_h := glob_max_h; best_h := glob_h
elif est_needed_step_err < estimated_step_error and not found_h
then glob_h := glob_h/2.0; best_h := glob_h; found_h := true
else glob_h := glob_h*2.0; best_h := glob_h
end if;
omniout_float(ALWAYS, "best_h", 32, best_h, 32, "");
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if;
if glob_display_interval < glob_h then glob_h := glob_display_interval
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := x_start;
array_x[2] := glob_h;
glob_next_display := x_start;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1);
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := 0;
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_current_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) <
convfloat(glob_max_sec) do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
glob_current_iter := glob_current_iter + 1;
atomall();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := glob_max_terms;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := glob_max_terms;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if convfloat(glob_max_sec) <=
elapsed_time_seconds() - convfloat(glob_orig_start_sec) then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));");
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, "2013-05-26T00:14:26-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"cos_sqrt_lin");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));");
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_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, " 189 | ");
logitem_str(html_log_file, "cos_sqrt_lin diffeq.mxt");
logitem_str(html_log_file, "cos_sqrt_lin 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 13
> main();
##############ECHO OF PROBLEM#################
##############temp/cos_sqrt_linpostode.ode#################
diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -1.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_display_interval := 0.1;
glob_max_minutes := 10;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
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(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0)));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 6
estimated_steps = 6000000
step_error = 1.6666666666666666666666666666667e-17
est_needed_step_err = 1.6666666666666666666666666666667e-17
opt_iter = 1
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.6153837606897130647130647130647e-185
estimated_step_error = 4.6153837606897130647130647130647e-185
best_h = 2.0e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.0153834900287545787545787545788e-176
estimated_step_error = 1.0153834900287545787545787545788e-176
best_h = 4.00e-06
opt_iter = 3
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.4461430199840252340252340252340e-169
estimated_step_error = 3.4461430199840252340252340252340e-169
best_h = 8.000e-06
opt_iter = 4
bytes used=4000484, alloc=3014104, time=0.29
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.9229686626617826617826617826617e-162
estimated_step_error = 4.9229686626617826617826617826617e-162
best_h = 1.60000e-05
opt_iter = 5
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.9938655263142043142043142043143e-153
estimated_step_error = 1.9938655263142043142043142043143e-153
best_h = 3.200000e-05
opt_iter = 6
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.4763760593813593813593813593814e-146
estimated_step_error = 1.4763760593813593813593813593814e-146
best_h = 6.4000000e-05
opt_iter = 7
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.9270197737077737077737077737077e-139
estimated_step_error = 3.9270197737077737077737077737077e-139
best_h = 0.000128
opt_iter = 8
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.1198997955229955229955229955230e-130
estimated_step_error = 5.1198997955229955229955229955230e-130
best_h = 0.000256
opt_iter = 9
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.0318459242328042328042328042328e-121
estimated_step_error = 1.0318459242328042328042328042328e-121
best_h = 0.000512
opt_iter = 10
bytes used=8001516, alloc=3996964, time=0.58
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.4985120872608872608872608872609e-114
estimated_step_error = 1.4985120872608872608872608872609e-114
best_h = 0.001024
opt_iter = 11
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.4883035115995115995115995115995e-107
estimated_step_error = 5.4883035115995115995115995115995e-107
best_h = 0.002048
opt_iter = 12
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 9.2254226129426129426129426129426e-100
estimated_step_error = 9.2254226129426129426129426129426e-100
best_h = 0.004096
opt_iter = 13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.5368150948310948310948310948311e-91
estimated_step_error = 1.5368150948310948310948310948311e-91
best_h = 0.008192
opt_iter = 14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.7703578412698412698412698412699e-82
estimated_step_error = 1.7703578412698412698412698412699e-82
best_h = 0.016384
opt_iter = 15
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.0633558323158323158323158323159e-75
estimated_step_error = 2.0633558323158323158323158323159e-75
best_h = 0.032768
opt_iter = 16
bytes used=12002224, alloc=4193536, time=0.89
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.1276361090761090761090761090761e-67
estimated_step_error = 2.1276361090761090761090761090761e-67
best_h = 0.065536
opt_iter = 17
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.7033032153032153032153032153020e-61
estimated_step_error = 6.7033032153032153032153032153020e-61
best_h = 0.131072
opt_iter = 18
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.6997023361823361823361823361823e-52
estimated_step_error = 6.6997023361823361823361823361823e-52
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -1
y[1] (analytic) = 1.3817732906760362240534389290733
y[1] (numeric) = 1.3817732906760362240534389290733
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02121
Order of pole (three term test) = -30.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (analytic) = 1.3871342903544166154371007094768
y[1] (numeric) = 1.3871342903544166154371007094768
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.006395
Order of pole (three term test) = -6.024
Radius of convergence (six term test) for eq 1 = 0.1155
Order of pole (six term test) = -11.4
TOP MAIN SOLVE Loop
x[1] = -0.98
y[1] (analytic) = 1.3924114437413490976852412826912
y[1] (numeric) = 1.3924114437413490976852412826912
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=16003156, alloc=4259060, time=1.21
x[1] = -0.97
y[1] (analytic) = 1.3976050510761118950933993659855
y[1] (numeric) = 1.3976050510761118950933993659855
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.001765
Order of pole (three term test) = -24.79
Radius of convergence (six term test) for eq 1 = 0.06964
Order of pole (six term test) = -11.22
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (analytic) = 1.4027154119794318390745075888768
y[1] (numeric) = 1.4027154119794318390745075888768
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.009669
Order of pole (three term test) = -27.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (analytic) = 1.407742825454382501814219222154
y[1] (numeric) = 1.4077428254543825018142192221541
absolute error = 1e-31
relative error = 7.1035702112509520306728117515007e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02477
Order of pole (three term test) = -96.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.94
y[1] (analytic) = 1.4126875898872813216838642202808
y[1] (numeric) = 1.4126875898872813216838642202808
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.004197
Order of pole (three term test) = -25.31
Radius of convergence (six term test) for eq 1 = 0.1493
Order of pole (six term test) = -12.43
TOP MAIN SOLVE Loop
x[1] = -0.93
y[1] (analytic) = 1.4175500030485857213341443069425
y[1] (numeric) = 1.4175500030485857213341443069425
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.001429
Order of pole (three term test) = 0.1818
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=20004064, alloc=4324584, time=1.52
x[1] = -0.92
y[1] (analytic) = 1.4223303620937882193919630535745
y[1] (numeric) = 1.4223303620937882193919630535745
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.009884
Order of pole (three term test) = -23.69
Radius of convergence (six term test) for eq 1 = 0.1486
Order of pole (six term test) = -10.74
TOP MAIN SOLVE Loop
x[1] = -0.91
y[1] (analytic) = 1.4270289635643105366820735985177
y[1] (numeric) = 1.4270289635643105366820735985176
absolute error = 1e-31
relative error = 7.0075662480058272858983638901397e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01149
Order of pole (three term test) = -19.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (analytic) = 1.4316461033883966978945138297226
y[1] (numeric) = 1.4316461033883966978945138297225
absolute error = 1e-31
relative error = 6.9849664496918356757024087441620e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (analytic) = 1.4361820768820051296180865063764
y[1] (numeric) = 1.4361820768820051296180865063763
absolute error = 1e-31
relative error = 6.9629054428184366801611892091008e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.88
y[1] (analytic) = 1.4406371787496997556594299241749
y[1] (numeric) = 1.4406371787496997556594299241748
absolute error = 1e-31
relative error = 6.9413729893315680944873940506986e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01515
Order of pole (three term test) = -9.356
Radius of convergence (six term test) for eq 1 = 0.03444
Order of pole (six term test) = -11.64
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (analytic) = 1.4450117030855400905665133349323
y[1] (numeric) = 1.4450117030855400905665133349322
absolute error = 1e-31
relative error = 6.9203591767782602168071063399857e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01071
Order of pole (three term test) = -24.38
Radius of convergence (six term test) for eq 1 = 0.1019
Order of pole (six term test) = -11.84
TOP MAIN SOLVE Loop
bytes used=24005104, alloc=4390108, time=1.85
x[1] = -0.86
y[1] (analytic) = 1.4493059433739703322746804135193
y[1] (numeric) = 1.4493059433739703322746804135192
absolute error = 1e-31
relative error = 6.8998544066686816552239827845285e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03455
Order of pole (three term test) = -40.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (analytic) = 1.453520192490707454792653623479
y[1] (numeric) = 1.453520192490707454792653623479
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.07296
Order of pole (six term test) = -11.27
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (analytic) = 1.4576547427036283018452023667972
y[1] (numeric) = 1.4576547427036283018452023667971
absolute error = 1e-31
relative error = 6.8603351033950631233284877114839e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.008074
Order of pole (three term test) = -34.03
Radius of convergence (six term test) for eq 1 = 0.1025
Order of pole (six term test) = -11
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (analytic) = 1.4617098856736556823884683129225
y[1] (numeric) = 1.4617098856736556823884683129224
absolute error = 1e-31
relative error = 6.8413028453941922020044391495495e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.001616
Order of pole (three term test) = -0.7587
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (analytic) = 1.4656859124556434689132322869684
y[1] (numeric) = 1.4656859124556434689132322869683
absolute error = 1e-31
relative error = 6.8227441602722188021590727741427e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=28005888, alloc=4390108, time=2.16
x[1] = -0.81
y[1] (analytic) = 1.469583113499260699450698556785
y[1] (numeric) = 1.4695831134992606994506985567849
absolute error = 1e-31
relative error = 6.8046508619636712245877710142776e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04456
Order of pole (three term test) = -26.43
Radius of convergence (six term test) for eq 1 = 0.1658
Order of pole (six term test) = -11.26
TOP MAIN SOLVE Loop
x[1] = -0.8
y[1] (analytic) = 1.4734017786498746841946642930075
y[1] (numeric) = 1.4734017786498746841946642930074
absolute error = 1e-31
relative error = 6.7870150185126834821965486944088e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1161
Order of pole (three term test) = -49.26
Radius of convergence (six term test) for eq 1 = 0.2445
Order of pole (six term test) = -12.18
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (analytic) = 1.4771421971494331176532343849659
y[1] (numeric) = 1.4771421971494331176532343849658
absolute error = 1e-31
relative error = 6.7698289435491384550747825882669e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0378
Order of pole (three term test) = -17.02
Radius of convergence (six term test) for eq 1 = 0.05663
Order of pole (six term test) = -11.75
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (analytic) = 1.4808046576373451972425346782169
y[1] (numeric) = 1.4808046576373451972425346782168
absolute error = 1e-31
relative error = 6.7530851881268452742161091100908e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.008522
Order of pole (three term test) = 12.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (analytic) = 1.4843894481513617492341700561392
y[1] (numeric) = 1.4843894481513617492341700561391
absolute error = 1e-31
relative error = 6.7367765329064166991973775982937e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (analytic) = 1.4878968561284543629674676182464
y[1] (numeric) = 1.4878968561284543629674676182463
absolute error = 1e-31
relative error = 6.7208959806664660283635114722191e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=32007080, alloc=4390108, time=2.49
x[1] = -0.75
y[1] (analytic) = 1.4913271684056935342368395113354
y[1] (numeric) = 1.4913271684056935342368395113353
absolute error = 1e-31
relative error = 6.7054367491276385482201746742027e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07084
Order of pole (three term test) = -66.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.74
y[1] (analytic) = 1.4946806712211258187638947460211
y[1] (numeric) = 1.494680671221125818763894746021
absolute error = 1e-31
relative error = 6.6903922640748336356554281685461e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1034
Order of pole (three term test) = -63.1
Radius of convergence (six term test) for eq 1 = 0.1968
Order of pole (six term test) = -11.48
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (analytic) = 1.497957650214649996663224580334
y[1] (numeric) = 1.4979576502146499966632245803339
absolute error = 1e-31
relative error = 6.6757561527637640250275146899207e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0005345
Order of pole (three term test) = -0.9465
Radius of convergence (six term test) for eq 1 = 0.06329
Order of pole (six term test) = -11.7
TOP MAIN SOLVE Loop
x[1] = -0.72
y[1] (analytic) = 1.5011583904288922488100817735946
y[1] (numeric) = 1.5011583904288922488100817735944
absolute error = 2e-31
relative error = 1.3323044475197483653963933475108e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (analytic) = 1.5042831763100803460174702074492
y[1] (numeric) = 1.504283176310080346017470207449
absolute error = 2e-31
relative error = 1.3295369060138559550972647314177e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=36008024, alloc=4455632, time=2.81
x[1] = -0.7
y[1] (analytic) = 1.5073322917089168519294580364768
y[1] (numeric) = 1.5073322917089168519294580364766
absolute error = 2e-31
relative error = 1.3268474449867507590662687489916e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1321
Order of pole (six term test) = -11.5
TOP MAIN SOLVE Loop
x[1] = -0.69
y[1] (analytic) = 1.5103060198814513405368246678763
y[1] (numeric) = 1.5103060198814513405368246678761
absolute error = 2e-31
relative error = 1.3242349389277984052690132006589e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1362
Order of pole (six term test) = -11.49
TOP MAIN SOLVE Loop
x[1] = -0.68
y[1] (analytic) = 1.513204643489951629220449478141
y[1] (numeric) = 1.5132046434899516292204494781408
absolute error = 2e-31
relative error = 1.3216982967930476843959519303217e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3942
Order of pole (six term test) = -12
TOP MAIN SOLVE Loop
x[1] = -0.67
y[1] (analytic) = 1.5160284446037740282271482540418
y[1] (numeric) = 1.5160284446037740282271482540417
absolute error = 1e-31
relative error = 6.5961823048864882899638059749342e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.0937
Order of pole (six term test) = -12.18
TOP MAIN SOLVE Loop
x[1] = -0.66
y[1] (analytic) = 1.5187777047002326074819618953976
y[1] (numeric) = 1.5187777047002326074819618953975
absolute error = 1e-31
relative error = 6.5842420316367108282850429113757e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01629
Order of pole (three term test) = -4.658
Radius of convergence (six term test) for eq 1 = 0.142
Order of pole (six term test) = -9.57
TOP MAIN SOLVE Loop
x[1] = -0.65
y[1] (analytic) = 1.5214527046654674816402009377242
y[1] (numeric) = 1.5214527046654674816402009377241
absolute error = 1e-31
relative error = 6.5726656959729618461001693380651e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.007494
Order of pole (three term test) = -7.979
Radius of convergence (six term test) for eq 1 = 0.06819
Order of pole (six term test) = -12.03
TOP MAIN SOLVE Loop
bytes used=40008980, alloc=4455632, time=3.14
x[1] = -0.64
y[1] (analytic) = 1.5240537247953121142818489436586
y[1] (numeric) = 1.5240537247953121142818489436585
absolute error = 1e-31
relative error = 6.5614484826268503212755576548993e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1475
Order of pole (six term test) = -12
TOP MAIN SOLVE Loop
x[1] = -0.63
y[1] (analytic) = 1.5265810447961596421502277727575
y[1] (numeric) = 1.5265810447961596421502277727574
absolute error = 1e-31
relative error = 6.5505857249362569795936489216569e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02004
Order of pole (three term test) = -46.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.62
y[1] (analytic) = 1.5290349437858282203361281696052
y[1] (numeric) = 1.5290349437858282203361281696051
absolute error = 1e-31
relative error = 6.5400729006496133107757072332159e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2073
Order of pole (six term test) = -11.31
TOP MAIN SOLVE Loop
x[1] = -0.61
y[1] (analytic) = 1.5314157002944253893079100098493
y[1] (numeric) = 1.5314157002944253893079100098492
absolute error = 1e-31
relative error = 6.5299056278954368780227167839947e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3824
Order of pole (three term test) = -91.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.6
y[1] (analytic) = 1.5337235922652114646873779125413
y[1] (numeric) = 1.5337235922652114646873779125412
absolute error = 1e-31
relative error = 6.5200796613101848427102652096127e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04402
Order of pole (three term test) = -21
Radius of convergence (six term test) for eq 1 = 0.1877
Order of pole (six term test) = -11.24
TOP MAIN SOLVE Loop
bytes used=44010524, alloc=4455632, time=3.47
x[1] = -0.59
y[1] (analytic) = 1.5359588970554619506705397647102
y[1] (numeric) = 1.5359588970554619506705397647101
absolute error = 1e-31
relative error = 6.5105908883178336310102773828795e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06107
Order of pole (three term test) = -52.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.58
y[1] (analytic) = 1.53812189143732897799165801017
y[1] (numeric) = 1.5381218914373289779916580101698
absolute error = 2e-31
relative error = 1.3002870651109839686426001890200e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01388
Order of pole (three term test) = -28.05
Radius of convergence (six term test) for eq 1 = 0.1427
Order of pole (six term test) = -11.05
TOP MAIN SOLVE Loop
x[1] = -0.57
y[1] (analytic) = 1.5402128515987017673283063288728
y[1] (numeric) = 1.5402128515987017673283063288726
absolute error = 2e-31
relative error = 1.2985218230870173992616740967599e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02715
Order of pole (three term test) = -23.12
Radius of convergence (six term test) for eq 1 = 0.1476
Order of pole (six term test) = -11.16
TOP MAIN SOLVE Loop
x[1] = -0.56
y[1] (analytic) = 1.5422320531440661190444475753984
y[1] (numeric) = 1.5422320531440661190444475753983
absolute error = 1e-31
relative error = 6.4841085228474755670574423365626e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04803
Order of pole (three term test) = -44.24
Radius of convergence (six term test) for eq 1 = 0.04255
Order of pole (six term test) = -11.62
TOP MAIN SOLVE Loop
x[1] = -0.55
y[1] (analytic) = 1.5441797710953629301678525551331
y[1] (numeric) = 1.5441797710953629301678525551329
absolute error = 2e-31
relative error = 1.2951859863967142134158088987469e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03022
Order of pole (three term test) = 3.593
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.54
y[1] (analytic) = 1.5460562798928457394974833940672
y[1] (numeric) = 1.5460562798928457394974833940671
absolute error = 1e-31
relative error = 6.4680698432873874688029393575103e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1031
Order of pole (three term test) = -64.33
Radius of convergence (six term test) for eq 1 = 0.2158
Order of pole (six term test) = -11.13
TOP MAIN SOLVE Loop
bytes used=48011676, alloc=4455632, time=3.79
x[1] = -0.53
y[1] (analytic) = 1.5478618533959373017357699026535
y[1] (numeric) = 1.5478618533959373017357699026535
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.001055
Order of pole (three term test) = -26.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.52
y[1] (analytic) = 1.5495967648840851915400124455322
y[1] (numeric) = 1.5495967648840851915400124455321
absolute error = 1e-31
relative error = 6.4532917379625738156096059866483e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.51
y[1] (analytic) = 1.5512612870576164383864504068832
y[1] (numeric) = 1.5512612870576164383864504068831
absolute error = 1e-31
relative error = 6.4463672776671202244279704799838e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1422
Order of pole (three term test) = -76.97
Radius of convergence (six term test) for eq 1 = 0.4931
Order of pole (six term test) = -13.44
TOP MAIN SOLVE Loop
x[1] = -0.5
y[1] (analytic) = 1.5528556920385911931398413854228
y[1] (numeric) = 1.5528556920385911931398413854227
absolute error = 1e-31
relative error = 6.4397484268947010593729509663601e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.49
y[1] (analytic) = 1.5543802513716554272207027633469
y[1] (numeric) = 1.5543802513716554272207027633469
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0111
Order of pole (three term test) = -26.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=52012720, alloc=4521156, time=4.11
x[1] = -0.48
y[1] (analytic) = 1.5558352360248926652616742695672
y[1] (numeric) = 1.5558352360248926652616742695671
absolute error = 1e-31
relative error = 6.4274158139969035189305761624579e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.47
y[1] (analytic) = 1.5572209163906747521437675991053
y[1] (numeric) = 1.5572209163906747521437675991053
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.46
y[1] (analytic) = 1.5585375622865116553025770572386
y[1] (numeric) = 1.5585375622865116553025770572385
absolute error = 1e-31
relative error = 6.4162714085178163052030200810629e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05655
Order of pole (three term test) = -49.04
Radius of convergence (six term test) for eq 1 = 0.1377
Order of pole (six term test) = -11.8
TOP MAIN SOLVE Loop
x[1] = -0.45
y[1] (analytic) = 1.559785442955900303193833568637
y[1] (numeric) = 1.5597854429559003031938335686369
absolute error = 1e-31
relative error = 6.4111381761899987482781103038629e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.44
y[1] (analytic) = 1.5609648270691724608069932280444
y[1] (numeric) = 1.5609648270691724608069932280442
absolute error = 2e-31
relative error = 1.2812588504989883237005477602691e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04575
Order of pole (three term test) = -25.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.43
y[1] (analytic) = 1.5620759827243416431148608697349
y[1] (numeric) = 1.5620759827243416431148608697348
absolute error = 1e-31
relative error = 6.4017372461994330339164628821696e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.234
Order of pole (three term test) = 54.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=56013664, alloc=4521156, time=4.44
x[1] = -0.42
y[1] (analytic) = 1.563119177447949067346558897768
y[1] (numeric) = 1.5631191774479490673465588977678
absolute error = 2e-31
relative error = 1.2794929707569266915039304972368e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3324
Order of pole (six term test) = -13.1
TOP MAIN SOLVE Loop
x[1] = -0.41
y[1] (analytic) = 1.5640946781959086449704618476762
y[1] (numeric) = 1.5640946781959086449704618476761
absolute error = 1e-31
relative error = 6.3934748576310052529881399450183e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.4
y[1] (analytic) = 1.5650027513543510142730278423965
y[1] (numeric) = 1.5650027513543510142730278423964
absolute error = 1e-31
relative error = 6.3897651242759893699678125138307e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1702
