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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
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<____ ____> 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,
> #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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
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,
> #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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
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,
> #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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
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,
> #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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
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,
> #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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
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,
> #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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
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,
> #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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
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,
> #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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> 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_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_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
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,
> #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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> 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 sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre sin 1 $eq_no = 1
> array_tmp3[1] := sin(array_x[1]);
> array_tmp3_g[1] := cos(array_x[1]);
> #emit pre add FULL FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp2[1] + array_tmp3[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_tmp4[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 sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1;
> array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1;
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp3[2] := array_tmp3_g[1] * array_x[2] / 1;
> array_tmp3_g[2] := -array_tmp3[1] * array_x[2] / 1;
> #emit pre add FULL FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp2[2] + array_tmp3[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_tmp4[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 sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2;
> array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2;
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := array_tmp3_g[2] * array_x[2] / 2;
> array_tmp3_g[3] := -array_tmp3[2] * array_x[2] / 2;
> #emit pre add FULL FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp2[3] + array_tmp3[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_tmp4[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 sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3;
> array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3;
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := array_tmp3_g[3] * array_x[2] / 3;
> array_tmp3_g[4] := -array_tmp3[3] * array_x[2] / 3;
> #emit pre add FULL FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp2[4] + array_tmp3[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_tmp4[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 sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4;
> array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4;
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := array_tmp3_g[4] * array_x[2] / 4;
> array_tmp3_g[5] := -array_tmp3[4] * array_x[2] / 4;
> #emit pre add FULL FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp2[5] + array_tmp3[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_tmp4[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 sin LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit sin LINEAR $eq_no = 1
> array_tmp3[kkk] := array_tmp3_g[kkk - 1] * array_x[2] / (kkk - 1);
> array_tmp3_g[kkk] := -array_tmp3[kkk - 1] * array_x[2] / (kkk - 1);
> #emit FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp2[kkk] + array_tmp3[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_tmp4[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_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_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
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] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := sin(array_x[1]);
array_tmp3_g[1] := cos(array_x[1]);
array_tmp4[1] := array_tmp2[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1_g[1]*array_x[2];
array_tmp1_g[2] := -array_tmp1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp3_g[1]*array_x[2];
array_tmp3_g[2] := -array_tmp3[1]*array_x[2];
array_tmp4[2] := array_tmp2[2] + array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2];
array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2];
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := 1/2*array_tmp3_g[2]*array_x[2];
array_tmp3_g[3] := -1/2*array_tmp3[2]*array_x[2];
array_tmp4[3] := array_tmp2[3] + array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := 1/3*array_tmp1_g[3]*array_x[2];
array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2];
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := 1/3*array_tmp3_g[3]*array_x[2];
array_tmp3_g[4] := -1/3*array_tmp3[3]*array_x[2];
array_tmp4[4] := array_tmp2[4] + array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := 1/4*array_tmp1_g[4]*array_x[2];
array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2];
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := 1/4*array_tmp3_g[4]*array_x[2];
array_tmp3_g[5] := -1/4*array_tmp3[4]*array_x[2];
array_tmp4[5] := array_tmp2[5] + array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] := array_tmp3_g[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp3_g[kkk] := -array_tmp3[kkk - 1]*array_x[2]/(kkk - 1);
array_tmp4[kkk] := array_tmp2[kkk] + array_tmp3[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_tmp4[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(2.0 - cos(x) - cos(x));
> end;
exact_soln_y := proc(x) return 2.0 - 2*cos(x) end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,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,
> #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_g,
> array_tmp1,
> array_tmp2,
> array_tmp3_g,
> array_tmp3,
> array_tmp4,
> 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/addpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -5.0;");
> 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 := 100;");
> 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(2.0 - cos(x) - cos(x));");
> 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
> max_terms:=30;
> Digits:=32;
> #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_g:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3_g:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= 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_g[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_g[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[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_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1_g[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_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3_g[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 := 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_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_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 := -5.0;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 100;
> 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 ) = sin ( x ) + sin ( x ) ;");
> 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,"2013-05-25T23:50:52-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"add")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;")
> ;
> 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,"add diffeq.mxt")
> ;
> logitem_str(html_log_file,"add 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_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_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4,
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/addpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -5.0;");
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 := 100;");
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(2.0 - cos(x) - cos(x));");
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;
max_terms := 30;
Digits := 32;
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_g := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3_g := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := 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_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_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_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp1_g[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp3_g[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_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_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 := -5.0;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 100;
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 ) = sin ( x ) + sin ( x ) ;");
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, "2013-05-25T23:50:52-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "add");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;");
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,
"add diffeq.mxt");
logitem_str(html_log_file,
"add 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/addpostode.ode#################
diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
max_terms:=30;
Digits:=32;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -5.0;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 100;
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(2.0 - cos(x) - cos(x));
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 = 10
estimated_steps = 10000000
step_error = 1.0000000000000000000000000000000e-17
est_needed_step_err = 1.0000000000000000000000000000000e-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 = 1.4067353021209587373088533999590e-183
estimated_step_error = 1.4067353021209587373088533999590e-183
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 = 9.4404402164116865043464570617934e-176
estimated_step_error = 9.4404402164116865043464570617934e-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 = 6.3353713926173167972978718673577e-168
estimated_step_error = 6.3353713926173167972978718673577e-168
best_h = 8.000e-06
opt_iter = 4
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.2515947071303265754442581571220e-160
estimated_step_error = 4.2515947071303265754442581571220e-160
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 = 2.8531954809087672667810583490172e-152
estimated_step_error = 2.8531954809087672667810583490172e-152
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 = 1.9147451570588862570582253255205e-144
estimated_step_error = 1.9147451570588862570582253255205e-144
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 = 1.2849611492638689738777494471502e-136
estimated_step_error = 1.2849611492638689738777494471502e-136
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 = 8.6231937516725606723920452632870e-129
estimated_step_error = 8.6231937516725606723920452632870e-129
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 = 5.7868809957316295545604444322444e-121
estimated_step_error = 5.7868809957316295545604444322444e-121
best_h = 0.000512
opt_iter = 10
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.8834478583206815928292968901601e-113
estimated_step_error = 3.8834478583206815928292968901601e-113
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 = 2.6060542057122508356940820194223e-105
estimated_step_error = 2.6060542057122508356940820194223e-105
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 = 1.7487812515942845088201533601559e-97
estimated_step_error = 1.7487812515942845088201533601559e-97
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 = 1.1734367429771466736806510441436e-89
estimated_step_error = 1.1734367429771466736806510441436e-89
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 = 7.8727807875006785840587221469819e-82
estimated_step_error = 7.8727807875006785840587221469819e-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 = 5.2806225223138969085011158615030e-74
estimated_step_error = 5.2806225223138969085011158615030e-74
best_h = 0.032768
opt_iter = 16
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.5401263640216604856691597924428e-66
estimated_step_error = 3.5401263640216604856691597924428e-66
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 = 2.3708525684792538752954511718038e-58
estimated_step_error = 2.3708525684792538752954511718038e-58
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 = 1.5844909190829553189763380039629e-50
estimated_step_error = 1.5844909190829553189763380039629e-50
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -5
y[1] (analytic) = 1.4326756290735474710667216569729
y[1] (numeric) = 1.4326756290735474710667216569729
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] = -4.99
y[1] (analytic) = 1.4518821609091455120738168046061
y[1] (numeric) = 1.4518821609091455120738168046061
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] = -4.98
y[1] (analytic) = 1.4711435040718892951674933586384
y[1] (numeric) = 1.4711435040718892951674933586384
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] = -4.97
y[1] (analytic) = 1.4904577324435136117680929719749
y[1] (numeric) = 1.4904577324435136117680929719749
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=4000360, alloc=3145152, time=0.14
x[1] = -4.96
y[1] (analytic) = 1.5098229146172764361031039541294
y[1] (numeric) = 1.5098229146172764361031039541293
absolute error = 1e-31
relative error = 6.6232933035957335552074366499358e-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] = -4.95
y[1] (analytic) = 1.5292371140910979899094851767305
y[1] (numeric) = 1.5292371140910979899094851767305
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] = -4.94
y[1] (analytic) = 1.5486983894612093366651383919206
y[1] (numeric) = 1.5486983894612093366651383919205
absolute error = 1e-31
relative error = 6.4570351903568455788146775456171e-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] = -4.93
y[1] (analytic) = 1.5682047946162911406514791070285
y[1] (numeric) = 1.5682047946162911406514791070284
absolute error = 1e-31
relative error = 6.3767181648279574693005125015443e-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] = -4.92
y[1] (analytic) = 1.5877543789320831771329815183765
y[1] (numeric) = 1.5877543789320831771329815183764
absolute error = 1e-31
relative error = 6.2982033825193776798338310355874e-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] = -4.91
y[1] (analytic) = 1.6073451874664451328648536009612
y[1] (numeric) = 1.6073451874664451328648536009612
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] = -4.9
y[1] (analytic) = 1.6269752611548491910113417117562
y[1] (numeric) = 1.6269752611548491910113417117562
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] = -4.89
y[1] (analytic) = 1.6466426370062848513790828205723
y[1] (numeric) = 1.6466426370062848513790828205724
absolute error = 1e-31
relative error = 6.0729631161383757667052432978067e-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] = -4.88
y[1] (analytic) = 1.6663453482995563956467345059368
y[1] (numeric) = 1.6663453482995563956467345059368
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] = -4.87
y[1] (analytic) = 1.6860814247799533680079404287439
y[1] (numeric) = 1.686081424779953368007940428744
absolute error = 1e-31
relative error = 5.9309116707131016153521868418806e-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] = -4.86
y[1] (analytic) = 1.7058488928562744043434585080292
y[1] (numeric) = 1.7058488928562744043434585080293
absolute error = 1e-31
relative error = 5.8621839495150089357840100419421e-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] = -4.85
y[1] (analytic) = 1.7256457757981847077037205630694
y[1] (numeric) = 1.7256457757981847077037205630695
absolute error = 1e-31
relative error = 5.7949320423970405291180884372253e-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] = -4.84
y[1] (analytic) = 1.7454700939338874345187391805346
y[1] (numeric) = 1.7454700939338874345187391805347
absolute error = 1e-31
relative error = 5.7291156318022636556024786906784e-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] = -4.83
y[1] (analytic) = 1.7653198648480892245614664220924
y[1] (numeric) = 1.7653198648480892245614664220924
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] = -4.82
y[1] (analytic) = 1.7851931035802400782765787616605
y[1] (numeric) = 1.7851931035802400782765787616605
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] = -4.81
y[1] (analytic) = 1.8050878228230277576521547209232
y[1] (numeric) = 1.8050878228230277576521547209233
absolute error = 1e-31
relative error = 5.5398966596321712233003319840919e-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] = -4.8
y[1] (analytic) = 1.825002033121106861359569484701
y[1] (numeric) = 1.8250020331211068613595694847011
absolute error = 1e-31
relative error = 5.4794459504782379050358995417346e-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] = -4.79
y[1] (analytic) = 1.8449337430700427014196995173048
y[1] (numeric) = 1.8449337430700427014196995173049
absolute error = 1e-31
relative error = 5.4202488504327556917303717753508e-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] = -4.78
y[1] (analytic) = 1.8648809595154500871735565706809
y[1] (numeric) = 1.864880959515450087173556570681
absolute error = 1e-31
relative error = 5.3622725616750833802878716448076e-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] = -4.77
y[1] (analytic) = 1.8848416877523071028449024544255
y[1] (numeric) = 1.8848416877523071028449024544256
absolute error = 1e-31
relative error = 5.3054853704584079860519453085827e-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] = -4.76
y[1] (analytic) = 1.9048139317244239474831825671789
y[1] (numeric) = 1.9048139317244239474831825671791
absolute error = 2e-31
relative error = 1.0499713209202561375821943934823e-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] = -4.75
y[1] (analytic) = 1.9247956942240468905690073752533
y[1] (numeric) = 1.9247956942240468905690073752535
absolute error = 2e-31
relative error = 1.0390713185828642559255802306881e-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] = -4.74
y[1] (analytic) = 1.944784977091577383052957365562
y[1] (numeric) = 1.9447849770915773830529573655622
absolute error = 2e-31
relative error = 1.0283913252924220905658288514537e-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] = -4.73
y[1] (analytic) = 1.9647797814153863520830396301143
y[1] (numeric) = 1.9647797814153863520830396301145
absolute error = 2e-31
relative error = 1.0179257843132128209552597794626e-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=8001788, alloc=4259060, time=0.30
x[1] = -4.72
y[1] (analytic) = 1.9847781077317036981578346936507
y[1] (numeric) = 1.9847781077317036981578346936509
absolute error = 2e-31
relative error = 1.0076693168918980998766221861335e-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] = -4.71
y[1] (analytic) = 2.0047779562245630059221922954494
y[1] (numeric) = 2.0047779562245630059221922954496
absolute error = 2e-31
relative error = 9.9761671550221903557712361455900e-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 = 0.002304
Order of pole (three term test) = -0.893
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.7
y[1] (analytic) = 2.0247773269257814743010165926542
y[1] (numeric) = 2.0247773269257814743010165926544
absolute error = 2e-31
relative error = 9.8776293738758874839623492773220e-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 = 0.01195
Order of pole (three term test) = -0.8966
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.69
y[1] (analytic) = 2.044774219914955068144776792884
y[1] (numeric) = 2.0447742199149550681447767928842
absolute error = 2e-31
relative error = 9.7810309838666819231987230180752e-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 = 0.02158
Order of pole (three term test) = -0.905
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.68
y[1] (analytic) = 2.0647666355194488920382407358891
y[1] (numeric) = 2.0647666355194488920382407358893
absolute error = 2e-31
relative error = 9.6863246702785127976950039258927e-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 = 0.03121
Order of pole (three term test) = -0.9182
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.67
y[1] (analytic) = 2.0847525745143627874017086402106
y[1] (numeric) = 2.0847525745143627874017086402107
absolute error = 1e-31
relative error = 4.7967322943968406903304045188291e-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 = 0.04083
Order of pole (three term test) = -0.9363
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.66
y[1] (analytic) = 2.1047300383224521564916743335919
y[1] (numeric) = 2.1047300383224521564916743335921
absolute error = 2e-31
relative error = 9.5024063114245004152029273785685e-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 = 0.05043
Order of pole (three term test) = -0.9592
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.65
y[1] (analytic) = 2.1246970292139840213851140323542
y[1] (numeric) = 2.1246970292139840213851140323543
absolute error = 1e-31
relative error = 4.7065533873784471599150664009714e-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 = 0.06
Order of pole (three term test) = -0.9868
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.64
y[1] (analytic) = 2.1446515505065083325080504015202
y[1] (numeric) = 2.1446515505065083325080504015204
absolute error = 2e-31
relative error = 9.3255242303937645592356643111852e-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 = 0.06956
Order of pole (three term test) = -1.019
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.63
y[1] (analytic) = 2.1645916067645245497440145748052
y[1] (numeric) = 2.1645916067645245497440145748054
absolute error = 2e-31
relative error = 9.2396181974920238408038097776135e-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 = 0.07909
Order of pole (three term test) = -1.057
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.62
y[1] (analytic) = 2.1845152039990235296306835512316
y[1] (numeric) = 2.1845152039990235296306835512318
absolute error = 2e-31
relative error = 9.1553494172929271713261672307516e-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 = 0.08858
Order of pole (three term test) = -1.099
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.61
y[1] (analytic) = 2.2044203498668847646222576563454
y[1] (numeric) = 2.2044203498668847646222576563455
absolute error = 1e-31
relative error = 4.5363399047753555505771014786574e-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 = 0.09804
Order of pole (three term test) = -1.145
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.6
y[1] (analytic) = 2.2243050538701090348598156424584
y[1] (numeric) = 2.2243050538701090348598156424585
absolute error = 1e-31
relative error = 4.4957862153848084591819074827995e-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 = 0.1075
Order of pole (three term test) = -1.197
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.59
y[1] (analytic) = 2.244167327554866549350497048793
y[1] (numeric) = 2.2441673275548665493504970487931
absolute error = 1e-31
relative error = 4.4559957170820698935084701819744e-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 = 0.1168
Order of pole (three term test) = -1.253
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.58
y[1] (analytic) = 2.2640051847103406719072668013646
y[1] (numeric) = 2.2640051847103406719072668013647
absolute error = 1e-31
relative error = 4.4169510156309165269893879563386e-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 = 0.1262
Order of pole (three term test) = -1.314
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.57
y[1] (analytic) = 2.2838166415673473476423706287492
y[1] (numeric) = 2.2838166415673473476423706287493
absolute error = 1e-31
relative error = 4.3786352275361115198056476191367e-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 = 0.1355
Order of pole (three term test) = -1.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.56
y[1] (analytic) = 2.3035997169967103682373475852198
y[1] (numeric) = 2.3035997169967103682373475852199
absolute error = 1e-31
relative error = 4.3410319623746856002179814072745e-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 = 0.1447
Order of pole (three term test) = -1.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.55
y[1] (analytic) = 2.3233524327073726386283848500159
y[1] (numeric) = 2.323352432707372638628384850016
absolute error = 1e-31
relative error = 4.3041253058396865402557992080671e-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 = 0.1538
Order of pole (three term test) = -1.525
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.54
y[1] (analytic) = 2.3430728134442236341454384391956
y[1] (numeric) = 2.3430728134442236341454384391957
absolute error = 1e-31
relative error = 4.2678998034638106823258605856865e-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 = 0.163
Order of pole (three term test) = -1.604
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.53
y[1] (analytic) = 2.3627588871856232655242615827628
y[1] (numeric) = 2.3627588871856232655242615827629
absolute error = 1e-31
relative error = 4.2323404449919985194791392336668e-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 = 0.172
Order of pole (three term test) = -1.688
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.52
y[1] (analytic) = 2.3824086853406023995694422363978
y[1] (numeric) = 2.3824086853406023995694422363979
absolute error = 1e-31
relative error = 4.1974326493736503347208933691486e-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 = 0.181
Order of pole (three term test) = -1.777
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.51
y[1] (analytic) = 2.4020202429457203155807166434815
y[1] (numeric) = 2.4020202429457203155807166434817
absolute error = 2e-31
relative error = 8.3263245006932068000353543773883e-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 = 0.1899
Order of pole (three term test) = -1.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.5
y[1] (analytic) = 2.4215915988615594119609636495877
y[1] (numeric) = 2.4215915988615594119609636495878
absolute error = 1e-31
relative error = 4.1295154825864146680687126966162e-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 = 0.1987
Order of pole (three term test) = -1.967
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.49
y[1] (analytic) = 2.4411207959688375136989640130322
y[1] (numeric) = 2.4411207959688375136989640130323
absolute error = 1e-31
relative error = 4.0964789683958173406733440034490e-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 = 0.2074
Order of pole (three term test) = -2.069
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=12002816, alloc=4324584, time=0.45
x[1] = -4.48
y[1] (analytic) = 2.4606058813641181696596028136977
y[1] (numeric) = 2.4606058813641181696596028136978
absolute error = 1e-31
relative error = 4.0640397049104709106496876647709e-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 = 0.2161
Order of pole (three term test) = -2.175
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.47
y[1] (analytic) = 2.4800449065550993688148773106603
y[1] (numeric) = 2.4800449065550993688148773106604
absolute error = 1e-31
relative error = 4.0321850517983066806621672466604e-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 = 0.2247
Order of pole (three term test) = -2.286
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.46
y[1] (analytic) = 2.4994359276554611467068272022253
y[1] (numeric) = 2.4994359276554611467068272022254
absolute error = 1e-31
relative error = 4.0009027194308885020917627543848e-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 = 0.2332
Order of pole (three term test) = -2.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.45
y[1] (analytic) = 2.5187770055792525975441134594889
y[1] (numeric) = 2.518777005579252597544113459489
absolute error = 1e-31
relative error = 3.9701807575062654200683556442469e-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 = 0.2415
Order of pole (three term test) = -2.519
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.44
y[1] (analytic) = 2.5380662062347988533930247123268
y[1] (numeric) = 2.5380662062347988533930247123269
absolute error = 1e-31
relative error = 3.9400075441037926755660692309145e-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 = 0.2498
Order of pole (three term test) = -2.643
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.43
y[1] (analytic) = 2.5573016007181086399265806978673
y[1] (numeric) = 2.5573016007181086399265806978674
absolute error = 1e-31
relative error = 3.9103717751523434869543981799336e-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 = 0.258
Order of pole (three term test) = -2.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.42
y[1] (analytic) = 2.5764812655057630681373302869864
y[1] (numeric) = 2.5764812655057630681373302869865
absolute error = 1e-31
relative error = 3.8812624542942293791024037924885e-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 = 0.2661
Order of pole (three term test) = -2.901
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.41
y[1] (analytic) = 2.5956032826472663732954129329813
y[1] (numeric) = 2.5956032826472663732954129329813
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 = 0.2741
Order of pole (three term test) = -3.037
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.4
y[1] (analytic) = 2.6146657399568393662382794844354
y[1] (numeric) = 2.6146657399568393662382794844355
absolute error = 1e-31
relative error = 3.8245806518140522714789189995086e-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 = 0.282
Order of pole (three term test) = -3.176
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.39
y[1] (analytic) = 2.6336667312046364178067707335115
y[1] (numeric) = 2.6336667312046364178067707335116
absolute error = 1e-31
relative error = 3.7969876300278928696899242934907e-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 = 0.2897
Order of pole (three term test) = -3.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.38
y[1] (analytic) = 2.6526043563073668548884570476882
y[1] (numeric) = 2.6526043563073668548884570476883
absolute error = 1e-31
relative error = 3.7698799582463114427332273735060e-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 = 0.2974
Order of pole (three term test) = -3.467
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.37
y[1] (analytic) = 2.6714767215183017060874853848457
y[1] (numeric) = 2.6714767215183017060874853848458
absolute error = 1e-31
relative error = 3.7432480393527891628200396906084e-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 = 0.3049
Order of pole (three term test) = -3.618
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.36
y[1] (analytic) = 2.6902819396166467965047051339269
y[1] (numeric) = 2.690281939616646796504705133927
absolute error = 1e-31
relative error = 3.7170825305488076449497641324066e-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 = 0.3123
Order of pole (three term test) = -3.772
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.35
y[1] (analytic) = 2.7090181300962632544764051548717
y[1] (numeric) = 2.7090181300962632544764051548719
absolute error = 2e-31
relative error = 7.3827486711169823680496829818369e-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 = 0.3196
Order of pole (three term test) = -3.931
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.34
y[1] (analytic) = 2.7276834193537165583782547088473
y[1] (numeric) = 2.7276834193537165583782547088475
absolute error = 2e-31
relative error = 7.3322291942291082732782180464257e-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 = 0.3267
Order of pole (three term test) = -4.093
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.33
y[1] (analytic) = 2.7462759408756353187464749013257
y[1] (numeric) = 2.7462759408756353187464749013259
absolute error = 2e-31
relative error = 7.2825893794281675596825582109261e-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 = 0.3338
Order of pole (three term test) = -4.258
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.32
y[1] (analytic) = 2.7647938354253610599941603188602
y[1] (numeric) = 2.7647938354253610599941603188603
absolute error = 1e-31
relative error = 3.6169062126332139117688940876409e-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 = 0.3406
Order of pole (three term test) = -4.428
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.31
y[1] (analytic) = 2.7832352512288703369001201936885
y[1] (numeric) = 2.7832352512288703369001201936886
absolute error = 1e-31
relative error = 3.5929409831902428670105256687859e-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 = 0.3474
Order of pole (three term test) = -4.6
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.3
y[1] (analytic) = 2.8015983441599505938135247926721
y[1] (numeric) = 2.8015983441599505938135247926722
absolute error = 1e-31
relative error = 3.5693910302472229706455336380633e-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 = 0.354
Order of pole (three term test) = -4.776
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.29
y[1] (analytic) = 2.8198812779246112491427492675585
y[1] (numeric) = 2.8198812779246112491427492675586
absolute error = 1e-31
relative error = 3.5462485879404981287563707948899e-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 = 0.3605
Order of pole (three term test) = -4.955
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.28
y[1] (analytic) = 2.8380822242447115641736414736721
y[1] (numeric) = 2.8380822242447115641736414736722
absolute error = 1e-31
relative error = 3.5235060896310935470032471212809e-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 = 0.3668
Order of pole (three term test) = -5.137
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.27
y[1] (analytic) = 2.8561993630407869335833546441886
y[1] (numeric) = 2.8561993630407869335833546441887
absolute error = 1e-31
relative error = 3.5011561620662677026697629336598e-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 = 0.373
Order of pole (three term test) = -5.323
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.26
y[1] (analytic) = 2.874230882614055315173048270972
y[1] (numeric) = 2.8742308826140553151730482709721
absolute error = 1e-31
relative error = 3.4791916197439228173287427509077e-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 = 0.379
Order of pole (three term test) = -5.511
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.25
y[1] (analytic) = 2.8921749798275855983281554410897
y[1] (numeric) = 2.8921749798275855983281554410898
absolute error = 1e-31
relative error = 3.4576054594719372672645682229952e-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 = 0.3849
Order of pole (three term test) = -5.703
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.24
y[1] (analytic) = 2.9100298602866097945203437394119
y[1] (numeric) = 2.910029860286609794520343739412
absolute error = 1e-31
relative error = 3.4363908551148326440622672861197e-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 = 0.3906
Order of pole (three term test) = -5.897
NO COMPLEX POLE (six term test) for Equation 1
bytes used=16006156, alloc=4390108, time=0.61
TOP MAIN SOLVE Loop
x[1] = -4.23
y[1] (analytic) = 2.9277937385179610187823791790897
y[1] (numeric) = 2.9277937385179610187823791790898
absolute error = 1e-31
relative error = 3.4155411525205204960880784747755e-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 = 0.3962
Order of pole (three term test) = -6.094
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.22
y[1] (analytic) = 2.9454648381486193185072768263104
y[1] (numeric) = 2.9454648381486193185072768263105
absolute error = 1e-31
relative error = 3.3950498646201900451347112316034e-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 = 0.4016
Order of pole (three term test) = -6.294
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.21
y[1] (analytic) = 2.9630413920833474951376458989737
y[1] (numeric) = 2.9630413920833474951376458989738
absolute error = 1e-31
relative error = 3.3749106666946992313962498559020e-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 = 0.4068
Order of pole (three term test) = -6.497
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.2
y[1] (analytic) = 2.9805216426813991553110897627543
y[1] (numeric) = 2.9805216426813991553110897627544
