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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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> #BEGIN OUTFILE1
> # Begin Function number 3
> display_poles := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ;
> local rad_given;
> if (glob_type_given_pole = 4) then # if number 1
> rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 2;
> if (array_poles[1,1] <> glob_large_float) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 2;
> if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 2;
> if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 2
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_large_float, array_pole,
glob_type_given_pole, array_given_rad_poles, array_given_ord_poles,
array_complex_poles, array_poles, array_real_poles, array_x;
if glob_type_given_pole = 4 then
rad_given := sqrt(
expt(array_x[1] - array_given_rad_poles[1, 1], 2.0)
+ expt(array_given_rad_poles[1, 2], 2.0));
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ")
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_poles[1, 1], 4, " ");
omniout_str(ALWAYS, "Order of pole (ratio test) \
Not computed")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if 0. < array_real_poles[1, 1] and
array_real_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_real_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_real_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if 0. < array_complex_poles[1, 1] and
array_complex_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_complex_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
> # End Function number 3
> # Begin Function number 4
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 2
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 2;
> ret;;
> end;
check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
> # End Function number 4
> # Begin Function number 5
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 2
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> if (min_size < 1.0) then # if number 2
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_pole, array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y[1]) < min_size then
min_size := omniabs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 5
> # Begin Function number 6
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 2
> max_estimated_step_error := est_tmp;
> fi;# end if 2;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_pole, array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
max_estimated_step_error := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := omniabs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
> # End Function number 6
> # Begin Function number 7
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2
> ret := true;
> else
> ret := false;
> fi;# end if 2;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_pole, array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 7
> # Begin Function number 8
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 2
> if (iter >= 0) then # if number 3
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 4
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 5
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 5;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 4;
> if (glob_iter = 1) then # if number 4
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 4;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 3;
> #BOTTOM DISPLAY ALOT
> fi;# end if 2;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_pole, array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 8
> # Begin Function number 9
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 3
> glob_normmax := tmp;
> fi;# end if 3
> fi;# end if 2;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 3
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 3
> fi;# end if 2;
> if ( not glob_reached_optimal_h) then # if number 2
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 2;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_pole, array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 9
> # Begin Function number 10
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 2
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 2;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_pole, array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # End Function number 10
> # Begin Function number 11
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad;
> #TOP CHECK FOR POLE
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> #TOP radius ratio test in Henrici1
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3
> if (tmp_rad < rad_c) then # if number 4
> rad_c := tmp_rad;
> fi;# end if 4;
> elif
> (cnt = 0) then # if number 4
> if (tmp_rad < rad_c) then # if number 5
> rad_c := tmp_rad;
> fi;# end if 5;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5
> fi;# end if 4;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 4
> if (rad_c < array_pole[1]) then # if number 5
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 5;
> fi;# end if 4;
> #BOTTOM radius ratio test in Henrici1
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 4
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 5
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[1,1] := rcs;
> array_real_poles[1,2] := ord_no;
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 5
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 4;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 1