Order of pole (six term test) = -11.69
TOP MAIN SOLVE Loop
x[1] = -0.39
y[1] (analytic) = 1.5658436627404666144187692606989
y[1] (numeric) = 1.5658436627404666144187692606988
absolute error = 1e-31
relative error = 6.3863336027419659336519606949168e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01138
Order of pole (three term test) = -0.1104
Radius of convergence (six term test) for eq 1 = 0.1166
Order of pole (six term test) = -12.44
TOP MAIN SOLVE Loop
x[1] = -0.38
y[1] (analytic) = 1.5666176776033478018759165548274
y[1] (numeric) = 1.5666176776033478018759165548273
absolute error = 1e-31
relative error = 6.3831783229321517414978631120714e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01085
Order of pole (three term test) = -5.79
Radius of convergence (six term test) for eq 1 = 0.1321
Order of pole (six term test) = -11.49
TOP MAIN SOLVE Loop
bytes used=60014748, alloc=4521156, time=4.76
x[1] = -0.37
y[1] (analytic) = 1.56732506062483001009164123525
y[1] (numeric) = 1.5673250606248300100916412352499
absolute error = 1e-31
relative error = 6.3802973940921985352940756997870e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7601
Order of pole (six term test) = -14.57
TOP MAIN SOLVE Loop
x[1] = -0.36
y[1] (analytic) = 1.5679660759203319533000165840625
y[1] (numeric) = 1.5679660759203319533000165840624
absolute error = 1e-31
relative error = 6.3776890033353617182185083736055e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.009464
Order of pole (three term test) = -4.776
Radius of convergence (six term test) for eq 1 = 0.1476
Order of pole (six term test) = -11.8
TOP MAIN SOLVE Loop
x[1] = -0.35
y[1] (analytic) = 1.5685409870396948753452076644143
y[1] (numeric) = 1.5685409870396948753452076644142
absolute error = 1e-31
relative error = 6.3753514142292102057325953115232e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.00507
Order of pole (three term test) = -25.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.34
y[1] (analytic) = 1.5690500569680208444016956610648
y[1] (numeric) = 1.5690500569680208444016956610646
absolute error = 2e-31
relative error = 1.2746565930883889203572923921582e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1754
Order of pole (three term test) = -76.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.33
y[1] (analytic) = 1.56949354812651009447265551655
y[1] (numeric) = 1.5694935481265100944726555165498
absolute error = 2e-31
relative error = 1.2742964138892966256989665232726e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.008479
Order of pole (three term test) = -25.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.32
y[1] (analytic) = 1.5698717223732974145469202181775
y[1] (numeric) = 1.5698717223732974145469202181773
absolute error = 2e-31
relative error = 1.2739894422561125889531248344484e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04442
Order of pole (three term test) = -35.93
Radius of convergence (six term test) for eq 1 = 0.117
Order of pole (six term test) = -11.47
TOP MAIN SOLVE Loop
bytes used=64015808, alloc=4521156, time=5.08
x[1] = -0.31
y[1] (analytic) = 1.570184841004287586294279942891
y[1] (numeric) = 1.5701848410042875862942799428908
absolute error = 2e-31
relative error = 1.2737353894722377781518523195586e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05637
Order of pole (three term test) = -34.81
Radius of convergence (six term test) for eq 1 = 0.2139
Order of pole (six term test) = -11.91
TOP MAIN SOLVE Loop
x[1] = -0.3
y[1] (analytic) = 1.5704331647539898711781795796907
y[1] (numeric) = 1.5704331647539898711781795796904
absolute error = 3e-31
relative error = 1.9103009713055527504981899095441e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0145
Order of pole (three term test) = -31.09
Radius of convergence (six term test) for eq 1 = 0.3684
Order of pole (six term test) = -9.11
TOP MAIN SOLVE Loop
x[1] = -0.29
y[1] (analytic) = 1.5706169537963515478641939224803
y[1] (numeric) = 1.57061695379635154786419392248
absolute error = 3e-31
relative error = 1.9100774334242824637027242397487e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2288
Order of pole (six term test) = -11.72
TOP MAIN SOLVE Loop
x[1] = -0.28
y[1] (analytic) = 1.5707364677455905008019760596691
y[1] (numeric) = 1.5707364677455905008019760596689
absolute error = 2e-31
relative error = 1.2732880665020229092520183665427e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02492
Order of pole (three term test) = -6.186
Radius of convergence (six term test) for eq 1 = 0.27
Order of pole (six term test) = -12.23
TOP MAIN SOLVE Loop
x[1] = -0.27
y[1] (analytic) = 1.5707919656570268608576911803111
y[1] (numeric) = 1.5707919656570268608576911803108
absolute error = 3e-31
relative error = 1.9098646196252777778274638202427e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=68017264, alloc=4521156, time=5.41
x[1] = -0.26
y[1] (analytic) = 1.5707837060279136988732651697435
y[1] (numeric) = 1.5707837060279136988732651697433
absolute error = 2e-31
relative error = 1.2732497748257511459028728294887e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2552
Order of pole (six term test) = -11.11
TOP MAIN SOLVE Loop
x[1] = -0.25
y[1] (analytic) = 1.570711946798266773028094980324
y[1] (numeric) = 1.5707119467982667730280949803238
absolute error = 2e-31
relative error = 1.2733079442585207003103249086572e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.04706
Order of pole (six term test) = -10.78
TOP MAIN SOLVE Loop
x[1] = -0.24
y[1] (analytic) = 1.5705769453516933308781858346734
y[1] (numeric) = 1.5705769453516933308781858346732
absolute error = 2e-31
relative error = 1.2734173934739297954554759146006e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.006351
Order of pole (three term test) = -28.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.23
y[1] (analytic) = 1.5703789585162199669469988495613
y[1] (numeric) = 1.5703789585162199669469988495611
absolute error = 2e-31
relative error = 1.2735779406326925819533074590839e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.003493
Order of pole (three term test) = -1.362
Radius of convergence (six term test) for eq 1 = 0.1622
Order of pole (six term test) = -11.51
TOP MAIN SOLVE Loop
x[1] = -0.22
y[1] (analytic) = 1.5701182425651195367416116579275
y[1] (numeric) = 1.5701182425651195367416116579273
absolute error = 2e-31
relative error = 1.2737894164789639550299805095617e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.21
y[1] (analytic) = 1.5697950532177371280671140542581
y[1] (numeric) = 1.5697950532177371280671140542579
absolute error = 2e-31
relative error = 1.2740516641968240739695185718579e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0281
Order of pole (three term test) = -35.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=72018268, alloc=4521156, time=5.74
x[1] = -0.2
y[1] (analytic) = 1.5694096456403150905114805943555
y[1] (numeric) = 1.5694096456403150905114805943552
absolute error = 3e-31
relative error = 1.9115468089123459745491492039572e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.306
Order of pole (three term test) = -395.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.19
y[1] (analytic) = 1.568962274446817123972482444179
y[1] (numeric) = 1.5689622744468171239724824441788
absolute error = 2e-31
relative error = 1.2747279093789285985622442657866e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1534
Order of pole (three term test) = -67.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.18
y[1] (analytic) = 1.5684531936997514270975215936278
y[1] (numeric) = 1.5684531936997514270975215936275
absolute error = 3e-31
relative error = 1.9127124813482251692220806901610e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.009612
Order of pole (three term test) = -2.975
Radius of convergence (six term test) for eq 1 = 0.2505
Order of pole (six term test) = -11.57
TOP MAIN SOLVE Loop
x[1] = -0.17
y[1] (analytic) = 1.5678826569109929065065918296025
y[1] (numeric) = 1.5678826569109929065065918296023
absolute error = 2e-31
relative error = 1.2756056655032813164985290793400e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.16
y[1] (analytic) = 1.5672509170426044476678925981676
y[1] (numeric) = 1.5672509170426044476678925981673
absolute error = 3e-31
relative error = 1.9141797700530217192783032514190e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=76019360, alloc=4521156, time=6.06
x[1] = -0.15
y[1] (analytic) = 1.566558226507657248294944077844
y[1] (numeric) = 1.5665582265076572482949440778437
absolute error = 3e-31
relative error = 1.9150261696227709089419427009447e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6403
Order of pole (six term test) = -11.25
TOP MAIN SOLVE Loop
x[1] = -0.14
y[1] (analytic) = 1.565804837171050215133374434752
y[1] (numeric) = 1.5658048371710502151333744347517
absolute error = 3e-31
relative error = 1.9159475873251991704019464467339e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6477
Order of pole (six term test) = -13.76
TOP MAIN SOLVE Loop
x[1] = -0.13
y[1] (analytic) = 1.5649910003503284250048733351949
y[1] (numeric) = 1.5649910003503284250048733351946
absolute error = 3e-31
relative error = 1.9169439308778389472354255736208e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3805
Order of pole (six term test) = -8.505
TOP MAIN SOLVE Loop
x[1] = -0.12
y[1] (analytic) = 1.5641169668165006509751293520824
y[1] (numeric) = 1.5641169668165006509751293520822
absolute error = 2e-31
relative error = 1.2786767501606140119747897574538e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.11
y[1] (analytic) = 1.563182986794855954511892918049
y[1] (numeric) = 1.5631829867948559545118929180487
absolute error = 3e-31
relative error = 1.9191611125138892485685397812971e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01422
Order of pole (three term test) = -9.259
Radius of convergence (six term test) for eq 1 = 0.1622
Order of pole (six term test) = -11.53
TOP MAIN SOLVE Loop
x[1] = -0.1
y[1] (analytic) = 1.5621893099657793444986309499634
y[1] (numeric) = 1.5621893099657793444986309499632
absolute error = 2e-31
relative error = 1.2802545678947266324092177617816e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1466
Order of pole (six term test) = -11.31
TOP MAIN SOLVE Loop
bytes used=80021236, alloc=4521156, time=6.39
x[1] = -0.09
y[1] (analytic) = 1.5611361854655665039685641964877
y[1] (numeric) = 1.5611361854655665039685641964875
absolute error = 2e-31
relative error = 1.2811182128890019114218485816895e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03973
Order of pole (three term test) = -7.028
Radius of convergence (six term test) for eq 1 = 0.2391
Order of pole (six term test) = -12.32
TOP MAIN SOLVE Loop
x[1] = -0.08
y[1] (analytic) = 1.5600238618872375854232037421401
y[1] (numeric) = 1.5600238618872375854232037421399
absolute error = 2e-31
relative error = 1.2820316719902615097932067036532e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3464
Order of pole (six term test) = -12.38
TOP MAIN SOLVE Loop
x[1] = -0.07
y[1] (analytic) = 1.5588525872813500755988289376984
y[1] (numeric) = 1.5588525872813500755988289376982
absolute error = 2e-31
relative error = 1.2829949517471784349888726599973e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.004372
Order of pole (three term test) = -25.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.06
y[1] (analytic) = 1.5576226091568107305436753174596
y[1] (numeric) = 1.5576226091568107305436753174594
absolute error = 2e-31
relative error = 1.2840080698897031460183569633661e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.05
y[1] (analytic) = 1.5563341744816865818679278085896
y[1] (numeric) = 1.5563341744816865818679278085893
absolute error = 3e-31
relative error = 1.9276065829493876897115498219068e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1508
Order of pole (six term test) = -11.5
TOP MAIN SOLVE Loop
bytes used=84022516, alloc=4521156, time=6.71
x[1] = -0.04
y[1] (analytic) = 1.554987529684015015027941736282
y[1] (numeric) = 1.5549875296840150150279417362817
absolute error = 3e-31
relative error = 1.9292759219809449039209354474528e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04881
Order of pole (three term test) = -28.63
Radius of convergence (six term test) for eq 1 = 0.2734
Order of pole (six term test) = -11.94
TOP MAIN SOLVE Loop
x[1] = -0.03
y[1] (analytic) = 1.5535829206526129205054417804259
y[1] (numeric) = 1.5535829206526129205054417804257
absolute error = 2e-31
relative error = 1.2873467990751731782377081453074e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.02
y[1] (analytic) = 1.5521205927378849187417771446912
y[1] (numeric) = 1.552120592737884918741777144691
absolute error = 2e-31
relative error = 1.2885596707869663081097942529655e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.01
y[1] (analytic) = 1.5506007907526306596866397571081
y[1] (numeric) = 1.5506007907526306596866397571079
absolute error = 2e-31
relative error = 1.2898226364435425950316558387711e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.009135
Order of pole (three term test) = -0.2586
Radius of convergence (six term test) for eq 1 = 0.4389
Order of pole (six term test) = -13.54
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (analytic) = 1.5490237589728511978199813320776
y[1] (numeric) = 1.5490237589728511978199813320774
absolute error = 2e-31
relative error = 1.2911357804648448842103164184123e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02636
Order of pole (three term test) = -23.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.01
y[1] (analytic) = 1.5473897411385544435051945870289
y[1] (numeric) = 1.5473897411385544435051945870287
absolute error = 2e-31
relative error = 1.2924991983780500538020687139928e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.005831
Order of pole (three term test) = -1.77
Radius of convergence (six term test) for eq 1 = 0.124
Order of pole (six term test) = -11.93
TOP MAIN SOLVE Loop
bytes used=88023740, alloc=4521156, time=7.04
x[1] = 0.02
y[1] (analytic) = 1.5456989804545596915309538223722
y[1] (numeric) = 1.5456989804545596915309538223719
absolute error = 3e-31
relative error = 1.9408694952478774107351010858161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05453
Order of pole (three term test) = -3.876
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.03
y[1] (analytic) = 1.5439517195913012276984404407148
y[1] (numeric) = 1.5439517195913012276984404407145
absolute error = 3e-31
relative error = 1.9430659404259925073000847482923e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1781
Order of pole (three term test) = -27.41
Radius of convergence (six term test) for eq 1 = 0.5088
Order of pole (six term test) = -11.39
TOP MAIN SOLVE Loop
x[1] = 0.04
y[1] (analytic) = 1.5421482006856310143100098002425
y[1] (numeric) = 1.5421482006856310143100098002422
absolute error = 3e-31
relative error = 1.9453383265410002164497270515287e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.05
y[1] (analytic) = 1.540288665341620455414687067451
y[1] (numeric) = 1.5402886653416204554146870674508
absolute error = 2e-31
relative error = 1.2984579092234118451519576989307e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09621
Order of pole (three term test) = -34.84
Radius of convergence (six term test) for eq 1 = 0.4976
Order of pole (six term test) = -11.66
TOP MAIN SOLVE Loop
x[1] = 0.06
y[1] (analytic) = 1.5383733546313612426652114557752
y[1] (numeric) = 1.538373354631361242665211455775
absolute error = 2e-31
relative error = 1.3000745196079256425699650082855e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08825
Order of pole (three term test) = -24.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=92024720, alloc=4521156, time=7.36
x[1] = 0.07
y[1] (analytic) = 1.5364025090957652826406804088408
y[1] (numeric) = 1.5364025090957652826406804088406
absolute error = 2e-31
relative error = 1.3017422115361426353847075857892e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02657
Order of pole (three term test) = -14.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.08
y[1] (analytic) = 1.5343763687453637064881779097844
y[1] (numeric) = 1.5343763687453637064881779097842
absolute error = 2e-31
relative error = 1.3034611590345135967570237105680e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.007031
Order of pole (three term test) = -25.4
Radius of convergence (six term test) for eq 1 = 0.3884
Order of pole (six term test) = -10.52
TOP MAIN SOLVE Loop
x[1] = 0.09
y[1] (analytic) = 1.5322951730611049627361041710849
y[1] (numeric) = 1.5322951730611049627361041710847
absolute error = 2e-31
relative error = 1.3052315475252390388666209601929e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2228
Order of pole (six term test) = -11.49
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 1.5301591609951519941312574823598
y[1] (numeric) = 1.5301591609951519941312574823597
absolute error = 1e-31
relative error = 6.5352678694524922149486840812907e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05358
Order of pole (three term test) = -34.77
Radius of convergence (six term test) for eq 1 = 0.2694
Order of pole (six term test) = -11.29
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 1.5279685709716784993510529663306
y[1] (numeric) = 1.5279685709716784993510529663304
absolute error = 2e-31
relative error = 1.3089274465430550989564128401877e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 1.5257236408876642804415974153874
y[1] (numeric) = 1.5257236408876642804415974153873
absolute error = 1e-31
relative error = 6.5542669275164481058731924537738e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.002151
Order of pole (three term test) = -24.62
Radius of convergence (six term test) for eq 1 = 0.2895
Order of pole (six term test) = -11.11
TOP MAIN SOLVE Loop
bytes used=96025540, alloc=4586680, time=7.69
x[1] = 0.13
y[1] (analytic) = 1.5234246081136896768316742526236
y[1] (numeric) = 1.5234246081136896768316742526235
absolute error = 1e-31
relative error = 6.5641581124136094994257069699212e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2902
Order of pole (six term test) = -12
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 1.5210717094947290867720279815834
y[1] (numeric) = 1.5210717094947290867720279815832
absolute error = 2e-31
relative error = 1.3148624009740880172633684557286e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04193
Order of pole (three term test) = -20.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 1.5186651813509435770486732580231
y[1] (numeric) = 1.5186651813509435770486732580229
absolute error = 2e-31
relative error = 1.3169459763480455197718525009254e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03934
Order of pole (three term test) = -31.14
Radius of convergence (six term test) for eq 1 = 0.1964
Order of pole (six term test) = -12.15
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 1.5162052594784725818182899344495
y[1] (numeric) = 1.5162052594784725818182899344493
absolute error = 2e-31
relative error = 1.3190826159565874023337811244913e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4963
Order of pole (six term test) = -11.3
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 1.5136921791502246914131020937992
y[1] (numeric) = 1.5136921791502246914131020937989
absolute error = 3e-31
relative error = 1.9819088988648783573183426497567e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2455
Order of pole (three term test) = -110.3
Radius of convergence (six term test) for eq 1 = 0.2558
Order of pole (six term test) = -11.49
TOP MAIN SOLVE Loop
bytes used=100026576, alloc=4586680, time=8.02
x[1] = 0.18
y[1] (analytic) = 1.5111261751166675319619762021087
y[1] (numeric) = 1.5111261751166675319619762021084
absolute error = 3e-31
relative error = 1.9852743267903376394270303046812e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04251
Order of pole (three term test) = -13.32
Radius of convergence (six term test) for eq 1 = 0.4041
Order of pole (six term test) = -11.84
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 1.5085074816066167366738110711143
y[1] (numeric) = 1.508507481606616736673811071114
absolute error = 3e-31
relative error = 1.9887206636886468054827083446556e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01508
Order of pole (three term test) = -27.41
Radius of convergence (six term test) for eq 1 = 0.1422
Order of pole (six term test) = -11.52
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 1.5058363323280240096286303301544
y[1] (numeric) = 1.5058363323280240096286303301541
absolute error = 3e-31
relative error = 1.9922483842330978482644945863831e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3119
Order of pole (six term test) = -11.68
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 1.5031129604687642829211265622632
y[1] (numeric) = 1.5031129604687642829211265622628
absolute error = 4e-31
relative error = 2.6611439760006797841329009013255e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02748
Order of pole (three term test) = -22.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 1.500337598697421968000745161669
y[1] (numeric) = 1.5003375986974219680007451616687
absolute error = 3e-31
relative error = 1.9995499696898683765592480067719e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01895
Order of pole (three term test) = -6.309
Radius of convergence (six term test) for eq 1 = 0.1365
Order of pole (six term test) = -11.03
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 1.4975104791640763020517353187854
y[1] (numeric) = 1.4975104791640763020517353187851
absolute error = 3e-31
relative error = 2.0033248793521810554139403291142e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.008239
Order of pole (three term test) = -0.9703
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=104027792, alloc=4586680, time=8.35
x[1] = 0.24
y[1] (analytic) = 1.494631833501085790255935333935
y[1] (numeric) = 1.4946318335010857902559353339347
absolute error = 3e-31
relative error = 2.0071832626317607599460766750048e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 1.4917018928238717447803997022225
y[1] (numeric) = 1.4917018928238717447803997022222
absolute error = 3e-31
relative error = 2.0111256910191613325159987966009e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04514
Order of pole (three term test) = -23.57
Radius of convergence (six term test) for eq 1 = 0.2738
Order of pole (six term test) = -11.69
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 1.4887208877317009213313160988903
y[1] (numeric) = 1.48872088773170092133131609889
absolute error = 3e-31
relative error = 2.0151527561160031415120325162015e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01046
Order of pole (three term test) = -1.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 1.4856890483084672541150015269043
y[1] (numeric) = 1.4856890483084672541150015269039
absolute error = 4e-31
relative error = 2.6923534265492526747126136024798e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 1.4826066041234726900461084661439
y[1] (numeric) = 1.4826066041234726900461084661435
absolute error = 4e-31
relative error = 2.6979510200987049764522500722470e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01556
Order of pole (three term test) = 2.227
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=108028908, alloc=4586680, time=8.69
x[1] = 0.29
y[1] (analytic) = 1.4794737842322071230425138861616
y[1] (numeric) = 1.4794737842322071230425138861612
absolute error = 4e-31
relative error = 2.7036639936650543328298707079280e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6141
Order of pole (six term test) = -13.06
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 1.4762908171771274292457064517528
y[1] (numeric) = 1.4762908171771274292457064517524
absolute error = 4e-31
relative error = 2.7094932471696560221645254128607e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03104
Order of pole (three term test) = -6.386
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 1.4730579309884356040048301622881
y[1] (numeric) = 1.4730579309884356040048301622877
absolute error = 4e-31
relative error = 2.7154397093642900457660938684891e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 1.4697753531848560014618860216289
y[1] (numeric) = 1.4697753531848560014618860216284
absolute error = 5e-31
relative error = 3.4018804228588407874729443023668e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.006491
Order of pole (three term test) = -1.402
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 1.4664433107744116775749371352182
y[1] (numeric) = 1.4664433107744116775749371352177
absolute error = 5e-31
relative error = 3.4096101521712135480917798533903e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.002633
Order of pole (three term test) = -0.8072
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 1.4630620302551998374155068743454
y[1] (numeric) = 1.463062030255199837415506874345
absolute error = 4e-31
relative error = 2.7339920777673969614661358334898e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02072
Order of pole (three term test) = 0.5737
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=112029980, alloc=4586680, time=9.02
x[1] = 0.35
y[1] (analytic) = 1.4596317376161663875757044343603
y[1] (numeric) = 1.4596317376161663875757044343599
absolute error = 4e-31
relative error = 2.7404172551993825271378496600933e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3039