absolute error = 1e-31
relative error = 3.3551173918011180954401442753502e-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 = 0.4119
Order of pole (three term test) = -6.702
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.19
y[1] (analytic) = 2.9979038419322813208038025029849
y[1] (numeric) = 2.997903841932281320803802502985
absolute error = 1e-31
relative error = 3.3356640263533465134092578897236e-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 = 0.4168
Order of pole (three term test) = -6.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.18
y[1] (analytic) = 3.0151862516305540211578360660934
y[1] (numeric) = 3.0151862516305540211578360660936
absolute error = 2e-31
relative error = 6.6330894117019767475557692735683e-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 = 0.4216
Order of pole (three term test) = -7.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.17
y[1] (analytic) = 3.0323671435496493891784410855156
y[1] (numeric) = 3.0323671435496493891784410855157
absolute error = 1e-31
relative error = 3.2977537107509120927131822853741e-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 = 0.4262
Order of pole (three term test) = -7.332
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.16
y[1] (analytic) = 3.0494447996146928775367804214184
y[1] (numeric) = 3.0494447996146928775367804214186
absolute error = 2e-31
relative error = 6.5585709249523270893653551616871e-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 = 0.4306
Order of pole (three term test) = -7.547
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.15
y[1] (analytic) = 3.0664175120743093145003723433254
y[1] (numeric) = 3.0664175120743093145003723433256
absolute error = 2e-31
relative error = 6.5222690391142452680841649927287e-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 = 0.4348
Order of pole (three term test) = -7.764
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.14
y[1] (analytic) = 3.0832835836713966183288615471946
y[1] (numeric) = 3.0832835836713966183288615471948
absolute error = 2e-31
relative error = 6.4865911478000188342990761526171e-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 = 0.4389
Order of pole (three term test) = -7.983
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.13
y[1] (analytic) = 3.100041327812850093105989384141
y[1] (numeric) = 3.1000413278128500931059893841412
absolute error = 2e-31
relative error = 6.4515268943561008737632383399972e-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 = 0.4428
Order of pole (three term test) = -8.204
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.12
y[1] (analytic) = 3.1166890687382203337196165455186
y[1] (numeric) = 3.1166890687382203337196165455188
absolute error = 2e-31
relative error = 6.4170661746816225130821004523842e-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 = 0.4465
Order of pole (three term test) = -8.427
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.11
y[1] (analytic) = 3.1332251416872878743398479877489
y[1] (numeric) = 3.1332251416872878743398479877492
absolute error = 3e-31
relative error = 9.5747986957121626636379778548214e-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 = 0.45
Order of pole (three term test) = -8.652
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.1
y[1] (analytic) = 3.1496478930665378230700573593196
y[1] (numeric) = 3.1496478930665378230700573593198
absolute error = 2e-31
relative error = 6.3499161426986500307154861151519e-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 = 0.4534
Order of pole (three term test) = -8.878
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.09
y[1] (analytic) = 3.1659556806145178354460742272886
y[1] (numeric) = 3.1659556806145178354460742272888
absolute error = 2e-31
relative error = 6.3172078252586161032927262322998e-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 = 0.4565
Order of pole (three term test) = -9.106
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.08
y[1] (analytic) = 3.1821468735660628911239820364958
y[1] (numeric) = 3.1821468735660628911239820364961
absolute error = 3e-31
relative error = 9.4275975283254585611840122620044e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.92
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4595
Order of pole (three term test) = -9.336
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.07
y[1] (analytic) = 3.1982198528153704514157115460792
y[1] (numeric) = 3.1982198528153704514157115460795
absolute error = 3e-31
relative error = 9.3802181778063852972369531862489e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.22
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4623
Order of pole (three term test) = -9.567
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.06
y[1] (analytic) = 3.2141730110779096902925716955787
y[1] (numeric) = 3.214173011077909690292571695579
absolute error = 3e-31
relative error = 9.3336606015303316829570607780944e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.52
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4649
Order of pole (three term test) = -9.799
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.05
y[1] (analytic) = 3.2300047530511486080685414569647
y[1] (numeric) = 3.2300047530511486080685414569651
absolute error = 4e-31
relative error = 1.2383882705502192688918770621852e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.82
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4674
Order of pole (three term test) = -10.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.04
y[1] (analytic) = 3.2457134955740829551858931583454
y[1] (numeric) = 3.2457134955740829551858931583457
absolute error = 3e-31
relative error = 9.2429599965950704501383320622772e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.13
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4696
Order of pole (three term test) = -10.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.03
y[1] (analytic) = 3.2612976677855510133437090437049
y[1] (numeric) = 3.2612976677855510133437090437052
absolute error = 3e-31
relative error = 9.1987923385019486345928346778274e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.44
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4717
Order of pole (three term test) = -10.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.02
y[1] (analytic) = 3.2767557112813184026231067615307
y[1] (numeric) = 3.276755711281318402623106761531
absolute error = 3e-31
relative error = 9.1553971804230169814521462479381e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.76
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4736
Order of pole (three term test) = -10.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4.01
y[1] (analytic) = 3.2920860802699172062593648293701
y[1] (numeric) = 3.2920860802699172062593648293703
absolute error = 2e-31
relative error = 6.0751752877495249634525702900627e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.08
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4752
Order of pole (three term test) = -10.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -4
y[1] (analytic) = 3.3072872417272238292783363661955
y[1] (numeric) = 3.3072872417272238292783363661957
absolute error = 2e-31
relative error = 6.0472521853151895944387674226035e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.41
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4767
Order of pole (three term test) = -11.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=20007080, alloc=4390108, time=0.77
x[1] = -3.99
y[1] (analytic) = 3.3223576755497601333401019040203
y[1] (numeric) = 3.3223576755497601333401019040205
absolute error = 2e-31
relative error = 6.0198214500461760658984462450592e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.74
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.478
Order of pole (three term test) = -11.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.98
y[1] (analytic) = 3.3372958747067025178041274333497
y[1] (numeric) = 3.3372958747067025178041274333499
absolute error = 2e-31
relative error = 5.9928758943968956336360039941063e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.09
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4791
Order of pole (three term test) = -11.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.97
y[1] (analytic) = 3.3521003453905837462344949786387
y[1] (numeric) = 3.3521003453905837462344949786389
absolute error = 2e-31
relative error = 5.9664085019118417279235511256579e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.43
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4801
Order of pole (three term test) = -11.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.96
y[1] (analytic) = 3.366769607166672448288139617503
y[1] (numeric) = 3.3667696071666724482881396175032
absolute error = 2e-31
relative error = 5.9404124230618602342655043267800e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.79
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4808
Order of pole (three term test) = -12.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.95
y[1] (analytic) = 3.3813021931210153591603866232805
y[1] (numeric) = 3.3813021931210153591603866232806
absolute error = 1e-31
relative error = 2.9574404856046843954592025702338e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4813
Order of pole (three term test) = -12.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.94
y[1] (analytic) = 3.3956966500071274924872122988712
y[1] (numeric) = 3.3956966500071274924872122988713
absolute error = 1e-31
relative error = 2.9449038093491096209148427145464e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = -12.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.93
y[1] (analytic) = 3.4099515383913155778091796790539
y[1] (numeric) = 3.409951538391315577809179679054
absolute error = 1e-31
relative error = 2.9325929965320318511467696692693e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.89
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.92
y[1] (analytic) = 3.4240654327966202303744051685852
y[1] (numeric) = 3.4240654327966202303744051685853
absolute error = 1e-31
relative error = 2.9205049366806220204649101186751e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.27
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.91
y[1] (analytic) = 3.4380369218453624591835272277488
y[1] (numeric) = 3.4380369218453624591835272277489
absolute error = 1e-31
relative error = 2.9086365933011886397411117951715e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.33
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4815
Order of pole (three term test) = -13.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.9
y[1] (analytic) = 3.4518646084002802587446609692287
y[1] (numeric) = 3.4518646084002802587446609692288
absolute error = 1e-31
relative error = 2.8969850021534778845412362295161e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.95
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4811
Order of pole (three term test) = -13.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.89
y[1] (analytic) = 3.4655471097042411709967766052634
y[1] (numeric) = 3.4655471097042411709967766052635
absolute error = 1e-31
relative error = 2.8855472695777106551824517790954e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4805
Order of pole (three term test) = -13.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.88
y[1] (analytic) = 3.4790830575185168462617361540826
y[1] (numeric) = 3.4790830575185168462617361540827
absolute error = 1e-31
relative error = 2.8743205708726534614737939116942e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4797
Order of pole (three term test) = -14.11
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.87
y[1] (analytic) = 3.4924710982596057758841216186546
y[1] (numeric) = 3.4924710982596057758841216186547
absolute error = 1e-31
relative error = 2.8633021487230845006952928139537e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.84
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4786
Order of pole (three term test) = -14.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.86
y[1] (analytic) = 3.5057098931345905143996092187297
y[1] (numeric) = 3.5057098931345905143996092187298
absolute error = 1e-31
relative error = 2.8524893116750781854333729379013e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4775
Order of pole (three term test) = -14.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.85
y[1] (analytic) = 3.5187981182750158556224701479056
y[1] (numeric) = 3.5187981182750158556224701479057
absolute error = 1e-31
relative error = 2.8418794326575907575984933628360e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.14
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4761
Order of pole (three term test) = -14.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.84
y[1] (analytic) = 3.5317344648692745749461538804954
y[1] (numeric) = 3.5317344648692745749461538804955
absolute error = 1e-31
relative error = 2.8314699475488866098602686370195e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.79
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4745
Order of pole (three term test) = -15.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.83
y[1] (analytic) = 3.544517639293487499393045054047
y[1] (numeric) = 3.5445176392934874993930450540471
absolute error = 1e-31
relative error = 2.8212583537863996338841440729793e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.45
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4727
Order of pole (three term test) = -15.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.82
y[1] (analytic) = 3.5571463632408648175154553133124
y[1] (numeric) = 3.5571463632408648175154553133125
absolute error = 1e-31
relative error = 2.8112422090186764289555242623877e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.12
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4708
Order of pole (three term test) = -15.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.81
y[1] (analytic) = 3.5696193738495356931246607487299
y[1] (numeric) = 3.56961937384953569312466074873
absolute error = 1e-31
relative error = 2.8014191297980986326953936334332e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.79
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4686
Order of pole (three term test) = -15.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.8
y[1] (analytic) = 3.5819354238288333999931363487015
y[1] (numeric) = 3.5819354238288333999931363487015
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 = 15.47
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4663
Order of pole (three term test) = -16.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.79
y[1] (analytic) = 3.5940932815840233491217545036803
y[1] (numeric) = 3.5940932815840233491217545036804
absolute error = 1e-31
relative error = 2.7823429211588809535908048689729e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4638
Order of pole (three term test) = -16.24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.78
y[1] (analytic) = 3.6060917313394615358731605184754
y[1] (numeric) = 3.6060917313394615358731605184755
absolute error = 1e-31
relative error = 2.7730853081448260591099923792344e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.84
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.461
Order of pole (three term test) = -16.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.77
y[1] (analytic) = 3.6179295732601710912292434923924
y[1] (numeric) = 3.6179295732601710912292434923925
absolute error = 1e-31
relative error = 2.7640117911385568135073772000287e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.53
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4582
Order of pole (three term test) = -16.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.76
y[1] (analytic) = 3.6296056235718247796188902751262
y[1] (numeric) = 3.6296056235718247796188902751263
absolute error = 1e-31
relative error = 2.7551202629444884907316082924142e-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 = 0.4551
Order of pole (three term test) = -16.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=24009716, alloc=4390108, time=0.92
x[1] = -3.75
y[1] (analytic) = 3.6411187146791214451662248045814
y[1] (numeric) = 3.6411187146791214451662248045815
absolute error = 1e-31
relative error = 2.7464086682164834728384455873944e-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 = 0.4518
Order of pole (three term test) = -17.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.74
y[1] (analytic) = 3.6524676952825445688133547124051
y[1] (numeric) = 3.6524676952825445688133547124051
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 = 0.4484
Order of pole (three term test) = -17.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.73
y[1] (analytic) = 3.6636514304934912605592113958433
y[1] (numeric) = 3.6636514304934912605592113958433
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 = 0.4448
Order of pole (three term test) = -17.61
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.72
y[1] (analytic) = 3.6746688019477601740112001789793
y[1] (numeric) = 3.6746688019477601740112001789794
absolute error = 1e-31
relative error = 2.7213336871882153362773104072683e-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 = 0.441
Order of pole (three term test) = -17.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.71
y[1] (analytic) = 3.6855187079173869945527783452195
y[1] (numeric) = 3.6855187079173869945527783452196
absolute error = 1e-31
relative error = 2.7133222736103814963377584601765e-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 = 0.437
Order of pole (three term test) = -18.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.7
y[1] (analytic) = 3.6962000634208163176713402127088
y[1] (numeric) = 3.6962000634208163176713402127089
absolute error = 1e-31
relative error = 2.7054812587024971703172639057409e-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 = 0.4329
Order of pole (three term test) = -18.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.69
y[1] (analytic) = 3.7067118003313989003503860567443
y[1] (numeric) = 3.7067118003313989003503860567444
absolute error = 1e-31
relative error = 2.6978088771579028897672490323384e-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 = 0.4286
Order of pole (three term test) = -18.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.68
y[1] (analytic) = 3.7170528674842034358912497370723
y[1] (numeric) = 3.7170528674842034358912497370724
absolute error = 1e-31
relative error = 2.6903034087777869224155574042177e-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 = 0.4241
Order of pole (three term test) = -18.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.67
y[1] (analytic) = 3.7272222307811321710759123729596
y[1] (numeric) = 3.7272222307811321710759123729597
absolute error = 1e-31
relative error = 2.6829631776220252764878413694650e-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 = 0.4194
Order of pole (three term test) = -18.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.66
y[1] (analytic) = 3.7372188732943298541967818403199
y[1] (numeric) = 3.7372188732943298541967818403199
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 = 0.4146
Order of pole (three term test) = -19.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.65
y[1] (analytic) = 3.7470417953678756731448089490565
y[1] (numeric) = 3.7470417953678756731448089490566
absolute error = 1e-31
relative error = 2.6687719396036850787911526187058e-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 = 0.4096
Order of pole (three term test) = -19.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.64
y[1] (analytic) = 3.7566900147177480144468744882682
y[1] (numeric) = 3.7566900147177480144468744882682
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 = 0.4044
Order of pole (three term test) = -19.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.63
y[1] (analytic) = 3.766162566530052046859847088796
y[1] (numeric) = 3.766162566530052046859847088796
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 = 0.3991
Order of pole (three term test) = -19.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.62
y[1] (analytic) = 3.775458503557500306844808544136
y[1] (numeric) = 3.775458503557500306844808544136
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 = 0.3937
Order of pole (three term test) = -19.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.61
y[1] (analytic) = 3.7845768962141366379432993870768
y[1] (numeric) = 3.7845768962141366379432993870768
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 = 0.388
Order of pole (three term test) = -20.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.6
y[1] (analytic) = 3.7935168326682940117405834505319
y[1] (numeric) = 3.7935168326682940117405834505318
absolute error = 1e-31
relative error = 2.6360763484384418204810552982960e-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 = 0.3822
Order of pole (three term test) = -20.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.59
y[1] (analytic) = 3.8022774189337769347112996786957
y[1] (numeric) = 3.8022774189337769347112996786956
absolute error = 1e-31
relative error = 2.6300027321005339938446384790204e-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 = 0.3763
Order of pole (three term test) = -20.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.58
y[1] (analytic) = 3.810857778959259322782801709098
y[1] (numeric) = 3.810857778959259322782801709098
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 = 0.3702
Order of pole (three term test) = -20.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.57
y[1] (analytic) = 3.8192570547158889039032268720735
y[1] (numeric) = 3.8192570547158889039032268720734
absolute error = 1e-31
relative error = 2.6183102778202215045598573092352e-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 = 0.364
Order of pole (three term test) = -20.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.56
y[1] (analytic) = 3.8274744062830893882470412262073
y[1] (numeric) = 3.8274744062830893882470412262072
absolute error = 1e-31
relative error = 2.6126889270857675566522054916209e-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 = 0.3576
Order of pole (three term test) = -21.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.55
y[1] (analytic) = 3.8355090119325518259125416454209
y[1] (numeric) = 3.8355090119325518259125416454208
absolute error = 1e-31
relative error = 2.6072158790109113033915910674702e-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 = 0.3511
Order of pole (three term test) = -21.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.54
y[1] (analytic) = 3.8433600682104067530455377722595
y[1] (numeric) = 3.8433600682104067530455377722594
absolute error = 1e-31
relative error = 2.6018899667280783072128704691273e-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 = 0.3444
Order of pole (three term test) = -21.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.53
y[1] (analytic) = 3.851026790017568909243078029368
y[1] (numeric) = 3.8510267900175689092430780293679
absolute error = 1e-31
relative error = 2.5967100581905789953377763568320e-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 = 0.3376
Order of pole (three term test) = -21.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.52
y[1] (analytic) = 3.8585084106882464918324330245445
y[1] (numeric) = 3.8585084106882464918324330245443
absolute error = 2e-31
relative error = 5.1833501113018378700274127000487e-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 = 0.3307
Order of pole (three term test) = -21.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.51
y[1] (analytic) = 3.8658041820666070961653326115152
y[1] (numeric) = 3.865804182066607096165332611515
absolute error = 2e-31
relative error = 5.1735677903137525429560685752881e-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 = 0.3236
Order of pole (three term test) = -21.91
NO COMPLEX POLE (six term test) for Equation 1
bytes used=28010784, alloc=4455632, time=1.08
TOP MAIN SOLVE Loop
x[1] = -3.5
y[1] (analytic) = 3.8729133745815926753973152533435
y[1] (numeric) = 3.8729133745815926753973152533434
absolute error = 1e-31
relative error = 2.5820355460649420243896016810803e-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 = 0.3164
Order of pole (three term test) = -22.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.49
y[1] (analytic) = 3.8798352773198760383185573455335
y[1] (numeric) = 3.8798352773198760383185573455334
absolute error = 1e-31
relative error = 2.5774290105707346551999801139591e-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 = 0.3091
Order of pole (three term test) = -22.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.48
y[1] (analytic) = 3.8865691980969515896471962947646
y[1] (numeric) = 3.8865691980969515896471962947644
absolute error = 2e-31
relative error = 5.1459266465120311055922675528656e-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 = 0.3016
Order of pole (three term test) = -22.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.47
y[1] (analytic) = 3.8931144635263532037703601070534
y[1] (numeric) = 3.8931144635263532037703601070532
absolute error = 2e-31
relative error = 5.1372751013038937180047136641699e-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 = 0.294
Order of pole (three term test) = -22.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.46
y[1] (analytic) = 3.8994704190869923102032107515641
y[1] (numeric) = 3.8994704190869923102032107515639
absolute error = 2e-31
relative error = 5.1289015816364947792692923089323e-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 = 0.2863
Order of pole (three term test) = -22.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.45
y[1] (analytic) = 3.9056364291886094570135702798955
y[1] (numeric) = 3.9056364291886094570135702798953
absolute error = 2e-31
relative error = 5.1208043458758326408603938868885e-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 = 0.2785
Order of pole (three term test) = -22.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.44
y[1] (analytic) = 3.911611877235332807110330025945
y[1] (numeric) = 3.9116118772353328071103300259448
absolute error = 2e-31
relative error = 5.1129817138544156385316278078409e-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 = 0.2706
Order of pole (three term test) = -22.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.43
y[1] (analytic) = 3.9173961656873372115989792824511
y[1] (numeric) = 3.9173961656873372115989792824509
absolute error = 2e-31
relative error = 5.1054320661211058697363848232826e-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 = 0.2626
Order of pole (three term test) = -23.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.42
y[1] (analytic) = 3.9229887161205976943483002912028
y[1] (numeric) = 3.9229887161205976943483002912026
absolute error = 2e-31
relative error = 5.0981538432202756305544032456300e-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 = 0.2545
Order of pole (three term test) = -23.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.41
y[1] (analytic) = 3.9283889692847313724695672819059
y[1] (numeric) = 3.9283889692847313724695672819057
absolute error = 2e-31
relative error = 5.0911455449997194871794037856253e-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 = 0.2463
Order of pole (three term test) = -23.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.4
y[1] (analytic) = 3.9335963851589220285644030795314
y[1] (numeric) = 3.9335963851589220285644030795312
absolute error = 2e-31
relative error = 5.0844057299467891206515794297204e-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 = 0.2379
Order of pole (three term test) = -23.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.39
y[1] (analytic) = 3.938610443005921742330672149345
y[1] (numeric) = 3.9386104430059217423306721493448
absolute error = 2e-31
relative error = 5.0779330145522416137856689157947e-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 = 0.2295
Order of pole (three term test) = -23.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.38
y[1] (analytic) = 3.9434306414241241814082506999811
y[1] (numeric) = 3.943430641424124181408250699981
absolute error = 1e-31
relative error = 2.5358630363506573883073746565044e-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 = 0.221
Order of pole (three term test) = -23.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.37
y[1] (analytic) = 3.9480564983977043441789835319417
y[1] (numeric) = 3.9480564983977043441789835319416
absolute error = 1e-31
relative error = 2.5328918175457827302922859200056e-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 = 0.2124
Order of pole (three term test) = -23.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.36
y[1] (analytic) = 3.9524875513448197405883306155566
y[1] (numeric) = 3.9524875513448197405883306155565
absolute error = 1e-31
relative error = 2.5300522443385143103344514061500e-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 = 0.2037
Order of pole (three term test) = -23.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.35
y[1] (analytic) = 3.9567233571638681909107887505431
y[1] (numeric) = 3.9567233571638681909107887505429
absolute error = 2e-31
relative error = 5.0546874761382761760935008938320e-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 = 0.1949
Order of pole (three term test) = -24
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.34
y[1] (analytic) = 3.9607634922777976167177598021398
y[1] (numeric) = 3.9607634922777976167177598021397
absolute error = 1e-31
relative error = 2.5247657476889877605752699982593e-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 = 0.1861
Order of pole (three term test) = -24.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.33
y[1] (analytic) = 3.9646075526764633931056934297185
y[1] (numeric) = 3.9646075526764633931056934297184
absolute error = 1e-31
relative error = 2.5223177495207839367674326521405e-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 = 0.1772
Order of pole (three term test) = -24.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.32
y[1] (analytic) = 3.9682551539570290264845791694624
y[1] (numeric) = 3.9682551539570290264845791694623
absolute error = 1e-31
relative error = 2.5199992470313532719229638317910e-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 = 0.1682
Order of pole (three term test) = -24.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.31
y[1] (analytic) = 3.9717059313624061178926761411711
y[1] (numeric) = 3.971705931362406117892676141171
absolute error = 1e-31
relative error = 2.5178097706165573453777950526511e-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 = 0.1591
Order of pole (three term test) = -24.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.3
y[1] (analytic) = 3.9749595398177297678731821022057
y[1] (numeric) = 3.9749595398177297678731821022056
absolute error = 1e-31
relative error = 2.5157488773982706077697999220608e-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 = 0.15
Order of pole (three term test) = -24.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.29
y[1] (analytic) = 3.978015653964865775402750251079
y[1] (numeric) = 3.9780156539648657754027502510789
absolute error = 1e-31
relative error = 2.5138161510332560851321869423148e-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 = 0.1408
Order of pole (three term test) = -24.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.28
y[1] (analytic) = 3.9808739681949461801807168322634
y[1] (numeric) = 3.9808739681949461801807168322634
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 = 0.1316
Order of pole (three term test) = -24.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.27
y[1] (analytic) = 3.9835341966789298947519234809895
y[1] (numeric) = 3.9835341966789298947519234809895
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 = 0.1223
Order of pole (three term test) = -24.64
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=32014220, alloc=4455632, time=1.24
x[1] = -3.26
y[1] (analytic) = 3.9859960733961853704253891343433
y[1] (numeric) = 3.9859960733961853704253891343433
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 = 0.113
Order of pole (three term test) = -24.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.25
y[1] (analytic) = 3.9882593521610924387460584503432
y[1] (numeric) = 3.9882593521610924387460584503432
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 = 0.1036
Order of pole (three term test) = -24.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.24
y[1] (analytic) = 3.9903238066476606683576476874849
y[1] (numeric) = 3.9903238066476606683576476874849
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 = 0.09415
Order of pole (three term test) = -24.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.23
y[1] (analytic) = 3.9921892304121617754414169891699
y[1] (numeric) = 3.9921892304121617754414169891698
absolute error = 1e-31
relative error = 2.5048912821618877925424464215853e-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 = 0.08469
Order of pole (three term test) = -24.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.22
y[1] (analytic) = 3.9938554369137738245086854749517
y[1] (numeric) = 3.9938554369137738245086854749516
absolute error = 1e-31
relative error = 2.5038462603261964504215374304257e-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 = 0.07519
Order of pole (three term test) = -24.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.21
y[1] (analytic) = 3.9953222595332351551442133304085
y[1] (numeric) = 3.9953222595332351551442133304084
absolute error = 1e-31
relative error = 2.5029270107408753400167080823310e-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 = 0.06567
Order of pole (three term test) = -24.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.2
y[1] (analytic) = 3.9965895515895061693233214445672
y[1] (numeric) = 3.9965895515895061693233214445671
absolute error = 1e-31
relative error = 2.5021333491758851256104861100514e-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 = 0.05612
Order of pole (three term test) = -24.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.19
y[1] (analytic) = 3.997657186354437313137901659399
y[1] (numeric) = 3.9976571863544373131379016593989
absolute error = 1e-31
relative error = 2.5014651166522980155171243704512e-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 = 0.04654
Order of pole (three term test) = -24.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.18
y[1] (analytic) = 3.9985250570654417861453683077206
y[1] (numeric) = 3.9985250570654417861453683077206
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 = 0.03695
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.17
y[1] (analytic) = 3.9991930769361717110801767002706
y[1] (numeric) = 3.9991930769361717110801767002705
absolute error = 1e-31
relative error = 2.5005044286736753918217190006149e-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 = 0.02734
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.16
y[1] (analytic) = 3.9996611791651966963198341885479
y[1] (numeric) = 3.9996611791651966963198341885478
absolute error = 1e-31
relative error = 2.5002117809607025399701645648812e-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 = 0.01772
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.15
y[1] (analytic) = 3.9999293169426839232563893135895
y[1] (numeric) = 3.9999293169426839232563893135893
absolute error = 2e-31
relative error = 5.0000883553829522452788791202668e-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 = 0.008096
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -3.14
y[1] (analytic) = 3.9999974634550790905702286126901
y[1] (numeric) = 3.9999974634550790905702286126899
absolute error = 2e-31
relative error = 5.0000031706831617818546719379572e-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] = -3.13
y[1] (analytic) = 3.9998656118877877473156544782784
y[1] (numeric) = 3.9998656118877877473156544782782
absolute error = 2e-31
relative error = 5.0001679907842564071740266332586e-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) = 3.9995337754258567466871699479512
y[1] (numeric) = 3.999533775425856746687169947951
absolute error = 2e-31
relative error = 5.0005828486522702403065175900700e-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] = -3.11
y[1] (analytic) = 3.9990019872526557523216616734337
y[1] (numeric) = 3.9990019872526557523216616734335
absolute error = 2e-31
relative error = 5.0012478272710610602789265917413e-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] = -3.1
y[1] (analytic) = 3.9982703005465589289847521090829
y[1] (numeric) = 3.9982703005465589289847521090828
absolute error = 1e-31
relative error = 2.5010815298387934296857728049953e-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] = -3.09
y[1] (analytic) = 3.9973387884756271494694870361715
y[1] (numeric) = 3.9973387884756271494694870361714
absolute error = 1e-31
relative error = 2.5016643645092362157268007393515e-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] = -3.08
y[1] (analytic) = 3.9962075441902912494822370747196
y[1] (numeric) = 3.9962075441902912494822370747195
absolute error = 1e-31