> if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 4;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 4
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) <> 0.0) then # if number 7
> if (rcs > 0.0) then # if number 8
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 8
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> fi;# end if 5;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 4;
> #BOTTOM RADII COMPLEX EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 4;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 4
> display_poles();
> fi;# end if 4
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test,
tmp_rad, tmp_ratio, prev_tmp_rad;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_pole, array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_y_higher[1, n]) = 0. or
omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[1, 1] := rad_c
end if
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or
omniabs(array_y_higher[1, m - 1]) = 0. or
omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[1, 1] := rcs;
array_real_poles[1, 2] := ord_no
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if omniabs(rcs) <> 0. then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_poles[1, 1] := rad_c;
array_complex_poles[1, 2] := ord_no
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
> # End Function number 11
> # Begin Function number 12
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 4
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 1;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 5;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 4;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_pole, array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 12
> # Begin Function number 13
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D2[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] + array_const_0D3[1];
> #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := expt(array_tmp2[1] , array_tmp4[1] ) ;
> array_tmp5_a1[1] := ln(array_tmp2[1] ) ;
> array_tmp5_a1[2] := array_tmp2[2] / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D2[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp5_a2[1] := (array_tmp5_a1[1] * array_tmp4[2] + array_tmp5_a1[2] * array_tmp4[1]) / glob_h;
> array_tmp5[2] := array_tmp5[1] * array_tmp5_a2[1] * glob_h;
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp6[2] := array_tmp5[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_tmp6[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp5_a1[3] := -array_tmp5_a1[2] * array_tmp2[2] * 1 / array_tmp2[1] / 2;
> array_tmp5_a2[2] := (array_tmp5_a1[2] * array_tmp4[2] + array_tmp5_a1[3] * array_tmp4[1]) * 2 / glob_h;
> array_tmp5[3] := ats(2,array_tmp5,array_tmp5_a2,1)*glob_h/2;
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp6[3] := array_tmp5[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_tmp6[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 4
> array_tmp5_a1[4] := -array_tmp5_a1[3] * array_tmp2[2] * 2 / array_tmp2[1] / 3;
> array_tmp5_a2[3] := (array_tmp5_a1[3] * array_tmp4[2] + array_tmp5_a1[4] * array_tmp4[1]) * 3 / glob_h;
> array_tmp5[4] := ats(3,array_tmp5,array_tmp5_a2,1)*glob_h/3;
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp6[4] := array_tmp5[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_tmp6[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre expt LINEAR - LINEAR $eq_no = 1 i = 5
> array_tmp5_a1[5] := -array_tmp5_a1[4] * array_tmp2[2] * 3 / array_tmp2[1] / 4;
> array_tmp5_a2[4] := (array_tmp5_a1[4] * array_tmp4[2] + array_tmp5_a1[5] * array_tmp4[1]) * 4 / glob_h;
> array_tmp5[5] := ats(4,array_tmp5,array_tmp5_a2,1)*glob_h/4;
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp6[5] := array_tmp5[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_tmp6[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit expt LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp5_a1[kkk] := -array_tmp5_a1[kkk-1] * array_tmp4[2] * (kkk-2) / array_tmp2[1] / (kkk - 1);
> array_tmp5_a2[kkk-1] := (array_tmp5_a1[kkk-1] * array_tmp4[2] + array_tmp5_a1[kkk] * array_tmp4[1]) * (kkk-1) / glob_h;
> array_tmp5[kkk] := ats(kkk-1,array_tmp5,array_tmp5_a2,1)*glob_h/(kkk-1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp6[kkk] := array_tmp5[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_tmp6[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_pole, array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_tmp1[1] := array_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := array_const_0D2[1]*array_x[1];
array_tmp4[1] := array_tmp3[1] + array_const_0D3[1];
array_tmp5[1] := expt(array_tmp2[1], array_tmp4[1]);
array_tmp5_a1[1] := ln(array_tmp2[1]);
array_tmp5_a1[2] := array_tmp2[2]/array_tmp2[1];
array_tmp6[1] := array_const_0D0[1] + array_tmp5[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp6[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_const_0D2[1]*array_x[2];
array_tmp4[2] := array_tmp3[2];
array_tmp5_a2[1] := (
array_tmp5_a1[1]*array_tmp4[2] + array_tmp5_a1[2]*array_tmp4[1])/
glob_h;
array_tmp5[2] := array_tmp5[1]*array_tmp5_a2[1]*glob_h;
array_tmp6[2] := array_tmp5[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp6[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp5_a1[3] := -1/2*array_tmp5_a1[2]*array_tmp2[2]/array_tmp2[1];
array_tmp5_a2[2] := 2*
(array_tmp5_a1[2]*array_tmp4[2] + array_tmp5_a1[3]*array_tmp4[1])/
glob_h;
array_tmp5[3] := 1/2*ats(2, array_tmp5, array_tmp5_a2, 1)*glob_h;