Order of pole (six term test) = -12.03
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 1.4561526583378795945199572434966
y[1] (numeric) = 1.4561526583378795945199572434962
absolute error = 4e-31
relative error = 2.7469647341548558087122862464810e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04471
Order of pole (three term test) = -21.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 1.4526250173933028497155752516978
y[1] (numeric) = 1.4526250173933028497155752516974
absolute error = 4e-31
relative error = 2.7536356266105716262600539112686e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07426
Order of pole (three term test) = -39.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 1.4490490392485665423757181441449
y[1] (numeric) = 1.4490490392485665423757181441445
absolute error = 4e-31
relative error = 2.7604310769732681156902343294427e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07885
Order of pole (three term test) = -21.19
Radius of convergence (six term test) for eq 1 = 0.3487
Order of pole (six term test) = -11.5
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 1.4454249478637390406476829818173
y[1] (numeric) = 1.4454249478637390406476829818168
absolute error = 5e-31
relative error = 3.4591903283458150140650936511041e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5556
Order of pole (six term test) = -12.17
TOP MAIN SOLVE Loop
bytes used=116030972, alloc=4586680, time=9.35
x[1] = 0.4
y[1] (analytic) = 1.4417529666935967820787766710982
y[1] (numeric) = 1.4417529666935967820787766710977
absolute error = 5e-31
relative error = 3.4680004935010523969749618046562e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.00567
Order of pole (three term test) = -26.14
Radius of convergence (six term test) for eq 1 = 0.2857
Order of pole (six term test) = -11.53
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 1.4380333186883934741913850059127
y[1] (numeric) = 1.4380333186883934741913850059122
absolute error = 5e-31
relative error = 3.4769708983936601137863533136497e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.208
Order of pole (three term test) = -43.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 1.4342662262946284059981978088856
y[1] (numeric) = 1.4342662262946284059981978088852
absolute error = 4e-31
relative error = 2.7888825147433374689009271014549e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 1.4304519114558138712878979222795
y[1] (numeric) = 1.4304519114558138712878979222791
absolute error = 4e-31
relative error = 2.7963190988567241434471615978741e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4752
Order of pole (six term test) = -11.62
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 1.4265905956132417045109704647401
y[1] (numeric) = 1.4265905956132417045109704647396
absolute error = 5e-31
relative error = 3.5048597792351728036661274799030e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3389
Order of pole (six term test) = -12.02
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 1.4226824997067489300946378758921
y[1] (numeric) = 1.4226824997067489300946378758916
absolute error = 5e-31
relative error = 3.5144875972190754072350079842357e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=120031912, alloc=4586680, time=9.68
x[1] = 0.46
y[1] (analytic) = 1.4187278441754825260152758173194
y[1] (numeric) = 1.418727844175482526015275817319
absolute error = 4e-31
relative error = 2.8194272893295239910383074341479e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 1.4147268489586633024560149851678
y[1] (numeric) = 1.4147268489586633024560149851673
absolute error = 5e-31
relative error = 3.5342511550412331723835257085370e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 1.4106797334963488963765843162729
y[1] (numeric) = 1.4106797334963488963765843162724
absolute error = 5e-31
relative error = 3.5443906092048078164270786246936e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01493
Order of pole (three term test) = -28.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 1.4065867167301958828218019360697
y[1] (numeric) = 1.4065867167301958828218019360694
absolute error = 3e-31
relative error = 2.1328226438636590157173401310940e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02078
Order of pole (three term test) = 1.101
Radius of convergence (six term test) for eq 1 = 0.9311
Order of pole (six term test) = -14.13
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 1.4024480171042210037944715023227
y[1] (numeric) = 1.4024480171042210037944715023223
absolute error = 4e-31
relative error = 2.8521556244624398637090281669615e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=124032820, alloc=4586680, time=10.01
x[1] = 0.51
y[1] (analytic) = 1.3982638525655615155177933436685
y[1] (numeric) = 1.3982638525655615155177933436681
absolute error = 4e-31
relative error = 2.8606904145170618297143149369672e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5265
Order of pole (six term test) = -11.43
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = 1.3940344405652346549117519758292
y[1] (numeric) = 1.3940344405652346549117519758288
absolute error = 4e-31
relative error = 2.8693695676400454515461583144037e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05104
Order of pole (three term test) = 1.801
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (analytic) = 1.3897599980588962261072942008533
y[1] (numeric) = 1.3897599980588962261072942008529
absolute error = 4e-31
relative error = 2.8781948002438369133891278651191e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09651
Order of pole (three term test) = -17.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 1.3854407415075983078214650556406
y[1] (numeric) = 1.3854407415075983078214650556402
absolute error = 4e-31
relative error = 2.8871678738473582052966232789852e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09349
Order of pole (three term test) = -50.12
Radius of convergence (six term test) for eq 1 = 0.2055
Order of pole (six term test) = -11.62
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = 1.3810768868785460824160223750185
y[1] (numeric) = 1.3810768868785460824160223750181
absolute error = 4e-31
relative error = 2.8962905961308480281313443203927e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2057
Order of pole (six term test) = -11.69
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = 1.3766686496458537874614046715186
y[1] (numeric) = 1.3766686496458537874614046715182
absolute error = 4e-31
relative error = 2.9055648220281581751764667662185e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1621
Order of pole (six term test) = -11.5
TOP MAIN SOLVE Loop
bytes used=128033772, alloc=4586680, time=10.34
x[1] = 0.57
y[1] (analytic) = 1.3722162447912997906272814084825
y[1] (numeric) = 1.3722162447912997906272814084821
absolute error = 4e-31
relative error = 2.9149924548578416921807586591469e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3343
Order of pole (three term test) = -53.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = 1.3677198868050807887202695549477
y[1] (numeric) = 1.3677198868050807887202695549473
absolute error = 4e-31
relative error = 2.9245754474944297856463638392864e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3418
Order of pole (six term test) = -11.6
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 1.3631797896865651316887555596704
y[1] (numeric) = 1.3631797896865651316887555596699
absolute error = 5e-31
relative error = 3.6678947544766975377099068875229e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.1536
Order of pole (six term test) = -11.79
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 1.3585961669450452724141175673624
y[1] (numeric) = 1.358596166945045272414117567362
absolute error = 4e-31
relative error = 2.9442155787870690828221323533926e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02282
Order of pole (three term test) = -27.81
Radius of convergence (six term test) for eq 1 = 0.4046
Order of pole (six term test) = -11.22
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 1.3539692316004893431069988225092
y[1] (numeric) = 1.3539692316004893431069988225089
absolute error = 3e-31
relative error = 2.2157076615794167642950163718098e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1196
Order of pole (three term test) = -24.09
Radius of convergence (six term test) for eq 1 = 0.9457
Order of pole (six term test) = -10.1
TOP MAIN SOLVE Loop
bytes used=132034748, alloc=4586680, time=10.67
x[1] = 0.62
y[1] (analytic) = 1.3492991961842918591266397647154
y[1] (numeric) = 1.3492991961842918591266397647151
absolute error = 3e-31
relative error = 2.2233764079040108078809376904785e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04838
Order of pole (three term test) = -31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 1.3445862727400235510406333141538
y[1] (numeric) = 1.3445862727400235510406333141534
absolute error = 4e-31
relative error = 2.9748927838216908986492442764567e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.242
Order of pole (six term test) = -11.27
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = 1.3398306728241803257418252760985
y[1] (numeric) = 1.3398306728241803257418252760981
absolute error = 4e-31
relative error = 2.9854518792054114862881266797137e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0885
Order of pole (three term test) = -31.65
Radius of convergence (six term test) for eq 1 = 0.3428
Order of pole (six term test) = -11.33
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 1.335032607506931357438439659449
y[1] (numeric) = 1.3350326075069313574384396594486
absolute error = 4e-31
relative error = 2.9961814996187142905239507650237e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04943
Order of pole (three term test) = -20.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (analytic) = 1.3301922873728663093328670053409
y[1] (numeric) = 1.3301922873728663093328670053406
absolute error = 3e-31
relative error = 2.2553130314151864824231228419976e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4464
Order of pole (six term test) = -11.53
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = 1.325309922521741686803912558129
y[1] (numeric) = 1.3253099225217416868039125581286
absolute error = 4e-31
relative error = 3.0181619650058721022164240488903e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6102
Order of pole (six term test) = -11.95
TOP MAIN SOLVE Loop
bytes used=136035784, alloc=4586680, time=11.00
x[1] = 0.68
y[1] (analytic) = 1.3203857225692263229066602819605
y[1] (numeric) = 1.3203857225692263229066602819601
absolute error = 4e-31
relative error = 3.0294177918076394117667707534036e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = 1.3154198966476459970034683315745
y[1] (numeric) = 1.3154198966476459970034683315742
absolute error = 3e-31
relative error = 2.2806405830149860039874964045415e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01996
Order of pole (three term test) = -0.365
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 1.310412653406727187338971625603
y[1] (numeric) = 1.3104126534067271873389716256026
absolute error = 4e-31
relative error = 3.0524735773888135735530929121177e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.379
Order of pole (six term test) = -5.191
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = 1.3053642010143399583713276442537
y[1] (numeric) = 1.3053642010143399583713276442533
absolute error = 4e-31
relative error = 3.0642789168660971788776695610444e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3796
Order of pole (six term test) = -10.81
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 1.3002747471572399836713024805746
y[1] (numeric) = 1.3002747471572399836713024805742
absolute error = 4e-31
relative error = 3.0762729251991593861764157301539e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3359
Order of pole (six term test) = -12
TOP MAIN SOLVE Loop
bytes used=140036736, alloc=4586680, time=11.32
x[1] = 0.73
y[1] (analytic) = 1.2951444990418097052001555152551
y[1] (numeric) = 1.2951444990418097052001555152546
absolute error = 5e-31
relative error = 3.8605730894885965749099229895524e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1395
Order of pole (three term test) = -44.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = 1.2899736633947986297766428588745
y[1] (numeric) = 1.289973663394798629776642858874
absolute error = 5e-31
relative error = 3.8760481255420340400296063887692e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01657
Order of pole (three term test) = -28.08
Radius of convergence (six term test) for eq 1 = 1.174
Order of pole (six term test) = -7.282
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = 1.284762446464062763542821912393
y[1] (numeric) = 1.2847624464640627635428219123925
absolute error = 5e-31
relative error = 3.8917700418167223104849129815707e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1265
Order of pole (three term test) = -23.51
Radius of convergence (six term test) for eq 1 = 0.6244
Order of pole (six term test) = -11.83
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 1.2795110540193031852377020362348
y[1] (numeric) = 1.2795110540193031852377020362343
absolute error = 5e-31
relative error = 3.9077427149172312805299703370023e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 1.274219691352803759087149390288
y[1] (numeric) = 1.2742196913528037590871493902875
absolute error = 5e-31
relative error = 3.9239701237795489300635115097695e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = 1.2688885632801679881178175112751
y[1] (numeric) = 1.2688885632801679881178175112746
absolute error = 5e-31
relative error = 3.9404563526639732754909080274852e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05553
Order of pole (three term test) = -34.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=144037616, alloc=4586680, time=11.65
x[1] = 0.79
y[1] (analytic) = 1.263517874141055008702239129979
y[1] (numeric) = 1.2635178741410550087022391299785
absolute error = 5e-31
relative error = 3.9572055942611986591215703335480e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3062
Order of pole (three term test) = -131.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 1.2581078277999147271415790984816
y[1] (numeric) = 1.2581078277999147271415790984812
absolute error = 4e-31
relative error = 3.1793777223331501750206208223820e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = 1.2526586276467220990919130966288
y[1] (numeric) = 1.2526586276467220990919130966284
absolute error = 4e-31
relative error = 3.1932083583813306445458136255238e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.944
Order of pole (six term test) = -5.444
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = 1.2471704765977105526392620171209
y[1] (numeric) = 1.2471704765977105526392620171205
absolute error = 4e-31
relative error = 3.2072600138130489585819824813602e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02099
Order of pole (three term test) = -25.8
Radius of convergence (six term test) for eq 1 = 0.2277
Order of pole (six term test) = -11.05
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 1.2416435770961045558279775896833
y[1] (numeric) = 1.2416435770961045558279775896828
absolute error = 5e-31
relative error = 4.0269205206970555544571074920928e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08069
Order of pole (three term test) = -26.09
Radius of convergence (six term test) for eq 1 = 0.3648
Order of pole (six term test) = -11.28
TOP MAIN SOLVE Loop
bytes used=148038716, alloc=4586680, time=11.98
x[1] = 0.84
y[1] (analytic) = 1.2360781311128513294464408964378
y[1] (numeric) = 1.2360781311128513294464408964374
absolute error = 4e-31
relative error = 3.2360413952140444643190436166266e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09922
Order of pole (three term test) = -25.94
Radius of convergence (six term test) for eq 1 = 0.4291
Order of pole (six term test) = -11.86
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 1.2304743401473517058734019526235
y[1] (numeric) = 1.2304743401473517058734019526232
absolute error = 3e-31
relative error = 2.4380841616256249112204494489637e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2031
Order of pole (three term test) = -46.91
Radius of convergence (six term test) for eq 1 = 0.4579
Order of pole (six term test) = -11.63
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 1.2248324052281901347876554789341
y[1] (numeric) = 1.2248324052281901347876554789339
absolute error = 2e-31
relative error = 1.6328764584142380694629527690598e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 1.2191525269138638365431153737114
y[1] (numeric) = 1.2191525269138638365431153737112
absolute error = 2e-31
relative error = 1.6404838244995943668789789523262e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04949
Order of pole (three term test) = -11.48
Radius of convergence (six term test) for eq 1 = 0.5057
Order of pole (six term test) = -11.74
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = 1.2134349052935111040107182047827
y[1] (numeric) = 1.2134349052935111040107182047825
absolute error = 2e-31
relative error = 1.6482136711867794718863880673918e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 1.2076797399876387536879542816159
y[1] (numeric) = 1.2076797399876387536879542816157
absolute error = 2e-31
relative error = 1.6560681890883348484382659350972e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9454
Order of pole (three term test) = -234.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=152039588, alloc=4586680, time=12.31
x[1] = 0.9
y[1] (analytic) = 1.2018872301488487268761935384199
y[1] (numeric) = 1.2018872301488487268761935384196
absolute error = 3e-31
relative error = 2.4960744442125926379888013397432e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5316
Order of pole (six term test) = -11.4
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = 1.1960575744625638417253425575932
y[1] (numeric) = 1.196057574462563841725342557593
absolute error = 2e-31
relative error = 1.6721603062450228710835260346599e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 1.1901909711477526969447385902606
y[1] (numeric) = 1.1901909711477526969447385902602
absolute error = 4e-31
relative error = 3.3608051959448379720511756086821e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = 1.1842876179576537279785563862737
y[1] (numeric) = 1.1842876179576537279785563862734
absolute error = 3e-31
relative error = 2.5331684250601277832525038463038e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06656
Order of pole (three term test) = -36.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 1.1783477121804984164433740297515
y[1] (numeric) = 1.1783477121804984164433740297512
absolute error = 3e-31
relative error = 2.5459378152893313853839539636477e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08047
Order of pole (three term test) = -37.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=156040720, alloc=4586680, time=12.64
x[1] = 0.95
y[1] (analytic) = 1.1723714506402336536249147877116
y[1] (numeric) = 1.1723714506402336536249147877113
absolute error = 3e-31
relative error = 2.5589159462742767186950549342695e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = 1.1663590296972432588303532183775
y[1] (numeric) = 1.1663590296972432588303532183772
absolute error = 3e-31
relative error = 2.5721068072656175816703739518532e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4415
Order of pole (six term test) = -11.44
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 1.1603106452490686533919454520502
y[1] (numeric) = 1.1603106452490686533919454520499
absolute error = 3e-31
relative error = 2.5855145018996437671107543234825e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 1.1542264927311286911171156507711
y[1] (numeric) = 1.1542264927311286911171156507707
absolute error = 4e-31
relative error = 3.4655243361597142478939367622060e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 1.1481067671174386459795031731133
y[1] (numeric) = 1.1481067671174386459795031731129
absolute error = 4e-31
relative error = 3.4839965363524803300575666802736e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7517
Order of pole (six term test) = -11.35
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 1.1419516629213283578448479170698
y[1] (numeric) = 1.1419516629213283578448479170694
absolute error = 4e-31
relative error = 3.5027752311050043801472383705838e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3211
Order of pole (three term test) = -76.93
Radius of convergence (six term test) for eq 1 = 0.4715
Order of pole (six term test) = -11.62
TOP MAIN SOLVE Loop
bytes used=160041736, alloc=4586680, time=12.96
x[1] = 1.01
y[1] (analytic) = 1.1357613741961595370249646868967
y[1] (numeric) = 1.1357613741961595370249646868964
absolute error = 3e-31
relative error = 2.6413999174107009340000119990293e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = 1.1295360945360422284524312286767
y[1] (numeric) = 1.1295360945360422284524312286764
absolute error = 3e-31
relative error = 2.6559576223478296014872178657997e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03537
Order of pole (three term test) = -34.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 1.1232760170765504362679888040208
y[1] (numeric) = 1.1232760170765504362679888040204
absolute error = 4e-31
relative error = 3.5610125554095249015964837557844e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1818
Order of pole (three term test) = -122.8
Radius of convergence (six term test) for eq 1 = 0.8903
Order of pole (six term test) = -10.48
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = 1.1169813344954369096120288214886
y[1] (numeric) = 1.1169813344954369096120288214884
absolute error = 2e-31
relative error = 1.7905402160578095110945376570194e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2259
Order of pole (three term test) = 27.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 1.1106522390133470904109141207111
y[1] (numeric) = 1.1106522390133470904109141207108
absolute error = 3e-31
relative error = 2.7011155198904235648380115656951e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.9485
Order of pole (six term test) = -9.871
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 1.1042889223945322239482590045896
y[1] (numeric) = 1.1042889223945322239482590045893
absolute error = 3e-31
relative error = 2.7166803353372606463065546463095e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3734
Order of pole (six term test) = -11.27
bytes used=164042980, alloc=4586680, time=13.30
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = 1.0978915759475616330106680400931
y[1] (numeric) = 1.0978915759475616330106680400929
absolute error = 2e-31
relative error = 1.8216735093115657388157463333363e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04483
Order of pole (three term test) = -26.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = 1.0914603905260341563968099977819
y[1] (numeric) = 1.0914603905260341563968099977816
absolute error = 3e-31
relative error = 2.7486109675076131241410537992569e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 1.0849955565292887525780800740422
y[1] (numeric) = 1.0849955565292887525780800740419
absolute error = 3e-31
relative error = 2.7649882821607822338786713677648e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07332
Order of pole (three term test) = 2.501
Radius of convergence (six term test) for eq 1 = 0.4233
Order of pole (six term test) = -12.24
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 1.078497263903114269298480737846
y[1] (numeric) = 1.0784972639031142692984807378457
absolute error = 3e-31
relative error = 2.7816482251822402591198094509418e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.9232
Order of pole (six term test) = -9.981
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = 1.0719657021404583799007291653952
y[1] (numeric) = 1.0719657021404583799007291653949
absolute error = 3e-31
relative error = 2.7985970017601492245670107749831e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03703
Order of pole (three term test) = -2.321
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=168043924, alloc=4586680, time=13.63
x[1] = 1.12
y[1] (analytic) = 1.0654010602821356871649772710374
y[1] (numeric) = 1.0654010602821356871649772710371
absolute error = 3e-31
relative error = 2.8158410122152035038066682623145e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5675
Order of pole (three term test) = -92.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = 1.0588035269175349954459088110772
y[1] (numeric) = 1.058803526917534995445908811077
absolute error = 2e-31
relative error = 1.8889245730249349400937875931230e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01143
Order of pole (three term test) = 1.072
Radius of convergence (six term test) for eq 1 = 0.1408
Order of pole (six term test) = -11.62
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 1.052173290185325751893356928312
y[1] (numeric) = 1.0521732901853257518933569283118
absolute error = 2e-31
relative error = 1.9008275715188775615931481445208e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.009298
Order of pole (three term test) = -0.5089
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = 1.0455105377741636575409648190359
y[1] (numeric) = 1.0455105377741636575409648190357
absolute error = 2e-31