relative error = 2.5023725343139536407860215962698e-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] = -3.07
y[1] (analytic) = 3.9948766808140370621842273254535
y[1] (numeric) = 3.9948766808140370621842273254535
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] = -3.06
y[1] (analytic) = 3.9933463314320931638774785435863
y[1] (numeric) = 3.9933463314320931638774785435863
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] = -3.05
y[1] (analytic) = 3.9916166490781224620511644031298
y[1] (numeric) = 3.9916166490781224620511644031298
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] = -3.04
y[1] (analytic) = 3.9896878067189189566184899096864
y[1] (numeric) = 3.9896878067189189566184899096863
absolute error = 1e-31
relative error = 2.5064617795806695539274336912426e-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) = 3.9875599972371112046552146174169
y[1] (numeric) = 3.9875599972371112046552146174168
absolute error = 1e-31
relative error = 2.5077992574227774552125522713633e-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] = -3.02
y[1] (analytic) = 3.9852334334118742182789330665261
y[1] (numeric) = 3.985233433411874218278933066526
absolute error = 1e-31
relative error = 2.5092633009049884530273995323494e-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=36016460, alloc=4521156, time=1.40
x[1] = -3.01
y[1] (analytic) = 3.9827083478976517244632511483648
y[1] (numeric) = 3.9827083478976517244632511483648
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] = -3
y[1] (analytic) = 3.9799849932008909145431455894625
y[1] (numeric) = 3.9799849932008909145431455894625
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] = -2.99
y[1] (analytic) = 3.9770636416547920099171683744217
y[1] (numeric) = 3.9770636416547920099171683744217
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] = -2.98
y[1] (analytic) = 3.9739445853920751689688839287908
y[1] (numeric) = 3.9739445853920751689688839287908
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] = -2.97
y[1] (analytic) = 3.9706281363157674584941527496123
y[1] (numeric) = 3.9706281363157674584941527496123
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] = -2.96
y[1] (analytic) = 3.9671146260680128109127746459523
y[1] (numeric) = 3.9671146260680128109127746459523
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] = -2.95
y[1] (analytic) = 3.9634044059969080862427788094039
y[1] (numeric) = 3.9634044059969080862427788094039
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] = -2.94
y[1] (analytic) = 3.9594978471213685552035267626566
y[1] (numeric) = 3.9594978471213685552035267626566
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] = -2.93
y[1] (analytic) = 3.9553953400940263168700392093527
y[1] (numeric) = 3.9553953400940263168700392093526
absolute error = 1e-31
relative error = 2.5281922893103988413701550743022e-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] = -2.92
y[1] (analytic) = 3.9510972951621653610058634703165
y[1] (numeric) = 3.9510972951621653610058634703165
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] = -2.91
y[1] (analytic) = 3.9466041421266971815356942132055
y[1] (numeric) = 3.9466041421266971815356942132055
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] = -2.9
y[1] (analytic) = 3.9419163302991810435622133386911
y[1] (numeric) = 3.9419163302991810435622133386911
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] = -2.89
y[1] (analytic) = 3.9370343284568932018646310144186
y[1] (numeric) = 3.9370343284568932018646310144186
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] = -2.88
y[1] (analytic) = 3.931958624795949563919635809531
y[1] (numeric) = 3.9319586247959495639196358095311
absolute error = 1e-31
relative error = 2.5432617568601586367287444519065e-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] = -2.87
y[1] (analytic) = 3.9266897268824864851393875174759
y[1] (numeric) = 3.9266897268824864851393875174759
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] = -2.86
y[1] (analytic) = 3.9212281616019045782063463327855
y[1] (numeric) = 3.9212281616019045782063463327856
absolute error = 1e-31
relative error = 2.5502214071406619329341812450230e-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] = -2.85
y[1] (analytic) = 3.9155744751061806120817082143499
y[1] (numeric) = 3.9155744751061806120817082143499
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] = -2.84
y[1] (analytic) = 3.9097292327592527694536389871725
y[1] (numeric) = 3.9097292327592527694536389871725
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] = -2.83
y[1] (analytic) = 3.9036930190804847240540502254491
y[1] (numeric) = 3.9036930190804847240540502254491
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] = -2.82
y[1] (analytic) = 3.8974664376862141913890721275201
y[1] (numeric) = 3.8974664376862141913890721275201
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] = -2.81
y[1] (analytic) = 3.8910501112293917979794409567177
y[1] (numeric) = 3.8910501112293917979794409567177
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] = -2.8
y[1] (analytic) = 3.8844446813373163051735762347323
y[1] (numeric) = 3.8844446813373163051735762347323
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] = -2.79
y[1] (analytic) = 3.8776508085474724139590792392482
y[1] (numeric) = 3.8776508085474724139590792392482
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] = -2.78
y[1] (analytic) = 3.8706691722414775669387033382352
y[1] (numeric) = 3.8706691722414775669387033382352
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] = -2.77
y[1] (analytic) = 3.8635004705771443527355544156581
y[1] (numeric) = 3.8635004705771443527355544156582
absolute error = 1e-31
relative error = 2.5883263315627763013321982233126e-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] = -2.76
y[1] (analytic) = 3.8561454204186653065304663942802
y[1] (numeric) = 3.8561454204186653065304663942803
absolute error = 1e-31
relative error = 2.5932631967272361499344115765650e-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
bytes used=40017472, alloc=4521156, time=1.56
TOP MAIN SOLVE Loop
x[1] = -2.75
y[1] (analytic) = 3.8486047572649270881933189790534
y[1] (numeric) = 3.8486047572649270881933189790535
absolute error = 1e-31
relative error = 2.5983442392007697210734012962417e-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] = -2.74
y[1] (analytic) = 3.8408792351759612065307465035586
y[1] (numeric) = 3.8408792351759612065307465035586
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] = -2.73
y[1] (analytic) = 3.8329696266975386445165222497856
y[1] (numeric) = 3.8329696266975386445165222497856
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] = -2.72
y[1] (analytic) = 3.8248767227839159259792575999741
y[1] (numeric) = 3.8248767227839159259792575999742
absolute error = 1e-31
relative error = 2.6144633473890248283125458504858e-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] = -2.71
y[1] (analytic) = 3.8166013327187403490763691874322
y[1] (numeric) = 3.8166013327187403490763691874322
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] = -2.7
y[1] (analytic) = 3.8081442840341222959650545638867
y[1] (numeric) = 3.8081442840341222959650545638867
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] = -2.69
y[1] (analytic) = 3.7995064224278827113718697686577
y[1] (numeric) = 3.7995064224278827113718697686578
absolute error = 1e-31
relative error = 2.6319208044949177848913455032412e-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] = -2.68
y[1] (analytic) = 3.7906886116789840252440916372413
y[1] (numeric) = 3.7906886116789840252440916372414
absolute error = 1e-31
relative error = 2.6380431168074150382337041622013e-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] = -2.67
y[1] (analytic) = 3.7816917335611529763201257168595
y[1] (numeric) = 3.7816917335611529763201257168596
absolute error = 1e-31
relative error = 2.6443191842565059808945709079016e-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] = -2.66
y[1] (analytic) = 3.7725166877547039742646220077652
y[1] (numeric) = 3.7725166877547039742646220077653
absolute error = 1e-31
relative error = 2.6507503684368641633412839992689e-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] = -2.65
y[1] (analytic) = 3.7631643917565718179586047321076
y[1] (numeric) = 3.7631643917565718179586047321077
absolute error = 1e-31
relative error = 2.6573380694995880412039346241472e-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] = -2.64
y[1] (analytic) = 3.753635780788562766597814632532
y[1] (numeric) = 3.7536357807885627665978146325321
absolute error = 1e-31
relative error = 2.6640837268178434632068390893046e-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] = -2.63
y[1] (analytic) = 3.7439318077038331384156967803899
y[1] (numeric) = 3.74393180770383313841569678039
absolute error = 1e-31
relative error = 2.6709888196743188053412604810374e-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] = -2.62
y[1] (analytic) = 3.7340534428916047890932273534967
y[1] (numeric) = 3.7340534428916047890932273534968
absolute error = 1e-31
relative error = 2.6780548679710710616719026487072e-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] = -2.61
y[1] (analytic) = 3.7240016741801269982283348974453
y[1] (numeric) = 3.7240016741801269982283348974454
absolute error = 1e-31
relative error = 2.6852834329623633664962233640851e-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] = -2.6
y[1] (analytic) = 3.7137775067378944675954043032904
y[1] (numeric) = 3.7137775067378944675954043032905
absolute error = 1e-31
relative error = 2.6926761180111173815411995474675e-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] = -2.59
y[1] (analytic) = 3.7033819629731313093127194908166
y[1] (numeric) = 3.7033819629731313093127194908167
absolute error = 1e-31
relative error = 2.7002345693696277710762006575522e-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] = -2.58
y[1] (analytic) = 3.6928160824315510754352649891385
y[1] (numeric) = 3.6928160824315510754352649891385
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] = -2.57
y[1] (analytic) = 3.6820809216924030528847274431343
y[1] (numeric) = 3.6820809216924030528847274431343
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] = -2.56
y[1] (analytic) = 3.6711775542628152190005762467649
y[1] (numeric) = 3.6711775542628152190005762467649
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] = -2.55
y[1] (analytic) = 3.6601070704704444233286209516646
y[1] (numeric) = 3.6601070704704444233286209516646
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] = -2.54
y[1] (analytic) = 3.6488705773544445305394087116131
y[1] (numeric) = 3.6488705773544445305394087116132
absolute error = 1e-31
relative error = 2.7405740455860017528387610770351e-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] = -2.53
y[1] (analytic) = 3.63746919855476342757131034511
y[1] (numeric) = 3.63746919855476342757131034511
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] = -2.52
y[1] (analytic) = 3.6259040741997799652053285209037
y[1] (numeric) = 3.6259040741997799652053285209037
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] = -2.51
y[1] (analytic) = 3.6141763607922920702838350157568
y[1] (numeric) = 3.6141763607922920702838350157568
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 = 14.63
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
bytes used=44020108, alloc=4521156, time=1.72
TOP MAIN SOLVE Loop
x[1] = -2.5
y[1] (analytic) = 3.6022872310938674296670055809347
y[1] (numeric) = 3.6022872310938674296670055809347
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 = 14.94
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] = -2.49
y[1] (analytic) = 3.5902378740075683107621826651431
y[1] (numeric) = 3.5902378740075683107621826651431
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 = 15.25
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] = -2.48
y[1] (analytic) = 3.5780294944590622460463840671807
y[1] (numeric) = 3.5780294944590622460463840671806
absolute error = 1e-31
relative error = 2.7948344236641994075594283747142e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.57
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] = -2.47
y[1] (analytic) = 3.5656633132761304704144311681231
y[1] (numeric) = 3.565663313276130470414431168123
absolute error = 1e-31
relative error = 2.8045272706390224918771925581896e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.9
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] = -2.46
y[1] (analytic) = 3.5531405670665861604085526293724
y[1] (numeric) = 3.5531405670665861604085526293723
absolute error = 1e-31
relative error = 2.8144115920119180408092772332402e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.23
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] = -2.45
y[1] (analytic) = 3.540462508094614683403806134673
y[1] (numeric) = 3.5404625080946146834038061346729
absolute error = 1e-31
relative error = 2.8244897318180446604652293665077e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.56
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] = -2.44
y[1] (analytic) = 3.5276304041555482226213501850748
y[1] (numeric) = 3.5276304041555482226213501850747
absolute error = 1e-31
relative error = 2.8347640921282459509946512959743e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.9
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] = -2.43
y[1] (analytic) = 3.5146455384490873004027104883558
y[1] (numeric) = 3.5146455384490873004027104883557
absolute error = 1e-31
relative error = 2.8452371343292599586008461085216e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.25
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] = -2.42
y[1] (analytic) = 3.5015092094509818774870651378215
y[1] (numeric) = 3.5015092094509818774870651378214
absolute error = 1e-31
relative error = 2.8559113804438478413011529330254e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
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] = -2.41
y[1] (analytic) = 3.4882227307831848600746887911359
y[1] (numeric) = 3.4882227307831848600746887911358
absolute error = 1e-31
relative error = 2.8667894144921112688086281775430e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.96
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] = -2.4
y[1] (analytic) = 3.4747874310824909992176444546696
y[1] (numeric) = 3.4747874310824909992176444546695
absolute error = 1e-31
relative error = 2.8778738838953171370830574372110e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.32
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] = -2.39
y[1] (analytic) = 3.4612046538676743185383165852361
y[1] (numeric) = 3.4612046538676743185383165852361
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 = 18.69
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] = -2.38
y[1] (analytic) = 3.4474757574051373564222952147351
y[1] (numeric) = 3.447475757405137356422295214735
absolute error = 1e-31
relative error = 2.9006730441889599025342394234058e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.07
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] = -2.37
y[1] (analytic) = 3.4336021145730856576494332176447
y[1] (numeric) = 3.4336021145730856576494332176446
absolute error = 1e-31
relative error = 2.9123933601850494247000304351270e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.46
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] = -2.36
y[1] (analytic) = 3.4195851127242410969007260692902
y[1] (numeric) = 3.4195851127242410969007260692901
absolute error = 1e-31
relative error = 2.9243313648752600618415443182982e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.15
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] = -2.35
y[1] (analytic) = 3.4054261535471077626942582245178
y[1] (numeric) = 3.4054261535471077626942582245177
absolute error = 1e-31
relative error = 2.9364900453307300072071606571541e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.77
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] = -2.34
y[1] (analytic) = 3.3911266529258042750462111441227
y[1] (numeric) = 3.3911266529258042750462111441226
absolute error = 1e-31
relative error = 2.9488724614199166951819874945628e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.39
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] = -2.33
y[1] (analytic) = 3.376688040798476553508360855632
y[1] (numeric) = 3.3766880407984765535083608556319
absolute error = 1e-31
relative error = 2.9614817475514635521193097238781e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.03
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] = -2.32
y[1] (analytic) = 3.3621117610143051941872723320165
y[1] (numeric) = 3.3621117610143051941872723320164
absolute error = 1e-31
relative error = 2.9743211144721526581287764625724e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
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] = -2.31
y[1] (analytic) = 3.3473992711891217548883286469421
y[1] (numeric) = 3.347399271189121754888328646942
absolute error = 1e-31
relative error = 2.9873938511218068650685445764915e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.32
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] = -2.3
y[1] (analytic) = 3.332552042559648386635761142332
y[1] (numeric) = 3.332552042559648386635761142332
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 = 16.98
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] = -2.29
y[1] (analytic) = 3.3175715598363753874840620363779
y[1] (numeric) = 3.3175715598363753874840620363779
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 = 16.64
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] = -2.28
y[1] (analytic) = 3.3024593210550913907427967009214
y[1] (numeric) = 3.3024593210550913907427967009214
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 = 16.3
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] = -2.27
y[1] (analytic) = 3.2872168374270810344722686962486
y[1] (numeric) = 3.2872168374270810344722686962486
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 = 15.98
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=48021748, alloc=4521156, time=1.87
x[1] = -2.26
y[1] (analytic) = 3.2718456331880050923582531374897
y[1] (numeric) = 3.2718456331880050923582531374897
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 = 15.66
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] = -2.25
y[1] (analytic) = 3.2563472454454781778267781147928
y[1] (numeric) = 3.2563472454454781778267781147928
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 = 15.34
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] = -2.24
y[1] (analytic) = 3.2407232240253592635015245326209
y[1] (numeric) = 3.2407232240253592635015245326209
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 = 15.03
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] = -2.23
y[1] (analytic) = 3.2249751313167703868238078213713
y[1] (numeric) = 3.2249751313167703868238078213713
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 = 14.72
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] = -2.22
y[1] (analytic) = 3.2091045421158590398354288750003
y[1] (numeric) = 3.2091045421158590398354288750003
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 = 14.42
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] = -2.21
y[1] (analytic) = 3.1931130434683198667552183550373
y[1] (numeric) = 3.1931130434683198667552183550373
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 = 14.12
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] = -2.2
y[1] (analytic) = 3.1770022345106914170482852253099
y[1] (numeric) = 3.1770022345106914170482852253099
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 = 13.83
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] = -2.19
y[1] (analytic) = 3.1607737263104438241804103275939
y[1] (numeric) = 3.1607737263104438241804103275939
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] = -2.18
y[1] (analytic) = 3.144429141704873401156449735325
y[1] (numeric) = 3.144429141704873401156449735325
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] = -2.17
y[1] (analytic) = 3.127970115138820263248939988833
y[1] (numeric) = 3.127970115138820263248939988833
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] = -2.16
y[1] (analytic) = 3.1113982925012252060193974879667
y[1] (numeric) = 3.1113982925012252060193974879667
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] = -2.15
y[1] (analytic) = 3.0947153309605421828083077645281
y[1] (numeric) = 3.094715330960542182808307764528
absolute error = 1e-31
relative error = 3.2313149774897666139071995704580e-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] = -2.14
y[1] (analytic) = 3.0779228987990228403088998240172
y[1] (numeric) = 3.0779228987990228403088998240171
absolute error = 1e-31
relative error = 3.2489442811910291433289135609377e-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] = -2.13
y[1] (analytic) = 3.0610226752458896836330524192194
y[1] (numeric) = 3.0610226752458896836330524192193
absolute error = 1e-31
relative error = 3.2668820394140685053442061193242e-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] = -2.12
y[1] (analytic) = 3.0440163503094145534138037659678
y[1] (numeric) = 3.0440163503094145534138037659676
absolute error = 2e-31
relative error = 6.5702669428720590768383238480885e-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] = -2.11
y[1] (analytic) = 3.0269056246079192069568203141434
y[1] (numeric) = 3.0269056246079192069568203141432
absolute error = 2e-31
relative error = 6.6074078548751045753860151201031e-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] = -2.1
y[1] (analytic) = 3.0096922091997149032418770474383
y[1] (numeric) = 3.0096922091997149032418770474382
absolute error = 1e-31
relative error = 3.3225988921501798271567572657832e-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] = -2.09
y[1] (analytic) = 2.9923778254119979976741326237409
y[1] (numeric) = 2.9923778254119979976741326237408
absolute error = 1e-31
relative error = 3.3418239886278983530784327098394e-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] = -2.08
y[1] (analytic) = 2.9749642046687186568831376995447
y[1] (numeric) = 2.9749642046687186568831376995446
absolute error = 1e-31
relative error = 3.3613849821475630600465308443733e-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] = -2.07
y[1] (analytic) = 2.9574530883174399065546542780235
y[1] (numeric) = 2.9574530883174399065546542780234
absolute error = 1e-31
relative error = 3.3812877842431711707122279559445e-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] = -2.06
y[1] (analytic) = 2.9398462274552043262462192529758
y[1] (numeric) = 2.9398462274552043262462192529757
absolute error = 1e-31
relative error = 3.4015384568791614482411895864399e-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] = -2.05
y[1] (analytic) = 2.9221453827534258043718599883348
y[1] (numeric) = 2.9221453827534258043718599883347
absolute error = 1e-31
relative error = 3.4221432167681481202329698407370e-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] = -2.04
y[1] (analytic) = 2.9043523242818238640345404105827
y[1] (numeric) = 2.9043523242818238640345404105826
absolute error = 1e-31
relative error = 3.4431084398387369600668011908329e-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] = -2.03
y[1] (analytic) = 2.8864688313314181661270334633922
y[1] (numeric) = 2.8864688313314181661270334633921
absolute error = 1e-31
relative error = 3.4644406658593229160231955709862e-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] = -2.02
y[1] (analytic) = 2.8684966922366008901034057481804
y[1] (numeric) = 2.8684966922366008901034057481803
absolute error = 1e-31
relative error = 3.4861466032240327961466686513681e-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=52022724, alloc=4521156, time=2.03
x[1] = -2.01
y[1] (analytic) = 2.8504377041963047850347646803309
y[1] (numeric) = 2.8504377041963047850347646803308
absolute error = 1e-31
relative error = 3.5082331339072537923447625470108e-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
y[1] (analytic) = 2.8322936730942847739951364590015
y[1] (numeric) = 2.8322936730942847739951364590015
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] = -1.99
y[1] (analytic) = 2.8140664133185310834672714322606
y[1] (numeric) = 2.8140664133185310834672714322606
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] = -1.98
y[1] (analytic) = 2.7957577475798319563049477198144
y[1] (numeric) = 2.7957577475798319563049477198144
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] = -1.97
y[1] (analytic) = 2.7773695067295040918292796277586
y[1] (numeric) = 2.7773695067295040918292796277586
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] = -1.96
y[1] (analytic) = 2.7589035295763090398631304308949
y[1] (numeric) = 2.7589035295763090398631304308949
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] = -1.95
y[1] (analytic) = 2.7403616627025738569116569182614
y[1] (numeric) = 2.7403616627025738569116569182614
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] = -1.94
y[1] (analytic) = 2.7217457602795344122701353716815
y[1] (numeric) = 2.7217457602795344122701353716815
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] = -1.93
y[1] (analytic) = 2.7030576838819198095745781294237
y[1] (numeric) = 2.7030576838819198095745781294238
absolute error = 1e-31
relative error = 3.6995140945859442224061099509459e-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] = -1.92
y[1] (analytic) = 2.6842993023017964651984732063181
y[1] (numeric) = 2.6842993023017964651984732063181
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] = -1.91
y[1] (analytic) = 2.6654724913616904589326778787951
y[1] (numeric) = 2.6654724913616904589326778787951
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] = -1.9
y[1] (analytic) = 2.6465791337270068445576673901606
y[1] (numeric) = 2.6465791337270068445576673901607
absolute error = 1e-31
relative error = 3.7784624961950955967737981189767e-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] = -1.89
y[1] (analytic) = 2.6276211187177646782207648311025
y[1] (numeric) = 2.6276211187177646782207648311025
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] = -1.88
y[1] (analytic) = 2.6086003421196665909586275190445
y[1] (numeric) = 2.6086003421196665909586275190445
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] = -1.87
y[1] (analytic) = 2.5895187059945217982502961296198
y[1] (numeric) = 2.5895187059945217982502961296198
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) = 2.5703781184900415041418709765782
y[1] (numeric) = 2.5703781184900415041418709765783
absolute error = 1e-31
relative error = 3.8904781860944492439283745360753e-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] = -1.85
y[1] (analytic) = 2.5511804936490257202438996709496
y[1] (numeric) = 2.5511804936490257202438996709497
absolute error = 1e-31
relative error = 3.9197540216751644874321928449834e-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] = -1.84
y[1] (analytic) = 2.5319277512179605807605659665632
y[1] (numeric) = 2.5319277512179605807605659665633
absolute error = 1e-31
relative error = 3.9495597752303918950340591298270e-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] = -1.83
y[1] (analytic) = 2.5126218164550452936596751672371
y[1] (numeric) = 2.5126218164550452936596751672372
absolute error = 1e-31
relative error = 3.9799065400572651319133416450721e-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] = -1.82
y[1] (analytic) = 2.4932646199376679251283420896617
y[1] (numeric) = 2.4932646199376679251283420896619
absolute error = 2e-31
relative error = 8.0216114407062029721151085526849e-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] = -1.81
y[1] (analytic) = 2.473858097369349269575499701684
y[1] (numeric) = 2.4738580973693492695754997016841
absolute error = 1e-31
relative error = 4.0422690414756602274521284258620e-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] = -1.8
y[1] (analytic) = 2.4544041893861741106333486130612
y[1] (numeric) = 2.4544041893861741106333486130613
absolute error = 1e-31
relative error = 4.0743085606046476296829126148877e-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] = -1.79
y[1] (analytic) = 2.4349048413627292298703405289292
y[1] (numeric) = 2.4349048413627292298703405289294
absolute error = 2e-31
relative error = 8.2138733556448615412048579907676e-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] = -1.78
y[1] (analytic) = 2.4153620032175675692531065806253
y[1] (numeric) = 2.4153620032175675692531065806254
absolute error = 1e-31
relative error = 4.1401661476328333691003774735024e-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] = -1.77
y[1] (analytic) = 2.3957776292182180007789716834608
y[1] (numeric) = 2.3957776292182180007789716834609
absolute error = 1e-31
relative error = 4.1740100909378496674844310660940e-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] = -1.76
y[1] (analytic) = 2.3761536777857602021396003530082
y[1] (numeric) = 2.3761536777857602021396003530083
absolute error = 1e-31
relative error = 4.2084820074931299685846569545754e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
bytes used=56024052, alloc=4521156, time=2.18
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] = -1.75
y[1] (analytic) = 2.3564921112989841807653538878853
y[1] (numeric) = 2.3564921112989841807653538878854
absolute error = 1e-31
relative error = 4.2435957888641673409646909106746e-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] = -1.74
y[1] (analytic) = 2.3367948958981540301347546306902
y[1] (numeric) = 2.3367948958981540301347546306903
absolute error = 1e-31
relative error = 4.2793657319062529111986249083347e-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] = -1.73
y[1] (analytic) = 2.3170640012883955418098967026851
y[1] (numeric) = 2.3170640012883955418098967026853
absolute error = 2e-31
relative error = 8.6316131055849420456821578853812e-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] = -1.72
y[1] (analytic) = 2.2973014005427273342727565606624
y[1] (numeric) = 2.2973014005427273342727565606625
absolute error = 1e-31
relative error = 4.3529334016152795879001757767515e-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) = 2.2775090699047551952853795661022
y[1] (numeric) = 2.2775090699047551952853795661023
absolute error = 1e-31
relative error = 4.3907618775885697164662986274691e-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] = -1.7
y[1] (analytic) = 2.2576889885910493681752857146697
y[1] (numeric) = 2.2576889885910493681752857146698
absolute error = 1e-31
relative error = 4.4293080448785270323605956900799e-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] = -1.69
y[1] (analytic) = 2.2378431385932245441527809396662
y[1] (numeric) = 2.2378431385932245441527809396662
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] = -1.68
y[1] (analytic) = 2.2179735044797423524960094683456
y[1] (numeric) = 2.2179735044797423524960094683457
absolute error = 1e-31
relative error = 4.5086201344617252786543916193572e-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] = -1.67
y[1] (analytic) = 2.1980820731974561681895646848972
y[1] (numeric) = 2.1980820731974561681895646848973
absolute error = 1e-31
relative error = 4.5494206617378152961492340403267e-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) = 2.1781708338729180823705158633012
y[1] (numeric) = 2.1781708338729180823705158633013
absolute error = 1e-31
relative error = 4.5910081268600046439763848973193e-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] = -1.65
y[1] (analytic) = 2.1582417776134679047192291946826
y[1] (numeric) = 2.1582417776134679047192291946826
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] = -1.64
y[1] (analytic) = 2.1382968973081240887289854149132
y[1] (numeric) = 2.1382968973081240887289854149133
absolute error = 1e-31
relative error = 4.6766190478922165398136456161881e-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] = -1.63
y[1] (analytic) = 2.1183381874282964905959433948396
y[1] (numeric) = 2.1183381874282964905959433948397
absolute error = 1e-31
relative error = 4.7206815509190217220591358450533e-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] = -1.62
y[1] (analytic) = 2.0983676438283408902874885494247
y[1] (numeric) = 2.0983676438283408902874885494248
absolute error = 1e-31
relative error = 4.7656091292732782055654246581825e-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] = -1.61
y[1] (analytic) = 2.078387263545975219170655219202
y[1] (numeric) = 2.0783872635459752191706552192022
absolute error = 2e-31
relative error = 9.6228457279311977262859895891363e-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] = -1.6
y[1] (analytic) = 2.058399044602577452411540925893
y[1] (numeric) = 2.0583990446025774524115409258932
absolute error = 2e-31
relative error = 9.7162890025833024657822769616757e-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] = -1.59
y[1] (analytic) = 2.0384049858033851361900546924868
y[1] (numeric) = 2.038404985803385136190054692487
absolute error = 2e-31
relative error = 9.8115929559098444104692907050142e-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] = -1.58
y[1] (analytic) = 2.0184070865376165296107781139655
y[1] (numeric) = 2.0184070865376165296107781139656
absolute error = 1e-31
relative error = 4.9544019473068930846946040521527e-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] = -1.57
y[1] (analytic) = 1.9984073465785333490291829327093
y[1] (numeric) = 1.9984073465785333490291829327094
absolute error = 1e-31
relative error = 5.0039848067617281022809994434768e-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 = 0.0007679
Order of pole (three term test) = -0.8929
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.56
y[1] (analytic) = 1.9784077658834651083521586724782
y[1] (numeric) = 1.9784077658834651083521586724783
absolute error = 1e-31
relative error = 5.0545697264458846323583578900401e-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 = 0.01041
Order of pole (three term test) = -0.8957
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.55
y[1] (analytic) = 1.9584103443938150527121744506089
y[1] (numeric) = 1.958410344393815052712174450609
absolute error = 1e-31
relative error = 5.1061821791465724590563267384745e-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 = 0.02005
Order of pole (three term test) = -0.9033
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.54
y[1] (analytic) = 1.9384170818350676847550463858472
y[1] (numeric) = 1.9384170818350676847550463858473
absolute error = 1e-31
relative error = 5.1588484716267377705781527230635e-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 = 0.02968
Order of pole (three term test) = -0.9158
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.53
y[1] (analytic) = 1.9184299775168178826220219858478
y[1] (numeric) = 1.9184299775168178826220219858479
absolute error = 1e-31
relative error = 5.2125957773782416700481346003982e-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 = 0.0393
Order of pole (three term test) = -0.9331
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.52
y[1] (analytic) = 1.8984510301328416065477414596946
y[1] (numeric) = 1.8984510301328416065477414596947
absolute error = 1e-31
relative error = 5.2674521708891607234165505446590e-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 = 0.0489
Order of pole (three term test) = -0.9552
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.51
y[1] (analytic) = 1.8784822375612281868368089701676
y[1] (numeric) = 1.8784822375612281868368089701678
bytes used=60025368, alloc=4521156, time=2.34
absolute error = 2e-31
relative error = 1.0646893327011355371488932734048e-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 = 0.05848
Order of pole (three term test) = -0.9821
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.5
y[1] (analytic) = 1.8585255966645941798236202971315
y[1] (numeric) = 1.8585255966645941798236202971316
absolute error = 1e-31
relative error = 5.3806092409738748707249848863757e-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 = 0.06804
Order of pole (three term test) = -1.014
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.49
y[1] (analytic) = 1.8385831030903987702633630308726
y[1] (numeric) = 1.8385831030903987702633630308727
absolute error = 1e-31
relative error = 5.4389709027519131502064139084487e-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 = 0.07757
Order of pole (three term test) = -1.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.48
y[1] (analytic) = 1.8186567510713806884475469187043
y[1] (numeric) = 1.8186567510713806884475469187045
absolute error = 2e-31
relative error = 1.0997127406377201232948552864748e-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 = 0.08707
Order of pole (three term test) = -1.092
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.47
y[1] (analytic) = 1.7987485332261365981860507970752
y[1] (numeric) = 1.7987485332261365981860507970754
absolute error = 2e-31
relative error = 1.1118841589340505656560808239990e-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 = 0.09654
Order of pole (three term test) = -1.138
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.46