array_tmp6[3] := array_tmp5[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp6[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp5_a1[4] := -2/3*array_tmp5_a1[3]*array_tmp2[2]/array_tmp2[1];
array_tmp5_a2[3] := 3*
(array_tmp5_a1[3]*array_tmp4[2] + array_tmp5_a1[4]*array_tmp4[1])/
glob_h;
array_tmp5[4] := 1/3*ats(3, array_tmp5, array_tmp5_a2, 1)*glob_h;
array_tmp6[4] := array_tmp5[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp6[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp5_a1[5] := -3/4*array_tmp5_a1[4]*array_tmp2[2]/array_tmp2[1];
array_tmp5_a2[4] := 4*
(array_tmp5_a1[4]*array_tmp4[2] + array_tmp5_a1[5]*array_tmp4[1])/
glob_h;
array_tmp5[5] := 1/4*ats(4, array_tmp5, array_tmp5_a2, 1)*glob_h;
array_tmp6[5] := array_tmp5[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp6[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp5_a1[kkk] := -array_tmp5_a1[kkk - 1]*array_tmp4[2]*
(kkk - 2)/(array_tmp2[1]*(kkk - 1));
array_tmp5_a2[kkk - 1] := (array_tmp5_a1[kkk - 1]*array_tmp4[2]
+ array_tmp5_a1[kkk]*array_tmp4[1])*(kkk - 1)/glob_h;
array_tmp5[kkk] :=
ats(kkk - 1, array_tmp5, array_tmp5_a2, 1)*glob_h/(kkk - 1);
array_tmp6[kkk] := array_tmp5[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_tmp6[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(0.0 ) ;
> end;
exact_soln_y := proc(x) return 0. end proc
> #END USER DEF BLOCK
> #END USER DEF BLOCK
> #END OUTFILE5
> # Begin Function number 2
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it;
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5_c1,
> array_tmp5_a1,
> array_tmp5_a2,
> array_tmp5,
> array_tmp6,
> 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/expt_lin_linpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3));");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1;");
> omniout_str(ALWAYS,"x_end := 5.0 ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_iter := 1000000;");
> omniout_str(ALWAYS,"#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(0.0 ) ;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_large_float := 1.0e100;
> glob_almost_1 := 0.99;
> #BEGIN FIRST INPUT BLOCK
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_max_terms := max_terms;
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> array_y_init:= Array(0..(max_terms + 1),[]);
> array_norms:= Array(0..(max_terms + 1),[]);
> array_fact_1:= Array(0..(max_terms + 1),[]);
> array_pole:= Array(0..(4 + 1),[]);
> array_real_pole:= Array(0..(4 + 1),[]);
> array_complex_pole:= Array(0..(4 + 1),[]);
> array_1st_rel_error:= Array(0..(2 + 1),[]);
> array_last_rel_error:= Array(0..(2 + 1),[]);
> array_type_pole:= Array(0..(2 + 1),[]);
> array_type_real_pole:= Array(0..(2 + 1),[]);
> array_type_complex_pole:= Array(0..(2 + 1),[]);
> array_y:= Array(0..(max_terms + 1),[]);
> array_x:= Array(0..(max_terms + 1),[]);
> array_tmp0:= Array(0..(max_terms + 1),[]);
> array_tmp1:= Array(0..(max_terms + 1),[]);
> array_tmp2:= Array(0..(max_terms + 1),[]);
> array_tmp3:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5_c1:= Array(0..(max_terms + 1),[]);
> array_tmp5_a1:= Array(0..(max_terms + 1),[]);
> array_tmp5_a2:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_tmp6:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5_c1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5_c1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5_c1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5_a1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5_a2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp6 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D0[1] := 0.0;
> array_const_0D1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D1[1] := 0.1;
> array_const_0D2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D2[1] := 0.2;
> array_const_0D3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D3[1] := 0.3;
> 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 := 0.1;
> x_end := 5.0 ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_iter := 1000000;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=10;
> glob_display_interval:=0.01;
> 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 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3));");
> 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,"2013-05-26T01:20:50-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"expt_lin_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3));")
> ;
> 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,"expt_lin_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"expt_lin_lin maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_pole, array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5_c1, array_tmp5_a1,
array_tmp5_a2, array_tmp5, array_tmp6, 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/expt_lin_linpostode.ode#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3));");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1;");
omniout_str(ALWAYS, "x_end := 5.0 ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_iter := 1000000;");
omniout_str(ALWAYS, "#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(0.0 ) ;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_large_float := 0.10*10^101;
glob_almost_1 := 0.99;
Digits := 32;
max_terms := 30;
glob_max_terms := max_terms;
glob_html_log := true;
array_y_init := Array(0 .. max_terms + 1, []);
array_norms := Array(0 .. max_terms + 1, []);
array_fact_1 := Array(0 .. max_terms + 1, []);
array_pole := Array(0 .. 5, []);
array_real_pole := Array(0 .. 5, []);
array_complex_pole := Array(0 .. 5, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_y := Array(0 .. max_terms + 1, []);