relative error = 1.9129410252123270367972024601248e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5813
Order of pole (six term test) = -11.78
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = 1.0388154569233954490467919406335
y[1] (numeric) = 1.0388154569233954490467919406333
absolute error = 2e-31
relative error = 1.9252697740205885543563215790625e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3567
Order of pole (three term test) = -149.1
Radius of convergence (six term test) for eq 1 = 2.254
Order of pole (six term test) = -10.09
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = 1.0320882344237628518691483364618
y[1] (numeric) = 1.0320882344237628518691483364617
absolute error = 1e-31
relative error = 9.6890940778752467219107057732310e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1109
Order of pole (three term test) = -14.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=172044940, alloc=4586680, time=13.96
x[1] = 1.18
y[1] (analytic) = 1.0253290566181057056603202352588
y[1] (numeric) = 1.0253290566181057056603202352587
absolute error = 1e-31
relative error = 9.7529665578614361665681232133079e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 1.0185381094020642626602310845493
y[1] (numeric) = 1.0185381094020642626602310845492
absolute error = 1e-31
relative error = 9.8179929721731559627288028783214e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0984
Order of pole (three term test) = -26.8
Radius of convergence (six term test) for eq 1 = 0.9004
Order of pole (six term test) = -10.98
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = 1.011715578224780659871463601209
y[1] (numeric) = 1.0117155782247806598714636012088
absolute error = 2e-31
relative error = 1.9768401743000981656925765091271e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6297
Order of pole (three term test) = -161.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 1.0048616480895995657964502672288
y[1] (numeric) = 1.0048616480895995657964502672286
absolute error = 2e-31
relative error = 1.9903237463608202674003399633547e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = 0.9979765035547680025170219645519
y[1] (numeric) = 0.99797650355476800251702196455176
absolute error = 1.4e-31
relative error = 1.4028386389992490738919620862976e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=176045976, alloc=4586680, time=14.29
x[1] = 1.23
y[1] (analytic) = 0.99106032873413434389588712937858
y[1] (numeric) = 0.99106032873413434389588712937846
absolute error = 1.2e-31
relative error = 1.2108243718449925121030843579620e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.005339
Order of pole (three term test) = -1.643
Radius of convergence (six term test) for eq 1 = 0.1755
Order of pole (six term test) = -12.01
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = 0.98411330729784649067899691329815
y[1] (numeric) = 0.98411330729784649067899691329806
absolute error = 9e-32
relative error = 9.1452883862651680899418352135496e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07664
Order of pole (three term test) = -38.81
Radius of convergence (six term test) for eq 1 = 0.3456
Order of pole (six term test) = -12.19
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = 0.97713562247304922327713536576483
y[1] (numeric) = 0.97713562247304922327713536576471
absolute error = 1.2e-31
relative error = 1.2280792680169611666678380211140e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.629
Order of pole (six term test) = -8.816
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = 0.97012745704458073300445759952675
y[1] (numeric) = 0.97012745704458073300445759952656
absolute error = 1.9e-31
relative error = 1.9585055408989299303930885355976e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1071
Order of pole (three term test) = -46.46
Radius of convergence (six term test) for eq 1 = 0.3996
Order of pole (six term test) = -12.49
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = 0.96308899335566833255108326740178
y[1] (numeric) = 0.96308899335566833255108326740171
absolute error = 7e-32
relative error = 7.2682795134124257870626537932003e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06764
Order of pole (three term test) = -49.74
Radius of convergence (six term test) for eq 1 = 0.6447
Order of pole (six term test) = -11.62
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = 0.95602041330862334646623746501355
y[1] (numeric) = 0.95602041330862334646623746501344
absolute error = 1.1e-31
relative error = 1.1506030464277304477987398731526e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3855
Order of pole (three term test) = -69.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=180046984, alloc=4586680, time=14.63
x[1] = 1.29
y[1] (analytic) = 0.94892189836553518242781637950302
y[1] (numeric) = 0.94892189836553518242781637950287
absolute error = 1.5e-31
relative error = 1.5807412628833479128972093463819e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.8208
Order of pole (six term test) = -10.01
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = 0.94179362954896458407364062857779
y[1] (numeric) = 0.94179362954896458407364062857763
absolute error = 1.6e-31
relative error = 1.6988859871204031692296694059692e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.272
Order of pole (six term test) = -10.65
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = 0.93463578744263606616904527728
y[1] (numeric) = 0.93463578744263606616904527727978
absolute error = 2.2e-31
relative error = 2.3538580798619660807078393192556e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08532
Order of pole (three term test) = 7.005
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = 0.92744855219212953288484198131523
y[1] (numeric) = 0.92744855219212953288484198131508
absolute error = 1.5e-31
relative error = 1.6173403866495671093540388115168e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = 0.92023210350557107995907558542752
y[1] (numeric) = 0.92023210350557107995907558542735
absolute error = 1.7e-31
relative error = 1.8473600231115042919148126504368e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4113
Order of pole (three term test) = -72.06
Radius of convergence (six term test) for eq 1 = 0.6806
Order of pole (six term test) = -12.43
TOP MAIN SOLVE Loop
bytes used=184048020, alloc=4586680, time=14.96
x[1] = 1.34
y[1] (analytic) = 0.91298662065432298151538480287687
y[1] (numeric) = 0.91298662065432298151538480287678
absolute error = 9e-32
relative error = 9.8577567254488825130328313291163e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05499
Order of pole (three term test) = -6.814
Radius of convergence (six term test) for eq 1 = 0.6167
Order of pole (six term test) = -6.314
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = 0.9057122824736728623101643173389
y[1] (numeric) = 0.90571228247367286231016431733873
absolute error = 1.7e-31
relative error = 1.8769757602899852462601868891452e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3037
Order of pole (three term test) = -43.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = 0.89840926736352205618011378123045
y[1] (numeric) = 0.89840926736352205618011378123025
absolute error = 2.0e-31
relative error = 2.2261569116146960471081760047973e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.393
Order of pole (six term test) = -11.27
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = 0.89107775328907315146114773434518
y[1] (numeric) = 0.89107775328907315146114773434502
absolute error = 1.6e-31
relative error = 1.7955784375653091659637836147205e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05318
Order of pole (three term test) = -29.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = 0.88371791778151672414902943348432
y[1] (numeric) = 0.88371791778151672414902943348418
absolute error = 1.4e-31
relative error = 1.5842159266325124860781109272545e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.043
Order of pole (six term test) = -10.5
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = 0.87632993793871725957148096726067
y[1] (numeric) = 0.87632993793871725957148096726056
absolute error = 1.1e-31
relative error = 1.2552349889898708903940940150239e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02494
Order of pole (three term test) = 1.108
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=188048888, alloc=4586680, time=15.29
x[1] = 1.4
y[1] (analytic) = 0.86891399042589826334091183017841
y[1] (numeric) = 0.86891399042589826334091183017826
absolute error = 1.5e-31
relative error = 1.7262928397145209706518069197060e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2198
Order of pole (three term test) = -38.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = 0.86147025147632656235629834619829
y[1] (numeric) = 0.86147025147632656235629834619816
absolute error = 1.3e-31
relative error = 1.5090480463743841244263717725148e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03732
Order of pole (three term test) = -1.676
Radius of convergence (six term test) for eq 1 = 0.8305
Order of pole (six term test) = -12.24
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = 0.85399889689199579662213696404437
y[1] (numeric) = 0.85399889689199579662213696404436
absolute error = 1e-32
relative error = 1.1709616998796531063686962497027e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5966
Order of pole (six term test) = -12.09
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (analytic) = 0.84650010204430910265178549423719
y[1] (numeric) = 0.84650010204430910265178549423705
absolute error = 1.4e-31
relative error = 1.6538686724537672450506967886651e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02169
Order of pole (three term test) = -27
Radius of convergence (six term test) for eq 1 = 0.5184
Order of pole (six term test) = -11.12
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 0.8389740418747609892218978210054
y[1] (numeric) = 0.83897404187476098922189782100522
absolute error = 1.8e-31
relative error = 2.1454775835230161867237075282033e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0147
Order of pole (three term test) = -29.4
Radius of convergence (six term test) for eq 1 = 0.5635
Order of pole (six term test) = -11.45
TOP MAIN SOLVE Loop
bytes used=192049872, alloc=4586680, time=15.62
x[1] = 1.45
y[1] (analytic) = 0.83142089089561840624404950058915
y[1] (numeric) = 0.83142089089561840624404950058905
absolute error = 1.0e-31
relative error = 1.2027602516972911040053134918917e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1062
Order of pole (three term test) = -23.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = 0.82384082319060100751904395073818
y[1] (numeric) = 0.82384082319060100751904395073804
absolute error = 1.4e-31
relative error = 1.6993574008362787422415233367840e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3733
Order of pole (three term test) = 79.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = 0.81623401241556060813878164419837
y[1] (numeric) = 0.81623401241556060813878164419822
absolute error = 1.5e-31
relative error = 1.8377082762832980686009939245553e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07827
Order of pole (three term test) = -37.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = 0.80860063179915983729996784141234
y[1] (numeric) = 0.80860063179915983729996784141228
absolute error = 6e-32
relative error = 7.4202267028283494320434427685618e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 0.80094085414354998729332793428085
y[1] (numeric) = 0.80094085414354998729332793428079
absolute error = 6e-32
relative error = 7.4911898537324951983093537737109e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02839
Order of pole (three term test) = -4.239
Radius of convergence (six term test) for eq 1 = 1.342
Order of pole (six term test) = -9.226
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = 0.7932548518250480594313934234041
y[1] (numeric) = 0.79325485182504805943139342340404
absolute error = 6e-32
relative error = 7.5637734659873178385498442660554e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=196052084, alloc=4652204, time=15.95
x[1] = 1.51
y[1] (analytic) = 0.78554279679481300767731591549317
y[1] (numeric) = 0.78554279679481300767731591549299
absolute error = 1.8e-31
relative error = 2.2914092107322414467134933493185e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.11
Order of pole (six term test) = -19.4
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = 0.77780486057952118073656130535769
y[1] (numeric) = 0.77780486057952118073656130535766
absolute error = 3e-32
relative error = 3.8570085532311817248357762887789e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = 0.77004121428204096337273149780351
y[1] (numeric) = 0.77004121428204096337273149780339
absolute error = 1.2e-31
relative error = 1.5583581472568806776463323156092e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = 0.76225202858210661770815662864271
y[1] (numeric) = 0.76225202858210661770815662864263
absolute error = 8e-32
relative error = 1.0495216411402797963619429008969e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2528
Order of pole (three term test) = -92.18
Radius of convergence (six term test) for eq 1 = 0.4904
Order of pole (six term test) = -11.89
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = 0.75443747373699132526929676061439
y[1] (numeric) = 0.7544374737369913252692967606144
absolute error = 1e-32
relative error = 1.3254908919710099168071190657738e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=200053164, alloc=4652204, time=16.28
x[1] = 1.56
y[1] (analytic) = 0.74659771958217943053638845904851
y[1] (numeric) = 0.7465977195821794305363884590483
absolute error = 2.1e-31
relative error = 2.8127597297983027219379145320353e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = 0.73873293553203788675616849336738
y[1] (numeric) = 0.73873293553203788675616849336736
absolute error = 2e-32
relative error = 2.7073383408302940093102779237895e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.537
Order of pole (six term test) = -9.985
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = 0.73084329058048690477590416374714
y[1] (numeric) = 0.73084329058048690477590416374711
absolute error = 3e-32
relative error = 4.1048471521400846166023051394772e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1103
Order of pole (three term test) = -45.83
Radius of convergence (six term test) for eq 1 = 0.5605
Order of pole (six term test) = -11.18
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = 0.72292895330166980565635741719035
y[1] (numeric) = 0.72292895330166980565635741719014
absolute error = 2.1e-31
relative error = 2.9048497648477699522672979661850e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = 0.71499009185062207782070799368926
y[1] (numeric) = 0.71499009185062207782070799368913
absolute error = 1.3e-31
relative error = 1.8182070140792943825226877710776e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05913
Order of pole (three term test) = -32.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = 0.70702687396393963949585933079012
y[1] (numeric) = 0.70702687396393963949585933079012
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01143
Order of pole (three term test) = -24.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=204053976, alloc=4652204, time=16.61
x[1] = 1.62
y[1] (analytic) = 0.69903946696044630720194985348533
y[1] (numeric) = 0.69903946696044630720194985348524
absolute error = 9e-32
relative error = 1.2874809542776854774479278693488e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04814
Order of pole (three term test) = 2.583
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = 0.69102803774186047104529158571374
y[1] (numeric) = 0.69102803774186047104529158571366
absolute error = 8e-32
relative error = 1.1576954281250841988110889452117e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.6997
Order of pole (six term test) = -10.83
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = 0.68299275279346097756935773958471
y[1] (numeric) = 0.68299275279346097756935773958464
absolute error = 7e-32
relative error = 1.0249010654022006352625153950378e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4685
Order of pole (six term test) = -11.97
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = 0.67493377818475222091784106851159
y[1] (numeric) = 0.67493377818475222091784106851161
absolute error = 2e-32
relative error = 2.9632536770926470093102591734562e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = 0.6668512795701284430632053105147
y[1] (numeric) = 0.66685127957012844306320531051454
absolute error = 1.6e-31
relative error = 2.3993355775389770869608641350315e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.007384
Order of pole (three term test) = -26.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=208055036, alloc=4652204, time=16.94
x[1] = 1.67
y[1] (analytic) = 0.65874542218953724385355299776381
y[1] (numeric) = 0.65874542218953724385355299776374
absolute error = 7e-32
relative error = 1.0626259802661562943706844292878e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = 0.65061637086914230163003426775646
y[1] (numeric) = 0.65061637086914230163003426775628
absolute error = 1.8e-31
relative error = 2.7666072982384758703543847690027e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1231
Order of pole (three term test) = -22.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = 0.6424642900219853051664230800898
y[1] (numeric) = 0.64246429002198530516642308008984
absolute error = 4e-32
relative error = 6.2260269747648058337770241745515e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03164
Order of pole (three term test) = -28.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = 0.6342893436486470976818894203837
y[1] (numeric) = 0.63428934364864709768188942038364
absolute error = 6e-32
relative error = 9.4594053330392848566706586950238e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = 0.62609169533790803367739865924558
y[1] (numeric) = 0.62609169533790803367739865924561
absolute error = 3e-32
relative error = 4.7916303990917330307888263827871e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05504
Order of pole (three term test) = -19.29
Radius of convergence (six term test) for eq 1 = 0.407
Order of pole (six term test) = -11.47
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = 0.6178715082674075493455722290549
y[1] (numeric) = 0.61787150826740754934557222905483
absolute error = 7e-32
relative error = 1.1329216360257353082378768065729e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.009527
Order of pole (three term test) = -27.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=212055908, alloc=4652204, time=17.27
x[1] = 1.73
y[1] (analytic) = 0.6096289452043029473032471844726
y[1] (numeric) = 0.6096289452043029473032471844725
absolute error = 1.0e-31
relative error = 1.6403420603082966844586655042344e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7098
Order of pole (six term test) = -10.73
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = 0.60136416850592739639537602376926
y[1] (numeric) = 0.60136416850592739639537602376925
absolute error = 1e-32
relative error = 1.6628859056974948717395141481739e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05416
Order of pole (three term test) = -0.1739
Radius of convergence (six term test) for eq 1 = 0.4421
Order of pole (six term test) = -12.45
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = 0.59307734012044714731831236701554
y[1] (numeric) = 0.59307734012044714731831236701547
absolute error = 7e-32
relative error = 1.1802845137496537926990647983756e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04427
Order of pole (three term test) = -16.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = 0.58476862158751796480993271368091
y[1] (numeric) = 0.58476862158751796480993271368083
absolute error = 8e-32
relative error = 1.3680624617445721779639788911071e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = 0.57643817403894077715344953598403
y[1] (numeric) = 0.57643817403894077715344953598394
absolute error = 9e-32
relative error = 1.5613122803681653575275518619014e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07294
Order of pole (three term test) = -20.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 0.56808615819931654374117640517919
y[1] (numeric) = 0.56808615819931654374117640517908
absolute error = 1.1e-31
relative error = 1.9363260028843339526483012487479e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
bytes used=216057272, alloc=4652204, time=17.60
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5545
Order of pole (six term test) = -11.52
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = 0.55971273438670034144391169561953
y[1] (numeric) = 0.55971273438670034144391169561942
absolute error = 1.1e-31
relative error = 1.9652938595462082045034520377371e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2666
Order of pole (three term test) = -46.73
Radius of convergence (six term test) for eq 1 = 1.137
Order of pole (six term test) = -13.64
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = 0.55131806251325467053101366565145
y[1] (numeric) = 0.55131806251325467053101366565138
absolute error = 7e-32
relative error = 1.2696845026425571722296672526613e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = 0.54290230208590198088564637492838
y[1] (numeric) = 0.54290230208590198088564637492823
absolute error = 1.5e-31
relative error = 2.7629280521316688159435529791654e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.002078
Order of pole (three term test) = -0.9762
Radius of convergence (six term test) for eq 1 = 0.2453
Order of pole (six term test) = -11.79
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = 0.53446561220697641925908296433907
y[1] (numeric) = 0.53446561220697641925908296433885
absolute error = 2.2e-31
relative error = 4.1162610835063996974239987277911e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1638
Order of pole (three term test) = -81.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = 0.52600815157487479830736029718629
y[1] (numeric) = 0.52600815157487479830736029718619
absolute error = 1.0e-31
relative error = 1.9011112223375015143042329373672e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=220058036, alloc=4652204, time=17.93
x[1] = 1.84
y[1] (analytic) = 0.51753007848470678815298683827532
y[1] (numeric) = 0.51753007848470678815298683827532
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = 0.5090315508289443312138139309396
y[1] (numeric) = 0.5090315508289443312138139309396
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = 0.50051272609807028104058932050237
y[1] (numeric) = 0.50051272609807028104058932050225
absolute error = 1.2e-31
relative error = 2.3975414358692498811265881921661e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.022
Order of pole (six term test) = -12.95
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = 0.49197376138122626590412086599556
y[1] (numeric) = 0.49197376138122626590412086599562
absolute error = 6e-32
relative error = 1.2195772358173897091387096811855e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.7843
Order of pole (six term test) = -11.7
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = 0.4834148133668597778723878798992
y[1] (numeric) = 0.48341481336685977787238787989908
absolute error = 1.2e-31
relative error = 2.4823401493270526739406458691012e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01863
Order of pole (three term test) = -23.6
Radius of convergence (six term test) for eq 1 = 0.1426
Order of pole (six term test) = -11.84
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = 0.4748360383433704881173474379656
y[1] (numeric) = 0.47483603834337048811734743796539
absolute error = 2.1e-31
relative error = 4.4225792282459757438620056533270e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3611
Order of pole (six term test) = -11.18
TOP MAIN SOLVE Loop
bytes used=224060616, alloc=4652204, time=18.25
x[1] = 1.9
y[1] (analytic) = 0.4662375921997557891905933076416
y[1] (numeric) = 0.46623759219975578919059330764162
absolute error = 2e-32
relative error = 4.2896583919022898148622616975946e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.4813
Order of pole (six term test) = -12.12
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = 0.45761963042625556500643585391184
y[1] (numeric) = 0.45761963042625556500643585391175
absolute error = 9e-32
relative error = 1.9666988480404209743603521296969e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1599
Order of pole (three term test) = -35.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = 0.44898230811499618927038239535099
y[1] (numeric) = 0.44898230811499618927038239535096
absolute error = 3e-32
relative error = 6.6817777577810950633350432510092e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.8479
Order of pole (six term test) = -11.76
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (analytic) = 0.44032577996063375309040900054392
y[1] (numeric) = 0.44032577996063375309040900054393
absolute error = 1e-32
relative error = 2.2710457699964843042455152455477e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07316
Order of pole (three term test) = -20.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = 0.43165020026099652250782663553908
y[1] (numeric) = 0.43165020026099652250782663553902
absolute error = 6e-32
relative error = 1.3900144136090081084458968692982e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02511