y[1] (analytic) = 1.7788604403598608976507037817533
y[1] (numeric) = 1.7788604403598608976507037817535
absolute error = 2e-31
relative error = 1.1243152945688099561391407450166e-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 = 0.106
Order of pole (three term test) = -1.188
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.45
y[1] (analytic) = 1.758994461265266858934266745504
y[1] (numeric) = 1.7589944612652668589342667455042
absolute error = 2e-31
relative error = 1.1370132448065668286282929550296e-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 = 0.1154
Order of pole (three term test) = -1.244
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.44
y[1] (analytic) = 1.7391525825237090140449596877417
y[1] (numeric) = 1.7391525825237090140449596877419
absolute error = 2e-31
relative error = 1.1499853549927008667550192381032e-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 = 0.1247
Order of pole (three term test) = -1.304
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.43
y[1] (analytic) = 1.7193367883065266749322047508502
y[1] (numeric) = 1.7193367883065266749322047508504
absolute error = 2e-31
relative error = 1.1632392289877741783000085837894e-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 = 0.134
Order of pole (three term test) = -1.369
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.42
y[1] (analytic) = 1.6995490601766284530260357940482
y[1] (numeric) = 1.6995490601766284530260357940484
absolute error = 2e-31
relative error = 1.1767827401182209385971942024681e-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 = 0.1432
Order of pole (three term test) = -1.438
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.41
y[1] (analytic) = 1.6797913768903376196728749012782
y[1] (numeric) = 1.6797913768903376196728749012784
absolute error = 2e-31
relative error = 1.1906240426727507046812268586386e-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) = -1.513
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.4
y[1] (analytic) = 1.6600657141995181227665039295927
y[1] (numeric) = 1.6600657141995181227665039295929
absolute error = 2e-31
relative error = 1.2047715839757571399385756415498e-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 = 0.1615
Order of pole (three term test) = -1.591
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.39
y[1] (analytic) = 1.6403740446540010468076735643919
y[1] (numeric) = 1.6403740446540010468076735643921
absolute error = 2e-31
relative error = 1.2192341170710572467043369891108e-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 = 0.1706
Order of pole (three term test) = -1.675
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.38
y[1] (analytic) = 1.6207183374043312735816998528036
y[1] (numeric) = 1.6207183374043312735816998528038
absolute error = 2e-31
relative error = 1.2340207140514674346288780941448e-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 = 0.1795
Order of pole (three term test) = -1.762
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.37
y[1] (analytic) = 1.6011005580048540686236032207094
y[1] (numeric) = 1.6011005580048540686236032207096
absolute error = 2e-31
relative error = 1.2491407800720637716078973123310e-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 = 0.1885
Order of pole (three term test) = -1.855
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.36
y[1] (analytic) = 1.5815226682171612846480494952163
y[1] (numeric) = 1.5815226682171612846480494952165
absolute error = 2e-31
relative error = 1.2646040680874875427349687237699e-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 = 0.1973
Order of pole (three term test) = -1.951
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.35
y[1] (analytic) = 1.5619866258139168371599556539787
y[1] (numeric) = 1.561986625813916837159955653979
absolute error = 3e-31
relative error = 1.9206310415345368641187810010832e-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 = 0.206
Order of pole (three term test) = -2.052
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.34
y[1] (analytic) = 1.5424943843830810695347210153997
y[1] (numeric) = 1.5424943843830810695347210154
absolute error = 3e-31
relative error = 1.9449017321381346204710667555095e-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 = 0.2147
Order of pole (three term test) = -2.158
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.33
y[1] (analytic) = 1.5230478931325535849684300279788
y[1] (numeric) = 1.5230478931325535849684300279791
absolute error = 3e-31
relative error = 1.9697345129638051565004877458097e-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 = 0.2233
Order of pole (three term test) = -2.268
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.32
y[1] (analytic) = 1.5036490966952540808520345411453
y[1] (numeric) = 1.5036490966952540808520345411455
absolute error = 2e-31
relative error = 1.3300975635842394979810562118441e-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 = 0.2318
Order of pole (three term test) = -2.382
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.31
y[1] (analytic) = 1.4842999349346606773236460427676
y[1] (numeric) = 1.4842999349346606773236460427678
absolute error = 2e-31
relative error = 1.3474365611206744358261933616895e-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 = 0.2402
Order of pole (three term test) = -2.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.3
y[1] (analytic) = 1.4650023427508251860040317814143
y[1] (numeric) = 1.4650023427508251860040317814144
absolute error = 1e-31
relative error = 6.8259276508889851330157218437498e-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 = 0.2485
Order of pole (three term test) = -2.623
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.29
y[1] (analytic) = 1.4457582498868847172267878198776
y[1] (numeric) = 1.4457582498868847172267878198778
absolute error = 2e-31
relative error = 1.3833571415943701751297561008642e-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 = 0.2567
Order of pole (three term test) = -2.749
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.28
y[1] (analytic) = 1.4265695807360889744412262128148
y[1] (numeric) = 1.426569580736088974441226212815
absolute error = 2e-31
relative error = 1.4019645638090988467753668089730e-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 = 0.2648
Order of pole (three term test) = -2.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.27
y[1] (analytic) = 1.4074382541493625328977259678241
y[1] (numeric) = 1.4074382541493625328977259678243
absolute error = 2e-31
relative error = 1.4210214864514778432912451482654e-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 = 0.2728
Order of pole (three term test) = -3.015
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=64026588, alloc=4521156, time=2.50
x[1] = -1.26
y[1] (analytic) = 1.388366183243421346227315021647
y[1] (numeric) = 1.3883661832434213462273150216472
absolute error = 2e-31
relative error = 1.4405421452485358408549029259662e-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 = 0.2807
Order of pole (three term test) = -3.154
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.25
y[1] (analytic) = 1.3693552752094626691049228951239
y[1] (numeric) = 1.3693552752094626691049228951241
absolute error = 2e-31
relative error = 1.4605413483320251647917090647585e-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 = 0.2885
Order of pole (three term test) = -3.296
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.24
y[1] (analytic) = 1.3504074311224475268446131686052
y[1] (numeric) = 1.3504074311224475268446131686054
absolute error = 2e-31
relative error = 1.4810345040367679876971585634013e-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 = 0.2962
Order of pole (three term test) = -3.443
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.23
y[1] (analytic) = 1.3315245457509948035209055090047
y[1] (numeric) = 1.3315245457509948035209055090048
absolute error = 1e-31
relative error = 7.5101882514376688788012953675962e-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 = 0.3037
Order of pole (three term test) = -3.593
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.22
y[1] (analytic) = 1.3127085073679059590489540511296
y[1] (numeric) = 1.3127085073679059590489540511297
absolute error = 1e-31
relative error = 7.6178374283951770071276414522781e-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 = 0.3111
Order of pole (three term test) = -3.748
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.21
y[1] (analytic) = 1.2939611975613393225939785726704
y[1] (numeric) = 1.2939611975613393225939785726705
absolute error = 1e-31
relative error = 7.7282070118072122615019220736677e-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 = 0.3184
Order of pole (three term test) = -3.905
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.2
y[1] (analytic) = 1.2752844910466528447232532887538
y[1] (numeric) = 1.2752844910466528447232532887539
absolute error = 1e-31
relative error = 7.8413876042613749324452115264341e-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 = 0.3256
Order of pole (three term test) = -4.067
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.19
y[1] (analytic) = 1.2566802554789341238686408832991
y[1] (numeric) = 1.2566802554789341238686408832991
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 = 0.3327
Order of pole (three term test) = -4.232
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.18
y[1] (analytic) = 1.2381503512662364539408010665745
y[1] (numeric) = 1.2381503512662364539408010665745
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 = 0.3396
Order of pole (three term test) = -4.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.17
y[1] (analytic) = 1.219696631383539569334676129899
y[1] (numeric) = 1.219696631383539569334676129899
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 = 0.3463
Order of pole (three term test) = -4.572
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.16
y[1] (analytic) = 1.201320941187453691096720753212
y[1] (numeric) = 1.201320941187453691096720753212
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 = 0.353
Order of pole (three term test) = -4.748
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.15
y[1] (analytic) = 1.1830251182316854036948465623802
y[1] (numeric) = 1.1830251182316854036948465623802
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 = 0.3595
Order of pole (three term test) = -4.926
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.14
y[1] (analytic) = 1.1648109920832838156496265183548
y[1] (numeric) = 1.1648109920832838156496265183549
absolute error = 1e-31
relative error = 8.5850838187188067520444821235886e-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 = 0.3658
Order of pole (three term test) = -5.108
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.13
y[1] (analytic) = 1.1466803841396853792575683286929
y[1] (numeric) = 1.146680384139685379257568328693
absolute error = 1e-31
relative error = 8.7208259060807550413890072911428e-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 = 0.372
Order of pole (three term test) = -5.293
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.12
y[1] (analytic) = 1.1286351074465756647720224120777
y[1] (numeric) = 1.1286351074465756647720224120778
absolute error = 1e-31
relative error = 8.8602595595524246767385107136981e-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 = 0.3781
Order of pole (three term test) = -5.481
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.11
y[1] (analytic) = 1.1106769665165863027125249761329
y[1] (numeric) = 1.1106769665165863027125249761329
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 = 0.384
Order of pole (three term test) = -5.672
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.1
y[1] (analytic) = 1.0928077571488452244572598964306
y[1] (numeric) = 1.0928077571488452244572598964306
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 = 0.3897
Order of pole (three term test) = -5.866
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.09
y[1] (analytic) = 1.0750292662493982459442058522497
y[1] (numeric) = 1.0750292662493982459442058522497
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 = 0.3953
Order of pole (three term test) = -6.063
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.08
y[1] (analytic) = 1.0573432716525199521729504229479
y[1] (numeric) = 1.0573432716525199521729504229479
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 = 0.4007
Order of pole (three term test) = -6.262
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.07
y[1] (analytic) = 1.0397515419429317512698138636482
y[1] (numeric) = 1.0397515419429317512698138636481
absolute error = 1e-31
relative error = 9.6176822987090739853220028140128e-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 = 0.406
Order of pole (three term test) = -6.464
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.06
y[1] (analytic) = 1.0222558362789448761627249200872
y[1] (numeric) = 1.0222558362789448761627249200871
absolute error = 1e-31
relative error = 9.7822870216133265079915273219518e-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 = 0.4111
Order of pole (three term test) = -6.669
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.05
y[1] (analytic) = 1.0048579042165460194183008543758
y[1] (numeric) = 1.0048579042165460194183008543757
absolute error = 1e-31
relative error = 9.9516558092824719900684299305615e-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 = 0.416
Order of pole (three term test) = -6.877
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.04
y[1] (analytic) = 0.9875594855344431925310531580157
y[1] (numeric) = 0.98755948553444319253105315801555
absolute error = 1.5e-31
relative error = 1.5188958457406102024124999860818e-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 = 0.4208
Order of pole (three term test) = -7.086
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.03
y[1] (analytic) = 0.9703623100600893049329954003253
y[1] (numeric) = 0.9703623100600893049329954003252
absolute error = 1.0e-31
relative error = 1.0305429112741151217609769623687e-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 = 0.4254
Order of pole (three term test) = -7.298
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.02
y[1] (analytic) = 0.9532680974967008602207723839324
y[1] (numeric) = 0.95326809749670086022077238393228
absolute error = 1.2e-31
relative error = 1.2588273992922049377071349637787e-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 = 0.4299
Order of pole (three term test) = -7.513
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=68031764, alloc=4521156, time=2.65
x[1] = -1.01
y[1] (analytic) = 0.9362785572512890675865372884416
y[1] (numeric) = 0.93627855725128906758653728844154
absolute error = 6e-32
relative error = 6.4083492605178310086573930906761e-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 = 0.4341
Order of pole (three term test) = -7.729
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1
y[1] (analytic) = 0.919395388263720565198126785114
y[1] (numeric) = 0.91939538826372056519812678511394
absolute error = 6e-32
relative error = 6.5260279490100642323303602789685e-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 = 0.4382
Order of pole (three term test) = -7.948
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (analytic) = 0.9026202788368248493137471826928
y[1] (numeric) = 0.90262027883682484931374718269267
absolute error = 1.3e-31
relative error = 1.4402512667622142106558973151563e-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 = 0.4422
Order of pole (three term test) = -8.169
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.98
y[1] (analytic) = 0.8859549064675653982466834652801
y[1] (numeric) = 0.88595490646756539824668346528002
absolute error = 8e-32
relative error = 9.0298049501155712911751054599910e-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 = 0.4459
Order of pole (three term test) = -8.391
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.97
y[1] (analytic) = 0.8694009376792913739269444903003
y[1] (numeric) = 0.86940093767929137392694449030018
absolute error = 1.2e-31
relative error = 1.3802607611663993078602196456530e-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 = 0.4495
Order of pole (three term test) = -8.616
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (analytic) = 0.8529600278550866757498983992963
y[1] (numeric) = 0.85296002785508667574989839929619
absolute error = 1.1e-31
relative error = 1.2896266695710670368355534157628e-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 = 0.4528
Order of pole (three term test) = -8.842
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (analytic) = 0.8366338210722330116676380524791
y[1] (numeric) = 0.83663382107223301166763805247899
absolute error = 1.1e-31
relative error = 1.3147926515691607058025927476455e-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 = 0.456
Order of pole (three term test) = -9.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.94
y[1] (analytic) = 0.820423949937803540078020369552
y[1] (numeric) = 0.82042394993780354007802036955187
absolute error = 1.3e-31
relative error = 1.5845466238504534034931852707701e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.88
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4591
Order of pole (three term test) = -9.299
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.93
y[1] (analytic) = 0.804332035425403523010185831134
y[1] (numeric) = 0.80433203542540352301018583113393
absolute error = 7e-32
relative error = 8.7028735543248217506070648305582e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.17
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4619
Order of pole (three term test) = -9.53
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.92
y[1] (analytic) = 0.7883596867130743164051905866512
y[1] (numeric) = 0.78835968671307431640519058665115
absolute error = 5e-32
relative error = 6.3422826969331878056431954095549e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.47
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4645
Order of pole (three term test) = -9.762
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.91
y[1] (analytic) = 0.7725085010223769069576435476506
y[1] (numeric) = 0.77250850102237690695764354765054
absolute error = 6e-32
relative error = 7.7669048198942741388632985563331e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.467
Order of pole (three term test) = -9.995
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (analytic) = 0.7567800634586710870305676971857
y[1] (numeric) = 0.75678006345867108703056769718563
absolute error = 7e-32
relative error = 9.2497151259617989017398536914670e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.08
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4693
Order of pole (three term test) = -10.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (analytic) = 0.7411759468526062395928938852395
y[1] (numeric) = 0.74117594685260623959289388523939
absolute error = 1.1e-31
relative error = 1.4841280328525707158272656691238e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4714
Order of pole (three term test) = -10.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.88
y[1] (analytic) = 0.7256977116028395839690027885558
y[1] (numeric) = 0.72569771160283958396900278855571
absolute error = 9e-32
relative error = 1.2401858041031727958835743389155e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.71
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4733
Order of pole (three term test) = -10.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (analytic) = 0.7103469055199976104446723890343
y[1] (numeric) = 0.71034690551999761044467238903424
absolute error = 6e-32
relative error = 8.4465772334262511106203491288066e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.475
Order of pole (three term test) = -10.94
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.86
y[1] (analytic) = 0.6951250636718963074559386715523
y[1] (numeric) = 0.69512506367189630745593867155218
absolute error = 1.2e-31
relative error = 1.7263080598204527536582465424132e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.36
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4765
Order of pole (three term test) = -11.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (analytic) = 0.6800337082300356592091679410771
y[1] (numeric) = 0.68003370823003565920916794107696
absolute error = 1.4e-31
relative error = 2.0587214766807127860545415333172e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4778
Order of pole (three term test) = -11.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (analytic) = 0.6650743483173837641546579262583
y[1] (numeric) = 0.66507434831738376415465792625818
absolute error = 1.2e-31
relative error = 1.8043095528130960817450923596830e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.479
Order of pole (three term test) = -11.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (analytic) = 0.6502484798574657957750741642711
y[1] (numeric) = 0.65024847985746579577507416427099
absolute error = 1.1e-31
relative error = 1.6916610097129631980651023502541e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.38
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4799
Order of pole (three term test) = -11.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (analytic) = 0.6355575854247728966668840431261
y[1] (numeric) = 0.63555758542477289666688404312604
absolute error = 6e-32
relative error = 9.4405292889233931931997180235529e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4807
Order of pole (three term test) = -12.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.81
y[1] (analytic) = 0.6210031340965059649007215186398
y[1] (numeric) = 0.6210031340965059649007215186397
absolute error = 1.0e-31
relative error = 1.6102978311935486206791468653127e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.09
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4812
Order of pole (three term test) = -12.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.8
y[1] (analytic) = 0.6065865813056691581585000367154
y[1] (numeric) = 0.60658658130566915815850003671526
absolute error = 1.4e-31
relative error = 2.3079969836894834061013925844631e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.45
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -12.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (analytic) = 0.5923093686955278061744382778301
y[1] (numeric) = 0.59230936869552780617443827783001
absolute error = 9e-32
relative error = 1.5194762189598899588780390859207e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.83
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (analytic) = 0.5781729239754452855674699524709
y[1] (numeric) = 0.57817292397544528556746995247079
absolute error = 1.1e-31
relative error = 1.9025449902367210279987157478748e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.21
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (analytic) = 0.5641786607781132732574188693513
y[1] (numeric) = 0.56417866077811327325741886935123
absolute error = 7e-32
relative error = 1.2407417165239153173367949433388e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -13.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=72034488, alloc=4521156, time=2.81
x[1] = -0.76
y[1] (analytic) = 0.550327978518189655320623266666
y[1] (numeric) = 0.5503279785181896553206232666659
absolute error = 1.0e-31
relative error = 1.8170982378409961385780431705115e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.01
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4812
Order of pole (three term test) = -13.59
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.75
y[1] (analytic) = 0.5366222622523582273763224939998
y[1] (numeric) = 0.53662226225235822737632249399974
absolute error = 6e-32
relative error = 1.1181049356424892793965828082818e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4806
Order of pole (three term test) = -13.83
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.74
y[1] (analytic) = 0.5230628825408241804171508786023
y[1] (numeric) = 0.52306288254082418041715087860225
absolute error = 5e-32
relative error = 9.5590801161651121148243125131636e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.26
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4798
Order of pole (three term test) = -14.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (analytic) = 0.5096511953102592224197356828993
y[1] (numeric) = 0.50965119531025922241973568289924
absolute error = 6e-32
relative error = 1.1772757633477918894904451788035e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4788
Order of pole (three term test) = -14.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.72
y[1] (analytic) = 0.4963885417182100411090260754961
y[1] (numeric) = 0.49638854171821004110902607549601
absolute error = 9e-32
relative error = 1.8130958399739053650671143613172e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4777
Order of pole (three term test) = -14.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (analytic) = 0.4832762480189836669170841117209
y[1] (numeric) = 0.4832762480189836669170841117208
absolute error = 1.0e-31
relative error = 2.0692099065475256055881542758270e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.19
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4763
Order of pole (three term test) = -14.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.7
y[1] (analytic) = 0.4703156254310231474882800196163
y[1] (numeric) = 0.47031562543102314748828001961618
absolute error = 1.2e-31
relative error = 2.5514780609303675493037244369476e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.85
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4747
Order of pole (three term test) = -15.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.69
y[1] (analytic) = 0.4575079700057867960529213690045
y[1] (numeric) = 0.45750797000578679605292136900438
absolute error = 1.2e-31
relative error = 2.6229051266250548224680302491422e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.51
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.473
Order of pole (three term test) = -15.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.68
y[1] (analytic) = 0.4448545624981441256352118319114
y[1] (numeric) = 0.44485456249814412563521183191128
absolute error = 1.2e-31
relative error = 2.6975108297445105807983284375358e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.17
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4711
Order of pole (three term test) = -15.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.67
y[1] (analytic) = 0.4323566682383014293941157103238
y[1] (numeric) = 0.43235666823830142939411571032368
absolute error = 1.2e-31
relative error = 2.7754862782377572875369371904382e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.85
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.469
Order of pole (three term test) = -15.73
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.66
y[1] (analytic) = 0.4200155370052698144323658175395
y[1] (numeric) = 0.42001553700526981443236581753943
absolute error = 7e-32
relative error = 1.6666050141645529194871245947658e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.52
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4667
Order of pole (three term test) = -15.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.65
y[1] (analytic) = 0.4078324029018883421647908586402
y[1] (numeric) = 0.40783240290188834216479085864011
absolute error = 9e-32
relative error = 2.2067888514893499345413151532873e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.2
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4642
Order of pole (three term test) = -16.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.64
y[1] (analytic) = 0.3958084842314147728277784414794
y[1] (numeric) = 0.39580848423141477282777844147927
absolute error = 1.3e-31
relative error = 3.2844167110878236074693438901327e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.89
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4615
Order of pole (three term test) = -16.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.63
y[1] (analytic) = 0.3839449833756962549525820684459
y[1] (numeric) = 0.38394498337569625495258206844581
absolute error = 9e-32
relative error = 2.3440858429431170025704033386603e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.58
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4586
Order of pole (three term test) = -16.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.62
y[1] (analytic) = 0.3722430866749321426320006912786
y[1] (numeric) = 0.37224308667493214263200069127853
absolute error = 7e-32
relative error = 1.8804916063123218652612714675184e-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 = 0.4556
Order of pole (three term test) = -16.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.61
y[1] (analytic) = 0.3607039643090409641985068426904
y[1] (numeric) = 0.36070396430904096419850684269028
absolute error = 1.2e-31
relative error = 3.3268278664436133239495099942435e-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 = 0.4524
Order of pole (three term test) = -17.12
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.6
y[1] (analytic) = 0.3493287701806434055180950020892
y[1] (numeric) = 0.34932877018064340551809500208917
absolute error = 3e-32
relative error = 8.5878984386217395715899328797487e-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 = 0.449
Order of pole (three term test) = -17.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.59
y[1] (analytic) = 0.3381186417996730095040069550186
y[1] (numeric) = 0.33811864179967300950400695501856
absolute error = 4e-32
relative error = 1.1830167005018024865899752349615e-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 = 0.4454
Order of pole (three term test) = -17.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.58
y[1] (analytic) = 0.3270747001696261306842253439
y[1] (numeric) = 0.32707470016962613068422534389988
absolute error = 1.2e-31
relative error = 3.6688866469270198953411804550964e-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 = 0.4416
Order of pole (three term test) = -17.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.57
y[1] (analytic) = 0.316198049675462519732487272168
y[1] (numeric) = 0.31619804967546251973248727216789
absolute error = 1.1e-31
relative error = 3.4788323366605565113793730026194e-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 = 0.4377
Order of pole (three term test) = -18.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.56
y[1] (analytic) = 0.3054897779731677478109489922674
y[1] (numeric) = 0.30548977797316774781094899226728
absolute error = 1.2e-31
relative error = 3.9281183415092869718469400940943e-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 = 0.4335
Order of pole (three term test) = -18.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.55
y[1] (analytic) = 0.2949509558809885143900364047645
y[1] (numeric) = 0.29495095588098851439003640476437
absolute error = 1.3e-31
relative error = 4.4075124154693182293308540874674e-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 = 0.4293
Order of pole (three term test) = -18.45
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.54
y[1] (analytic) = 0.2845826372723517149240624421644
y[1] (numeric) = 0.28458263727235171492406244216432
absolute error = 8e-32
relative error = 2.8111342549488806823548260918642e-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 = 0.4248
Order of pole (three term test) = -18.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.53
y[1] (analytic) = 0.2743858589704779763866099628716
y[1] (numeric) = 0.27438585897047797638660996287151
absolute error = 9e-32
relative error = 3.2800524173398957302601570098463e-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 = 0.4202
Order of pole (three term test) = -18.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.52
y[1] (analytic) = 0.264361640644700199224304856023
y[1] (numeric) = 0.26436164064470019922430485602289
absolute error = 1.1e-31
relative error = 4.1609667624902913268990099902670e-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 = 0.4154
Order of pole (three term test) = -19.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.51
y[1] (analytic) = 0.254510984708497473788383052849
y[1] (numeric) = 0.2545109847084974737883830528489
absolute error = 1.0e-31
relative error = 3.9291034968307697802240923805290e-29 %
Correct digits = 31
h = 0.01
bytes used=76035140, alloc=4586680, time=2.97
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4104
Order of pole (three term test) = -19.29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.5
y[1] (analytic) = 0.2448348762192545677674368347923
y[1] (numeric) = 0.24483487621925456776743683479226
absolute error = 4e-32
relative error = 1.6337541700627321395365592147389e-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 = 0.4053
Order of pole (three term test) = -19.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.49
y[1] (analytic) = 0.2353342827797570085890636817267
y[1] (numeric) = 0.2353342827797570085890636817266
absolute error = 1.0e-31
relative error = 4.2492746411107172102283847733567e-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 = 0.4
Order of pole (three term test) = -19.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.48
y[1] (analytic) = 0.2260101544414316112000903376825
y[1] (numeric) = 0.22601015444143161120009033768243
absolute error = 7e-32
relative error = 3.0972059716962777596955697711048e-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 = 0.3945
Order of pole (three term test) = -19.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.47
y[1] (analytic) = 0.2168634236093421270919614469332
y[1] (numeric) = 0.21686342360934212709196144693313
absolute error = 7e-32
relative error = 3.2278380021380660669038855020917e-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 = 0.3889
Order of pole (three term test) = -20.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.46
y[1] (analytic) = 0.2078950049489495149272201929992
y[1] (numeric) = 0.2078950049489495149272201929991
absolute error = 1.0e-31
relative error = 4.8101203790132378534399575722065e-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 = 0.3832
Order of pole (three term test) = -20.28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.45
y[1] (analytic) = 0.1991057952946461566623187770271
y[1] (numeric) = 0.19910579529464615666231877702702
absolute error = 8e-32
relative error = 4.0179644134221318268471330804715e-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 = 0.3773
Order of pole (three term test) = -20.47
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.44
y[1] (analytic) = 0.1904966735600731656689252220033
y[1] (numeric) = 0.19049667356007316566892522200317
absolute error = 1.3e-31
relative error = 6.8242661444166621068982618367850e-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 = 0.3712
Order of pole (three term test) = -20.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.43
y[1] (analytic) = 0.1820685006502297550481790446731
y[1] (numeric) = 0.18206850065022975504817904467302
absolute error = 8e-32
relative error = 4.3939506127799293637192063319412e-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 = 0.365
Order of pole (three term test) = -20.85
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.42
y[1] (analytic) = 0.1738221193753834551278224206687
y[1] (numeric) = 0.17382211937538345512782242066858
absolute error = 1.2e-31
relative error = 6.9036093007731616010457240758315e-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 = 0.3586
Order of pole (three term test) = -21.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.41
y[1] (analytic) = 0.165758354366789789048715883446
y[1] (numeric) = 0.16575835436678978904871588344588
absolute error = 1.2e-31
relative error = 7.2394541112820301877213695380697e-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 = 0.3521
Order of pole (three term test) = -21.21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.4
y[1] (analytic) = 0.1578780119942298344029465358964
y[1] (numeric) = 0.15787801199422983440294653589631
absolute error = 9e-32
relative error = 5.7006038309685165538307241611507e-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 = 0.3455
Order of pole (three term test) = -21.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.39
y[1] (analytic) = 0.1501818802853739170986464942378
y[1] (numeric) = 0.15018188028537391709864649423771
absolute error = 9e-32
relative error = 5.9927335993518668072625469029424e-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 = 0.3387
Order of pole (three term test) = -21.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.38
y[1] (analytic) = 0.1426707288469795010149383845509
y[1] (numeric) = 0.1426707288469795010149383845508
absolute error = 1.0e-31
relative error = 7.0091462213846475281943636390537e-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 = 0.3318
Order of pole (three term test) = -21.72
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.37
y[1] (analytic) = 0.1353453087879311535923741910182