array_x := Array(0 .. max_terms + 1, []);
array_tmp0 := Array(0 .. max_terms + 1, []);
array_tmp1 := Array(0 .. max_terms + 1, []);
array_tmp2 := Array(0 .. max_terms + 1, []);
array_tmp3 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5_c1 := Array(0 .. max_terms + 1, []);
array_tmp5_a1 := Array(0 .. max_terms + 1, []);
array_tmp5_a2 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_tmp6 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_real_poles := Array(0 .. 3, 0 .. 4, []);
array_complex_poles := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do
array_type_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5_c1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5_a1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5_a2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5_c1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp5_c1[term] := 0.; term := term + 1
end do;
array_tmp5_a1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp5_a1[term] := 0.; term := term + 1
end do;
array_tmp5_a2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp5_a2[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_tmp6 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp6[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_0D1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D1[term] := 0.; term := term + 1
end do;
array_const_0D1[1] := 0.1;
array_const_0D2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D2[term] := 0.; term := term + 1
end do;
array_const_0D2[1] := 0.2;
array_const_0D3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D3[term] := 0.; term := term + 1
end do;
array_const_0D3[1] := 0.3;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 0.1;
x_end := 5.0;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
glob_desired_digits_correct := 10;
glob_display_interval := 0.01;
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 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3));")
;
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, "2013-05-26T01:20:50-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"expt_lin_lin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = expt((0.1 * \
x + 0.2) , (0.2 * x + 0.3));");
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, "expt_lin_lin diffeq.mxt");
logitem_str(html_log_file, "expt_lin_lin maple results");
logitem_str(html_log_file, "All Tests - All Languages");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
> # End Function number 13
> main();
##############ECHO OF PROBLEM#################
##############temp/expt_lin_linpostode.ode#################
diff ( y , x , 1 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3));
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1;
x_end := 5.0 ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_iter := 1000000;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=10;
glob_display_interval:=0.01;
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(0.0 ) ;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 10
desired_abs_gbl_error = 1.0000000000000000000000000000000e-10
range = 4.9
estimated_steps = 4900000
step_error = 2.0408163265306122448979591836735e-17
est_needed_step_err = 2.0408163265306122448979591836735e-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 = 3.4344981665902949603036122703651e-196
estimated_step_error = 3.4344981665902949603036122703651e-196
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 = 7.8889630804708215156296805510342e-155
estimated_step_error = 7.8889630804708215156296805510342e-155
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 = 5.2941888228882317422471966437998e-147
estimated_step_error = 5.2941888228882317422471966437998e-147
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 = 3.5528636932729090382664689101979e-139
estimated_step_error = 3.5528636932729090382664689101979e-139
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 = 2.3842780301188516281047131185572e-131
estimated_step_error = 2.3842780301188516281047131185572e-131
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 = 1.6000505809390507879004397042175e-123
estimated_step_error = 1.6000505809390507879004397042175e-123
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 = 1.0737605756059140680118574323109e-115
estimated_step_error = 1.0737605756059140680118574323109e-115
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 = 7.2056813395662606512729615043512e-108
estimated_step_error = 7.2056813395662606512729615043512e-108
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 = 4.8353772382574764555876191820193e-100
estimated_step_error = 4.8353772382574764555876191820193e-100
best_h = 0.000512
opt_iter = 10
bytes used=4000252, alloc=3014104, time=0.12
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.2445995074996670632988895553425e-92
estimated_step_error = 3.2445995074996670632988895553425e-92
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 = 2.1769211546853024359606276156794e-84
estimated_step_error = 2.1769211546853024359606276156794e-84
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 = 1.4602461952888146354992092175540e-76
estimated_step_error = 1.4602461952888146354992092175540e-76
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 = 9.7906884920338036884879736838536e-69
estimated_step_error = 9.7906884920338036884879736838536e-69
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 = 6.5585635031589350694959844271618e-61
estimated_step_error = 6.5585635031589350694959844271618e-61
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 = 4.3855513391997814892455661765302e-53