Order of pole (three term test) = -18.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=228061404, alloc=4652204, time=18.59
x[1] = 1.95
y[1] (analytic) = 0.42295572291772662668395689644434
y[1] (numeric) = 0.42295572291772662668395689644425
absolute error = 9e-32
relative error = 2.1278823083215924602234213276199e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05966
Order of pole (three term test) = -30.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = 0.41424250143692097747824528737794
y[1] (numeric) = 0.41424250143692097747824528737784
absolute error = 1.0e-31
relative error = 2.4140449049317929365746642990835e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.113
Order of pole (three term test) = -23.66
Radius of convergence (six term test) for eq 1 = 0.5394
Order of pole (six term test) = -11.59
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = 0.4055106889297714211528531325236
y[1] (numeric) = 0.40551068892977142115285313252354
absolute error = 6e-32
relative error = 1.4796157447378934837222135106302e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5188
Order of pole (six term test) = -12.29
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = 0.39676043811320412293818274176717
y[1] (numeric) = 0.3967604381132041229381827417672
absolute error = 3e-32
relative error = 7.5612377440314165417365528569349e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = 0.38799190131051818519320438206401
y[1] (numeric) = 0.38799190131051818519320438206402
absolute error = 1e-32
relative error = 2.5773733849142348307707731958681e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0688
Order of pole (three term test) = -32.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 0.37920523045202349989386794106468
y[1] (numeric) = 0.37920523045202349989386794106468
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.153
Order of pole (three term test) = -29.23
Radius of convergence (six term test) for eq 1 = 0.683
Order of pole (six term test) = -11.21
TOP MAIN SOLVE Loop
bytes used=232062464, alloc=4652204, time=18.92
x[1] = 2.01
y[1] (analytic) = 0.37040057707567783618229690537076
y[1] (numeric) = 0.37040057707567783618229690537076
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = 0.36157809232772316370887741285511
y[1] (numeric) = 0.36157809232772316370887741285489
absolute error = 2.2e-31
relative error = 6.0844394245157648058020952678573e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.309
Order of pole (three term test) = -311.8
Radius of convergence (six term test) for eq 1 = 0.6927
Order of pole (six term test) = -11.48
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 0.35273792696332121249877067652739
y[1] (numeric) = 0.35273792696332121249877067652724
absolute error = 1.5e-31
relative error = 4.2524488730580272094606302157033e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5828
Order of pole (six term test) = -11.23
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = 0.34388023134718827007379301621636
y[1] (numeric) = 0.34388023134718827007379301621626
absolute error = 1.0e-31
relative error = 2.9079892033409162712200218486568e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = 0.33500515545422921656002407361727
y[1] (numeric) = 0.33500515545422921656002407361728
absolute error = 1e-32
relative error = 2.9850286890185697505995074208792e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5354
Order of pole (six term test) = -11.86
TOP MAIN SOLVE Loop
bytes used=236063688, alloc=4652204, time=19.25
x[1] = 2.06
y[1] (analytic) = 0.32611284887017079851092052580639
y[1] (numeric) = 0.32611284887017079851092052580631
absolute error = 8e-32
relative error = 2.4531385462781597379052510527128e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1064
Order of pole (three term test) = -16.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = 0.31720346079219414217512975187826
y[1] (numeric) = 0.31720346079219414217512975187809
absolute error = 1.7e-31
relative error = 5.3593362309300322005008711271210e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.478
Order of pole (six term test) = -5.972
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 0.30827714002956650693761544670587
y[1] (numeric) = 0.30827714002956650693761544670586
absolute error = 1e-32
relative error = 3.2438344273730161986665631018336e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06195
Order of pole (three term test) = -75.45
Radius of convergence (six term test) for eq 1 = 0.3818
Order of pole (six term test) = -12.01
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = 0.29933403500427227966212511469582
y[1] (numeric) = 0.29933403500427227966212511469567
absolute error = 1.5e-31
relative error = 5.0111241108235188704049102902376e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3191
Order of pole (three term test) = -77.69
Radius of convergence (six term test) for eq 1 = 0.8767
Order of pole (six term test) = -11.07
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = 0.2903742937516432106624477145795
y[1] (numeric) = 0.29037429375164321066244771457936
absolute error = 1.4e-31
relative error = 4.8213634268790278692134293975251e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1187
Order of pole (three term test) = -19.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = 0.28139806392098789202932846351791
y[1] (numeric) = 0.28139806392098789202932846351774
absolute error = 1.7e-31
relative error = 6.0412640240386764187072641190626e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06051
Order of pole (three term test) = -4.203
Radius of convergence (six term test) for eq 1 = 1.993
Order of pole (six term test) = -9.351
TOP MAIN SOLVE Loop
bytes used=240064608, alloc=4652204, time=19.58
x[1] = 2.12
y[1] (analytic) = 0.27240549277622047903932694482916
y[1] (numeric) = 0.27240549277622047903932694482916
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 0.26339672719648865537132419827793
y[1] (numeric) = 0.26339672719648865537132419827795
absolute error = 2e-32
relative error = 7.5931087727906363359866739811625e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.077
Order of pole (six term test) = -12.22
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 0.25437191367680084285580440481315
y[1] (numeric) = 0.25437191367680084285580440481301
absolute error = 1.4e-31
relative error = 5.5037522805242095170769083801516e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01906
Order of pole (three term test) = -20.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = 0.24533119832865265648145710869903
y[1] (numeric) = 0.24533119832865265648145710869904
absolute error = 1e-32
relative error = 4.0761224288334153719016565401677e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1471
Order of pole (three term test) = -18.17
Radius of convergence (six term test) for eq 1 = 0.997
Order of pole (six term test) = -12.17
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 0.23627472688065260538306664889203
y[1] (numeric) = 0.23627472688065260538306664889203
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01854
Order of pole (three term test) = 2.268
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=244065648, alloc=4652204, time=19.91
x[1] = 2.17
y[1] (analytic) = 0.22720264467914704053407659803758
y[1] (numeric) = 0.22720264467914704053407659803753
absolute error = 5e-32
relative error = 2.2006786087639703510285757621221e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01748
Order of pole (three term test) = -2.061
Radius of convergence (six term test) for eq 1 = 0.1765
Order of pole (six term test) = -11.38
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 0.21811509668884434986663853137507
y[1] (numeric) = 0.218115096688844349866638531375
absolute error = 7e-32
relative error = 3.2093147637487762793276333828097e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.326
Order of pole (six term test) = -11.46
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 0.20901222749343840154137636887588
y[1] (numeric) = 0.20901222749343840154137636887574
absolute error = 1.4e-31
relative error = 6.6981727183590286352236471886084e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09824
Order of pole (three term test) = -30.07
Radius of convergence (six term test) for eq 1 = 0.7745
Order of pole (six term test) = -12.22
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = 0.19989418129623123608851985188585
y[1] (numeric) = 0.19989418129623123608851985188584
absolute error = 1e-32
relative error = 5.0026468680349416202748132665377e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.486
Order of pole (three term test) = 445.4
Radius of convergence (six term test) for eq 1 = 0.431
Order of pole (six term test) = -12.41
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 0.19076110192075500814148343015091
y[1] (numeric) = 0.19076110192075500814148343015088
absolute error = 3e-32
relative error = 1.5726476570921908953041476234324e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1193
Order of pole (three term test) = -12.05
Radius of convergence (six term test) for eq 1 = 0.767
Order of pole (six term test) = -12.02
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 0.18161313281139317848338994612652
y[1] (numeric) = 0.18161313281139317848338994612639
absolute error = 1.3e-31
relative error = 7.1580726562878100444828613475707e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2437
Order of pole (six term test) = -12.01
TOP MAIN SOLVE Loop
bytes used=248066908, alloc=4652204, time=20.25
x[1] = 2.23
y[1] (analytic) = 0.17245041703400095712646201068961
y[1] (numeric) = 0.17245041703400095712646201068942
absolute error = 1.9e-31
relative error = 1.1017659641990828162965352909623e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2149
Order of pole (three term test) = -17.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = 0.16327309727652499814362786752253
y[1] (numeric) = 0.16327309727652499814362786752257
absolute error = 4e-32
relative error = 2.4498830895732080295118267092756e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1128
Order of pole (three term test) = -8.154
Radius of convergence (six term test) for eq 1 = 0.8648
Order of pole (six term test) = -11.78
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 0.15408131584962234697111284230509
y[1] (numeric) = 0.15408131584962234697111284230502
absolute error = 7e-32
relative error = 4.5430556984804961914850769442398e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2104
Order of pole (three term test) = -34.23
Radius of convergence (six term test) for eq 1 = 4.72
Order of pole (six term test) = 7.863
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 0.14487521468727864090021216717645
y[1] (numeric) = 0.14487521468727864090021216717624
absolute error = 2.1e-31
relative error = 1.4495233049579729560592785310661e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07006
Order of pole (three term test) = -29.16
Radius of convergence (six term test) for eq 1 = 0.6907
Order of pole (six term test) = -11.23
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = 0.13565493534742556347586606050004
y[1] (numeric) = 0.13565493534742556347586606049988
absolute error = 1.6e-31
relative error = 1.1794631694764686868605772377683e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08655
Order of pole (three term test) = 2.051
Radius of convergence (six term test) for eq 1 = 2.646
Order of pole (six term test) = -12.81
TOP MAIN SOLVE Loop
bytes used=252068960, alloc=4652204, time=20.57
x[1] = 2.28
y[1] (analytic) = 0.12642061901255755351908342650922
y[1] (numeric) = 0.12642061901255755351908342650918
absolute error = 4e-32
relative error = 3.1640408275509819167351453167487e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1214
Order of pole (three term test) = -29.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 0.11717240649034776948968641872355
y[1] (numeric) = 0.11717240649034776948968641872358
absolute error = 3e-32
relative error = 2.5603297652226071935831211042982e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01134
Order of pole (three term test) = -1.149
Radius of convergence (six term test) for eq 1 = 0.8377
Order of pole (six term test) = -11.57
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 0.10791043821426330990527438485121
y[1] (numeric) = 0.10791043821426330990527438485102
absolute error = 1.9e-31
relative error = 1.7607193812218836287647409582074e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.879
Order of pole (three term test) = -643
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 0.09863485424417969053173237899442
y[1] (numeric) = 0.098634854244179690531732378994331
absolute error = 8.9e-32
relative error = 9.0231795527037816592554109013264e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3264
Order of pole (three term test) = -46.72
Radius of convergence (six term test) for eq 1 = 0.5514
Order of pole (six term test) = -11.07
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = 0.08934579426699457906003648912541
y[1] (numeric) = 0.089345794266994579060036489125365
absolute error = 4.5e-32
relative error = 5.0366108857374102766756161342998e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.006761
Order of pole (three term test) = -26.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = 0.08004339759724078798353568373989
y[1] (numeric) = 0.080043397597240787983535683739891
absolute error = 1e-33
relative error = 1.2493222801857569455288232283254e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04146
Order of pole (three term test) = -1.158
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=256069976, alloc=4652204, time=20.90
x[1] = 2.34
y[1] (analytic) = 0.0707278031776985263893177311225
y[1] (numeric) = 0.070727803177698526389317731122432
absolute error = 6.8e-32
relative error = 9.6143237800211160533358106448234e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.349
Order of pole (three term test) = -210.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 0.06139914958000691137669498749622
y[1] (numeric) = 0.061399149580006911376694987496052
absolute error = 1.68e-31
relative error = 2.7361942494184801236921563614911e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.02138
Order of pole (three term test) = -28.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 0.05205757500527473981527448627069
y[1] (numeric) = 0.052057575005274739815274486270619
absolute error = 7.1e-32
relative error = 1.3638745176433192821361444320778e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.472
Order of pole (three term test) = -71.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = 0.0427032172846905211545057893973
y[1] (numeric) = 0.042703217284690521154505789397376
absolute error = 7.6e-32
relative error = 1.7797253891511042704503152855900e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.005635
Order of pole (three term test) = -25.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = 0.03333621388013177199602948325097
y[1] (numeric) = 0.03333621388013177199602948325101
absolute error = 4.0e-32
relative error = 1.1998963092758357137195783125150e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.8968
Order of pole (six term test) = -11.15
TOP MAIN SOLVE Loop
bytes used=260071008, alloc=4652204, time=21.23
x[1] = 2.39
y[1] (analytic) = 0.02395670188477357313957901525618
y[1] (numeric) = 0.023956701884773573139579015256198
absolute error = 1.8e-32
relative error = 7.5135551156315301243492714756292e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0808
Order of pole (three term test) = -23.75
Radius of convergence (six term test) for eq 1 = 1.264
Order of pole (six term test) = -10.4
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 0.01456481802369638981261877341731
y[1] (numeric) = 0.014564818023696389812618773417324
absolute error = 1.4e-32
relative error = 9.6122038581069444479113801318287e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1524
Order of pole (three term test) = -42.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 0.00516069865449315579333190876149
y[1] (numeric) = 0.0051606986544931557933319087613674
absolute error = 1.226e-31
relative error = 2.3756473339759620373168664449967e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = -0.00425552023212437786399760977137
y[1] (numeric) = -0.004255520232124377863997609771433
absolute error = 6.30e-32
relative error = 1.4804300429456558329107550641054e-27 %
Correct digits = 29
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.258
Order of pole (six term test) = -11.59
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = -0.0136837030117200287927328374927
y[1] (numeric) = -0.013683703011720028792732837492705
absolute error = 5e-33
relative error = 3.6539816712753287326197516219171e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = -0.02312371442552830325885395052728
y[1] (numeric) = -0.023123714425528303258853950527358
absolute error = 7.8e-32
relative error = 3.3731604950928184764505047204631e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.26
Order of pole (six term test) = -10.88
TOP MAIN SOLVE Loop
bytes used=264072064, alloc=4652204, time=21.56
x[1] = 2.45
y[1] (analytic) = -0.03257541957985024937981079098334
y[1] (numeric) = -0.032575419579850249379810790983368
absolute error = 2.8e-32
relative error = 8.5954380207951621470538241583011e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.794
Order of pole (six term test) = -10.7
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = -0.04203868394545004291048550108396
y[1] (numeric) = -0.042038683945450042910485501083959
absolute error = 1e-33
relative error = 2.3787614314891811079035421989401e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07062
Order of pole (three term test) = -10.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = -0.05151337335695230489005994226394
y[1] (numeric) = -0.051513373356952304890059942264116
absolute error = 1.76e-31
relative error = 3.4165885192654896270773515399498e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03042
Order of pole (three term test) = -1.554
Radius of convergence (six term test) for eq 1 = 2.82
Order of pole (six term test) = -6.346
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = -0.06099935401224015044414926062277
y[1] (numeric) = -0.06099935401224015044414926062275
absolute error = 2.0e-32
relative error = 3.2787232461489335477619586835563e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.8935
Order of pole (six term test) = -10.72
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = -0.070496492471853968037129235488
y[1] (numeric) = -0.070496492471853968037129235487999
absolute error = 1e-33
relative error = 1.4185102902804055956385827600976e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08574
Order of pole (three term test) = -12.92
Radius of convergence (six term test) for eq 1 = 1.47
Order of pole (six term test) = -10.36
TOP MAIN SOLVE Loop
bytes used=268073184, alloc=4652204, time=21.89
x[1] = 2.5
y[1] (analytic) = -0.08000465565839092847015093343133
y[1] (numeric) = -0.080004655658390928470150933431384
absolute error = 5.4e-32
relative error = 6.7496072016824501983725112796738e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = -0.08952371085590522292090168609172
y[1] (numeric) = -0.089523710855905222920901686091873
absolute error = 1.53e-31
relative error = 1.7090444368002615210958671135652e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09898
Order of pole (three term test) = -18.42
Radius of convergence (six term test) for eq 1 = 1.175
Order of pole (six term test) = -11.1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = -0.09905352570930902932173651687829
y[1] (numeric) = -0.099053525709309029321736516878398
absolute error = 1.08e-31
relative error = 1.0903195946497256576031380006151e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0617
Order of pole (three term test) = -8.636
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = -0.10859396822377420637336885924381
y[1] (numeric) = -0.10859396822377420637336885924377
absolute error = 4e-32
relative error = 3.6834458353684970004146445471164e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 76.21
Order of pole (six term test) = -24.02
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = -0.11814490676413471449187373799895
y[1] (numeric) = -0.11814490676413471449187373799907
absolute error = 1.2e-31
relative error = 1.0157018468817179407140042536044e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = -0.12770621005428976298732052529978
y[1] (numeric) = -0.12770621005428976298732052529999
absolute error = 2.1e-31
relative error = 1.6443992810586576234217992030891e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03252
Order of pole (three term test) = -16.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=272074064, alloc=4652204, time=22.22
x[1] = 2.56
y[1] (analytic) = -0.13727774717660768277291593471962
y[1] (numeric) = -0.13727774717660768277291593471973
absolute error = 1.1e-31
relative error = 8.0129520087829756818361590100732e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6287
Order of pole (three term test) = 59.3
Radius of convergence (six term test) for eq 1 = 2.107
Order of pole (six term test) = -10.97
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = -0.1468593875713305239041010804611
y[1] (numeric) = -0.1468593875713305239041010804613
absolute error = 2.0e-31
relative error = 1.3618468884248802138813455481964e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3519
Order of pole (three term test) = -18.36
Radius of convergence (six term test) for eq 1 = 5.303
Order of pole (six term test) = -11.43
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = -0.15645100103597937724760920448954
y[1] (numeric) = -0.15645100103597937724760920448964
absolute error = 1.0e-31
relative error = 6.3917775749483879834563872978601e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1465
Order of pole (three term test) = -28.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = -0.1660524577247604195810530624148
y[1] (numeric) = -0.16605245772476041958105306241498
absolute error = 1.8e-31
relative error = 1.0839947957792848376060318929641e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1594
Order of pole (three term test) = -15.97
Radius of convergence (six term test) for eq 1 = 0.458
Order of pole (six term test) = -11.14
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = -0.17566362814797168142417295956683
y[1] (numeric) = -0.17566362814797168142417295956704
absolute error = 2.1e-31
relative error = 1.1954665983734822859985526156940e-28 %
Correct digits = 30
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = -0.18528438317141053690343804209945
y[1] (numeric) = -0.18528438317141053690343804209954
absolute error = 9e-32
relative error = 4.8573980418381553166022265099050e-29 %
Correct digits = 31
h = 0.01
bytes used=276075216, alloc=4652204, time=22.55
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.01051
Order of pole (three term test) = -26.19
Radius of convergence (six term test) for eq 1 = 0.6704
Order of pole (six term test) = -11.15
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = -0.1949145940157819149522546743886
y[1] (numeric) = -0.19491459401578191495225467438856
absolute error = 4e-32
relative error = 2.0521808642384810658864456073803e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.113
Order of pole (three term test) = -25.56
Radius of convergence (six term test) for eq 1 = 0.8348
Order of pole (six term test) = -10.87
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = -0.20455413225610723114959657367169
y[1] (numeric) = -0.20455413225610723114959657367176
absolute error = 7e-32
relative error = 3.4220770427828919329396583024865e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = -0.21420286982113403950043182604996
y[1] (numeric) = -0.21420286982113403950043182605007
absolute error = 1.1e-31
relative error = 5.1353186860593124137570113345014e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = -0.22386067899274640346188197487397
y[1] (numeric) = -0.22386067899274640346188197487409
absolute error = 1.2e-31
relative error = 5.3604769064373414892179234438156e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.9858
Order of pole (six term test) = -11
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = -0.23352743240537598551960805339605
y[1] (numeric) = -0.2335274324053759855196080533961
absolute error = 5e-32
relative error = 2.1410760819399545883377410786912e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8631
Order of pole (three term test) = 77.01
Radius of convergence (six term test) for eq 1 = 1.376
Order of pole (six term test) = -10.82
TOP MAIN SOLVE Loop
bytes used=280076536, alloc=4652204, time=22.88
x[1] = 2.67
y[1] (analytic) = -0.24320300304541385461947772861921
y[1] (numeric) = -0.24320300304541385461947772861924
absolute error = 3e-32
relative error = 1.2335373997992134655419116834120e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = -0.25288726425062301076012663275029
y[1] (numeric) = -0.25288726425062301076012663275041
absolute error = 1.2e-31
relative error = 4.7451974442285252051134885551883e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03315
Order of pole (three term test) = -34.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = -0.262580089709551626052585482796
y[1] (numeric) = -0.26258008970955162605258548279604
absolute error = 4e-32
relative error = 1.5233447457591053623565660643602e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.05141