y[1] (numeric) = 0.13534530878793115359237419101816
absolute error = 4e-32
relative error = 2.9554035051687606846439935225585e-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 = 0.3247
Order of pole (three term test) = -21.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.36
y[1] (analytic) = 0.1282063526441302832981752637505
y[1] (numeric) = 0.12820635264413028329817526375043
absolute error = 7e-32
relative error = 5.4599478540898054875773198227703e-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 = 0.3175
Order of pole (three term test) = -22.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.35
y[1] (analytic) = 0.1212545743052421599299352853927
y[1] (numeric) = 0.12125457430524215992993528539258
absolute error = 1.2e-31
relative error = 9.8965338575941937620284222263957e-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 = 0.3102
Order of pole (three term test) = -22.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.34
y[1] (analytic) = 0.1144906689433075429947118799468
y[1] (numeric) = 0.11449066894330754299471187994676
absolute error = 4e-32
relative error = 3.4937344998662589081522414404844e-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 = 0.3028
Order of pole (three term test) = -22.36
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.33
y[1] (analytic) = 0.1079153129432260569411788432676
y[1] (numeric) = 0.1079153129432260569411788432675
absolute error = 1.0e-31
relative error = 9.2665255071455632204467224053840e-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 = 0.2952
Order of pole (three term test) = -22.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.32
y[1] (analytic) = 0.1015291638351182648493854524678
y[1] (numeric) = 0.10152916383511826484938545246773
absolute error = 7e-32
relative error = 6.8945707179937853433072067425026e-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 = 0.2876
Order of pole (three term test) = -22.65
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.31
y[1] (analytic) = 0.0953328602285732043143891275956
y[1] (numeric) = 0.095332860228573204314389127595498
absolute error = 1.02e-31
relative error = 1.0699353796313405668132907923076e-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 = 0.2798
Order of pole (three term test) = -22.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.3
y[1] (analytic) = 0.0893270217487879607153795448639
y[1] (numeric) = 0.089327021748787960715379544863814
absolute error = 8.6e-32
relative error = 9.6275458776466927692928876742371e-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 = 0.2719
Order of pole (three term test) = -22.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.29
y[1] (analytic) = 0.0835122489746056638597504441363
y[1] (numeric) = 0.08351224897460566385975044413619
absolute error = 1.10e-31
relative error = 1.3171720478207778805825441964067e-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 = 0.2639
Order of pole (three term test) = -23.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.28
y[1] (analytic) = 0.077889123378458104150819892807
y[1] (numeric) = 0.07788912337845810415081989280696
absolute error = 4.0e-32
relative error = 5.1355052239633822694625362964229e-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 = 0.2558
Order of pole (three term test) = -23.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.27
y[1] (analytic) = 0.0724582072682189739675345810156
y[1] (numeric) = 0.072458207268218973967534581015508
absolute error = 9.2e-32
relative error = 1.2696974361985393374917292370888e-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 = 0.2476
Order of pole (three term test) = -23.32
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.26
y[1] (analytic) = 0.0672200437309735488835647070999
y[1] (numeric) = 0.067220043730973548883564707099784
absolute error = 1.16e-31
relative error = 1.7256757592162900887065564316821e-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 = 0.2393
Order of pole (three term test) = -23.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=80036052, alloc=4586680, time=3.13
x[1] = -0.25
y[1] (analytic) = 0.0621751565787104317108091010116
y[1] (numeric) = 0.062175156578710431710809101011536
absolute error = 6.4e-32
relative error = 1.0293500414265851322428798681076e-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 = 0.2309
Order of pole (three term test) = -23.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.24
y[1] (analytic) = 0.0573240502959407901476495060732
y[1] (numeric) = 0.057324050295940790147649506073156
absolute error = 4.4e-32
relative error = 7.6756613974145005655277519831361e-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 = 0.2224
Order of pole (three term test) = -23.67
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.23
y[1] (analytic) = 0.0526672099892503260645387038568
y[1] (numeric) = 0.052667209989250326064538703856717
absolute error = 8.3e-32
relative error = 1.5759331093661647744352498966996e-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 = 0.2138
Order of pole (three term test) = -23.78
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.22
y[1] (analytic) = 0.0482051013387890211879540379106
y[1] (numeric) = 0.048205101338789021187954037910521
absolute error = 7.9e-32
relative error = 1.6388307006095091689100586625267e-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 = 0.2051
Order of pole (three term test) = -23.89
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.21
y[1] (analytic) = 0.0439381705517035101677228638013
y[1] (numeric) = 0.043938170551703510167722863801221
absolute error = 7.9e-32
relative error = 1.7979810949806857837718260131276e-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 = 0.1963
Order of pole (three term test) = -23.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.2
y[1] (analytic) = 0.0398668443175167377516069665037
y[1] (numeric) = 0.039866844317516737751606966503576
absolute error = 1.24e-31
relative error = 3.1103540328502184481130251803942e-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 = 0.1875
Order of pole (three term test) = -24.09
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.19
y[1] (analytic) = 0.0359915297654593620642449916202
y[1] (numeric) = 0.035991529765459362064244991620086
absolute error = 1.14e-31
relative error = 3.1674119089376531013698142054682e-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 = 0.1786
Order of pole (three term test) = -24.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.18
y[1] (analytic) = 0.0323126144237571708145679507769
y[1] (numeric) = 0.032312614423757170814567950776848
absolute error = 5.2e-32
relative error = 1.6092786339742318283115958493891e-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 = 0.1696
Order of pole (three term test) = -24.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.17
y[1] (analytic) = 0.028830466180878581656140019575
y[1] (numeric) = 0.028830466180878581656140019574907
absolute error = 9.3e-32
relative error = 3.2257542911907889049799895301939e-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 = 0.1606
Order of pole (three term test) = -24.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.16
y[1] (analytic) = 0.0255454332487461019180949519633
y[1] (numeric) = 0.025545433248746101918094951963238
absolute error = 6.2e-32
relative error = 2.4270482867243314885416778874309e-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 = 0.1515
Order of pole (three term test) = -24.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.15
y[1] (analytic) = 0.0224578441279154265300380026913
y[1] (numeric) = 0.022457844127915426530038002691236
absolute error = 6.4e-32
relative error = 2.8497837831391424689463186801419e-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 = 0.1423
Order of pole (three term test) = -24.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.14
y[1] (analytic) = 0.0195680075747256562021035459772
y[1] (numeric) = 0.019568007574725656202103545977113
absolute error = 8.7e-32
relative error = 4.4460326207339860698486921192693e-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 = 0.1331
Order of pole (three term test) = -24.57
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.13
y[1] (analytic) = 0.0168762125704239208109756576964
y[1] (numeric) = 0.016876212570423920810975657696284
absolute error = 1.16e-31
relative error = 6.8735801659249985568151017205301e-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 = 0.1238
Order of pole (three term test) = -24.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.12
y[1] (analytic) = 0.0143827282922674955038036642847
y[1] (numeric) = 0.014382728292267495503803664284646
absolute error = 5.4e-32
relative error = 3.7545032418523621278868981069253e-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 = 0.1145
Order of pole (three term test) = -24.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.11
y[1] (analytic) = 0.0120878040866062992843207771603
y[1] (numeric) = 0.012087804086606299284320777160218
absolute error = 8.2e-32
relative error = 6.7836969736181286235851644389869e-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 = 0.1051
Order of pole (three term test) = -24.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.1
y[1] (analytic) = 0.0099916694439484678088760243923
y[1] (numeric) = 0.0099916694439484678088760243921736
absolute error = 1.264e-31
relative error = 1.2650538602090678808996052298809e-27 %
Correct digits = 29
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 = 0.09566
Order of pole (three term test) = -24.8
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.09
y[1] (analytic) = 0.0080945339760114938143212563497
y[1] (numeric) = 0.0080945339760114938143212563496257
absolute error = 7.43e-32
relative error = 9.1790336812707570617057245372510e-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 = 0.0862
Order of pole (three term test) = -24.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.08
y[1] (analytic) = 0.006396587394761230044586450733
y[1] (numeric) = 0.0063965873947612300445864507328915
absolute error = 1.085e-31
relative error = 1.6962169560734979447542395940044e-27 %
Correct digits = 29
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 = 0.07671
Order of pole (three term test) = -24.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.07
y[1] (analytic) = 0.0048979994934408507581832201205
y[1] (numeric) = 0.0048979994934408507581832201204376
absolute error = 6.24e-32
relative error = 1.2739895151798785121506498978079e-27 %
Correct digits = 29
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 = 0.06719
Order of pole (three term test) = -24.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.06
y[1] (analytic) = 0.0035989201295916689046766256343
y[1] (numeric) = 0.0035989201295916689046766256342362
absolute error = 6.38e-32
relative error = 1.7727539846025620402616827434341e-27 %
Correct digits = 29
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 = 0.05764
Order of pole (three term test) = -24.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.05
y[1] (analytic) = 0.002499479210067506874258377687
y[1] (numeric) = 0.0024994792100675068742583776868721
absolute error = 1.279e-31
relative error = 5.1170659665757183358298663753132e-27 %
Correct digits = 29
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 = 0.04807
Order of pole (three term test) = -24.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.04
y[1] (analytic) = 0.0015997866780441193708584837417
y[1] (numeric) = 0.001599786678044119370858483741645
absolute error = 5.50e-32
relative error = 3.4379583700023281727051855204901e-27 %
Correct digits = 29
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 = 0.03848
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.03
y[1] (analytic) = 0.0008999325020249674556825870668
y[1] (numeric) = 0.00089993250202496745568258706668665
absolute error = 1.1335e-31
relative error = 1.2595389070285545905955849247405e-26 %
Correct digits = 28
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 = 0.02887
Order of pole (three term test) = -25.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.02
y[1] (analytic) = 0.000399986666844443174608818325
y[1] (numeric) = 0.00039998666684444317460881832496378
absolute error = 3.622e-32
relative error = 9.0553018393700958214473190104746e-27 %
Correct digits = 29
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 = 0.01925
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.01
y[1] (analytic) = 9.99991666694444394841324956e-05
y[1] (numeric) = 9.9999166669444439484132495500950e-05
absolute error = 9.9050e-32
relative error = 9.9050825420793766377372135589553e-26 %
Correct digits = 28
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 = 0.009629
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0
y[1] (analytic) = 0
y[1] (numeric) = -8.57000e-32
absolute error = 8.57000e-32
relative error = -1 %
Correct digits = -1
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=84037128, alloc=4586680, time=3.29
x[1] = 0.01
y[1] (analytic) = 9.99991666694444394841324956e-05
y[1] (numeric) = 9.9999166669444439484132495500954e-05
absolute error = 9.9046e-32
relative error = 9.9046825387460266376710757613356e-26 %
Correct digits = 28
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) = 0.000399986666844443174608818325
y[1] (numeric) = 0.00039998666684444317460881832496377
absolute error = 3.623e-32
relative error = 9.0578019227050958479027158406818e-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] = 0.03
y[1] (analytic) = 0.0008999325020249674556825870668
y[1] (numeric) = 0.00089993250202496745568258706668665
absolute error = 1.1335e-31
relative error = 1.2595389070285545905955849247405e-26 %
Correct digits = 28
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] = 0.04
y[1] (analytic) = 0.0015997866780441193708584837417
y[1] (numeric) = 0.001599786678044119370858483741645
absolute error = 5.50e-32
relative error = 3.4379583700023281727051855204901e-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] = 0.05
y[1] (analytic) = 0.002499479210067506874258377687
y[1] (numeric) = 0.0024994792100675068742583776868721
absolute error = 1.279e-31
relative error = 5.1170659665757183358298663753132e-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] = 0.06
y[1] (analytic) = 0.0035989201295916689046766256343
y[1] (numeric) = 0.0035989201295916689046766256342361
absolute error = 6.39e-32
relative error = 1.7755325958636945826445380455398e-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] = 0.07
y[1] (analytic) = 0.0048979994934408507581832201205
y[1] (numeric) = 0.0048979994934408507581832201204376
absolute error = 6.24e-32
relative error = 1.2739895151798785121506498978079e-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] = 0.08
y[1] (analytic) = 0.006396587394761230044586450733
y[1] (numeric) = 0.0063965873947612300445864507328915
absolute error = 1.085e-31
relative error = 1.6962169560734979447542395940044e-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] = 0.09
y[1] (analytic) = 0.0080945339760114938143212563497
y[1] (numeric) = 0.0080945339760114938143212563496257
absolute error = 7.43e-32
relative error = 9.1790336812707570617057245372510e-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] = 0.1
y[1] (analytic) = 0.0099916694439484678088760243923
y[1] (numeric) = 0.0099916694439484678088760243921736
absolute error = 1.264e-31
relative error = 1.2650538602090678808996052298809e-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] = 0.11
y[1] (analytic) = 0.0120878040866062992843207771603
y[1] (numeric) = 0.012087804086606299284320777160218
absolute error = 8.2e-32
relative error = 6.7836969736181286235851644389869e-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] = 0.12
y[1] (analytic) = 0.0143827282922674955038036642847
y[1] (numeric) = 0.014382728292267495503803664284646
absolute error = 5.4e-32
relative error = 3.7545032418523621278868981069253e-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] = 0.13
y[1] (analytic) = 0.0168762125704239208109756576964
y[1] (numeric) = 0.016876212570423920810975657696284
absolute error = 1.16e-31
relative error = 6.8735801659249985568151017205301e-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] = 0.14
y[1] (analytic) = 0.0195680075747256562021035459772
y[1] (numeric) = 0.019568007574725656202103545977113
absolute error = 8.7e-32
relative error = 4.4460326207339860698486921192693e-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] = 0.15
y[1] (analytic) = 0.0224578441279154265300380026913
y[1] (numeric) = 0.022457844127915426530038002691236
absolute error = 6.4e-32
relative error = 2.8497837831391424689463186801419e-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] = 0.16
y[1] (analytic) = 0.0255454332487461019180949519633
y[1] (numeric) = 0.025545433248746101918094951963238
absolute error = 6.2e-32
relative error = 2.4270482867243314885416778874309e-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] = 0.17
y[1] (analytic) = 0.028830466180878581656140019575
y[1] (numeric) = 0.028830466180878581656140019574907
absolute error = 9.3e-32
relative error = 3.2257542911907889049799895301939e-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] = 0.18
y[1] (analytic) = 0.0323126144237571708145679507769
y[1] (numeric) = 0.032312614423757170814567950776848
absolute error = 5.2e-32
relative error = 1.6092786339742318283115958493891e-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] = 0.19
y[1] (analytic) = 0.0359915297654593620642449916202
y[1] (numeric) = 0.035991529765459362064244991620086
absolute error = 1.14e-31
relative error = 3.1674119089376531013698142054682e-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] = 0.2
y[1] (analytic) = 0.0398668443175167377516069665037
y[1] (numeric) = 0.039866844317516737751606966503576
absolute error = 1.24e-31
relative error = 3.1103540328502184481130251803942e-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] = 0.21
y[1] (analytic) = 0.0439381705517035101677228638013
y[1] (numeric) = 0.043938170551703510167722863801221
absolute error = 7.9e-32
relative error = 1.7979810949806857837718260131276e-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] = 0.22
y[1] (analytic) = 0.0482051013387890211879540379106
y[1] (numeric) = 0.048205101338789021187954037910521
absolute error = 7.9e-32
relative error = 1.6388307006095091689100586625267e-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] = 0.23
y[1] (analytic) = 0.0526672099892503260645387038568
y[1] (numeric) = 0.052667209989250326064538703856717
absolute error = 8.3e-32
relative error = 1.5759331093661647744352498966996e-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] = 0.24
y[1] (analytic) = 0.0573240502959407901476495060732
y[1] (numeric) = 0.057324050295940790147649506073156
absolute error = 4.4e-32
relative error = 7.6756613974145005655277519831361e-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) = 0.0621751565787104317108091010116
y[1] (numeric) = 0.062175156578710431710809101011536
absolute error = 6.4e-32
relative error = 1.0293500414265851322428798681076e-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] = 0.26
y[1] (analytic) = 0.0672200437309735488835647070999
y[1] (numeric) = 0.067220043730973548883564707099785
absolute error = 1.15e-31
relative error = 1.7107992440506324155280516348572e-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
bytes used=88041584, alloc=4586680, time=3.44
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 0.0724582072682189739675345810156
y[1] (numeric) = 0.072458207268218973967534581015509
absolute error = 9.1e-32
relative error = 1.2558963771094247794755147888596e-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] = 0.28
y[1] (analytic) = 0.077889123378458104150819892807
y[1] (numeric) = 0.077889123378458104150819892806961
absolute error = 3.9e-32
relative error = 5.0071175933642977127259728890123e-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] = 0.29
y[1] (analytic) = 0.0835122489746056638597504441363
y[1] (numeric) = 0.083512248974605663859750444136191
absolute error = 1.09e-31
relative error = 1.3051977564769526271227028855303e-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] = 0.3
y[1] (analytic) = 0.0893270217487879607153795448639
y[1] (numeric) = 0.089327021748787960715379544863815
absolute error = 8.5e-32
relative error = 9.5155976697670800626732029338390e-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] = 0.31
y[1] (analytic) = 0.0953328602285732043143891275956
y[1] (numeric) = 0.095332860228573204314389127595499
absolute error = 1.01e-31
relative error = 1.0594458170859352671386506865006e-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] = 0.32
y[1] (analytic) = 0.1015291638351182648493854524678
y[1] (numeric) = 0.10152916383511826484938545246773
absolute error = 7e-32
relative error = 6.8945707179937853433072067425026e-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] = 0.33
y[1] (analytic) = 0.1079153129432260569411788432676
y[1] (numeric) = 0.1079153129432260569411788432675
absolute error = 1.0e-31
relative error = 9.2665255071455632204467224053840e-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] = 0.34
y[1] (analytic) = 0.1144906689433075429947118799468
y[1] (numeric) = 0.11449066894330754299471187994676
absolute error = 4e-32
relative error = 3.4937344998662589081522414404844e-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] = 0.35
y[1] (analytic) = 0.1212545743052421599299352853927
y[1] (numeric) = 0.12125457430524215992993528539258
absolute error = 1.2e-31
relative error = 9.8965338575941937620284222263957e-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] = 0.36
y[1] (analytic) = 0.1282063526441302832981752637505
y[1] (numeric) = 0.12820635264413028329817526375043
absolute error = 7e-32
relative error = 5.4599478540898054875773198227703e-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] = 0.37
y[1] (analytic) = 0.1353453087879311535923741910182
y[1] (numeric) = 0.13534530878793115359237419101816
absolute error = 4e-32
relative error = 2.9554035051687606846439935225585e-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] = 0.38
y[1] (analytic) = 0.1426707288469795010149383845509
y[1] (numeric) = 0.1426707288469795010149383845508
absolute error = 1.0e-31
relative error = 7.0091462213846475281943636390537e-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] = 0.39
y[1] (analytic) = 0.1501818802853739170986464942378
y[1] (numeric) = 0.15018188028537391709864649423771
absolute error = 9e-32
relative error = 5.9927335993518668072625469029424e-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] = 0.4
y[1] (analytic) = 0.1578780119942298344029465358964
y[1] (numeric) = 0.15787801199422983440294653589631
absolute error = 9e-32
relative error = 5.7006038309685165538307241611507e-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] = 0.41
y[1] (analytic) = 0.165758354366789789048715883446
y[1] (numeric) = 0.16575835436678978904871588344588
absolute error = 1.2e-31
relative error = 7.2394541112820301877213695380697e-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] = 0.42
y[1] (analytic) = 0.1738221193753834551278224206687
y[1] (numeric) = 0.17382211937538345512782242066858
absolute error = 1.2e-31
relative error = 6.9036093007731616010457240758315e-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) = 0.1820685006502297550481790446731
y[1] (numeric) = 0.18206850065022975504817904467302
absolute error = 8e-32
relative error = 4.3939506127799293637192063319412e-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] = 0.44
y[1] (analytic) = 0.1904966735600731656689252220033
y[1] (numeric) = 0.19049667356007316566892522200317
absolute error = 1.3e-31
relative error = 6.8242661444166621068982618367850e-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] = 0.45
y[1] (analytic) = 0.1991057952946461566623187770271
y[1] (numeric) = 0.19910579529464615666231877702702
absolute error = 8e-32
relative error = 4.0179644134221318268471330804715e-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] = 0.46
y[1] (analytic) = 0.2078950049489495149272201929992
y[1] (numeric) = 0.2078950049489495149272201929991
absolute error = 1.0e-31
relative error = 4.8101203790132378534399575722065e-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) = 0.2168634236093421270919614469332
y[1] (numeric) = 0.21686342360934212709196144693313
absolute error = 7e-32
relative error = 3.2278380021380660669038855020917e-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) = 0.2260101544414316112000903376825
y[1] (numeric) = 0.22601015444143161120009033768243
absolute error = 7e-32
relative error = 3.0972059716962777596955697711048e-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] = 0.49
y[1] (analytic) = 0.2353342827797570085890636817267
y[1] (numeric) = 0.2353342827797570085890636817266
absolute error = 1.0e-31
relative error = 4.2492746411107172102283847733567e-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] = 0.5
y[1] (analytic) = 0.2448348762192545677674368347923
y[1] (numeric) = 0.24483487621925456776743683479226
absolute error = 4e-32
relative error = 1.6337541700627321395365592147389e-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] = 0.51
y[1] (analytic) = 0.254510984708497473788383052849
y[1] (numeric) = 0.2545109847084974737883830528489
absolute error = 1.0e-31
relative error = 3.9291034968307697802240923805290e-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] = 0.52
y[1] (analytic) = 0.264361640644700199224304856023
y[1] (numeric) = 0.26436164064470019922430485602289
absolute error = 1.1e-31
relative error = 4.1609667624902913268990099902670e-29 %
Correct digits = 31
h = 0.01
bytes used=92042276, alloc=4586680, time=3.61
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] = 0.53
y[1] (analytic) = 0.2743858589704779763866099628716
y[1] (numeric) = 0.27438585897047797638660996287151
absolute error = 9e-32
relative error = 3.2800524173398957302601570098463e-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] = 0.54
y[1] (analytic) = 0.2845826372723517149240624421644
y[1] (numeric) = 0.28458263727235171492406244216432
absolute error = 8e-32
relative error = 2.8111342549488806823548260918642e-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] = 0.55
y[1] (analytic) = 0.2949509558809885143900364047645
y[1] (numeric) = 0.29495095588098851439003640476437
absolute error = 1.3e-31
relative error = 4.4075124154693182293308540874674e-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] = 0.56
y[1] (analytic) = 0.3054897779731677478109489922674
y[1] (numeric) = 0.30548977797316774781094899226728
absolute error = 1.2e-31
relative error = 3.9281183415092869718469400940943e-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] = 0.57
y[1] (analytic) = 0.316198049675462519732487272168
y[1] (numeric) = 0.31619804967546251973248727216789
absolute error = 1.1e-31
relative error = 3.4788323366605565113793730026194e-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] = 0.58
y[1] (analytic) = 0.3270747001696261306842253439
y[1] (numeric) = 0.32707470016962613068422534389988
absolute error = 1.2e-31
relative error = 3.6688866469270198953411804550964e-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] = 0.59
y[1] (analytic) = 0.3381186417996730095040069550186
y[1] (numeric) = 0.33811864179967300950400695501856
absolute error = 4e-32
relative error = 1.1830167005018024865899752349615e-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] = 0.6
y[1] (analytic) = 0.3493287701806434055180950020892
y[1] (numeric) = 0.34932877018064340551809500208916
absolute error = 4e-32
relative error = 1.1450531251495652762119910506332e-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] = 0.61
y[1] (analytic) = 0.3607039643090409641985068426904
y[1] (numeric) = 0.36070396430904096419850684269027
absolute error = 1.3e-31
relative error = 3.6040635219805811009453024937638e-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] = 0.62
y[1] (analytic) = 0.3722430866749321426320006912786
y[1] (numeric) = 0.37224308667493214263200069127852
absolute error = 8e-32
relative error = 2.1491332643569392745843102485924e-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] = 0.63
y[1] (analytic) = 0.3839449833756962549525820684459
y[1] (numeric) = 0.3839449833756962549525820684458
absolute error = 1.0e-31
relative error = 2.6045398254923522250782259318448e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.58
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] = 0.64
y[1] (analytic) = 0.3958084842314147728277784414794
y[1] (numeric) = 0.39580848423141477282777844147926
absolute error = 1.4e-31
relative error = 3.5370641504022715772746780355275e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.89
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] = 0.65
y[1] (analytic) = 0.4078324029018883421647908586402
y[1] (numeric) = 0.4078324029018883421647908586401
absolute error = 1.0e-31
relative error = 2.4519876127659443717125723925415e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.2
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] = 0.66
y[1] (analytic) = 0.4200155370052698144323658175395
y[1] (numeric) = 0.42001553700526981443236581753942
absolute error = 8e-32
relative error = 1.9046914447594890508424281083038e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.52
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] = 0.67
y[1] (analytic) = 0.4323566682383014293941157103238
y[1] (numeric) = 0.43235666823830142939411571032367
absolute error = 1.3e-31
relative error = 3.0067768014242370614983486229747e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.85
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] = 0.68
y[1] (analytic) = 0.4448545624981441256352118319114
y[1] (numeric) = 0.44485456249814412563521183191127
absolute error = 1.3e-31
relative error = 2.9223033988898864625315224739971e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.17
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] = 0.69
y[1] (analytic) = 0.4575079700057867960529213690045
y[1] (numeric) = 0.45750797000578679605292136900437
absolute error = 1.3e-31
relative error = 2.8414805538438093910070327699040e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.51
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] = 0.7
y[1] (analytic) = 0.4703156254310231474882800196163
y[1] (numeric) = 0.47031562543102314748828001961618
absolute error = 1.2e-31
relative error = 2.5514780609303675493037244369476e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.85
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] = 0.71
y[1] (analytic) = 0.4832762480189836669170841117209
y[1] (numeric) = 0.4832762480189836669170841117208
absolute error = 1.0e-31
relative error = 2.0692099065475256055881542758270e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.19
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] = 0.72
y[1] (analytic) = 0.4963885417182100411090260754961
y[1] (numeric) = 0.49638854171821004110902607549601
absolute error = 9e-32
relative error = 1.8130958399739053650671143613172e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.54
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] = 0.73
y[1] (analytic) = 0.5096511953102592224197356828993
y[1] (numeric) = 0.50965119531025922241973568289924
absolute error = 6e-32
relative error = 1.1772757633477918894904451788035e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.9
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] = 0.74
y[1] (analytic) = 0.5230628825408241804171508786023
y[1] (numeric) = 0.52306288254082418041715087860225
absolute error = 5e-32
relative error = 9.5590801161651121148243125131636e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.26
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] = 0.75
y[1] (analytic) = 0.5366222622523582273763224939998
y[1] (numeric) = 0.53662226225235822737632249399974
absolute error = 6e-32
relative error = 1.1181049356424892793965828082818e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.63
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] = 0.76
y[1] (analytic) = 0.550327978518189655320623266666
y[1] (numeric) = 0.5503279785181896553206232666659
absolute error = 1.0e-31
relative error = 1.8170982378409961385780431705115e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.01
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] = 0.77
y[1] (analytic) = 0.5641786607781132732574188693513
y[1] (numeric) = 0.56417866077811327325741886935123
absolute error = 7e-32
relative error = 1.2407417165239153173367949433388e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.39
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=96043192, alloc=4586680, time=3.76
x[1] = 0.78
y[1] (analytic) = 0.5781729239754452855674699524709
y[1] (numeric) = 0.57817292397544528556746995247079
absolute error = 1.1e-31
relative error = 1.9025449902367210279987157478748e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.21
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] = 0.79
y[1] (analytic) = 0.5923093686955278061744382778301
y[1] (numeric) = 0.59230936869552780617443827783001
absolute error = 9e-32
relative error = 1.5194762189598899588780390859207e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.83
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] = 0.8
y[1] (analytic) = 0.6065865813056691581585000367154
y[1] (numeric) = 0.60658658130566915815850003671526
absolute error = 1.4e-31
relative error = 2.3079969836894834061013925844631e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.45
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] = 0.81
y[1] (analytic) = 0.6210031340965059649007215186398
y[1] (numeric) = 0.6210031340965059649007215186397
absolute error = 1.0e-31
relative error = 1.6102978311935486206791468653127e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.09
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] = 0.82
y[1] (analytic) = 0.6355575854247728966668840431261
y[1] (numeric) = 0.63555758542477289666688404312604
absolute error = 6e-32
relative error = 9.4405292889233931931997180235529e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.73
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] = 0.83
y[1] (analytic) = 0.6502484798574657957750741642711
y[1] (numeric) = 0.65024847985746579577507416427099
absolute error = 1.1e-31
relative error = 1.6916610097129631980651023502541e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.38
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] = 0.84
y[1] (analytic) = 0.6650743483173837641546579262583
y[1] (numeric) = 0.66507434831738376415465792625818
absolute error = 1.2e-31
relative error = 1.8043095528130960817450923596830e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.03
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] = 0.85
y[1] (analytic) = 0.6800337082300356592091679410771
y[1] (numeric) = 0.68003370823003565920916794107696
absolute error = 1.4e-31
relative error = 2.0587214766807127860545415333172e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.69
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] = 0.86
y[1] (analytic) = 0.6951250636718963074559386715523
y[1] (numeric) = 0.69512506367189630745593867155218
absolute error = 1.2e-31
relative error = 1.7263080598204527536582465424132e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.36
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] = 0.87
y[1] (analytic) = 0.7103469055199976104446723890343
y[1] (numeric) = 0.71034690551999761044467238903424
absolute error = 6e-32
relative error = 8.4465772334262511106203491288066e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.03
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] = 0.88
y[1] (analytic) = 0.7256977116028395839690027885558
y[1] (numeric) = 0.72569771160283958396900278855572
absolute error = 8e-32
relative error = 1.1023873814250424852298438568138e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.71
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] = 0.89
y[1] (analytic) = 0.7411759468526062395928938852395
y[1] (numeric) = 0.7411759468526062395928938852394
absolute error = 1.0e-31
relative error = 1.3492073025932461052975142446580e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.39
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] = 0.9
y[1] (analytic) = 0.7567800634586710870305676971857
y[1] (numeric) = 0.75678006345867108703056769718564
absolute error = 6e-32
relative error = 7.9283272508243990586341603069717e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.08
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] = 0.91
y[1] (analytic) = 0.7725085010223769069576435476506
y[1] (numeric) = 0.77250850102237690695764354765055
absolute error = 5e-32
relative error = 6.4724206832452284490527487969442e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.77
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] = 0.92
y[1] (analytic) = 0.7883596867130743164051905866512
y[1] (numeric) = 0.78835968671307431640519058665116
absolute error = 4e-32
relative error = 5.0738261575465502445145563276439e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.47
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] = 0.93