estimated_step_error = 4.3855513391997814892455661765302e-53
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 = 2.9220861982860473282019531979045e-45
estimated_step_error = 2.9220861982860473282019531979045e-45
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 = 1.9334111586478532343541342645598e-37
estimated_step_error = 1.9334111586478532343541342645598e-37
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 = 1.2621755102892284966377549473513e-29
estimated_step_error = 1.2621755102892284966377549473513e-29
best_h = 0.1
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (analytic) = 0
y[1] (numeric) = 0
absolute error = 0
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.137
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] = 0.11
y[1] (analytic) = 0
y[1] (numeric) = 0.0061204845427376375559001978568783
absolute error = 0.0061204845427376375559001978568783
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.151
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.454
Order of pole (six term test) = -0.8616
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 0
y[1] (numeric) = 0.012174945832448542362009098003338
absolute error = 0.012174945832448542362009098003338
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.156
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.462
Order of pole (six term test) = -0.8606
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (analytic) = 0
y[1] (numeric) = 0.018219884635457830531736587481055
absolute error = 0.018219884635457830531736587481055
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.162
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.47
Order of pole (six term test) = -0.8596
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 0
y[1] (numeric) = 0.024255386099563737492822252172528
absolute error = 0.024255386099563737492822252172528
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.167
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.478
Order of pole (six term test) = -0.8587
TOP MAIN SOLVE Loop
bytes used=8001340, alloc=4062488, time=0.26
x[1] = 0.15
y[1] (analytic) = 0
y[1] (numeric) = 0.03028153462997530237106722797931
absolute error = 0.03028153462997530237106722797931
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.173
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.486
Order of pole (six term test) = -0.8577
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 0
y[1] (numeric) = 0.036298413899428191665096646543569
absolute error = 0.036298413899428191665096646543569
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.178
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.494
Order of pole (six term test) = -0.8567
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (analytic) = 0
y[1] (numeric) = 0.042306106858126130131511793191383
absolute error = 0.042306106858126130131511793191383
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.184
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.502
Order of pole (six term test) = -0.8557
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 0
y[1] (numeric) = 0.048304695743511707022815587919666
absolute error = 0.048304695743511707022815587919666
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.189
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.509
Order of pole (six term test) = -0.8548
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 0
y[1] (numeric) = 0.054294262089870227919632033960384
absolute error = 0.054294262089870227919632033960384
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.195
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.517
Order of pole (six term test) = -0.8539
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 0
y[1] (numeric) = 0.060274886737770187477885010166921
absolute error = 0.060274886737770187477885010166921
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.2
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.525
Order of pole (six term test) = -0.8529
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 0
y[1] (numeric) = 0.066246649843343846366743006848599
absolute error = 0.066246649843343846366743006848599
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.206
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.533
Order of pole (six term test) = -0.852
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 0
y[1] (numeric) = 0.072209630887411306404355814141878
absolute error = 0.072209630887411306404355814141878
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.211
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.541
Order of pole (six term test) = -0.8511
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 0
y[1] (numeric) = 0.078163908684451391309702232234473
absolute error = 0.078163908684451391309702232234473
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.217
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.549
Order of pole (six term test) = -0.8502
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 0
y[1] (numeric) = 0.084109561391422556487973312004542
absolute error = 0.084109561391422556487973312004542
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.222
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.557
Order of pole (six term test) = -0.8493
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 0
y[1] (numeric) = 0.090046666516436969765153109245627
absolute error = 0.090046666516436969765153109245627
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.228
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.564