Order of pole (three term test) = -17.39
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = -0.2722813534609470015537027278625
y[1] (numeric) = -0.27228135346094700155370272786245
absolute error = 5e-32
relative error = 1.8363358108975847278130392344774e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 565.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.0659
Order of pole (three term test) = -3.842
Radius of convergence (six term test) for eq 1 = 4.887
Order of pole (six term test) = -11.13
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = -0.28199092989317023918065021786787
y[1] (numeric) = -0.28199092989317023918065021786803
absolute error = 1.6e-31
relative error = 5.6739413590577037293048784651590e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = -0.29170869374361162801435675687512
y[1] (numeric) = -0.29170869374361162801435675687506
absolute error = 6e-32
relative error = 2.0568464803018573060047144786700e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.8868
Order of pole (six term test) = -11.08
bytes used=284079624, alloc=4652204, time=23.21
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = -0.30143452009810674430027138933691
y[1] (numeric) = -0.30143452009810674430027138933697
absolute error = 6e-32
relative error = 1.9904820450050654018537981675530e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = -0.31116828439035326445541486846486
y[1] (numeric) = -0.31116828439035326445541486846497
absolute error = 1.1e-31
relative error = 3.5350646424494726999842129711599e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.005866
Order of pole (three term test) = -0.8046
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = -0.3209098624013284903912339728774
y[1] (numeric) = -0.32090986240132849039123397287743
absolute error = 3e-32
relative error = 9.3484194519650285281629278369413e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.9903
Order of pole (six term test) = -11
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = -0.33065913025870758646232917093895
y[1] (numeric) = -0.33065913025870758646232917093907
absolute error = 1.2e-31
relative error = 3.6291149712428035021911210199427e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.31
Order of pole (six term test) = -10.97
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = -0.34041596443628252735168158195616
y[1] (numeric) = -0.34041596443628252735168158195609
absolute error = 7e-32
relative error = 2.0563077914373864080555943567223e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08384
Order of pole (three term test) = -9.134
Radius of convergence (six term test) for eq 1 = 1.231
Order of pole (six term test) = -11.03
TOP MAIN SOLVE Loop
bytes used=288080520, alloc=4652204, time=23.54
x[1] = 2.78
y[1] (analytic) = -0.35018024175338175620356024989981
y[1] (numeric) = -0.35018024175338175620356024989987
absolute error = 6e-32
relative error = 1.7134033519302797373930045566835e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.05299
Order of pole (three term test) = 1.833
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = -0.35995183937429055231584542881732
y[1] (numeric) = -0.35995183937429055231584542881731
absolute error = 1e-32
relative error = 2.7781494372644805759981751194358e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.201
Order of pole (six term test) = -11.01
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = -0.36973063480767210770405787978151
y[1] (numeric) = -0.36973063480767210770405787978169
absolute error = 1.8e-31
relative error = 4.8684091350351070253499897342651e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.2559
Order of pole (six term test) = -10.94
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = -0.37951650590598931184993809737539
y[1] (numeric) = -0.37951650590598931184993809737551
absolute error = 1.2e-31
relative error = 3.1619178120733807277066274200997e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04598
Order of pole (three term test) = -22.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = -0.38930933086492724394797291950733
y[1] (numeric) = -0.38930933086492724394797291950732
absolute error = 1e-32
relative error = 2.5686515085017441788224887315402e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.9085
Order of pole (three term test) = 363.6
Radius of convergence (six term test) for eq 1 = 3.712
Order of pole (six term test) = -11.21
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = -0.39910898822281637196382012807913
y[1] (numeric) = -0.39910898822281637196382012807912
absolute error = 1e-32
relative error = 2.5055812560195098259054523430164e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.337
Order of pole (six term test) = -11.11
TOP MAIN SOLVE Loop
bytes used=292081412, alloc=4652204, time=23.87
x[1] = 2.84
y[1] (analytic) = -0.40891535686005645781913441987036
y[1] (numeric) = -0.40891535686005645781913441987046
absolute error = 1.0e-31
relative error = 2.4454938735456469419063261052193e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1153
Order of pole (three term test) = -21.03
Radius of convergence (six term test) for eq 1 = 1.423
Order of pole (six term test) = -11.01
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = -0.41872831599854116801785051722084
y[1] (numeric) = -0.41872831599854116801785051722098
absolute error = 1.4e-31
relative error = 3.3434567152723379270753013598673e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.03184
Order of pole (three term test) = -0.1266
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = -0.42854774520108338902953119690498
y[1] (numeric) = -0.42854774520108338902953119690496
absolute error = 2e-32
relative error = 4.6669245665067237533163363818007e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.339
Order of pole (six term test) = -10.95
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = -0.43837352437084124674593964323076
y[1] (numeric) = -0.4383735243708412467459396432308
absolute error = 4e-32
relative error = 9.1246386417629720493394626531175e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 484.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.05
Order of pole (three term test) = -11.27
Radius of convergence (six term test) for eq 1 = 1.817
Order of pole (six term test) = -10.94
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = -0.44820553375074482932754677809521
y[1] (numeric) = -0.4482055337507448293275467780952
absolute error = 1e-32
relative error = 2.2311192626999514303517599794305e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=296082192, alloc=4652204, time=24.20
x[1] = 2.89
y[1] (analytic) = -0.45804365392292361275723508670654
y[1] (numeric) = -0.45804365392292361275723508670658
absolute error = 4e-32
relative error = 8.7327920946877523276432279929421e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1675
Order of pole (three term test) = -28.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = -0.46788776580813458841901094319542
y[1] (numeric) = -0.46788776580813458841901094319543
absolute error = 1e-32
relative error = 2.1372646884083461355110141148255e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = -0.47773775066519109202008754558054
y[1] (numeric) = -0.47773775066519109202008754558051
absolute error = 3e-32
relative error = 6.2795958573984759926806910428998e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.084
Order of pole (six term test) = -11.09
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = -0.48759349009039233317525029478961
y[1] (numeric) = -0.48759349009039233317525029478962
absolute error = 1e-32
relative error = 2.0508887430277532651940554862913e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = -0.49745486601695362497296579787143
y[1] (numeric) = -0.4974548660169536249729657978714
absolute error = 3e-32
relative error = 6.0306978681715374154521898357095e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.502
Order of pole (six term test) = -11.19
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = -0.50732176071443731284324464141016
y[1] (numeric) = -0.50732176071443731284324464141019
absolute error = 3e-32
relative error = 5.9134068993516884926806144689551e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.593
Order of pole (six term test) = -11.03
TOP MAIN SOLVE Loop
bytes used=300083280, alloc=4652204, time=24.53
x[1] = 2.95
y[1] (analytic) = -0.51719405678818440204781666769916
y[1] (numeric) = -0.51719405678818440204781666769918
absolute error = 2e-32
relative error = 3.8670204611788399789712273177069e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 575.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1285
Order of pole (three term test) = -18.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = -0.52707163717874688311372569366704
y[1] (numeric) = -0.52707163717874688311372569366716
absolute error = 1.2e-31
relative error = 2.2767303633017185932724311497151e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = -0.53695438516132075453199844112039
y[1] (numeric) = -0.53695438516132075453199844112048
absolute error = 9e-32
relative error = 1.6761200296922932329230231069792e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03671
Order of pole (three term test) = -24.01
Radius of convergence (six term test) for eq 1 = 0.8032
Order of pole (six term test) = -10.99
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = -0.5468421843451797420435898967836
y[1] (numeric) = -0.54684218434517974204358989678378
absolute error = 1.8e-31
relative error = 3.2916260879826296576384914607638e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.5759
Order of pole (six term test) = -11.01
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = -0.55673491867310971383535439212944
y[1] (numeric) = -0.55673491867310971383535439212958
absolute error = 1.4e-31
relative error = 2.5146617412406612422337492347562e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.185
Order of pole (three term test) = -9.692
Radius of convergence (six term test) for eq 1 = 7.447
Order of pole (six term test) = -12.59
TOP MAIN SOLVE Loop
bytes used=304084724, alloc=4652204, time=24.86
x[1] = 3
y[1] (analytic) = -0.56663247242084379096933838630693
y[1] (numeric) = -0.566632472420843790969338386307
absolute error = 7e-32
relative error = 1.2353686632348574059827596372599e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2361
Order of pole (three term test) = -61.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = -0.57653473019649815236923725084239
y[1] (numeric) = -0.57653473019649815236923725084259
absolute error = 2.0e-31
relative error = 3.4690017708358134148573330379124e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06106
Order of pole (three term test) = -4.651
Radius of convergence (six term test) for eq 1 = 0.3848
Order of pole (six term test) = -11.05
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = -0.58644157694000853368840429242015
y[1] (numeric) = -0.58644157694000853368840429242014
absolute error = 1e-32
relative error = 1.7051996981828889499901231435802e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = -0.59635289792256741938434581017999
y[1] (numeric) = -0.59635289792256741938434581018005
absolute error = 6e-32
relative error = 1.0061156776300366587918574286217e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = -0.60626857874606192732518116684082
y[1] (numeric) = -0.60626857874606192732518116684104
absolute error = 2.2e-31
relative error = 3.6287547749055934395522622706765e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.111
Order of pole (three term test) = -4.968
Radius of convergence (six term test) for eq 1 = 2.834
Order of pole (six term test) = -11.05
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = -0.61618850534251238525409165876576
y[1] (numeric) = -0.61618850534251238525409165876578
absolute error = 2e-32
relative error = 3.2457599949682394710708207035368e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1102
Order of pole (three term test) = -18.96
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=308085940, alloc=4652204, time=25.19
x[1] = 3.06
y[1] (analytic) = -0.6261125639735115984383263990955
y[1] (numeric) = -0.62611256397351159843832639909571
absolute error = 2.1e-31
relative error = 3.3540294842076398259712688801892e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.06077
Order of pole (three term test) = -8.177
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = -0.63604064122966480782987748049712
y[1] (numeric) = -0.63604064122966480782987748049731
absolute error = 1.9e-31
relative error = 2.9872304957222667195198867344151e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1279
Order of pole (three term test) = -4.516
Radius of convergence (six term test) for eq 1 = 1.029
Order of pole (six term test) = -11.19
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = -0.64597262403003033806548036011992
y[1] (numeric) = -0.64597262403003033806548036012002
absolute error = 1.0e-31
relative error = 1.5480532189759042149297003340295e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1505
Order of pole (three term test) = -33.62
Radius of convergence (six term test) for eq 1 = 0.3266
Order of pole (six term test) = -10.97
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = -0.65590839962156093463413870929279
y[1] (numeric) = -0.6559083996215609346341387092928
absolute error = 1e-32
relative error = 1.5246031314387334940603591564932e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.3566
Order of pole (six term test) = -11
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = -0.66584785557854578954091589451004
y[1] (numeric) = -0.66584785557854578954091589451021
absolute error = 1.7e-31
relative error = 2.5531358038585166434928194023709e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08592
Order of pole (three term test) = -7.861
Radius of convergence (six term test) for eq 1 = 1.811
Order of pole (six term test) = -11.03
TOP MAIN SOLVE Loop
bytes used=312086848, alloc=4652204, time=25.52
x[1] = 3.11
y[1] (analytic) = -0.67579087980205325479627780460661
y[1] (numeric) = -0.67579087980205325479627780460665
absolute error = 4e-32
relative error = 5.9189907995971253173334154319017e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = -0.68573736051937424306081391191724
y[1] (numeric) = -0.68573736051937424306081391191741
absolute error = 1.7e-31
relative error = 2.4790832436378091122975501525947e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1506
Order of pole (three term test) = -13.15
Radius of convergence (six term test) for eq 1 = 0.3889
Order of pole (six term test) = -11.02
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = -0.69568718628346631477570525290438
y[1] (numeric) = -0.69568718628346631477570525290431
absolute error = 7e-32
relative error = 1.0061993577020928140862811761874e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1406
Order of pole (three term test) = -12.43
Radius of convergence (six term test) for eq 1 = 1.255
Order of pole (six term test) = -11
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = -0.70564024597239845110984943640911
y[1] (numeric) = -0.70564024597239845110984943640926
absolute error = 1.5e-31
relative error = 2.1257290929217682624716612281315e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = -0.71559642878879651205509383561824
y[1] (numeric) = -0.71559642878879651205509383561844
absolute error = 2.0e-31
relative error = 2.7948714101119230014675442465834e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = -0.7255556242592893790015687931998
y[1] (numeric) = -0.72555562425928937900156879319987
absolute error = 7e-32
relative error = 9.6477785657663560291523500294735e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=316087880, alloc=4652204, time=25.85
x[1] = 3.17
y[1] (analytic) = -0.73551772223395578112565296814446
y[1] (numeric) = -0.73551772223395578112565296814451
absolute error = 5e-32
relative error = 6.7979327334407645140441914405381e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.04464
Order of pole (three term test) = -2.684
Radius of convergence (six term test) for eq 1 = 1.079
Order of pole (six term test) = -11.01
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = -0.7454826128857718049236428778232
y[1] (numeric) = -0.74548261288577180492364287782318
absolute error = 2e-32
relative error = 2.6828258170341182065691724386916e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.132
Order of pole (three term test) = -16.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = -0.75545018671005908622473823989437
y[1] (numeric) = -0.75545018671005908622473823989441
absolute error = 4e-32
relative error = 5.2948560611517796932901285592268e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 0.287
Order of pole (six term test) = -11
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = -0.76542033452393368401749389618871
y[1] (numeric) = -0.76542033452393368401749389618881
absolute error = 1.0e-31
relative error = 1.3064716926053018510855675321853e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = -0.77539294746575563542442790478019
y[1] (numeric) = -0.77539294746575563542442790478012
absolute error = 7e-32
relative error = 9.0276807686713544573659702952235e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07524
Order of pole (three term test) = -8.989
Radius of convergence (six term test) for eq 1 = 1.152
Order of pole (six term test) = -11
TOP MAIN SOLVE Loop
bytes used=320088948, alloc=4652204, time=26.19
x[1] = 3.22
y[1] (analytic) = -0.78536791699457919116001381735737
y[1] (numeric) = -0.7853679169945791911600138173576
absolute error = 2.3e-31
relative error = 2.9285637345634978162480563329301e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07305
Order of pole (three term test) = -35.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (analytic) = -0.79534513488960373080782321696572
y[1] (numeric) = -0.79534513488960373080782321696567
absolute error = 5e-32
relative error = 6.2865789713971342320767899831656e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1848
Order of pole (three term test) = -45.66
Radius of convergence (six term test) for eq 1 = 1.432
Order of pole (six term test) = -11.01
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = -0.8053244932496253572531222764
y[1] (numeric) = -0.80532449324962535725312227640018
absolute error = 1.8e-31
relative error = 2.2351238725357585824889087608169e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1069
Order of pole (three term test) = -28.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = -0.81530588449248916960776341027239
y[1] (numeric) = -0.81530588449248916960776341027255
absolute error = 1.6e-31
relative error = 1.9624536390976332471642915017131e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.03042
Order of pole (three term test) = -29.18
Radius of convergence (six term test) for eq 1 = 2.177
Order of pole (six term test) = -10.99
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = -0.82528920135454221396475003419928
y[1] (numeric) = -0.82528920135454221396475003419924
absolute error = 4e-32
relative error = 4.8467858217880762311468741109456e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.923
Order of pole (six term test) = -10.99
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = -0.83527433689008711132038901296983
y[1] (numeric) = -0.83527433689008711132038901296982
absolute error = 1e-32
relative error = 1.1972114499808809148504992573962e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.688
Order of pole (three term test) = -417.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=324089808, alloc=4652204, time=26.52
x[1] = 3.28
y[1] (analytic) = -0.8452611844708363620024815761181
y[1] (numeric) = -0.84526118447083636200248157611829
absolute error = 1.9e-31
relative error = 2.2478259204454866121032803904500e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07326
Order of pole (three term test) = -2.109
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = -0.85524963778536732594353930429454
y[1] (numeric) = -0.8552496377853673259435393042945
absolute error = 4e-32
relative error = 4.6769970114899205314017997547324e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 615
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1632
Order of pole (three term test) = -22.48
Radius of convergence (six term test) for eq 1 = 1.854
Order of pole (six term test) = -10.96
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = -0.86523959083857787813854724343072
y[1] (numeric) = -0.86523959083857787813854724343088
absolute error = 1.6e-31
relative error = 1.8491987848698680173978703143152e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 590.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.09809
Order of pole (three term test) = 3.206
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = -0.8752309379511427386273312861491
y[1] (numeric) = -0.87523093795114273862733128614925
absolute error = 1.5e-31
relative error = 1.7138333838054216561318433900770e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.01249
Order of pole (three term test) = -0.7965
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = -0.88522357375897047634212167137868
y[1] (numeric) = -0.88522357375897047634212167137877
absolute error = 9e-32
relative error = 1.0166923099192711548444031072896e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 579.8
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=328091080, alloc=4652204, time=26.85
x[1] = 3.33
y[1] (analytic) = -0.89521739321266118616143879398318
y[1] (numeric) = -0.89521739321266118616143879398337
absolute error = 1.9e-31
relative error = 2.1223895049463701945539791874776e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 641.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.436
Order of pole (six term test) = -10.99
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = -0.90521229157696483851196148655062
y[1] (numeric) = -0.90521229157696483851196148655082
absolute error = 2.0e-31
relative error = 2.2094264722320685018676705498542e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.2
Order of pole (six term test) = -11.07
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = -0.91520816443024030086057153560008
y[1] (numeric) = -0.91520816443024030086057153560002
absolute error = 6e-32
relative error = 6.5558855713828551679754907259441e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1398
Order of pole (three term test) = -35.89
Radius of convergence (six term test) for eq 1 = 1.525
Order of pole (six term test) = -11
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = -0.92520490766391503043930142454326
y[1] (numeric) = -0.92520490766391503043930142454326
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 660
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2273
Order of pole (three term test) = -35.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = -0.9352024174819454375464451560199
y[1] (numeric) = -0.93520241748194543754644515602007
absolute error = 1.7e-31
relative error = 1.8177882864944790117010738123379e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.115
Order of pole (six term test) = -11.01
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = -0.94520059040027791876762449692352
y[1] (numeric) = -0.94520059040027791876762449692374
absolute error = 2.2e-31
relative error = 2.3275482710694603165928342474328e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 642.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.07203
Order of pole (three term test) = 4.242
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=332091944, alloc=4652204, time=27.17
x[1] = 3.39
y[1] (analytic) = -0.95519932324631055946113511079392
y[1] (numeric) = -0.95519932324631055946113511079417
absolute error = 2.5e-31
relative error = 2.6172547856331997311291575629792e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.729
Order of pole (six term test) = -11.01
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = -0.96519851315835550485242879447624
y[1] (numeric) = -0.9651985131583555048524287944763
absolute error = 6e-32
relative error = 6.2163377980832101526987098529174e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.068
Order of pole (six term test) = -10.98
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = -0.97519805758510199908311941926515
y[1] (numeric) = -0.97519805758510199908311941926534
absolute error = 1.9e-31
relative error = 1.9483221743745053430879702229017e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1229
Order of pole (three term test) = -7.696
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = -0.98519785428508009156043119140224
y[1] (numeric) = -0.98519785428508009156043119140245
absolute error = 2.1e-31
relative error = 2.1315515364412650180473762840706e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.545
Order of pole (six term test) = -10.98
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = -0.99519780132612500995353849297114
y[1] (numeric) = -0.99519780132612500995353849297114
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.688
Order of pole (six term test) = -10.97
TOP MAIN SOLVE Loop
bytes used=336092968, alloc=4652204, time=27.50
x[1] = 3.44
y[1] (analytic) = -1.0051977970848421991837768421992
y[1] (numeric) = -1.0051977970848421991837768421993
absolute error = 1e-31
relative error = 9.9482908030646680079704274938162e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3011
Order of pole (three term test) = -96.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = -1.0151977402460730257562344221173