y[1] (analytic) = 0.804332035425403523010185831134
y[1] (numeric) = 0.80433203542540352301018583113394
absolute error = 6e-32
relative error = 7.4596059037069900719489127119070e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.17
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] = 0.94
y[1] (analytic) = 0.820423949937803540078020369552
y[1] (numeric) = 0.82042394993780354007802036955188
absolute error = 1.2e-31
relative error = 1.4626584220158031416860171730186e-29 %
Correct digits = 31
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.88
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] = 0.95
y[1] (analytic) = 0.8366338210722330116676380524791
y[1] (numeric) = 0.836633821072233011667638052479
absolute error = 1.0e-31
relative error = 1.1952660468810551870932661342232e-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) = 0.8529600278550866757498983992963
y[1] (numeric) = 0.8529600278550866757498983992962
absolute error = 1.0e-31
relative error = 1.1723878814282427607595940143299e-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] = 0.97
y[1] (analytic) = 0.8694009376792913739269444903003
y[1] (numeric) = 0.86940093767929137392694449030019
absolute error = 1.1e-31
relative error = 1.2652390310691993655385346751819e-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) = 0.8859549064675653982466834652801
y[1] (numeric) = 0.88595490646756539824668346528004
absolute error = 6e-32
relative error = 6.7723537125866784683813290949933e-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] = 0.99
y[1] (analytic) = 0.9026202788368248493137471826928
y[1] (numeric) = 0.90262027883682484931374718269269
absolute error = 1.1e-31
relative error = 1.2186741487987966397857592666707e-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
y[1] (analytic) = 0.919395388263720565198126785114
y[1] (numeric) = 0.91939538826372056519812678511396
absolute error = 4e-32
relative error = 4.3506852993400428215535735193124e-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] = 1.01
y[1] (analytic) = 0.9362785572512890675865372884416
y[1] (numeric) = 0.93627855725128906758653728844156
absolute error = 4e-32
relative error = 4.2722328403452206724382620604507e-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] = 1.02
y[1] (analytic) = 0.9532680974967008602207723839324
y[1] (numeric) = 0.9532680974967008602207723839323
absolute error = 1.0e-31
relative error = 1.0490228327435041147559458031489e-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=100046560, alloc=4586680, time=3.92
x[1] = 1.03
y[1] (analytic) = 0.9703623100600893049329954003253
y[1] (numeric) = 0.97036231006008930493299540032522
absolute error = 8e-32
relative error = 8.2443432901929209740878156989499e-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] = 1.04
y[1] (analytic) = 0.9875594855344431925310531580157
y[1] (numeric) = 0.98755948553444319253105315801557
absolute error = 1.3e-31
relative error = 1.3163763996418621754241666546042e-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] = 1.05
y[1] (analytic) = 1.0048579042165460194183008543758
y[1] (numeric) = 1.0048579042165460194183008543757
absolute error = 1e-31
relative error = 9.9516558092824719900684299305615e-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] = 1.06
y[1] (analytic) = 1.0222558362789448761627249200872
y[1] (numeric) = 1.0222558362789448761627249200871
absolute error = 1e-31
relative error = 9.7822870216133265079915273219518e-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] = 1.07
y[1] (analytic) = 1.0397515419429317512698138636482
y[1] (numeric) = 1.0397515419429317512698138636481
absolute error = 1e-31
relative error = 9.6176822987090739853220028140128e-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] = 1.08
y[1] (analytic) = 1.0573432716525199521729504229479
y[1] (numeric) = 1.0573432716525199521729504229479
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] = 1.09
y[1] (analytic) = 1.0750292662493982459442058522497
y[1] (numeric) = 1.0750292662493982459442058522497
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] = 1.1
y[1] (analytic) = 1.0928077571488452244572598964306
y[1] (numeric) = 1.0928077571488452244572598964306
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] = 1.11
y[1] (analytic) = 1.1106769665165863027125249761329
y[1] (numeric) = 1.1106769665165863027125249761329
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] = 1.12
y[1] (analytic) = 1.1286351074465756647720224120777
y[1] (numeric) = 1.1286351074465756647720224120778
absolute error = 1e-31
relative error = 8.8602595595524246767385107136981e-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] = 1.13
y[1] (analytic) = 1.1466803841396853792575683286929
y[1] (numeric) = 1.146680384139685379257568328693
absolute error = 1e-31
relative error = 8.7208259060807550413890072911428e-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] = 1.14
y[1] (analytic) = 1.1648109920832838156496265183548
y[1] (numeric) = 1.1648109920832838156496265183549
absolute error = 1e-31
relative error = 8.5850838187188067520444821235886e-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] = 1.15
y[1] (analytic) = 1.1830251182316854036948465623802
y[1] (numeric) = 1.1830251182316854036948465623802
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] = 1.16
y[1] (analytic) = 1.201320941187453691096720753212
y[1] (numeric) = 1.201320941187453691096720753212
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] = 1.17
y[1] (analytic) = 1.219696631383539569334676129899
y[1] (numeric) = 1.219696631383539569334676129899
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] = 1.18
y[1] (analytic) = 1.2381503512662364539408010665745
y[1] (numeric) = 1.2381503512662364539408010665745
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] = 1.19
y[1] (analytic) = 1.2566802554789341238686408832991
y[1] (numeric) = 1.2566802554789341238686408832991
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] = 1.2
y[1] (analytic) = 1.2752844910466528447232532887538
y[1] (numeric) = 1.2752844910466528447232532887539
absolute error = 1e-31
relative error = 7.8413876042613749324452115264341e-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] = 1.21
y[1] (analytic) = 1.2939611975613393225939785726704
y[1] (numeric) = 1.2939611975613393225939785726705
absolute error = 1e-31
relative error = 7.7282070118072122615019220736677e-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] = 1.22
y[1] (analytic) = 1.3127085073679059590489540511296
y[1] (numeric) = 1.3127085073679059590489540511297
absolute error = 1e-31
relative error = 7.6178374283951770071276414522781e-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] = 1.23
y[1] (analytic) = 1.3315245457509948035209055090047
y[1] (numeric) = 1.3315245457509948035209055090048
absolute error = 1e-31
relative error = 7.5101882514376688788012953675962e-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] = 1.24
y[1] (analytic) = 1.3504074311224475268446131686052
y[1] (numeric) = 1.3504074311224475268446131686054
absolute error = 2e-31
relative error = 1.4810345040367679876971585634013e-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] = 1.25
y[1] (analytic) = 1.3693552752094626691049228951239
y[1] (numeric) = 1.3693552752094626691049228951241
absolute error = 2e-31
relative error = 1.4605413483320251647917090647585e-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] = 1.26
y[1] (analytic) = 1.388366183243421346227315021647
y[1] (numeric) = 1.3883661832434213462273150216472
absolute error = 2e-31
relative error = 1.4405421452485358408549029259662e-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] = 1.27
y[1] (analytic) = 1.4074382541493625328977259678241
y[1] (numeric) = 1.4074382541493625328977259678242
absolute error = 1e-31
relative error = 7.1051074322573892164562257413270e-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] = 1.28
y[1] (analytic) = 1.4265695807360889744412262128148
y[1] (numeric) = 1.4265695807360889744412262128149
bytes used=104048216, alloc=4586680, time=4.08
absolute error = 1e-31
relative error = 7.0098228190454942338768340448648e-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] = 1.29
y[1] (analytic) = 1.4457582498868847172267878198776
y[1] (numeric) = 1.4457582498868847172267878198777
absolute error = 1e-31
relative error = 6.9167857079718508756487805043211e-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] = 1.3
y[1] (analytic) = 1.4650023427508251860040317814143
y[1] (numeric) = 1.4650023427508251860040317814143
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] = 1.31
y[1] (analytic) = 1.4842999349346606773236460427676
y[1] (numeric) = 1.4842999349346606773236460427677
absolute error = 1e-31
relative error = 6.7371828056033721791309668084476e-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] = 1.32
y[1] (analytic) = 1.5036490966952540808520345411453
y[1] (numeric) = 1.5036490966952540808520345411454
absolute error = 1e-31
relative error = 6.6504878179211974899052810592204e-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] = 1.33
y[1] (analytic) = 1.5230478931325535849684300279788
y[1] (numeric) = 1.523047893132553584968430027979
absolute error = 2e-31
relative error = 1.3131563419758701043336584972065e-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] = 1.34
y[1] (analytic) = 1.5424943843830810695347210153997
y[1] (numeric) = 1.5424943843830810695347210153999
absolute error = 2e-31
relative error = 1.2966011547587564136473778370063e-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] = 1.35
y[1] (analytic) = 1.5619866258139168371599556539787
y[1] (numeric) = 1.5619866258139168371599556539789
absolute error = 2e-31
relative error = 1.2804206943563579094125206673888e-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] = 1.36
y[1] (analytic) = 1.5815226682171612846480494952163
y[1] (numeric) = 1.5815226682171612846480494952164
absolute error = 1e-31
relative error = 6.3230203404374377136748436188494e-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] = 1.37
y[1] (analytic) = 1.6011005580048540686236032207094
y[1] (numeric) = 1.6011005580048540686236032207095
absolute error = 1e-31
relative error = 6.2457039003603188580394865616551e-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] = 1.38
y[1] (analytic) = 1.6207183374043312735816998528036
y[1] (numeric) = 1.6207183374043312735816998528037
absolute error = 1e-31
relative error = 6.1701035702573371731443904707241e-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] = 1.39
y[1] (analytic) = 1.6403740446540010468076735643919
y[1] (numeric) = 1.640374044654001046807673564392
absolute error = 1e-31
relative error = 6.0961705853552862335216849455541e-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] = 1.4
y[1] (analytic) = 1.6600657141995181227665039295927
y[1] (numeric) = 1.6600657141995181227665039295928
absolute error = 1e-31
relative error = 6.0238579198787856996928782077488e-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] = 1.41
y[1] (analytic) = 1.6797913768903376196728749012782
y[1] (numeric) = 1.6797913768903376196728749012783
absolute error = 1e-31
relative error = 5.9531202133637535234061342931929e-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] = 1.42
y[1] (analytic) = 1.6995490601766284530260357940482
y[1] (numeric) = 1.6995490601766284530260357940483
absolute error = 1e-31
relative error = 5.8839137005911046929859710123407e-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] = 1.43
y[1] (analytic) = 1.7193367883065266749322047508502
y[1] (numeric) = 1.7193367883065266749322047508503
absolute error = 1e-31
relative error = 5.8161961449388708915000429189470e-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] = 1.44
y[1] (analytic) = 1.7391525825237090140449596877417
y[1] (numeric) = 1.7391525825237090140449596877418
absolute error = 1e-31
relative error = 5.7499267749635043337750961905158e-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] = 1.45
y[1] (analytic) = 1.758994461265266858934266745504
y[1] (numeric) = 1.7589944612652668589342667455041
absolute error = 1e-31
relative error = 5.6850662240328341431414647751480e-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] = 1.46
y[1] (analytic) = 1.7788604403598608976507037817533
y[1] (numeric) = 1.7788604403598608976507037817534
absolute error = 1e-31
relative error = 5.6215764728440497806957037250832e-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] = 1.47
y[1] (analytic) = 1.7987485332261365981860507970752
y[1] (numeric) = 1.7987485332261365981860507970753
absolute error = 1e-31
relative error = 5.5594207946702528282804041199949e-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] = 1.48
y[1] (analytic) = 1.8186567510713806884475469187043
y[1] (numeric) = 1.8186567510713806884475469187044
absolute error = 1e-31
relative error = 5.4985637031886006164742764323742e-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) = 1.8385831030903987702633630308726
y[1] (numeric) = 1.8385831030903987702633630308726
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] = 1.5
y[1] (analytic) = 1.8585255966645941798236202971315
y[1] (numeric) = 1.8585255966645941798236202971315
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] = 1.51
y[1] (analytic) = 1.8784822375612281868368089701676
y[1] (numeric) = 1.8784822375612281868368089701677
absolute error = 1e-31
relative error = 5.3234466635056776857444663670241e-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] = 1.52
y[1] (analytic) = 1.8984510301328416065477414596946
y[1] (numeric) = 1.8984510301328416065477414596946
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] = 1.53
y[1] (analytic) = 1.9184299775168178826220219858478
y[1] (numeric) = 1.9184299775168178826220219858478
absolute error = 0
relative error = 0 %
Correct digits = 32
h = 0.01
bytes used=108048988, alloc=4586680, time=4.24
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) = 1.9384170818350676847550463858472
y[1] (numeric) = 1.9384170818350676847550463858472
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] = 1.55
y[1] (analytic) = 1.9584103443938150527121744506089
y[1] (numeric) = 1.9584103443938150527121744506089
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] = 1.56
y[1] (analytic) = 1.9784077658834651083521586724782
y[1] (numeric) = 1.9784077658834651083521586724782
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] = 1.57
y[1] (analytic) = 1.9984073465785333490291829327093
y[1] (numeric) = 1.9984073465785333490291829327093
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] = 1.58
y[1] (analytic) = 2.0184070865376165296107781139655
y[1] (numeric) = 2.0184070865376165296107781139655
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 = 0.008874
Order of pole (three term test) = -0.8949
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = 2.0384049858033851361900546924868
y[1] (numeric) = 2.0384049858033851361900546924869
absolute error = 1e-31
relative error = 4.9057964779549222052346453525071e-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 = 0.01851
Order of pole (three term test) = -0.9018
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = 2.058399044602577452411540925893
y[1] (numeric) = 2.0583990446025774524115409258931
absolute error = 1e-31
relative error = 4.8581445012916512328911384808379e-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 = 0.02814
Order of pole (three term test) = -0.9135
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = 2.078387263545975219170655219202
y[1] (numeric) = 2.0783872635459752191706552192021
absolute error = 1e-31
relative error = 4.8114228639655988631429947945682e-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 = 0.03776
Order of pole (three term test) = -0.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = 2.0983676438283408902874885494247
y[1] (numeric) = 2.0983676438283408902874885494247
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 = 0.04737
Order of pole (three term test) = -0.9513
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = 2.1183381874282964905959433948396
y[1] (numeric) = 2.1183381874282964905959433948396
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 = 0.05696
Order of pole (three term test) = -0.9775
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = 2.1382968973081240887289854149132
y[1] (numeric) = 2.1382968973081240887289854149132
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 = 0.06652
Order of pole (three term test) = -1.008
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = 2.1582417776134679047192291946826
y[1] (numeric) = 2.1582417776134679047192291946825
absolute error = 1e-31
relative error = 4.6334011804079525452219666154322e-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 = 0.07606
Order of pole (three term test) = -1.044
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = 2.1781708338729180823705158633012
y[1] (numeric) = 2.1781708338729180823705158633012
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 = 0.08556
Order of pole (three term test) = -1.085
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = 2.1980820731974561681895646848972
y[1] (numeric) = 2.1980820731974561681895646848972
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 = 0.09503
Order of pole (three term test) = -1.13
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = 2.2179735044797423524960094683456
y[1] (numeric) = 2.2179735044797423524960094683456
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 = 0.1045
Order of pole (three term test) = -1.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = 2.2378431385932245441527809396662
y[1] (numeric) = 2.2378431385932245441527809396661
absolute error = 1e-31
relative error = 4.4685884490931301612438331253267e-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 = 0.1139
Order of pole (three term test) = -1.235
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = 2.2576889885910493681752857146697
y[1] (numeric) = 2.2576889885910493681752857146697
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 = 0.1232
Order of pole (three term test) = -1.294
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = 2.2775090699047551952853795661022
y[1] (numeric) = 2.2775090699047551952853795661022
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 = 0.1325
Order of pole (three term test) = -1.358
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = 2.2973014005427273342727565606624
y[1] (numeric) = 2.2973014005427273342727565606624
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 = 0.1417
Order of pole (three term test) = -1.427
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = 2.3170640012883955418098967026851
y[1] (numeric) = 2.3170640012883955418098967026852
absolute error = 1e-31
relative error = 4.3158065527924710228410789426906e-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 = 0.1509
Order of pole (three term test) = -1.5
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = 2.3367948958981540301347546306902
y[1] (numeric) = 2.3367948958981540301347546306902
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 = 0.1601
Order of pole (three term test) = -1.578
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = 2.3564921112989841807653538878853
y[1] (numeric) = 2.3564921112989841807653538878853
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 = 0.1691
Order of pole (three term test) = -1.661
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = 2.3761536777857602021396003530082
y[1] (numeric) = 2.3761536777857602021396003530082
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 = 0.1781
Order of pole (three term test) = -1.748
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = 2.3957776292182180007789716834608
y[1] (numeric) = 2.3957776292182180007789716834608
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 = 0.187
Order of pole (three term test) = -1.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 2.4153620032175675692531065806253
y[1] (numeric) = 2.4153620032175675692531065806253
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 = 0.1959
Order of pole (three term test) = -1.936
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=112050708, alloc=4586680, time=4.40
x[1] = 1.79
y[1] (analytic) = 2.4349048413627292298703405289292
y[1] (numeric) = 2.4349048413627292298703405289293
absolute error = 1e-31
relative error = 4.1069366778224307706024289953838e-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 = 0.2047
Order of pole (three term test) = -2.036
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = 2.4544041893861741106333486130612
y[1] (numeric) = 2.4544041893861741106333486130612
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 = 0.2133
Order of pole (three term test) = -2.141
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = 2.473858097369349269575499701684
y[1] (numeric) = 2.473858097369349269575499701684
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 = 0.2219
Order of pole (three term test) = -2.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = 2.4932646199376679251283420896617
y[1] (numeric) = 2.4932646199376679251283420896618
absolute error = 1e-31
relative error = 4.0108057203531014860575542763424e-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 = 0.2305
Order of pole (three term test) = -2.363
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = 2.5126218164550452936596751672371
y[1] (numeric) = 2.5126218164550452936596751672371
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 = 0.2389
Order of pole (three term test) = -2.481
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = 2.5319277512179605807605659665632
y[1] (numeric) = 2.5319277512179605807605659665632
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 = 0.2472
Order of pole (three term test) = -2.603
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = 2.5511804936490257202438996709496
y[1] (numeric) = 2.5511804936490257202438996709496
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 = 0.2554
Order of pole (three term test) = -2.729
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = 2.5703781184900415041418709765782
y[1] (numeric) = 2.5703781184900415041418709765782
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 = 0.2636
Order of pole (three term test) = -2.859
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = 2.5895187059945217982502961296198
y[1] (numeric) = 2.5895187059945217982502961296197
absolute error = 1e-31
relative error = 3.8617214762151848650703939108721e-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 = 0.2716
Order of pole (three term test) = -2.993
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = 2.6086003421196665909586275190445
y[1] (numeric) = 2.6086003421196665909586275190444
absolute error = 1e-31
relative error = 3.8334733912801355094412915485393e-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 = 0.2795
Order of pole (three term test) = -3.131
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = 2.6276211187177646782207648311025
y[1] (numeric) = 2.6276211187177646782207648311024
absolute error = 1e-31
relative error = 3.8057237128919991972065356930738e-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 = 0.2873
Order of pole (three term test) = -3.273
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = 2.6465791337270068445576673901606
y[1] (numeric) = 2.6465791337270068445576673901606
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 = 0.295
Order of pole (three term test) = -3.419
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = 2.6654724913616904589326778787951
y[1] (numeric) = 2.665472491361690458932677878795
absolute error = 1e-31
relative error = 3.7516800613805521044601510372439e-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 = 0.3025
Order of pole (three term test) = -3.569
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = 2.6842993023017964651984732063181
y[1] (numeric) = 2.684299302301796465198473206318
absolute error = 1e-31
relative error = 3.7253669855015658802300488155690e-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 = 0.31
Order of pole (three term test) = -3.723
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (analytic) = 2.7030576838819198095745781294237
y[1] (numeric) = 2.7030576838819198095745781294237
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 = 0.3173
Order of pole (three term test) = -3.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = 2.7217457602795344122701353716815
y[1] (numeric) = 2.7217457602795344122701353716814
absolute error = 1e-31
relative error = 3.6741124560337182757247065485320e-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 = 0.3245
Order of pole (three term test) = -4.041
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = 2.7403616627025738569116569182614
y[1] (numeric) = 2.7403616627025738569116569182613
absolute error = 1e-31
relative error = 3.6491533712881873770250850161475e-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 = 0.3315
Order of pole (three term test) = -4.205
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = 2.7589035295763090398631304308949
y[1] (numeric) = 2.7589035295763090398631304308948
absolute error = 1e-31
relative error = 3.6246283687692850477099479166557e-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 = 0.3385
Order of pole (three term test) = -4.373
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = 2.7773695067295040918292796277586
y[1] (numeric) = 2.7773695067295040918292796277585
absolute error = 1e-31
relative error = 3.6005291970586643353154586295515e-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 = 0.3453
Order of pole (three term test) = -4.545
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = 2.7957577475798319563049477198144
y[1] (numeric) = 2.7957577475798319563049477198143
absolute error = 1e-31
relative error = 3.5768478183263813851804127894301e-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 = 0.3519
Order of pole (three term test) = -4.719
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = 2.8140664133185310834672714322606
y[1] (numeric) = 2.8140664133185310834672714322605
absolute error = 1e-31
relative error = 3.5535764019895131943677237842610e-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 = 0.3584
Order of pole (three term test) = -4.898
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 2.8322936730942847739951364590015
y[1] (numeric) = 2.8322936730942847739951364590014
absolute error = 1e-31
relative error = 3.5307073185934797865233375113541e-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 = 0.3648
Order of pole (three term test) = -5.079
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = 2.8504377041963047850347646803309
y[1] (numeric) = 2.8504377041963047850347646803307
absolute error = 2e-31
relative error = 7.0164662678145075846895250940217e-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 = 0.371
Order of pole (three term test) = -5.263
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = 2.8684966922366008901034057481804
y[1] (numeric) = 2.8684966922366008901034057481802
absolute error = 2e-31
relative error = 6.9722932064480655922933373027362e-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 = 0.3771
Order of pole (three term test) = -5.451
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 2.8864688313314181661270334633922
y[1] (numeric) = 2.886468831331418166127033463392
absolute error = 2e-31
relative error = 6.9288813317186458320463911419724e-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 = 0.383
Order of pole (three term test) = -5.641
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=116052852, alloc=4586680, time=4.56
x[1] = 2.04
y[1] (analytic) = 2.9043523242818238640345404105827
y[1] (numeric) = 2.9043523242818238640345404105825
absolute error = 2e-31
relative error = 6.8862168796774739201336023816658e-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 = 0.3888
Order of pole (three term test) = -5.835
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = 2.9221453827534258043718599883348
y[1] (numeric) = 2.9221453827534258043718599883346
absolute error = 2e-31
relative error = 6.8442864335362962404659396814740e-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 = 0.3944
Order of pole (three term test) = -6.031
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = 2.9398462274552043262462192529758
y[1] (numeric) = 2.9398462274552043262462192529756
absolute error = 2e-31
relative error = 6.8030769137583228964823791728797e-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 = 0.3999
Order of pole (three term test) = -6.23
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = 2.9574530883174399065546542780235
y[1] (numeric) = 2.9574530883174399065546542780233
absolute error = 2e-31
relative error = 6.7625755684863423414244559118891e-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 = 0.4052
Order of pole (three term test) = -6.432
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 2.9749642046687186568831376995447
y[1] (numeric) = 2.9749642046687186568831376995445
absolute error = 2e-31
relative error = 6.7227699642951261200930616887466e-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 = 0.4103
Order of pole (three term test) = -6.636
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = 2.9923778254119979976741326237409
y[1] (numeric) = 2.9923778254119979976741326237407
absolute error = 2e-31
relative error = 6.6836479772557967061568654196788e-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 = 0.4153
Order of pole (three term test) = -6.843
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = 3.0096922091997149032418770474383
y[1] (numeric) = 3.0096922091997149032418770474381
absolute error = 2e-31
relative error = 6.6451977843003596543135145315664e-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 = 0.4201
Order of pole (three term test) = -7.053
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = 3.0269056246079192069568203141434
y[1] (numeric) = 3.0269056246079192069568203141431
absolute error = 3e-31
relative error = 9.9111117823126568630790226801547e-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 = 0.4247
Order of pole (three term test) = -7.265
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = 3.0440163503094145534138037659678
y[1] (numeric) = 3.0440163503094145534138037659675
absolute error = 3e-31
relative error = 9.8554004143080886152574857721327e-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 = 0.4292
Order of pole (three term test) = -7.479
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 3.0610226752458896836330524192194
y[1] (numeric) = 3.0610226752458896836330524192192
absolute error = 2e-31
relative error = 6.5337640788281370106884122386484e-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 = 0.4335
Order of pole (three term test) = -7.695
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 3.0779228987990228403088998240172
y[1] (numeric) = 3.077922898799022840308899824017
absolute error = 2e-31
relative error = 6.4978885623820582866578271218755e-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 = 0.4376
Order of pole (three term test) = -7.913
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = 3.0947153309605421828083077645281
y[1] (numeric) = 3.0947153309605421828083077645279
absolute error = 2e-31
relative error = 6.4626299549795332278143991409161e-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 = 0.4415
Order of pole (three term test) = -8.133
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 3.1113982925012252060193974879667
y[1] (numeric) = 3.1113982925012252060193974879666
absolute error = 1e-31
relative error = 3.2139890364088004979472792474441e-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 = 0.4453
Order of pole (three term test) = -8.356
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = 3.127970115138820263248939988833
y[1] (numeric) = 3.1279701151388202632489399888329
absolute error = 1e-31
relative error = 3.1969614900096949821274525547725e-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 = 0.4489
Order of pole (three term test) = -8.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 3.144429141704873401156449735325
y[1] (numeric) = 3.1444291417048734011564497353249
absolute error = 1e-31
relative error = 3.1802274910154644925282756913345e-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 = 0.4523
Order of pole (three term test) = -8.806
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 3.1607737263104438241804103275939
y[1] (numeric) = 3.1607737263104438241804103275938
absolute error = 1e-31
relative error = 3.1637823096159915753895002482284e-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 = 0.4555
Order of pole (three term test) = -9.033
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = 3.1770022345106914170482852253099
y[1] (numeric) = 3.1770022345106914170482852253098
absolute error = 1e-31
relative error = 3.1476213303766083541440031391683e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.83
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4586
Order of pole (three term test) = -9.262
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 3.1931130434683198667552183550373
y[1] (numeric) = 3.1931130434683198667552183550372
absolute error = 1e-31
relative error = 3.1317400492461500109268327139118e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.12
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4615
Order of pole (three term test) = -9.493
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 3.2091045421158590398354288750003
y[1] (numeric) = 3.2091045421158590398354288750002
absolute error = 1e-31
relative error = 3.1161340706609388166746601279342e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.42
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4641
Order of pole (three term test) = -9.725
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = 3.2249751313167703868238078213713
y[1] (numeric) = 3.2249751313167703868238078213712
absolute error = 1e-31
relative error = 3.1007991047413006138087274507528e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.72
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4666
Order of pole (three term test) = -9.958
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = 3.2407232240253592635015245326209
y[1] (numeric) = 3.2407232240253592635015245326208
absolute error = 1e-31
relative error = 3.0857309645773526679223962786792e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4689
Order of pole (three term test) = -10.19
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 3.2563472454454781778267781147928
y[1] (numeric) = 3.2563472454454781778267781147927
absolute error = 1e-31
relative error = 3.0709255636009327609916444491444e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.34
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4711
Order of pole (three term test) = -10.43
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 3.2718456331880050923582531374897
y[1] (numeric) = 3.2718456331880050923582531374896
absolute error = 1e-31
relative error = 3.0563789130406645930449899432921e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.66
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.473
Order of pole (three term test) = -10.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = 3.2872168374270810344722686962486
y[1] (numeric) = 3.2872168374270810344722686962485
absolute error = 1e-31
relative error = 3.0420871194572742710940985812731e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.98
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4747
Order of pole (three term test) = -10.9
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = 3.3024593210550913907427967009214
y[1] (numeric) = 3.3024593210550913907427967009213
absolute error = 1e-31
relative error = 3.0280463823563871579214199480644e-30 %
Correct digits = 32
h = 0.01
bytes used=120053832, alloc=4586680, time=4.72
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.3
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4763
Order of pole (three term test) = -11.14
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 3.3175715598363753874840620363779
y[1] (numeric) = 3.3175715598363753874840620363778
absolute error = 1e-31
relative error = 3.0142529918761438797180732839552e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.64
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4776
Order of pole (three term test) = -11.38
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 3.332552042559648386635761142332
y[1] (numeric) = 3.3325520425596483866357611423319
absolute error = 1e-31
relative error = 3.0007033265470790882026878968656e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.98
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4788
Order of pole (three term test) = -11.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 3.3473992711891217548883286469421
y[1] (numeric) = 3.3473992711891217548883286469419
absolute error = 2e-31
relative error = 5.9747877022436137301370891529831e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.32
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4798
Order of pole (three term test) = -11.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = 3.3621117610143051941872723320165