Order of pole (six term test) = -0.8484
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (analytic) = 0
y[1] (numeric) = 0.095975300927290825899574438951034
absolute error = 0.095975300927290825899574438951034
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.233
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.572
Order of pole (six term test) = -0.8475
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (analytic) = 0
y[1] (numeric) = 0.10189554085985388094224572898762
absolute error = 0.10189554085985388094224572898762
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.239
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.58
Order of pole (six term test) = -0.8467
bytes used=12002956, alloc=4324584, time=0.39
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 0
y[1] (numeric) = 0.10780746192632111801483067539425
absolute error = 0.10780746192632111801483067539425
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.244
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.588
Order of pole (six term test) = -0.8458
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 0
y[1] (numeric) = 0.11371113912332938374848398951953
absolute error = 0.11371113912332938374848398951953
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.25
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.596
Order of pole (six term test) = -0.845
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (analytic) = 0
y[1] (numeric) = 0.11960664683994176440535078871432
absolute error = 0.11960664683994176440535078871432
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.255
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.604
Order of pole (six term test) = -0.8441
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 0
y[1] (numeric) = 0.12549405886550240251722702210419
absolute error = 0.12549405886550240251722702210419
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.261
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.611
Order of pole (six term test) = -0.8433
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 0
y[1] (numeric) = 0.1313734483973643886550970268604
absolute error = 0.1313734483973643886550970268604
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.266
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.619
Order of pole (six term test) = -0.8425
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 0
y[1] (numeric) = 0.13724488804849329862398506585065
absolute error = 0.13724488804849329862398506585065
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.272
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.627
Order of pole (six term test) = -0.8417
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 0
y[1] (numeric) = 0.14310844985494888389717820055947
absolute error = 0.14310844985494888389717820055947
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.277
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.635
Order of pole (six term test) = -0.8408
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (analytic) = 0
y[1] (numeric) = 0.14896420528324736240211974575776
absolute error = 0.14896420528324736240211974575776
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.283
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.643
Order of pole (six term test) = -0.84
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 0
y[1] (numeric) = 0.15481222523760669778908544958739
absolute error = 0.15481222523760669778908544958739
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.288
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.651
Order of pole (six term test) = -0.8393
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 0
y[1] (numeric) = 0.16065258006707719799722442043435
absolute error = 0.16065258006707719799722442043435
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.294
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.658
Order of pole (six term test) = -0.8385
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 0
y[1] (numeric) = 0.16648533957255970822680854987937
absolute error = 0.16648533957255970822680854987937
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.299
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.666
Order of pole (six term test) = -0.8377
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (analytic) = 0
y[1] (numeric) = 0.17231057301371361927968799589308
absolute error = 0.17231057301371361927968799589308
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.305
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.674
Order of pole (six term test) = -0.8369
TOP MAIN SOLVE Loop
bytes used=16003740, alloc=4390108, time=0.53
x[1] = 0.4
y[1] (analytic) = 0
y[1] (numeric) = 0.17812834911575685959198201628797
absolute error = 0.17812834911575685959198201628797
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.31
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.682
Order of pole (six term test) = -0.8362
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 0
y[1] (numeric) = 0.18393873607615998810573927429558
absolute error = 0.18393873607615998810573927429558
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.315
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.69
Order of pole (six term test) = -0.8354
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 0
y[1] (numeric) = 0.18974180157123645536321141589686
absolute error = 0.18974180157123645536321141589686
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.321
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.697
Order of pole (six term test) = -0.8347