y[1] (numeric) = -1.0151977402460730257562344221174
absolute error = 1e-31
relative error = 9.8502977336967943132630015273744e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1111
Order of pole (three term test) = -23.92
Radius of convergence (six term test) for eq 1 = 1.239
Order of pole (six term test) = -11
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = -1.0251975298023611467807631686836
y[1] (numeric) = -1.0251975298023611467807631686837
absolute error = 1e-31
relative error = 9.7542178061312851790175961250932e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = -1.0351970650534195430309775840861
y[1] (numeric) = -1.0351970650534195430309775840861
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1044
Order of pole (three term test) = -37.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = -1.0451962456055982153903382481896
y[1] (numeric) = -1.0451962456055982153903382481896
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.08764
Order of pole (three term test) = -28.91
Radius of convergence (six term test) for eq 1 = 3.366
Order of pole (six term test) = -10.79
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = -1.0551949713713525440349454412415
y[1] (numeric) = -1.0551949713713525440349454412415
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1749
Order of pole (three term test) = 4.761
Radius of convergence (six term test) for eq 1 = 3.051
Order of pole (six term test) = -10.97
TOP MAIN SOLVE Loop
bytes used=340094176, alloc=4652204, time=27.84
x[1] = 3.5
y[1] (analytic) = -1.0651931425687123097031963641976
y[1] (numeric) = -1.0651931425687123097031963641977
absolute error = 1e-31
relative error = 9.3879688108815730378988590381405e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2128
Order of pole (three term test) = -17.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (analytic) = -1.0751906597207513764029871496127
y[1] (numeric) = -1.0751906597207513764029871496129
absolute error = 2e-31
relative error = 1.8601352066427364576988877773435e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.8
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = -1.0851874236550580349076681961711
y[1] (numeric) = -1.0851874236550580349076681961713
absolute error = 2e-31
relative error = 1.8429996113148173633749526510430e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1045
Order of pole (three term test) = 4.027
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = -1.0951833355032060063924883338409
y[1] (numeric) = -1.095183335503206006392488333841
absolute error = 1e-31
relative error = 9.1308913090841367208640841182552e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3993
Order of pole (three term test) = -19.27
Radius of convergence (six term test) for eq 1 = 1.937
Order of pole (six term test) = -11.03
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = -1.1051782967002261055637899345408
y[1] (numeric) = -1.1051782967002261055637899345409
absolute error = 1e-31
relative error = 9.0483137696943466641582620863522e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2383
Order of pole (three term test) = 51.09
Radius of convergence (six term test) for eq 1 = 4.531
Order of pole (six term test) = -10.91
TOP MAIN SOLVE Loop
bytes used=344095164, alloc=4652204, time=28.17
x[1] = 3.55
y[1] (analytic) = -1.1151722089840785626337433253337
y[1] (numeric) = -1.1151722089840785626337433253337
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.8
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.895
Order of pole (six term test) = -11.04
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = -1.125164974395126003493934737724
y[1] (numeric) = -1.1251649743951260034939347377241
absolute error = 1e-31
relative error = 8.8875855786178106088204759364928e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1315
Order of pole (three term test) = 1.305
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = -1.1351564952756070874416475378731
y[1] (numeric) = -1.1351564952756070874416475378731
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1594
Order of pole (three term test) = -43.72
Radius of convergence (six term test) for eq 1 = 1.627
Order of pole (six term test) = -10.99
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = -1.1451466742691108018132016286544
y[1] (numeric) = -1.1451466742691108018132016286544
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.7
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.464
Order of pole (six term test) = -10.98
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = -1.1551354143200514128792406957032
y[1] (numeric) = -1.1551354143200514128792406957034
absolute error = 2e-31
relative error = 1.7313987392354879245788113783901e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2783
Order of pole (three term test) = -57.82
Radius of convergence (six term test) for eq 1 = 2.587
Order of pole (six term test) = -11
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = -1.1651226186731440723573813861608
y[1] (numeric) = -1.165122618673144072357381386161
absolute error = 2e-31
relative error = 1.7165575261749055466322702423029e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.0372
Order of pole (three term test) = -24.02
Radius of convergence (six term test) for eq 1 = 1.744
Order of pole (six term test) = -11.01
TOP MAIN SOLVE Loop
bytes used=348096408, alloc=4652204, time=28.50
x[1] = 3.61
y[1] (analytic) = -1.1751081908728810788981625609214
y[1] (numeric) = -1.1751081908728810788981625609213
absolute error = 1e-31
relative error = 8.5098547330964554159971694166802e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.7
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.028
Order of pole (six term test) = -10.97
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = -1.1850920347630087939007564490647
y[1] (numeric) = -1.1850920347630087939007564490648
absolute error = 1e-31
relative error = 8.4381632030796413839369871431732e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.7
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = -1.195074054486005211015426857032
y[1] (numeric) = -1.1950740544860052110154268570322
absolute error = 2e-31
relative error = 1.6735364578391663088234580368048e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3442
Order of pole (three term test) = -37.3
Radius of convergence (six term test) for eq 1 = 2.235
Order of pole (six term test) = -11
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = -1.2050541544825581786902425451768
y[1] (numeric) = -1.2050541544825581786902425451769
absolute error = 1e-31
relative error = 8.2983822451480863304885911695150e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.7
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = -1.2150322394910442751200764808554
y[1] (numeric) = -1.2150322394910442751200764808555
absolute error = 1e-31
relative error = 8.2302342892471930280758700376140e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.08016
Order of pole (three term test) = -4.581
Radius of convergence (six term test) for eq 1 = 1.152
Order of pole (six term test) = -11.04
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = -1.2250082145470083349564439103938
y[1] (numeric) = -1.2250082145470083349564439103938
absolute error = 0
bytes used=352097440, alloc=4652204, time=28.83
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.7227
Order of pole (three term test) = -87.86
Radius of convergence (six term test) for eq 1 = 1.383
Order of pole (six term test) = -11.02
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = -1.2349819849826436271372540623215
y[1] (numeric) = -1.2349819849826436271372540623218
absolute error = 3e-31
relative error = 2.4291852322381543441246242068641e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1351
Order of pole (three term test) = -22.57
Radius of convergence (six term test) for eq 1 = 1.336
Order of pole (six term test) = -11.02
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = -1.244953456426272683196071801424
y[1] (numeric) = -1.2449534564262726831960718014244
absolute error = 4e-31
relative error = 3.2129715206239790613272963173488e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.385
Order of pole (six term test) = -10.98
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = -1.2549225348018287754110066976287
y[1] (numeric) = -1.254922534801828775411006697629
absolute error = 3e-31
relative error = 2.3905858065364531180136908959159e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2694
Order of pole (three term test) = -36.4
Radius of convergence (six term test) for eq 1 = 4.998
Order of pole (six term test) = -10.88
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = -1.2648891263283380441538677557636
y[1] (numeric) = -1.2648891263283380441538677557638
absolute error = 2e-31
relative error = 1.5811662527335561623725777951586e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = -1.2748531375194022738007424719941
y[1] (numeric) = -1.2748531375194022738007424719943
absolute error = 2e-31
relative error = 1.5688081561234433206342993449112e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.019
Order of pole (six term test) = -11.02
TOP MAIN SOLVE Loop
bytes used=356098364, alloc=4652204, time=29.16
x[1] = 3.72
y[1] (analytic) = -1.2848144751826823165656789404977
y[1] (numeric) = -1.2848144751826823165656789404978
absolute error = 1e-31
relative error = 7.7832248882299854592364385583616e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2486
Order of pole (three term test) = -35.41
Radius of convergence (six term test) for eq 1 = 2.694
Order of pole (six term test) = -10.91
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = -1.294773046419382163619669429891
y[1] (numeric) = -1.2947730464193821636196694298912
absolute error = 2e-31
relative error = 1.5446722539760006774533004225131e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 9.762
Order of pole (six term test) = -12.3
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = -1.3047287586237336628576531833007
y[1] (numeric) = -1.3047287586237336628576531833008
absolute error = 1e-31
relative error = 7.6644282835830909714422979488800e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.148
Order of pole (six term test) = -11.03
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = -1.314681519482481882676775168978
y[1] (numeric) = -1.3146815194824818826767751689781
absolute error = 1e-31
relative error = 7.6064049367153592928323932449889e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.31
Order of pole (three term test) = -66.03
Radius of convergence (six term test) for eq 1 = 4.447
Order of pole (six term test) = -11.04
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = -1.3246312369743711211296561202402
y[1] (numeric) = -1.3246312369743711211296561202402
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.6126
Order of pole (three term test) = -45.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = -1.3345778193696315598169474544683
y[1] (numeric) = -1.3345778193696315598169474544685
absolute error = 2e-31
relative error = 1.4986012587446350171855955985413e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.5
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.42
Order of pole (six term test) = -11.04
bytes used=360100668, alloc=4652204, time=29.49
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = -1.3445211752294665618839625511538
y[1] (numeric) = -1.3445211752294665618839625511539
absolute error = 1e-31
relative error = 7.4375920470671064918438403149204e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1025
Order of pole (three term test) = -48.87
Radius of convergence (six term test) for eq 1 = 3.863
Order of pole (six term test) = -11.01
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = -1.3544612134055406134866933987487
y[1] (numeric) = -1.3544612134055406134866933987488
absolute error = 1e-31
relative error = 7.3830094956036882835232561687462e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.06695
Order of pole (three term test) = -31.78
Radius of convergence (six term test) for eq 1 = 2.117
Order of pole (six term test) = -10.96
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = -1.3643978430394679080930387895985
y[1] (numeric) = -1.3643978430394679080930387895985
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3461
Order of pole (three term test) = -62.35
Radius of convergence (six term test) for eq 1 = 1.348
Order of pole (six term test) = -11.03
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = -1.3743309735623015729855870516918
y[1] (numeric) = -1.374330973562301572985587051692
absolute error = 2e-31
relative error = 1.4552535295162183987686370503251e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.5
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.158
Order of pole (six term test) = -11.01
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = -1.3842605146940235373328127556177
y[1] (numeric) = -1.3842605146940235373328127556179
absolute error = 2e-31
relative error = 1.4448147431569839325515794412461e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.5
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.216
Order of pole (six term test) = -11.01
TOP MAIN SOLVE Loop
bytes used=364101388, alloc=4652204, time=29.82
x[1] = 3.83
y[1] (analytic) = -1.3941863764430350411960629251505
y[1] (numeric) = -1.3941863764430350411960629251507
absolute error = 2e-31
relative error = 1.4345284344999607397715570834679e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.5
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = -1.4041084691056477848402240105472
y[1] (numeric) = -1.4041084691056477848402240105472
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.05474
Order of pole (three term test) = -9.845
Radius of convergence (six term test) for eq 1 = 4.207
Order of pole (six term test) = -10.6
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = -1.4140267032655757177164762551204
y[1] (numeric) = -1.4140267032655757177164762551204
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.8396
Order of pole (three term test) = 4.159
Radius of convergence (six term test) for eq 1 = 4.363
Order of pole (six term test) = -10.39
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = -1.4239409897934274664860570981963
y[1] (numeric) = -1.4239409897934274664860570981962
absolute error = 1e-31
relative error = 7.0227629316652440288708133381893e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.03944
Order of pole (three term test) = -9.464
Radius of convergence (six term test) for eq 1 = 2.839
Order of pole (six term test) = -10.82
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = -1.4338512398461994014544699113681
y[1] (numeric) = -1.4338512398461994014544699113682
absolute error = 1e-31
relative error = 6.9742241887468325198226120388754e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.519
Order of pole (six term test) = -11.12
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (analytic) = -1.443757364866769340786088660261
y[1] (numeric) = -1.4437573648667693407860886602611
absolute error = 1e-31
relative error = 6.9263715935556838204388542362174e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=368102176, alloc=4652204, time=30.15
x[1] = 3.89
y[1] (analytic) = -1.4536592765833908918696230210185
y[1] (numeric) = -1.4536592765833908918696230210187
absolute error = 2e-31
relative error = 1.3758382257916046279796284266394e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.963
Order of pole (six term test) = -11.09
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = -1.4635568870091884292054220596594
y[1] (numeric) = -1.4635568870091884292054220596596
absolute error = 2e-31
relative error = 1.3665338312110608794088527895351e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 5.666
Order of pole (three term test) = -798.8
Radius of convergence (six term test) for eq 1 = 11.98
Order of pole (six term test) = -10.6
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = -1.4734501084416527081861078035146
y[1] (numeric) = -1.4734501084416527081861078035147
absolute error = 1e-31
relative error = 6.7867924015263601690740007541453e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.002636
Order of pole (three term test) = -0.8334
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = -1.4833388534621371141425428973935
y[1] (numeric) = -1.4833388534621371141425428973936
absolute error = 1e-31
relative error = 6.7415479454743847983228675473199e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = -1.4932230349353545460276490431345
y[1] (numeric) = -1.4932230349353545460276490431348
absolute error = 3e-31
relative error = 2.0090769629266251523730236294235e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.03359
Order of pole (three term test) = 2.091
Radius of convergence (six term test) for eq 1 = 1.954
Order of pole (six term test) = -10.81
TOP MAIN SOLVE Loop
bytes used=372103136, alloc=4652204, time=30.48
x[1] = 3.94
y[1] (analytic) = -1.5031025660088749341111050700025
y[1] (numeric) = -1.5031025660088749341111050700025
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2253
Order of pole (three term test) = 26.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = -1.5129773601126233910584652752119
y[1] (numeric) = -1.512977360112623391058465275212
absolute error = 1e-31
relative error = 6.6094842286705582118027707948557e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.979
Order of pole (six term test) = -10.65
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = -1.522847330958378995768750108915
y[1] (numeric) = -1.5228473309583789957687501089153
absolute error = 3e-31
relative error = 1.9699939311132385113280936672837e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.02625
Order of pole (three term test) = -23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = -1.5327123925392742093450723564781
y[1] (numeric) = -1.5327123925392742093450723564784
absolute error = 3e-31
relative error = 1.9573143758757258338326752333109e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.523
Order of pole (six term test) = -11.24
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = -1.542572459129294922573372693046
y[1] (numeric) = -1.5425724591292949225733726930462
absolute error = 2e-31
relative error = 1.2965355294420983430167393667161e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.07894
Order of pole (three term test) = -12.02
Radius of convergence (six term test) for eq 1 = 4.138
Order of pole (six term test) = -10.76
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = -1.5524274452827811342848488514365
y[1] (numeric) = -1.5524274452827811342848488514366
absolute error = 1e-31
relative error = 6.4415248715075752157364253694672e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3193
Order of pole (three term test) = -29.72
Radius of convergence (six term test) for eq 1 = 5.136
Order of pole (six term test) = -10.9
TOP MAIN SOLVE Loop
bytes used=376104264, alloc=4652204, time=30.82
x[1] = 4
y[1] (analytic) = -1.5622772658339282599781726545535
y[1] (numeric) = -1.5622772658339282599781726545536
absolute error = 1e-31
relative error = 6.4009124492137432589179742324456e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1457
Order of pole (three term test) = -14.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = -1.5721218358962890700780988179698
y[1] (numeric) = -1.5721218358962890700780988179699
absolute error = 1e-31
relative error = 6.3608301670200118075943621940925e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.08211
Order of pole (three term test) = -30.54
Radius of convergence (six term test) for eq 1 = 3.617
Order of pole (six term test) = -10.77
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = -1.5819610708622762572075787273268
y[1] (numeric) = -1.5819610708622762572075787273268
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = -1.5917948864026656318510013389437
y[1] (numeric) = -1.5917948864026656318510013389436
absolute error = 1e-31
relative error = 6.2822164371938856379091153649324e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3299
Order of pole (three term test) = -35.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = -1.6016231984660999457866919407409
y[1] (numeric) = -1.6016231984660999457866919407409
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.154
Order of pole (six term test) = -11.43
TOP MAIN SOLVE Loop
bytes used=380106168, alloc=4652204, time=31.14
x[1] = 4.05
y[1] (analytic) = -1.611445923278593342667307744475
y[1] (numeric) = -1.6114459232785933426673077444749
absolute error = 1e-31
relative error = 6.2056069369391796960466051640211e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = -1.6212629773430364351272771595745
y[1] (numeric) = -1.6212629773430364351272771595744
absolute error = 1e-31
relative error = 6.1680308128593876465246107099776e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = -1.6310742774387020077969371237776
y[1] (numeric) = -1.6310742774387020077969371237775
absolute error = 1e-31
relative error = 6.1309286390704016334506092841796e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.108
Order of pole (six term test) = -11.07
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = -1.6408797406207513456035300365047
y[1] (numeric) = -1.6408797406207513456035300365048
absolute error = 1e-31
relative error = 6.0942918316591319148086940915722e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.07236
Order of pole (three term test) = -5.683
Radius of convergence (six term test) for eq 1 = 6.942
Order of pole (six term test) = -10.32
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = -1.6506792842197411867397286576904
y[1] (numeric) = -1.6506792842197411867397286576904
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2153
Order of pole (three term test) = -16.34
Radius of convergence (six term test) for eq 1 = 9.087
Order of pole (six term test) = -10.56
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = -1.6604728258411312996808637978402
y[1] (numeric) = -1.6604728258411312996808637978403
absolute error = 1e-31
relative error = 6.0223810015887413520063598282793e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.753
Order of pole (six term test) = -11.04
TOP MAIN SOLVE Loop
bytes used=384106840, alloc=4652204, time=31.47
x[1] = 4.11
y[1] (analytic) = -1.6702602833647926836325357346123
y[1] (numeric) = -1.6702602833647926836325357346121
absolute error = 2e-31
relative error = 1.1974181628571902137129275550267e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 20.86
Order of pole (three term test) = -1951
Radius of convergence (six term test) for eq 1 = 4.823
Order of pole (six term test) = -10.98
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = -1.680041574944516391790796047431
y[1] (numeric) = -1.680041574944516391790796047431
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1533
Order of pole (three term test) = -41.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = -1.6898166190075229767975919647854
y[1] (numeric) = -1.6898166190075229767975919647852
absolute error = 2e-31
relative error = 1.1835603801640064842571400075087e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.261
Order of pole (six term test) = -11.14
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = -1.6995853342539725577746703690964
y[1] (numeric) = -1.6995853342539725577746703690965
absolute error = 1e-31
relative error = 5.8837881208179919970712299201678e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.8397
Order of pole (three term test) = -85.11
Radius of convergence (six term test) for eq 1 = 17.37
Order of pole (six term test) = -10.06
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = -1.7093476396564755083196433016555
y[1] (numeric) = -1.7093476396564755083196433016555
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1602
Order of pole (three term test) = -19.37
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=388108020, alloc=4652204, time=31.81
x[1] = 4.16
y[1] (analytic) = -1.7191034544596037648484211552572
y[1] (numeric) = -1.7191034544596037648484211552574
absolute error = 2e-31
relative error = 1.1633971154043753702715531703423e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.01783
Order of pole (three term test) = -25.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = -1.728852698179402754668723735093
y[1] (numeric) = -1.728852698179402754668723735093
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.02851
Order of pole (three term test) = -29.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = -1.7385952906029039431698830093492
y[1] (numeric) = -1.7385952906029039431698830093492
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.89
Order of pole (six term test) = -11.46
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = -1.7483311517876379995146546600768
y[1] (numeric) = -1.7483311517876379995146546600768
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 17.96
Order of pole (six term test) = -13.69
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = -1.7580602020611485802192584823961
y[1] (numeric) = -1.7580602020611485802192584823963
absolute error = 2e-31
relative error = 1.1376174704684181838092891503221e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.453
Order of pole (six term test) = -10.85
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (analytic) = -1.7677823620205067300083702662566
y[1] (numeric) = -1.7677823620205067300083702662566
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.286
Order of pole (six term test) = -11.18
TOP MAIN SOLVE Loop