y[1] (numeric) = 3.3621117610143051941872723320163
absolute error = 2e-31
relative error = 5.9486422289443053162575529251449e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.67
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4806
Order of pole (three term test) = -12.1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (analytic) = 3.376688040798476553508360855632
y[1] (numeric) = 3.3766880407984765535083608556318
absolute error = 2e-31
relative error = 5.9229634951029271042386194477562e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.03
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4812
Order of pole (three term test) = -12.34
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = 3.3911266529258042750462111441227
y[1] (numeric) = 3.3911266529258042750462111441225
absolute error = 2e-31
relative error = 5.8977449228398333903639749891255e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.39
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -12.58
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 3.4054261535471077626942582245178
y[1] (numeric) = 3.4054261535471077626942582245176
absolute error = 2e-31
relative error = 5.8729800906614600144143213143081e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.77
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -12.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 3.4195851127242410969007260692902
y[1] (numeric) = 3.41958511272424109690072606929
absolute error = 2e-31
relative error = 5.8486627297505201236830886365964e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.15
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4818
Order of pole (three term test) = -13.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = 3.4336021145730856576494332176447
y[1] (numeric) = 3.4336021145730856576494332176445
absolute error = 2e-31
relative error = 5.8247867203700988494000608702539e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.46
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4816
Order of pole (three term test) = -13.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = 3.4474757574051373564222952147351
y[1] (numeric) = 3.4474757574051373564222952147349
absolute error = 2e-31
relative error = 5.8013460883779198050684788468116e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.07
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4813
Order of pole (three term test) = -13.55
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = 3.4612046538676743185383165852361
y[1] (numeric) = 3.461204653867674318538316585236
absolute error = 1e-31
relative error = 2.8891675009235992603679955986649e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.69
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4807
Order of pole (three term test) = -13.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 3.4747874310824909992176444546696
y[1] (numeric) = 3.4747874310824909992176444546694
absolute error = 2e-31
relative error = 5.7557477677906342741661148744220e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.32
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4799
Order of pole (three term test) = -14.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 3.4882227307831848600746887911359
y[1] (numeric) = 3.4882227307831848600746887911357
absolute error = 2e-31
relative error = 5.7335788289842225376172563550861e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.96
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.479
Order of pole (three term test) = -14.27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = 3.5015092094509818774870651378215
y[1] (numeric) = 3.5015092094509818774870651378213
absolute error = 2e-31
relative error = 5.7118227608876956826023058660508e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.6
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4779
Order of pole (three term test) = -14.51
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = 3.5146455384490873004027104883558
y[1] (numeric) = 3.5146455384490873004027104883556
absolute error = 2e-31
relative error = 5.6904742686585199172016922170432e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.25
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4765
Order of pole (three term test) = -14.75
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = 3.5276304041555482226213501850748
y[1] (numeric) = 3.5276304041555482226213501850746
absolute error = 2e-31
relative error = 5.6695281842564919019893025919485e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.475
Order of pole (three term test) = -14.99
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = 3.540462508094614683403806134673
y[1] (numeric) = 3.5404625080946146834038061346728
absolute error = 2e-31
relative error = 5.6489794636360893209304587330155e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.56
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4733
Order of pole (three term test) = -15.22
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = 3.5531405670665861604085526293724
y[1] (numeric) = 3.5531405670665861604085526293722
absolute error = 2e-31
relative error = 5.6288231840238360816185544664803e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.23
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4714
Order of pole (three term test) = -15.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = 3.5656633132761304704144311681231
y[1] (numeric) = 3.5656633132761304704144311681229
absolute error = 2e-31
relative error = 5.6090545412780449837543851163792e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.9
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4693
Order of pole (three term test) = -15.7
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 3.5780294944590622460463840671807
y[1] (numeric) = 3.5780294944590622460463840671805
absolute error = 2e-31
relative error = 5.5896688473283988151188567494283e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.57
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.467
Order of pole (three term test) = -15.93
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 3.5902378740075683107621826651431
y[1] (numeric) = 3.590237874007568310762182665143
absolute error = 1e-31
relative error = 2.7853307638464625453404546069250e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.25
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4646
Order of pole (three term test) = -16.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 3.6022872310938674296670055809347
y[1] (numeric) = 3.6022872310938674296670055809346
absolute error = 1e-31
relative error = 2.7760140595350051072903962067798e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.94
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4619
Order of pole (three term test) = -16.4
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = 3.6141763607922920702838350157568
y[1] (numeric) = 3.6141763607922920702838350157567
absolute error = 1e-31
relative error = 2.7668821335015929400347991173521e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.63
Order of pole (ratio test) Not computed
Radius of convergence (three term test) for eq 1 = 0.4591
Order of pole (three term test) = -16.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 3.6259040741997799652053285209037
y[1] (numeric) = 3.6259040741997799652053285209036
absolute error = 1e-31
relative error = 2.7579328618082520924488514984891e-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 = 0.4561
Order of pole (three term test) = -16.86
NO COMPLEX POLE (six term test) for Equation 1
bytes used=124054948, alloc=4586680, time=4.88
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = 3.63746919855476342757131034511
y[1] (numeric) = 3.6374691985547634275713103451099
absolute error = 1e-31
relative error = 2.7491641727091991888233712683959e-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 = 0.4529
Order of pole (three term test) = -17.08
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 3.6488705773544445305394087116131
y[1] (numeric) = 3.648870577354444530539408711613
absolute error = 1e-31
relative error = 2.7405740455860017528387610770351e-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 = 0.4495
Order of pole (three term test) = -17.31
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = 3.6601070704704444233286209516646
y[1] (numeric) = 3.6601070704704444233286209516644
absolute error = 2e-31
relative error = 5.4643210198299856427270092053541e-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 = 0.446
Order of pole (three term test) = -17.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = 3.6711775542628152190005762467649
y[1] (numeric) = 3.6711775542628152190005762467647
absolute error = 2e-31
relative error = 5.4478432885319999624958599698602e-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 = 0.4422
Order of pole (three term test) = -17.76
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 3.6820809216924030528847274431343
y[1] (numeric) = 3.6820809216924030528847274431341
absolute error = 2e-31
relative error = 5.4317111506629668166635455740972e-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 = 0.4383
Order of pole (three term test) = -17.98
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = 3.6928160824315510754352649891385
y[1] (numeric) = 3.6928160824315510754352649891383
absolute error = 2e-31
relative error = 5.4159209539704212888665811435832e-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 = 0.4342
Order of pole (three term test) = -18.2
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = 3.7033819629731313093127194908166
y[1] (numeric) = 3.7033819629731313093127194908165
absolute error = 1e-31
relative error = 2.7002345693696277710762006575522e-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 = 0.43
Order of pole (three term test) = -18.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = 3.7137775067378944675954043032904
y[1] (numeric) = 3.7137775067378944675954043032903
absolute error = 1e-31
relative error = 2.6926761180111173815411995474675e-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 = 0.4255
Order of pole (three term test) = -18.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = 3.7240016741801269982283348974453
y[1] (numeric) = 3.7240016741801269982283348974452
absolute error = 1e-31
relative error = 2.6852834329623633664962233640851e-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 = 0.4209
Order of pole (three term test) = -18.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 3.7340534428916047890932273534967
y[1] (numeric) = 3.7340534428916047890932273534966
absolute error = 1e-31
relative error = 2.6780548679710710616719026487072e-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 = 0.4161
Order of pole (three term test) = -19.05
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = 3.7439318077038331384156967803899
y[1] (numeric) = 3.7439318077038331384156967803898
absolute error = 1e-31
relative error = 2.6709888196743188053412604810374e-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 = 0.4112
Order of pole (three term test) = -19.26
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = 3.753635780788562766597814632532
y[1] (numeric) = 3.7536357807885627665978146325319
absolute error = 1e-31
relative error = 2.6640837268178434632068390893046e-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 = 0.4061
Order of pole (three term test) = -19.46
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = 3.7631643917565718179586047321076
y[1] (numeric) = 3.7631643917565718179586047321075
absolute error = 1e-31
relative error = 2.6573380694995880412039346241472e-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 = 0.4008
Order of pole (three term test) = -19.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 3.7725166877547039742646220077652
y[1] (numeric) = 3.7725166877547039742646220077651
absolute error = 1e-31
relative error = 2.6507503684368641633412839992689e-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 = 0.3954
Order of pole (three term test) = -19.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 3.7816917335611529763201257168595
y[1] (numeric) = 3.7816917335611529763201257168594
absolute error = 1e-31
relative error = 2.6443191842565059808945709079016e-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 = 0.3898
Order of pole (three term test) = -20.06
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 3.7906886116789840252440916372413
y[1] (numeric) = 3.7906886116789840252440916372412
absolute error = 1e-31
relative error = 2.6380431168074150382337041622013e-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 = 0.3841
Order of pole (three term test) = -20.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = 3.7995064224278827113718697686577
y[1] (numeric) = 3.7995064224278827113718697686576
absolute error = 1e-31
relative error = 2.6319208044949177848913455032412e-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 = 0.3782
Order of pole (three term test) = -20.44
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = 3.8081442840341222959650545638867
y[1] (numeric) = 3.8081442840341222959650545638865
absolute error = 2e-31
relative error = 5.2519018472727576544702007858731e-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 = 0.3722
Order of pole (three term test) = -20.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = 3.8166013327187403490763691874322
y[1] (numeric) = 3.816601332718740349076369187432
absolute error = 2e-31
relative error = 5.2402643756750673778192875791742e-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 = 0.366
Order of pole (three term test) = -20.82
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = 3.8248767227839159259792575999741
y[1] (numeric) = 3.824876722783915925979257599974
absolute error = 1e-31
relative error = 2.6144633473890248283125458504858e-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 = 0.3596
Order of pole (three term test) = -21
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 3.8329696266975386445165222497856
y[1] (numeric) = 3.8329696266975386445165222497854
absolute error = 2e-31
relative error = 5.2178863773652879473904263967015e-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 = 0.3532
Order of pole (three term test) = -21.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = 3.8408792351759612065307465035586
y[1] (numeric) = 3.8408792351759612065307465035584
absolute error = 2e-31
relative error = 5.2071410672936050214615035115348e-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 = 0.3465
Order of pole (three term test) = -21.35
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = 3.8486047572649270881933189790534
y[1] (numeric) = 3.8486047572649270881933189790533
absolute error = 1e-31
relative error = 2.5983442392007697210734012962417e-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 = 0.3398
Order of pole (three term test) = -21.52
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = 3.8561454204186653065304663942802
y[1] (numeric) = 3.8561454204186653065304663942801
absolute error = 1e-31
relative error = 2.5932631967272361499344115765650e-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 = 0.3329
Order of pole (three term test) = -21.69
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=128057788, alloc=4586680, time=5.04
x[1] = 2.77
y[1] (analytic) = 3.8635004705771443527355544156581
y[1] (numeric) = 3.863500470577144352735554415658
absolute error = 1e-31
relative error = 2.5883263315627763013321982233126e-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 = 0.3258
Order of pole (three term test) = -21.86
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = 3.8706691722414775669387033382352
y[1] (numeric) = 3.870669172241477566938703338235
absolute error = 2e-31
relative error = 5.1670652050116024914774519179122e-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 = 0.3187
Order of pole (three term test) = -22.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = 3.8776508085474724139590792392482
y[1] (numeric) = 3.877650808547472413959079239248
absolute error = 2e-31
relative error = 5.1577620026832151993415404109440e-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 = 0.3114
Order of pole (three term test) = -22.18
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = 3.8844446813373163051735762347323
y[1] (numeric) = 3.8844446813373163051735762347321
absolute error = 2e-31
relative error = 5.1487411047682894455523444815608e-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 = 0.304
Order of pole (three term test) = -22.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = 3.8910501112293917979794409567177
y[1] (numeric) = 3.8910501112293917979794409567175
absolute error = 2e-31
relative error = 5.1400006240682737933594117351850e-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 = 0.2965
Order of pole (three term test) = -22.48
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = 3.8974664376862141913890721275201
y[1] (numeric) = 3.8974664376862141913890721275199
absolute error = 2e-31
relative error = 5.1315387367064234439767417907712e-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 = 0.2888
Order of pole (three term test) = -22.63
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = 3.9036930190804847240540502254491
y[1] (numeric) = 3.9036930190804847240540502254489
absolute error = 2e-31
relative error = 5.1233536813074000306602160941704e-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 = 0.281
Order of pole (three term test) = -22.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = 3.9097292327592527694536389871725
y[1] (numeric) = 3.9097292327592527694536389871723
absolute error = 2e-31
relative error = 5.1154437582075722525627241608078e-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 = 0.2732
Order of pole (three term test) = -22.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = 3.9155744751061806120817082143499
y[1] (numeric) = 3.9155744751061806120817082143497
absolute error = 2e-31
relative error = 5.1078073286954016859668305175902e-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 = 0.2652
Order of pole (three term test) = -23.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = 3.9212281616019045782063463327855
y[1] (numeric) = 3.9212281616019045782063463327854
absolute error = 1e-31
relative error = 2.5502214071406619329341812450230e-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 = 0.2571
Order of pole (three term test) = -23.17
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = 3.9266897268824864851393875174759
y[1] (numeric) = 3.9266897268824864851393875174757
absolute error = 2e-31
relative error = 5.0933486959965597780161134022414e-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 = 0.2489
Order of pole (three term test) = -23.3
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = 3.931958624795949563919635809531
y[1] (numeric) = 3.9319586247959495639196358095309
absolute error = 1e-31
relative error = 2.5432617568601586367287444519065e-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 = 0.2406
Order of pole (three term test) = -23.42
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = 3.9370343284568932018646310144186
y[1] (numeric) = 3.9370343284568932018646310144184
absolute error = 2e-31
relative error = 5.0799658655348656462953613388534e-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 = 0.2322
Order of pole (three term test) = -23.54
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = 3.9419163302991810435622133386911
y[1] (numeric) = 3.9419163302991810435622133386909
absolute error = 2e-31
relative error = 5.0736744071079897315290143640964e-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 = 0.2237
Order of pole (three term test) = -23.66
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = 3.9466041421266971815356942132055
y[1] (numeric) = 3.9466041421266971815356942132053
absolute error = 2e-31
relative error = 5.0676478511023524132940299788416e-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 = 0.2151
Order of pole (three term test) = -23.77
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = 3.9510972951621653610058634703165
y[1] (numeric) = 3.9510972951621653610058634703163
absolute error = 2e-31
relative error = 5.0618849666113164133102732705303e-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 = 0.2065
Order of pole (three term test) = -23.87
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = 3.9553953400940263168700392093527
y[1] (numeric) = 3.9553953400940263168700392093524
absolute error = 3e-31
relative error = 7.5845768679311965241104652229065e-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 = 0.1977
Order of pole (three term test) = -23.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = 3.9594978471213685552035267626566
y[1] (numeric) = 3.9594978471213685552035267626564
absolute error = 2e-31
relative error = 5.0511455674967436749183871820173e-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 = 0.1889
Order of pole (three term test) = -24.07
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = 3.9634044059969080862427788094039
y[1] (numeric) = 3.9634044059969080862427788094037
absolute error = 2e-31
relative error = 5.0461668684978502576660713026906e-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 = 0.18
Order of pole (three term test) = -24.16
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = 3.9671146260680128109127746459523
y[1] (numeric) = 3.9671146260680128109127746459521
absolute error = 2e-31
relative error = 5.0414474713131510575129252078004e-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 = 0.1711
Order of pole (three term test) = -24.25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (analytic) = 3.9706281363157674584941527496123
y[1] (numeric) = 3.9706281363157674584941527496121
absolute error = 2e-31
relative error = 5.0369864196241326386968728295454e-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 = 0.162
Order of pole (three term test) = -24.33
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = 3.9739445853920751689688839287908
y[1] (numeric) = 3.9739445853920751689688839287906
absolute error = 2e-31
relative error = 5.0327828106910481312397597827789e-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 = 0.1529
Order of pole (three term test) = -24.41
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = 3.9770636416547920099171683744217
y[1] (numeric) = 3.9770636416547920099171683744215
absolute error = 2e-31
relative error = 5.0288357949631207579342572875621e-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 = 0.1438
Order of pole (three term test) = -24.49
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (analytic) = 3.9799849932008909145431455894625
y[1] (numeric) = 3.9799849932008909145431455894623
absolute error = 2e-31
relative error = 5.0251445757123471923788782132044e-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 = 0.1345
Order of pole (three term test) = -24.56
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = 3.9827083478976517244632511483648
y[1] (numeric) = 3.9827083478976517244632511483646
absolute error = 2e-31
relative error = 5.0217084086906288313225684109678e-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 = 0.1253
Order of pole (three term test) = -24.62
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=132058596, alloc=4586680, time=5.20
x[1] = 3.02
y[1] (analytic) = 3.9852334334118742182789330665261
y[1] (numeric) = 3.9852334334118742182789330665258
absolute error = 3e-31
relative error = 7.5277899027149653590821985970483e-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 = 0.1159
Order of pole (three term test) = -24.68
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = 3.9875599972371112046552146174169
y[1] (numeric) = 3.9875599972371112046552146174166
absolute error = 3e-31
relative error = 7.5233977722683323656376568140899e-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 = 0.1066
Order of pole (three term test) = -24.74
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = 3.9896878067189189566184899096864
y[1] (numeric) = 3.9896878067189189566184899096861
absolute error = 3e-31
relative error = 7.5193853387420086617823010737279e-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 = 0.09716
Order of pole (three term test) = -24.79
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = 3.9916166490781224620511644031298
y[1] (numeric) = 3.9916166490781224620511644031296
absolute error = 2e-31
relative error = 5.0105011974581949165390051382900e-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 = 0.08771
Order of pole (three term test) = -24.84
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = 3.9933463314320931638774785435863
y[1] (numeric) = 3.9933463314320931638774785435861
absolute error = 2e-31
relative error = 5.0083309435441837806525367102764e-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 = 0.07822
Order of pole (three term test) = -24.88
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = 3.9948766808140370621842273254535
y[1] (numeric) = 3.9948766808140370621842273254533
absolute error = 2e-31
relative error = 5.0064123621269317351371643491289e-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 = 0.06871
Order of pole (three term test) = -24.91
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = 3.9962075441902912494822370747196
y[1] (numeric) = 3.9962075441902912494822370747193
absolute error = 3e-31
relative error = 7.5071176029418609223580647888096e-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 = 0.05916
Order of pole (three term test) = -24.95
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = 3.9973387884756271494694870361715
y[1] (numeric) = 3.9973387884756271494694870361712
absolute error = 3e-31
relative error = 7.5049930935277086471804022180546e-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 = 0.04959
Order of pole (three term test) = -24.97
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (analytic) = 3.9982703005465589289847521090829
y[1] (numeric) = 3.9982703005465589289847521090826
absolute error = 3e-31
relative error = 7.5032445895163802890573184149859e-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 = 0.04001
Order of pole (three term test) = -25
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = 3.9990019872526557523216616734337
y[1] (numeric) = 3.9990019872526557523216616734333
absolute error = 4e-31
relative error = 1.0002495654542122120557853183483e-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 = 0.0304
Order of pole (three term test) = -25.01
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = 3.9995337754258567466871699479512
y[1] (numeric) = 3.9995337754258567466871699479508
absolute error = 4e-31
relative error = 1.0001165697304540480613035180140e-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 = 0.02079
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = 3.9998656118877877473156544782784
y[1] (numeric) = 3.999865611887787747315654478278
absolute error = 4e-31
relative error = 1.0000335981568512814348053266517e-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 = 0.01116
Order of pole (three term test) = -25.03
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = 3.9999974634550790905702286126901
y[1] (numeric) = 3.9999974634550790905702286126897
absolute error = 4e-31
relative error = 1.0000006341366323563709343875914e-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 = 0.001534
Order of pole (three term test) = -25.04
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = 3.9999293169426839232563893135895
y[1] (numeric) = 3.9999293169426839232563893135891
absolute error = 4e-31
relative error = 1.0000176710765904490557758240534e-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] = 3.16
y[1] (analytic) = 3.9996611791651966963198341885479
y[1] (numeric) = 3.9996611791651966963198341885476
absolute error = 3e-31
relative error = 7.5006353428821076199104936946435e-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] = 3.17
y[1] (analytic) = 3.9991930769361717110801767002706
y[1] (numeric) = 3.9991930769361717110801767002703
absolute error = 3e-31
relative error = 7.5015132860210261754651570018446e-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] = 3.18
y[1] (analytic) = 3.9985250570654417861453683077206
y[1] (numeric) = 3.9985250570654417861453683077204
absolute error = 2e-31
relative error = 5.0018443587491742386103345761494e-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] = 3.19
y[1] (analytic) = 3.997657186354437313137901659399
y[1] (numeric) = 3.9976571863544373131379016593987
absolute error = 3e-31
relative error = 7.5043953499568940465513731113535e-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] = 3.2
y[1] (analytic) = 3.9965895515895061693233214445672
y[1] (numeric) = 3.9965895515895061693233214445669
absolute error = 3e-31
relative error = 7.5064000475276553768314583301541e-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] = 3.21
y[1] (analytic) = 3.9953222595332351551442133304085
y[1] (numeric) = 3.9953222595332351551442133304082
absolute error = 3e-31
relative error = 7.5087810322226260200501242469929e-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] = 3.22
y[1] (analytic) = 3.9938554369137738245086854749517
y[1] (numeric) = 3.9938554369137738245086854749514
absolute error = 3e-31
relative error = 7.5115387809785893512646122912770e-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] = 3.23
y[1] (analytic) = 3.9921892304121617754414169891699
y[1] (numeric) = 3.9921892304121617754414169891696
absolute error = 3e-31
relative error = 7.5146738464856633776273392647560e-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] = 3.24
y[1] (analytic) = 3.9903238066476606683576476874849
y[1] (numeric) = 3.9903238066476606683576476874847
absolute error = 2e-31
relative error = 5.0121245716152400014165379387955e-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] = 3.25
y[1] (analytic) = 3.9882593521610924387460584503432
y[1] (numeric) = 3.988259352161092438746058450343
absolute error = 2e-31
relative error = 5.0147190124841627111547735416959e-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] = 3.26
y[1] (analytic) = 3.9859960733961853704253891343433
y[1] (numeric) = 3.9859960733961853704253891343431
absolute error = 2e-31
relative error = 5.0175664079265924540316559927987e-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
bytes used=136060212, alloc=4586680, time=5.35
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = 3.9835341966789298947519234809895
y[1] (numeric) = 3.9835341966789298947519234809893
absolute error = 2e-31
relative error = 5.0206673301998984165173116825552e-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] = 3.28
y[1] (analytic) = 3.9808739681949461801807168322634
y[1] (numeric) = 3.9808739681949461801807168322632
absolute error = 2e-31
relative error = 5.0240224030675934283633736393246e-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] = 3.29
y[1] (analytic) = 3.978015653964865775402750251079
y[1] (numeric) = 3.9780156539648657754027502510787
absolute error = 3e-31
relative error = 7.5414484530997682553965608269443e-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] = 3.3
y[1] (analytic) = 3.9749595398177297678731821022057
y[1] (numeric) = 3.9749595398177297678731821022054
absolute error = 3e-31
relative error = 7.5472466321948118233093997661825e-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] = 3.31
y[1] (analytic) = 3.9717059313624061178926761411711
y[1] (numeric) = 3.9717059313624061178926761411708
absolute error = 3e-31
relative error = 7.5534293118496720361333851579534e-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] = 3.32
y[1] (analytic) = 3.9682551539570290264845791694624
y[1] (numeric) = 3.9682551539570290264845791694621
absolute error = 3e-31
relative error = 7.5599977410940598157688914953730e-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] = 3.33
y[1] (analytic) = 3.9646075526764633931056934297185
y[1] (numeric) = 3.9646075526764633931056934297182
absolute error = 3e-31
relative error = 7.5669532485623518103022979564216e-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] = 3.34
y[1] (analytic) = 3.9607634922777976167177598021398
y[1] (numeric) = 3.9607634922777976167177598021395
absolute error = 3e-31
relative error = 7.5742972430669632817258099947780e-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] = 3.35
y[1] (analytic) = 3.9567233571638681909107887505431
y[1] (numeric) = 3.9567233571638681909107887505427
absolute error = 4e-31
relative error = 1.0109374952276552352187001787664e-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] = 3.36
y[1] (analytic) = 3.9524875513448197405883306155566
y[1] (numeric) = 3.9524875513448197405883306155563
absolute error = 3e-31
relative error = 7.5901567330155429310033542184499e-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] = 3.37
y[1] (analytic) = 3.9480564983977043441789835319417
y[1] (numeric) = 3.9480564983977043441789835319414
absolute error = 3e-31
relative error = 7.5986754526373481908768577600168e-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] = 3.38
y[1] (analytic) = 3.9434306414241241814082506999811
y[1] (numeric) = 3.9434306414241241814082506999808
absolute error = 3e-31
relative error = 7.6075891090519721649221239695131e-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] = 3.39
y[1] (analytic) = 3.938610443005921742330672149345
y[1] (numeric) = 3.9386104430059217423306721493446
absolute error = 4e-31
relative error = 1.0155866029104483227571337831589e-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] = 3.4
y[1] (analytic) = 3.9335963851589220285644030795314
y[1] (numeric) = 3.933596385158922028564403079531
absolute error = 4e-31
relative error = 1.0168811459893578241303158859441e-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] = 3.41
y[1] (analytic) = 3.9283889692847313724695672819059
y[1] (numeric) = 3.9283889692847313724695672819055
absolute error = 4e-31
relative error = 1.0182291089999438974358807571251e-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] = 3.42
y[1] (analytic) = 3.9229887161205976943483002912028
y[1] (numeric) = 3.9229887161205976943483002912024
absolute error = 4e-31
relative error = 1.0196307686440551261108806491260e-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] = 3.43
y[1] (analytic) = 3.9173961656873372115989792824511
y[1] (numeric) = 3.9173961656873372115989792824507
absolute error = 4e-31
relative error = 1.0210864132242211739472769646565e-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] = 3.44
y[1] (analytic) = 3.911611877235332807110330025945
y[1] (numeric) = 3.9116118772353328071103300259446
absolute error = 4e-31
relative error = 1.0225963427708831277063255615682e-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] = 3.45
y[1] (analytic) = 3.9056364291886094570135702798955
y[1] (numeric) = 3.9056364291886094570135702798951
absolute error = 4e-31
relative error = 1.0241608691751665281720787773777e-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] = 3.46
y[1] (analytic) = 3.8994704190869923102032107515641
y[1] (numeric) = 3.8994704190869923102032107515637
absolute error = 4e-31
relative error = 1.0257803163272989558538584617865e-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] = 3.47
y[1] (analytic) = 3.8931144635263532037703601070534
y[1] (numeric) = 3.893114463526353203770360107053
absolute error = 4e-31
relative error = 1.0274550202607787436009427328340e-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] = 3.48
y[1] (analytic) = 3.8865691980969515896471962947646
y[1] (numeric) = 3.8865691980969515896471962947642
absolute error = 4e-31
relative error = 1.0291853293024062211184535105731e-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] = 3.49
y[1] (analytic) = 3.8798352773198760383185573455335
y[1] (numeric) = 3.8798352773198760383185573455332
absolute error = 3e-31
relative error = 7.7322870317122039655999403418772e-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] = 3.5
y[1] (analytic) = 3.8729133745815926753973152533435
y[1] (numeric) = 3.8729133745815926753973152533432
absolute error = 3e-31
relative error = 7.7461066381948260731688050432408e-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] = 3.51
y[1] (analytic) = 3.8658041820666070961653326115152
y[1] (numeric) = 3.8658041820666070961653326115148
absolute error = 4e-31
relative error = 1.0347135580627505085912137150576e-29 %
Correct digits = 31
h = 0.01
bytes used=140061176, alloc=4586680, time=5.51
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] = 3.52
y[1] (analytic) = 3.8585084106882464918324330245445
y[1] (numeric) = 3.8585084106882464918324330245441
absolute error = 4e-31
relative error = 1.0366700222603675740054825400097e-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] = 3.53
y[1] (analytic) = 3.851026790017568909243078029368
y[1] (numeric) = 3.8510267900175689092430780293677
absolute error = 3e-31
relative error = 7.7901301745717369860133290704960e-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] = 3.54
y[1] (analytic) = 3.8433600682104067530455377722595