bytes used=392108820, alloc=4652204, time=32.15
x[1] = 4.22
y[1] (analytic) = -1.7774975525318258993322900299476
y[1] (numeric) = -1.7774975525318258993322900299477
absolute error = 1e-31
relative error = 5.6258867899740475695352191825358e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.09645
Order of pole (three term test) = -31.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = -1.7872056947297775779340133586105
y[1] (numeric) = -1.7872056947297775779340133586105
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.1
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 9.461
Order of pole (six term test) = -10.92
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = -1.7969067100171075438544341343024
y[1] (numeric) = -1.7969067100171075438544341343026
absolute error = 2e-31
relative error = 1.1130238363798857960233787436379e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659.1
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4144
Order of pole (three term test) = -55.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = -1.8066005200641527272644081269767
y[1] (numeric) = -1.8066005200641527272644081269767
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.09054
Order of pole (three term test) = -30.18
Radius of convergence (six term test) for eq 1 = 6.12
Order of pole (six term test) = -10.41
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = -1.8162870468083586885129077482284
y[1] (numeric) = -1.8162870468083586885129077482283
absolute error = 1e-31
relative error = 5.5057376627622488277292853492848e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.06978
Order of pole (three term test) = -4.653
Radius of convergence (six term test) for eq 1 = 4.07
Order of pole (six term test) = -10.69
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = -1.8259662124537977097809987520794
y[1] (numeric) = -1.8259662124537977097809987520792
bytes used=396110256, alloc=4652204, time=32.48
absolute error = 2e-31
relative error = 1.0953105190880446559647558348611e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 9.802
Order of pole (six term test) = -11.64
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = -1.8356379394706874997318697996024
y[1] (numeric) = -1.8356379394706874997318697996024
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.06934
Order of pole (three term test) = -0.441
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = -1.8453021505949105105476455870719
y[1] (numeric) = -1.8453021505949105105476455870719
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.481
Order of pole (six term test) = -11.39
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = -1.8549587688275338667442136707527
y[1] (numeric) = -1.8549587688275338667442136707526
absolute error = 1e-31
relative error = 5.3909554045347933192656850702162e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = -1.8646077174343299051557942056431
y[1] (numeric) = -1.8646077174343299051557942056432
absolute error = 1e-31
relative error = 5.3630583561886349163981286999367e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 3.128
Order of pole (three term test) = -544.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = -1.8742489199452973254814805506658
y[1] (numeric) = -1.8742489199452973254814805506658
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=400111548, alloc=4652204, time=32.81
x[1] = 4.33
y[1] (analytic) = -1.883882300154182950786477079166
y[1] (numeric) = -1.8838823001541829507864770791659
absolute error = 1e-31
relative error = 5.3081872467200143166977909220458e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.06083
Order of pole (three term test) = -37.5
Radius of convergence (six term test) for eq 1 = 6.172
Order of pole (six term test) = -10.32
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = -1.8935077821180040973512585713662
y[1] (numeric) = -1.8935077821180040973512585713661
absolute error = 1e-31
relative error = 5.2812035389758943929467712465932e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 659
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2185
Order of pole (three term test) = -35.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = -1.903125290156571553262373254814
y[1] (numeric) = -1.9031252901565715532623732548138
absolute error = 2e-31
relative error = 1.0509029596445846669823941127045e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.01435
Order of pole (three term test) = -0.7876
Radius of convergence (six term test) for eq 1 = 6.123
Order of pole (six term test) = -7.637
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = -1.9127347488520131651391089000926
y[1] (numeric) = -1.9127347488520131651391089000924
absolute error = 2e-31
relative error = 1.0456232894813887657703572201584e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = -1.9223360830482980323907383723393
y[1] (numeric) = -1.9223360830482980323907383723394
absolute error = 1e-31
relative error = 5.2020040034533094919513412527668e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.52
Order of pole (six term test) = -11.72
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = -1.9319292178507613083995576846453
y[1] (numeric) = -1.9319292178507613083995576846454
absolute error = 1e-31
relative error = 5.1761730748732251417254141123782e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1666
Order of pole (three term test) = -28.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=404112952, alloc=4652204, time=33.14
x[1] = 4.39
y[1] (analytic) = -1.9415140786256296080254258974095
y[1] (numeric) = -1.9415140786256296080254258974093
absolute error = 2e-31
relative error = 1.0301238718885684051232107033611e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.392
Order of pole (six term test) = -11.22
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = -1.9510905909995470208280121584055
y[1] (numeric) = -1.9510905909995470208280121584054
absolute error = 1e-31
relative error = 5.1253386419525415422672134401091e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1347
Order of pole (three term test) = -13.79
Radius of convergence (six term test) for eq 1 = 8.73
Order of pole (six term test) = -10.28
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = -1.9606586808591017294034507818954
y[1] (numeric) = -1.9606586808591017294034507818954
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.0451
Order of pole (three term test) = -1.789
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = -1.9702182743503532322326005217996
y[1] (numeric) = -1.9702182743503532322326005217994
absolute error = 2e-31
relative error = 1.0151159523984553424085876277709e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 9.877
Order of pole (six term test) = -14.65
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = -1.9797692978783601704385991039411
y[1] (numeric) = -1.9797692978783601704385991039411
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.05423
Order of pole (three term test) = -33.52
Radius of convergence (six term test) for eq 1 = 8.061
Order of pole (six term test) = -7.668
TOP MAIN SOLVE Loop
bytes used=408114448, alloc=4652204, time=33.49
x[1] = 4.44
y[1] (analytic) = -1.9893116781067087578518986459106
y[1] (numeric) = -1.9893116781067087578518986459102
absolute error = 4e-31
relative error = 2.0107457489049314366807678663107e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.00962
Order of pole (three term test) = -24.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = -1.9988453419570418137814618103582
y[1] (numeric) = -1.9988453419570418137814618103582
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3475
Order of pole (three term test) = -46.97
Radius of convergence (six term test) for eq 1 = 22.88
Order of pole (six term test) = -8.303
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = -2.0083702166085883978912924087664
y[1] (numeric) = -2.0083702166085883978912924087663
absolute error = 1e-31
relative error = 4.9791616691500168995387341797010e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.03951
Order of pole (three term test) = -0.3071
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = -2.0178862294976940465819676981146
y[1] (numeric) = -2.0178862294976940465819676981144
absolute error = 2e-31
relative error = 9.9113615562848337174095716120042e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = -12.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = -2.0273933083173516102773327926444
y[1] (numeric) = -2.0273933083173516102773327926444
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.8
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = -2.0368913810167326910170104472626
y[1] (numeric) = -2.0368913810167326910170104472626
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.8
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.889
Order of pole (six term test) = -11.59
TOP MAIN SOLVE Loop
bytes used=412115324, alloc=4652204, time=33.82
x[1] = 4.5
y[1] (analytic) = -2.0463803758007196797558719582775
y[1] (numeric) = -2.0463803758007196797558719582776
absolute error = 1e-31
relative error = 4.8866770412060570725983013120751e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.02762
Order of pole (three term test) = -24.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = -2.0558602211294383927721070713289
y[1] (numeric) = -2.0558602211294383927721070713289
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1034
Order of pole (three term test) = -8.572
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = -2.0653308457177913065860225857425
y[1] (numeric) = -2.0653308457177913065860225857424
absolute error = 1e-31
relative error = 4.8418392727411040346611613040221e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.8
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.03821
Order of pole (three term test) = 1.271
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = -2.0747921785349913907921907993594
y[1] (numeric) = -2.0747921785349913907921907993593
absolute error = 1e-31
relative error = 4.8197598311079954267454342085948e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.8
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.827
Order of pole (six term test) = -11.55
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = -2.0842441488040965382080600483396
y[1] (numeric) = -2.0842441488040965382080600483397
absolute error = 1e-31
relative error = 4.7979023982088797453781266852731e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.7
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.828
Order of pole (six term test) = -11.59
TOP MAIN SOLVE Loop
bytes used=416116256, alloc=4652204, time=34.16
x[1] = 4.55
y[1] (analytic) = -2.0936866860015445917426303627453
y[1] (numeric) = -2.0936866860015445917426303627454
absolute error = 1e-31
relative error = 4.7762638349187184076691217577543e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.7
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = -2.1031197198566889673892876810772
y[1] (numeric) = -2.1031197198566889673892876810774
absolute error = 2e-31
relative error = 9.5096821218351004595591058418337e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1366
Order of pole (three term test) = -18.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = -2.1125431803513348727473801455827
y[1] (numeric) = -2.112543180351334872747380145583
absolute error = 3e-31
relative error = 1.4200893159973530580682170251660e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.7
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = -2.1219569977192761204776097352735
y[1] (numeric) = -2.1219569977192761204776097352736
absolute error = 1e-31
relative error = 4.7126308453697269569593188407296e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.07939
Order of pole (three term test) = -40.07
Radius of convergence (six term test) for eq 1 = 13.26
Order of pole (six term test) = -8.354
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = -2.1313611024458325360968018854121
y[1] (numeric) = -2.1313611024458325360968018854122
absolute error = 1e-31
relative error = 4.6918375251028796232714773445166e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1163
Order of pole (three term test) = -28.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = -2.1407554252673879595181047909527
y[1] (numeric) = -2.1407554252673879595181047909527
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.01602
Order of pole (three term test) = -17.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=420117508, alloc=4652204, time=34.49
x[1] = 4.61
y[1] (analytic) = -2.1501398971709288397431587972472
y[1] (numeric) = -2.1501398971709288397431587972473
absolute error = 1e-31
relative error = 4.6508601664280609681393103856475e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.7
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.03599
Order of pole (three term test) = -19.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = -2.1595144493935834221132646444976
y[1] (numeric) = -2.1595144493935834221132646444979
absolute error = 3e-31
relative error = 1.3892011701252726600572718099474e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.7
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.636
Order of pole (six term test) = -11.64
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = -2.1688790134221615275270673531188
y[1] (numeric) = -2.1688790134221615275270673531188
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 28.53
Order of pole (six term test) = -25.91
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = -2.1782335209926949230327602156121
y[1] (numeric) = -2.1782335209926949230327602156124
absolute error = 3e-31
relative error = 1.3772628008372574350646183099126e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2198
Order of pole (three term test) = -26.71
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = -2.1875779040899782832033006969447
y[1] (numeric) = -2.1875779040899782832033006969447
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.96
Order of pole (six term test) = -11.4
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (analytic) = -2.1969120949471107417036170399549
y[1] (numeric) = -2.1969120949471107417036170399551
absolute error = 2e-31
relative error = 9.1036869640801386963517303945314e-30 %
Correct digits = 32
h = 0.01
bytes used=424118400, alloc=4652204, time=34.82
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3219
Order of pole (three term test) = -26.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = -2.2062360260450380324592710252519
y[1] (numeric) = -2.206236026045038032459271025252
absolute error = 1e-31
relative error = 4.5326066123243788950208304426628e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.141
Order of pole (six term test) = -11.4
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = -2.2155496301120952198365286465438
y[1] (numeric) = -2.2155496301120952198365286465439
absolute error = 1e-31
relative error = 4.5135526932403009715505549371908e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.732
Order of pole (three term test) = -209.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = -2.224852840123550017244276432638
y[1] (numeric) = -2.2248528401235500172442764326383
absolute error = 3e-31
relative error = 1.3484037891842791222964816994054e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = -2.2341455893011466935687067766265
y[1] (numeric) = -2.2341455893011466935687067766267
absolute error = 2e-31
relative error = 8.9519680793300997413097118876640e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 1.791
Order of pole (three term test) = 68.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = -2.2434278111126505668521809212603
y[1] (numeric) = -2.2434278111126505668521809212605
absolute error = 2e-31
relative error = 8.9149291548101113280099240047534e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=428119668, alloc=4652204, time=35.15
x[1] = 4.72
y[1] (analytic) = -2.252699439271393084628163197426
y[1] (numeric) = -2.2526994392713930846281631974264
absolute error = 4e-31
relative error = 1.7756474433596649744335950118109e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3492
Order of pole (three term test) = -19.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = -2.261960407735817490324604720157
y[1] (numeric) = -2.2619604077358174903246047201573
absolute error = 3e-31
relative error = 1.3262831611641457227736590713437e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.5
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.605
Order of pole (six term test) = -11.62
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = -2.2712106507090250751486390139724
y[1] (numeric) = -2.2712106507090250751486390139727
absolute error = 3e-31
relative error = 1.3208814422666880045382047026011e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.008831
Order of pole (three term test) = -25.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = -2.2804501026383220148659359667396
y[1] (numeric) = -2.2804501026383220148659359667399
absolute error = 3e-31
relative error = 1.3155297704296221370789902986744e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2821
Order of pole (three term test) = -37.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = -2.2896786982147667908885440988956
y[1] (numeric) = -2.2896786982147667908885440988956
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1977
Order of pole (three term test) = -36.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = -2.2988963723727181950855343829676
y[1] (numeric) = -2.2988963723727181950855343829678
absolute error = 2e-31
relative error = 8.6998266822082819405355763612840e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.5
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.103
Order of pole (six term test) = -11.59
TOP MAIN SOLVE Loop
bytes used=432120676, alloc=4652204, time=35.49
x[1] = 4.78
y[1] (analytic) = -2.3081030602893839177312417571066
y[1] (numeric) = -2.3081030602893839177312417571067
absolute error = 1e-31
relative error = 4.3325621684961615994159361255001e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2069
Order of pole (three term test) = -44.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = -2.3172986973843697180063830459698
y[1] (numeric) = -2.3172986973843697180063830459701
absolute error = 3e-31
relative error = 1.2946108343245621730406814951083e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3343
Order of pole (three term test) = -32.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = -2.3264832193192291764678122330291
y[1] (numeric) = -2.3264832193192291764678122330293
absolute error = 2e-31
relative error = 8.5966663476955400646096805418557e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.5
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 37.71
Order of pole (six term test) = -25.71
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = -2.3356565619970140289031559203648
y[1] (numeric) = -2.335656561997014028903155920365
absolute error = 2e-31
relative error = 8.5629027509505777160227142518630e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.1009
Order of pole (three term test) = -31.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = -2.3448186615618250809870533655252
y[1] (numeric) = -2.3448186615618250809870533655254
absolute error = 2e-31
relative error = 8.5294442286119047162792780724604e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.5
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.3495
Order of pole (three term test) = -95.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=436121868, alloc=4652204, time=35.83
x[1] = 4.83
y[1] (analytic) = -2.3539694543983637031562067002198
y[1] (numeric) = -2.35396945439836370315620670022
absolute error = 2e-31
relative error = 8.4962869686478895405800813199450e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 8.487
Order of pole (six term test) = -11.65
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = -2.3631088771314839051209278127357
y[1] (numeric) = -2.3631088771314839051209278127361
absolute error = 4e-31
relative error = 1.6926854444622523872059195360495e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.06631
Order of pole (three term test) = -24.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = -2.3722368666257449894313489151934
y[1] (numeric) = -2.3722368666257449894313489151937
absolute error = 3e-31
relative error = 1.2646291954256580622054106101135e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.5419
Order of pole (three term test) = -78.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = -2.3813533599849647835169440183069
y[1] (numeric) = -2.3813533599849647835169440183072
absolute error = 3e-31
relative error = 1.2597878376264752169587444312907e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 100
Order of pole (six term test) = 5.757
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = -2.3904582945517734496184884004058
y[1] (numeric) = -2.3904582945517734496184884004062
absolute error = 4e-31
relative error = 1.6733192999503997360069289841123e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 143.8
Order of pole (six term test) = -17.77
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = -2.399551607907167872032062684288
y[1] (numeric) = -2.3995516079071678720320626842882
absolute error = 2e-31
relative error = 8.3348905412555501183138485535313e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.2607
Order of pole (three term test) = -34.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=440122940, alloc=4652204, time=36.16
x[1] = 4.89
y[1] (analytic) = -2.4086332378700666210851873252424
y[1] (numeric) = -2.4086332378700666210851873252427
absolute error = 3e-31
relative error = 1.2455196386199809533437363184111e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.4
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 8.519
Order of pole (six term test) = -11.71
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = -2.4177031224968654932656521664999
y[1] (numeric) = -2.4177031224968654932656521665004
absolute error = 5e-31
relative error = 2.0680785632754967855586030235508e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.09546
Order of pole (three term test) = -32.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = -2.4267612000809936269240842346364
y[1] (numeric) = -2.4267612000809936269240842346366
absolute error = 2e-31
relative error = 8.2414371876938266983589700634699e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.4
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.05029
Order of pole (three term test) = -26.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = -2.4358074091524701929717751272934
y[1] (numeric) = -2.4358074091524701929717751272938
absolute error = 4e-31
relative error = 1.6421659548986200821449788215509e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.262
Order of pole (three term test) = -20.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = -2.4448416884774616599957671891963
y[1] (numeric) = -2.4448416884774616599957671891968
absolute error = 5e-31
relative error = 2.0451221948500792096901999262420e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.01916
Order of pole (three term test) = -25.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=444123960, alloc=4652204, time=36.48
x[1] = 4.94
y[1] (analytic) = -2.4538639770578396332136751800153
y[1] (numeric) = -2.4538639770578396332136751800157
absolute error = 4e-31
relative error = 1.6300822039842498748305361919755e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.002
Order of pole (six term test) = -11.68
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = -2.4628742141307392666911973093993
y[1] (numeric) = -2.4628742141307392666911973093998
absolute error = 5e-31
relative error = 2.0301483410368678676736063082738e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 8.012
Order of pole (six term test) = -12.07
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = -2.4718723391681182482457463506563
y[1] (numeric) = -2.4718723391681182482457463506567
absolute error = 4e-31
relative error = 1.6182065459521896248682922112781e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.002133
Order of pole (three term test) = -25.28
Radius of convergence (six term test) for eq 1 = 3.105
Order of pole (six term test) = -12.71
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = -2.4808582918763163564601080453001
y[1] (numeric) = -2.4808582918763163564601080453007
absolute error = 6e-31
relative error = 2.4185178249186072803517097633935e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.27
Order of pole (six term test) = -12.2
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = -2.4898320121956155892305101762396
y[1] (numeric) = -2.4898320121956155892305101762401
absolute error = 5e-31
relative error = 2.0081676095050428284850271171829e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 8.834
Order of pole (six term test) = -12.14
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = -2.4987934402998008632739615179273
y[1] (numeric) = -2.4987934402998008632739615179277
absolute error = 4e-31
relative error = 1.6007725710693745863556143250935e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 658.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 10.04
Order of pole (six term test) = -12.28
Finished!
diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));
Iterations = 600
Total Elapsed Time = 36 Seconds
Elapsed Time(since restart) = 35 Seconds
Time to Timeout = 2 Minutes 23 Seconds
Percent Done = 100.2 %
> quit
bytes used=447920036, alloc=4652204, time=36.77