y[1] (numeric) = 3.8433600682104067530455377722592
absolute error = 3e-31
relative error = 7.8056699001842349216386114073820e-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] = 3.55
y[1] (analytic) = 3.8355090119325518259125416454209
y[1] (numeric) = 3.8355090119325518259125416454206
absolute error = 3e-31
relative error = 7.8216476370327339101747732024105e-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] = 3.56
y[1] (analytic) = 3.8274744062830893882470412262073
y[1] (numeric) = 3.827474406283089388247041226207
absolute error = 3e-31
relative error = 7.8380667812573026699566164748626e-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] = 3.57
y[1] (analytic) = 3.8192570547158889039032268720735
y[1] (numeric) = 3.8192570547158889039032268720732
absolute error = 3e-31
relative error = 7.8549308334606645136795719277057e-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] = 3.58
y[1] (analytic) = 3.810857778959259322782801709098
y[1] (numeric) = 3.8108577789592593227828017090978
absolute error = 2e-31
relative error = 5.2481622668852197238869066720920e-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] = 3.59
y[1] (analytic) = 3.8022774189337769347112996786957
y[1] (numeric) = 3.8022774189337769347112996786954
absolute error = 3e-31
relative error = 7.8900081963016019815339154370611e-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] = 3.6
y[1] (analytic) = 3.7935168326682940117405834505319
y[1] (numeric) = 3.7935168326682940117405834505316
absolute error = 3e-31
relative error = 7.9082290453153254614431658948879e-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] = 3.61
y[1] (analytic) = 3.7845768962141366379432993870768
y[1] (numeric) = 3.7845768962141366379432993870766
absolute error = 2e-31
relative error = 5.2846065883895234011144949020697e-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] = 3.62
y[1] (analytic) = 3.775458503557500306844808544136
y[1] (numeric) = 3.7754585035575003068448085441358
absolute error = 2e-31
relative error = 5.2973698376381584321829567878835e-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] = 3.63
y[1] (analytic) = 3.766162566530052046859847088796
y[1] (numeric) = 3.7661625665300520468598470887958
absolute error = 2e-31
relative error = 5.3104452202197337759013344406152e-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] = 3.64
y[1] (analytic) = 3.7566900147177480144468744882682
y[1] (numeric) = 3.756690014717748014446874488268
absolute error = 2e-31
relative error = 5.3238355897465932296158246825700e-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] = 3.65
y[1] (analytic) = 3.7470417953678756731448089490565
y[1] (numeric) = 3.7470417953678756731448089490564
absolute error = 1e-31
relative error = 2.6687719396036850787911526187058e-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] = 3.66
y[1] (analytic) = 3.7372188732943298541967818403199
y[1] (numeric) = 3.7372188732943298541967818403197
absolute error = 2e-31
relative error = 5.3515731023722870589964895782512e-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] = 3.67
y[1] (analytic) = 3.7272222307811321710759123729596
y[1] (numeric) = 3.7272222307811321710759123729595
absolute error = 1e-31
relative error = 2.6829631776220252764878413694650e-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] = 3.68
y[1] (analytic) = 3.7170528674842034358912497370723
y[1] (numeric) = 3.7170528674842034358912497370722
absolute error = 1e-31
relative error = 2.6903034087777869224155574042177e-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] = 3.69
y[1] (analytic) = 3.7067118003313989003503860567443
y[1] (numeric) = 3.7067118003313989003503860567442
absolute error = 1e-31
relative error = 2.6978088771579028897672490323384e-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] = 3.7
y[1] (analytic) = 3.6962000634208163176713402127088
y[1] (numeric) = 3.6962000634208163176713402127087
absolute error = 1e-31
relative error = 2.7054812587024971703172639057409e-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] = 3.71
y[1] (analytic) = 3.6855187079173869945527783452195
y[1] (numeric) = 3.6855187079173869945527783452194
absolute error = 1e-31
relative error = 2.7133222736103814963377584601765e-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] = 3.72
y[1] (analytic) = 3.6746688019477601740112001789793
y[1] (numeric) = 3.6746688019477601740112001789792
absolute error = 1e-31
relative error = 2.7213336871882153362773104072683e-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] = 3.73
y[1] (analytic) = 3.6636514304934912605592113958433
y[1] (numeric) = 3.6636514304934912605592113958431
absolute error = 2e-31
relative error = 5.4590346214530605940376679683122e-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] = 3.74
y[1] (analytic) = 3.6524676952825445688133547124051
y[1] (numeric) = 3.6524676952825445688133547124049
absolute error = 2e-31
relative error = 5.4757500048067794275076109914291e-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] = 3.75
y[1] (analytic) = 3.6411187146791214451662248045814
y[1] (numeric) = 3.6411187146791214451662248045813
absolute error = 1e-31
relative error = 2.7464086682164834728384455873944e-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=144063072, alloc=4586680, time=5.67
x[1] = 3.76
y[1] (analytic) = 3.6296056235718247796188902751262
y[1] (numeric) = 3.6296056235718247796188902751261
absolute error = 1e-31
relative error = 2.7551202629444884907316082924142e-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] = 3.77
y[1] (analytic) = 3.6179295732601710912292434923924
y[1] (numeric) = 3.6179295732601710912292434923923
absolute error = 1e-31
relative error = 2.7640117911385568135073772000287e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.53
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] = 3.78
y[1] (analytic) = 3.6060917313394615358731605184754
y[1] (numeric) = 3.6060917313394615358731605184753
absolute error = 1e-31
relative error = 2.7730853081448260591099923792344e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.84
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] = 3.79
y[1] (analytic) = 3.5940932815840233491217545036803
y[1] (numeric) = 3.5940932815840233491217545036802
absolute error = 1e-31
relative error = 2.7823429211588809535908048689729e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.15
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] = 3.8
y[1] (analytic) = 3.5819354238288333999931363487015
y[1] (numeric) = 3.5819354238288333999931363487013
absolute error = 2e-31
relative error = 5.5835735806262601415574672630399e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.47
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] = 3.81
y[1] (analytic) = 3.5696193738495356931246607487299
y[1] (numeric) = 3.5696193738495356931246607487298
absolute error = 1e-31
relative error = 2.8014191297980986326953936334332e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.79
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] = 3.82
y[1] (analytic) = 3.5571463632408648175154553133124
y[1] (numeric) = 3.5571463632408648175154553133123
absolute error = 1e-31
relative error = 2.8112422090186764289555242623877e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.12
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] = 3.83
y[1] (analytic) = 3.544517639293487499393045054047
y[1] (numeric) = 3.5445176392934874993930450540469
absolute error = 1e-31
relative error = 2.8212583537863996338841440729793e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.45
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) = 3.5317344648692745749461538804954
y[1] (numeric) = 3.5317344648692745749461538804953
absolute error = 1e-31
relative error = 2.8314699475488866098602686370195e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 16.79
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] = 3.85
y[1] (analytic) = 3.5187981182750158556224701479056
y[1] (numeric) = 3.5187981182750158556224701479055
absolute error = 1e-31
relative error = 2.8418794326575907575984933628360e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.14
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] = 3.86
y[1] (analytic) = 3.5057098931345905143996092187297
y[1] (numeric) = 3.5057098931345905143996092187296
absolute error = 1e-31
relative error = 2.8524893116750781854333729379013e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.49
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] = 3.87
y[1] (analytic) = 3.4924710982596057758841216186546
y[1] (numeric) = 3.4924710982596057758841216186545
absolute error = 1e-31
relative error = 2.8633021487230845006952928139537e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 17.84
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] = 3.88
y[1] (analytic) = 3.4790830575185168462617361540826
y[1] (numeric) = 3.4790830575185168462617361540825
absolute error = 1e-31
relative error = 2.8743205708726534614737939116942e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.2
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] = 3.89
y[1] (analytic) = 3.4655471097042411709967766052634
y[1] (numeric) = 3.4655471097042411709967766052633
absolute error = 1e-31
relative error = 2.8855472695777106551824517790954e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.57
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] = 3.9
y[1] (analytic) = 3.4518646084002802587446609692287
y[1] (numeric) = 3.4518646084002802587446609692286
absolute error = 1e-31
relative error = 2.8969850021534778845412362295161e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.95
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] = 3.91
y[1] (analytic) = 3.4380369218453624591835272277488
y[1] (numeric) = 3.4380369218453624591835272277487
absolute error = 1e-31
relative error = 2.9086365933011886397411117951715e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.33
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] = 3.92
y[1] (analytic) = 3.4240654327966202303744051685852
y[1] (numeric) = 3.4240654327966202303744051685851
absolute error = 1e-31
relative error = 2.9205049366806220204649101186751e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 19.27
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) = 3.4099515383913155778091796790539
y[1] (numeric) = 3.4099515383913155778091796790538
absolute error = 1e-31
relative error = 2.9325929965320318511467696692693e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.89
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] = 3.94
y[1] (analytic) = 3.3956966500071274924872122988712
y[1] (numeric) = 3.3956966500071274924872122988711
absolute error = 1e-31
relative error = 2.9449038093491096209148427145464e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.51
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] = 3.95
y[1] (analytic) = 3.3813021931210153591603866232805
y[1] (numeric) = 3.3813021931210153591603866232804
absolute error = 1e-31
relative error = 2.9574404856046843954592025702338e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 18.15
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] = 3.96
y[1] (analytic) = 3.366769607166672448288139617503
y[1] (numeric) = 3.366769607166672448288139617503
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 = 17.79
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] = 3.97
y[1] (analytic) = 3.3521003453905837462344949786387
y[1] (numeric) = 3.3521003453905837462344949786387
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 = 17.43
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] = 3.98
y[1] (analytic) = 3.3372958747067025178041274333497
y[1] (numeric) = 3.3372958747067025178041274333497
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 = 17.09
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] = 3.99
y[1] (analytic) = 3.3223576755497601333401019040203
y[1] (numeric) = 3.3223576755497601333401019040203
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 = 16.74
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
y[1] (analytic) = 3.3072872417272238292783363661955
y[1] (numeric) = 3.3072872417272238292783363661955
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 = 16.41
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
bytes used=148064344, alloc=4586680, time=5.83
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = 3.2920860802699172062593648293701
y[1] (numeric) = 3.2920860802699172062593648293701
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 = 16.08
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] = 4.02
y[1] (analytic) = 3.2767557112813184026231067615307
y[1] (numeric) = 3.2767557112813184026231067615308
absolute error = 1e-31
relative error = 3.0517990601410056604840487493127e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.76
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) = 3.2612976677855510133437090437049
y[1] (numeric) = 3.261297667785551013343709043705
absolute error = 1e-31
relative error = 3.0662641128339828781976115592758e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.44
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] = 4.04
y[1] (analytic) = 3.2457134955740829551858931583454
y[1] (numeric) = 3.2457134955740829551858931583455
absolute error = 1e-31
relative error = 3.0809866655316901500461106874257e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 15.13
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] = 4.05
y[1] (analytic) = 3.2300047530511486080685414569647
y[1] (numeric) = 3.2300047530511486080685414569649
absolute error = 2e-31
relative error = 6.1919413527510963444593853109260e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.82
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) = 3.2141730110779096902925716955787
y[1] (numeric) = 3.2141730110779096902925716955788
absolute error = 1e-31
relative error = 3.1112202005101105609856869260315e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.52
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) = 3.1982198528153704514157115460792
y[1] (numeric) = 3.1982198528153704514157115460793
absolute error = 1e-31
relative error = 3.1267393926021284324123177287496e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 14.22
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] = 4.08
y[1] (analytic) = 3.1821468735660628911239820364958
y[1] (numeric) = 3.1821468735660628911239820364959
absolute error = 1e-31
relative error = 3.1425325094418195203946707540015e-30 %
Correct digits = 32
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 13.92
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] = 4.09
y[1] (analytic) = 3.1659556806145178354460742272886
y[1] (numeric) = 3.1659556806145178354460742272886
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] = 4.1
y[1] (analytic) = 3.1496478930665378230700573593196
y[1] (numeric) = 3.1496478930665378230700573593196
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] = 4.11
y[1] (analytic) = 3.1332251416872878743398479877489
y[1] (numeric) = 3.133225141687287874339847987749
absolute error = 1e-31
relative error = 3.1915995652373875545459926182738e-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] = 4.12
y[1] (analytic) = 3.1166890687382203337196165455186
y[1] (numeric) = 3.1166890687382203337196165455186
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] = 4.13
y[1] (analytic) = 3.100041327812850093105989384141
y[1] (numeric) = 3.100041327812850093105989384141
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] = 4.14
y[1] (analytic) = 3.0832835836713966183288615471946
y[1] (numeric) = 3.0832835836713966183288615471946
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] = 4.15
y[1] (analytic) = 3.0664175120743093145003723433254
y[1] (numeric) = 3.0664175120743093145003723433254
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] = 4.16
y[1] (analytic) = 3.0494447996146928775367804214184
y[1] (numeric) = 3.0494447996146928775367804214184
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] = 4.17
y[1] (analytic) = 3.0323671435496493891784410855156
y[1] (numeric) = 3.0323671435496493891784410855155
absolute error = 1e-31
relative error = 3.2977537107509120927131822853741e-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] = 4.18
y[1] (analytic) = 3.0151862516305540211578360660934
y[1] (numeric) = 3.0151862516305540211578360660934
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] = 4.19
y[1] (analytic) = 2.9979038419322813208038025029849
y[1] (numeric) = 2.9979038419322813208038025029848
absolute error = 1e-31
relative error = 3.3356640263533465134092578897236e-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] = 4.2
y[1] (analytic) = 2.9805216426813991553110897627543
y[1] (numeric) = 2.9805216426813991553110897627542
absolute error = 1e-31
relative error = 3.3551173918011180954401442753502e-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] = 4.21
y[1] (analytic) = 2.9630413920833474951376458989737
y[1] (numeric) = 2.9630413920833474951376458989736
absolute error = 1e-31
relative error = 3.3749106666946992313962498559020e-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] = 4.22
y[1] (analytic) = 2.9454648381486193185072768263104
y[1] (numeric) = 2.9454648381486193185072768263103
absolute error = 1e-31
relative error = 3.3950498646201900451347112316034e-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] = 4.23
y[1] (analytic) = 2.9277937385179610187823791790897
y[1] (numeric) = 2.9277937385179610187823791790896
absolute error = 1e-31
relative error = 3.4155411525205204960880784747755e-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] = 4.24
y[1] (analytic) = 2.9100298602866097945203437394119
y[1] (numeric) = 2.9100298602866097945203437394118
absolute error = 1e-31
relative error = 3.4363908551148326440622672861197e-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] = 4.25
y[1] (analytic) = 2.8921749798275855983281554410897
y[1] (numeric) = 2.8921749798275855983281554410896
absolute error = 1e-31
relative error = 3.4576054594719372672645682229952e-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=152065500, alloc=4586680, time=5.98
x[1] = 4.26
y[1] (analytic) = 2.874230882614055315173048270972
y[1] (numeric) = 2.8742308826140553151730482709719
absolute error = 1e-31
relative error = 3.4791916197439228173287427509077e-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] = 4.27
y[1] (analytic) = 2.8561993630407869335833546441886
y[1] (numeric) = 2.8561993630407869335833546441885
absolute error = 1e-31
relative error = 3.5011561620662677026697629336598e-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] = 4.28
y[1] (analytic) = 2.8380822242447115641736414736721
y[1] (numeric) = 2.838082224244711564173641473672
absolute error = 1e-31
relative error = 3.5235060896310935470032471212809e-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] = 4.29
y[1] (analytic) = 2.8198812779246112491427492675585
y[1] (numeric) = 2.8198812779246112491427492675584
absolute error = 1e-31
relative error = 3.5462485879404981287563707948899e-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] = 4.3
y[1] (analytic) = 2.8015983441599505938135247926721
y[1] (numeric) = 2.801598344159950593813524792672
absolute error = 1e-31
relative error = 3.5693910302472229706455336380633e-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] = 4.31
y[1] (analytic) = 2.7832352512288703369001201936885
y[1] (numeric) = 2.7832352512288703369001201936884
absolute error = 1e-31
relative error = 3.5929409831902428670105256687859e-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] = 4.32
y[1] (analytic) = 2.7647938354253610599941603188602
y[1] (numeric) = 2.7647938354253610599941603188601
absolute error = 1e-31
relative error = 3.6169062126332139117688940876409e-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] = 4.33
y[1] (analytic) = 2.7462759408756353187464749013257
y[1] (numeric) = 2.7462759408756353187464749013257
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] = 4.34
y[1] (analytic) = 2.7276834193537165583782547088473
y[1] (numeric) = 2.7276834193537165583782547088473
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] = 4.35
y[1] (analytic) = 2.7090181300962632544764051548717
y[1] (numeric) = 2.7090181300962632544764051548717
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] = 4.36
y[1] (analytic) = 2.6902819396166467965047051339269
y[1] (numeric) = 2.6902819396166467965047051339268
absolute error = 1e-31
relative error = 3.7170825305488076449497641324066e-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] = 4.37
y[1] (analytic) = 2.6714767215183017060874853848457
y[1] (numeric) = 2.6714767215183017060874853848456
absolute error = 1e-31
relative error = 3.7432480393527891628200396906084e-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] = 4.38
y[1] (analytic) = 2.6526043563073668548884570476882
y[1] (numeric) = 2.6526043563073668548884570476881
absolute error = 1e-31
relative error = 3.7698799582463114427332273735060e-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] = 4.39
y[1] (analytic) = 2.6336667312046364178067707335115
y[1] (numeric) = 2.6336667312046364178067707335114
absolute error = 1e-31
relative error = 3.7969876300278928696899242934907e-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] = 4.4
y[1] (analytic) = 2.6146657399568393662382794844354
y[1] (numeric) = 2.6146657399568393662382794844353
absolute error = 1e-31
relative error = 3.8245806518140522714789189995086e-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] = 4.41
y[1] (analytic) = 2.5956032826472663732954129329813
y[1] (numeric) = 2.5956032826472663732954129329811
absolute error = 2e-31
relative error = 7.7053377662559890263766848497259e-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] = 4.42
y[1] (analytic) = 2.5764812655057630681373302869864
y[1] (numeric) = 2.5764812655057630681373302869863
absolute error = 1e-31
relative error = 3.8812624542942293791024037924885e-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] = 4.43
y[1] (analytic) = 2.5573016007181086399265806978673
y[1] (numeric) = 2.5573016007181086399265806978672
absolute error = 1e-31
relative error = 3.9103717751523434869543981799336e-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] = 4.44
y[1] (analytic) = 2.5380662062347988533930247123268
y[1] (numeric) = 2.5380662062347988533930247123267
absolute error = 1e-31
relative error = 3.9400075441037926755660692309145e-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] = 4.45
y[1] (analytic) = 2.5187770055792525975441134594889
y[1] (numeric) = 2.5187770055792525975441134594888
absolute error = 1e-31
relative error = 3.9701807575062654200683556442469e-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] = 4.46
y[1] (analytic) = 2.4994359276554611467068272022253
y[1] (numeric) = 2.4994359276554611467068272022252
absolute error = 1e-31
relative error = 4.0009027194308885020917627543848e-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] = 4.47
y[1] (analytic) = 2.4800449065550993688148773106603
y[1] (numeric) = 2.4800449065550993688148773106602
absolute error = 1e-31
relative error = 4.0321850517983066806621672466604e-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] = 4.48
y[1] (analytic) = 2.4606058813641181696596028136977
y[1] (numeric) = 2.4606058813641181696596028136976
absolute error = 1e-31
relative error = 4.0640397049104709106496876647709e-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] = 4.49
y[1] (analytic) = 2.4411207959688375136989640130322
y[1] (numeric) = 2.4411207959688375136989640130321
absolute error = 1e-31
relative error = 4.0964789683958173406733440034490e-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] = 4.5
y[1] (analytic) = 2.4215915988615594119609636495877
y[1] (numeric) = 2.4215915988615594119609636495876
absolute error = 1e-31
relative error = 4.1295154825864146680687126966162e-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=156066596, alloc=4586680, time=6.14
x[1] = 4.51
y[1] (analytic) = 2.4020202429457203155807166434815
y[1] (numeric) = 2.4020202429457203155807166434815
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] = 4.52
y[1] (analytic) = 2.3824086853406023995694422363978
y[1] (numeric) = 2.3824086853406023995694422363977
absolute error = 1e-31
relative error = 4.1974326493736503347208933691486e-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] = 4.53
y[1] (analytic) = 2.3627588871856232655242615827628
y[1] (numeric) = 2.3627588871856232655242615827627
absolute error = 1e-31
relative error = 4.2323404449919985194791392336668e-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] = 4.54
y[1] (analytic) = 2.3430728134442236341454384391956
y[1] (numeric) = 2.3430728134442236341454384391955
absolute error = 1e-31
relative error = 4.2678998034638106823258605856865e-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] = 4.55
y[1] (analytic) = 2.3233524327073726386283848500159
y[1] (numeric) = 2.3233524327073726386283848500158
absolute error = 1e-31
relative error = 4.3041253058396865402557992080671e-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] = 4.56
y[1] (analytic) = 2.3035997169967103682373475852198
y[1] (numeric) = 2.3035997169967103682373475852197
absolute error = 1e-31
relative error = 4.3410319623746856002179814072745e-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] = 4.57
y[1] (analytic) = 2.2838166415673473476423706287492
y[1] (numeric) = 2.2838166415673473476423706287491
absolute error = 1e-31
relative error = 4.3786352275361115198056476191367e-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] = 4.58
y[1] (analytic) = 2.2640051847103406719072668013646
y[1] (numeric) = 2.2640051847103406719072668013645
absolute error = 1e-31
relative error = 4.4169510156309165269893879563386e-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] = 4.59
y[1] (analytic) = 2.244167327554866549350497048793
y[1] (numeric) = 2.2441673275548665493504970487929
absolute error = 1e-31
relative error = 4.4559957170820698935084701819744e-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] = 4.6
y[1] (analytic) = 2.2243050538701090348598156424584
y[1] (numeric) = 2.2243050538701090348598156424583
absolute error = 1e-31
relative error = 4.4957862153848084591819074827995e-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] = 4.61
y[1] (analytic) = 2.2044203498668847646222576563454
y[1] (numeric) = 2.2044203498668847646222576563453
absolute error = 1e-31
relative error = 4.5363399047753555505771014786574e-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] = 4.62
y[1] (analytic) = 2.1845152039990235296306835512316
y[1] (numeric) = 2.1845152039990235296306835512316
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] = 4.63
y[1] (analytic) = 2.1645916067645245497440145748052
y[1] (numeric) = 2.1645916067645245497440145748052
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] = 4.64
y[1] (analytic) = 2.1446515505065083325080504015202
y[1] (numeric) = 2.1446515505065083325080504015202
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] = 4.65
y[1] (analytic) = 2.1246970292139840213851140323542
y[1] (numeric) = 2.1246970292139840213851140323541
absolute error = 1e-31
relative error = 4.7065533873784471599150664009714e-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] = 4.66
y[1] (analytic) = 2.1047300383224521564916743335919
y[1] (numeric) = 2.1047300383224521564916743335919
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] = 4.67
y[1] (analytic) = 2.0847525745143627874017086402106
y[1] (numeric) = 2.0847525745143627874017086402105
absolute error = 1e-31
relative error = 4.7967322943968406903304045188291e-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] = 4.68
y[1] (analytic) = 2.0647666355194488920382407358891
y[1] (numeric) = 2.0647666355194488920382407358891
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] = 4.69
y[1] (analytic) = 2.044774219914955068144776792884
y[1] (numeric) = 2.044774219914955068144776792884
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] = 4.7
y[1] (analytic) = 2.0247773269257814743010165926542
y[1] (numeric) = 2.0247773269257814743010165926542
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] = 4.71
y[1] (analytic) = 2.0047779562245630059221922954494
y[1] (numeric) = 2.0047779562245630059221922954494
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] = 4.72
y[1] (analytic) = 1.9847781077317036981578346936507
y[1] (numeric) = 1.9847781077317036981578346936507
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 = 0.007339
Order of pole (three term test) = -0.8943
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = 1.9647797814153863520830396301143
y[1] (numeric) = 1.9647797814153863520830396301143
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 = 0.01698
Order of pole (three term test) = -0.9004
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = 1.944784977091577383052957365562
y[1] (numeric) = 1.944784977091577383052957365562
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 = 0.02661
Order of pole (three term test) = -0.9113
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = 1.9247956942240468905690073752533
y[1] (numeric) = 1.9247956942240468905690073752533
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 = 0.03623
Order of pole (three term test) = -0.927
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
bytes used=160067380, alloc=4652204, time=6.29
x[1] = 4.76
y[1] (analytic) = 1.9048139317244239474831825671789
y[1] (numeric) = 1.9048139317244239474831825671789
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 = 0.04584
Order of pole (three term test) = -0.9476
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = 1.8848416877523071028449024544255
y[1] (numeric) = 1.8848416877523071028449024544254
absolute error = 1e-31
relative error = 5.3054853704584079860519453085827e-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 = 0.05543
Order of pole (three term test) = -0.973
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = 1.8648809595154500871735565706809
y[1] (numeric) = 1.8648809595154500871735565706808
absolute error = 1e-31
relative error = 5.3622725616750833802878716448076e-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 = 0.065
Order of pole (three term test) = -1.003
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (analytic) = 1.8449337430700427014196995173048
y[1] (numeric) = 1.8449337430700427014196995173047
absolute error = 1e-31
relative error = 5.4202488504327556917303717753508e-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 = 0.07454
Order of pole (three term test) = -1.038
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = 1.825002033121106861359569484701
y[1] (numeric) = 1.8250020331211068613595694847009
absolute error = 1e-31
relative error = 5.4794459504782379050358995417346e-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 = 0.08405
Order of pole (three term test) = -1.078
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = 1.8050878228230277576521547209232
y[1] (numeric) = 1.8050878228230277576521547209231
absolute error = 1e-31
relative error = 5.5398966596321712233003319840919e-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 = 0.09353
Order of pole (three term test) = -1.122
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = 1.7851931035802400782765787616605
y[1] (numeric) = 1.7851931035802400782765787616603
absolute error = 2e-31
relative error = 1.1203269808677618361412225977487e-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 = 0.103
Order of pole (three term test) = -1.172
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = 1.7653198648480892245614664220924
y[1] (numeric) = 1.7653198648480892245614664220922
absolute error = 2e-31
relative error = 1.1329391572739740658309354887712e-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 = 0.1124
Order of pole (three term test) = -1.226
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = 1.7454700939338874345187391805346
y[1] (numeric) = 1.7454700939338874345187391805345
absolute error = 1e-31
relative error = 5.7291156318022636556024786906784e-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 = 0.1217
Order of pole (three term test) = -1.284
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = 1.7256457757981847077037205630694
y[1] (numeric) = 1.7256457757981847077037205630693
absolute error = 1e-31
relative error = 5.7949320423970405291180884372253e-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 = 0.131
Order of pole (three term test) = -1.348
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = 1.7058488928562744043434585080292
y[1] (numeric) = 1.7058488928562744043434585080291
absolute error = 1e-31
relative error = 5.8621839495150089357840100419421e-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 = 0.1403
Order of pole (three term test) = -1.416
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = 1.6860814247799533680079404287439
y[1] (numeric) = 1.6860814247799533680079404287438
absolute error = 1e-31
relative error = 5.9309116707131016153521868418806e-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 = 0.1495
Order of pole (three term test) = -1.488
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = 1.6663453482995563956467345059368
y[1] (numeric) = 1.6663453482995563956467345059366
absolute error = 2e-31
relative error = 1.2002313938349729228642100357713e-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 = 0.1586
Order of pole (three term test) = -1.566
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (analytic) = 1.6466426370062848513790828205723
y[1] (numeric) = 1.6466426370062848513790828205722
absolute error = 1e-31
relative error = 6.0729631161383757667052432978067e-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 = 0.1677
Order of pole (three term test) = -1.648
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = 1.6269752611548491910113417117562
y[1] (numeric) = 1.626975261154849191011341711756
absolute error = 2e-31
relative error = 1.2292749912991134055521807762218e-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 = 0.1767
Order of pole (three term test) = -1.734
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = 1.6073451874664451328648536009612
y[1] (numeric) = 1.607345187466445132864853600961
absolute error = 2e-31
relative error = 1.2442877955496736830573012850513e-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 = 0.1856
Order of pole (three term test) = -1.825
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = 1.5877543789320831771329815183765
y[1] (numeric) = 1.5877543789320831771329815183762
absolute error = 3e-31
relative error = 1.8894610147558133039501493106762e-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 = 0.1945
Order of pole (three term test) = -1.92
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = 1.5682047946162911406514791070285
y[1] (numeric) = 1.5682047946162911406514791070282
absolute error = 3e-31
relative error = 1.9130154494483872407901537504633e-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 = 0.2033
Order of pole (three term test) = -2.02
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = 1.5486983894612093366651383919206
y[1] (numeric) = 1.5486983894612093366651383919203
absolute error = 3e-31
relative error = 1.9371105571070536736444032636851e-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 = 0.212
Order of pole (three term test) = -2.124
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = 1.5292371140910979899094851767305
y[1] (numeric) = 1.5292371140910979899094851767303
absolute error = 2e-31
relative error = 1.3078416561899231109043080697272e-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 = 0.2206
Order of pole (three term test) = -2.232
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = 1.5098229146172764361031039541294
y[1] (numeric) = 1.5098229146172764361031039541291
absolute error = 3e-31
relative error = 1.9869879910787200665622309949807e-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 = 0.2291
Order of pole (three term test) = -2.345
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = 1.4904577324435136117680929719749
y[1] (numeric) = 1.4904577324435136117680929719747
absolute error = 2e-31
relative error = 1.3418696528355240494327011818336e-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 = 0.2375
Order of pole (three term test) = -2.462
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = 1.4711435040718892951674933586384
y[1] (numeric) = 1.4711435040718892951674933586382
absolute error = 2e-31
relative error = 1.3594866812546299770732698998444e-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 = 0.2459
Order of pole (three term test) = -2.583
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = 1.4518821609091455120738168046061
y[1] (numeric) = 1.4518821609091455120738168046059
absolute error = 2e-31
relative error = 1.3775222630655037573794760349050e-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 = 0.2541
Order of pole (three term test) = -2.709
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ;
Iterations = 1000
Total Elapsed Time = 6 Seconds
Elapsed Time(since restart) = 6 Seconds
Time to Timeout = 2 Minutes 53 Seconds
Percent Done = 100.1 %
> quit
bytes used=163912544, alloc=4652204, time=6.44