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 0
y[1] (numeric) = 0.19553761276263105181369692635332
absolute error = 0.19553761276263105181369692635332
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.326
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.705
Order of pole (six term test) = -0.8339
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (analytic) = 0
y[1] (numeric) = 0.20132623630370851525542810890221
absolute error = 0.20132623630370851525542810890221
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.332
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.713
Order of pole (six term test) = -0.8332
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 0
y[1] (numeric) = 0.20710773834584422355202839427423
absolute error = 0.20710773834584422355202839427423
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.337
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.721
Order of pole (six term test) = -0.8325
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 0
y[1] (numeric) = 0.2128821845446188542244719664523
absolute error = 0.2128821845446188542244719664523
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.343
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.729
Order of pole (six term test) = -0.8317
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 0
y[1] (numeric) = 0.21864964006591884918646256023039
absolute error = 0.21864964006591884918646256023039
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.348
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.736
Order of pole (six term test) = -0.831
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (analytic) = 0
y[1] (numeric) = 0.22441016959194448072630508004341
absolute error = 0.22441016959194448072630508004341
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.354
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.744
Order of pole (six term test) = -0.8303
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 0
y[1] (numeric) = 0.23016383732712727380557313656265
absolute error = 0.23016383732712727380557313656265
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.359
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.752
Order of pole (six term test) = -0.8296
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 0
y[1] (numeric) = 0.23591070700395849980933636780007
absolute error = 0.23591070700395849980933636780007
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.365
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.76
Order of pole (six term test) = -0.8289
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = 0
y[1] (numeric) = 0.24165084188873041801077134110824
absolute error = 0.24165084188873041801077134110824
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.37
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.767
Order of pole (six term test) = -0.8282
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = 0
y[1] (numeric) = 0.24738430478719190317216923042169
absolute error = 0.24738430478719190317216923042169
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.376
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.775
Order of pole (six term test) = -0.8276
TOP MAIN SOLVE Loop
bytes used=20004828, alloc=4455632, time=0.67
x[1] = 0.53
y[1] (analytic) = 0
y[1] (numeric) = 0.25311115805012006086332040226605
absolute error = 0.25311115805012006086332040226605
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.381
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.783
Order of pole (six term test) = -0.8269
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 0
y[1] (numeric) = 0.25883146357880939620672354513457
absolute error = 0.25883146357880939620672354513457
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.387
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.791
Order of pole (six term test) = -0.8262
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = 0
y[1] (numeric) = 0.26454528283048006682779199717001
absolute error = 0.26454528283048006682779199717001
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.392
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.798
Order of pole (six term test) = -0.8256
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = 0
y[1] (numeric) = 0.27025267682360671676896407185829
absolute error = 0.27025267682360671676896407185829
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.398
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.806
Order of pole (six term test) = -0.8249
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (analytic) = 0
y[1] (numeric) = 0.27595370614316935499207605795083
absolute error = 0.27595370614316935499207605795083
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.403
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.814
Order of pole (six term test) = -0.8242
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = 0
y[1] (numeric) = 0.28164843094582770981715571020229
absolute error = 0.28164843094582770981715571020229
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.409
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.822
Order of pole (six term test) = -0.8236
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 0
y[1] (numeric) = 0.28733691096502045920245632834803
absolute error = 0.28733691096502045920245632834803
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.414
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.83
Order of pole (six term test) = -0.823
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 0
y[1] (numeric) = 0.29301920551599070613544601311239
absolute error = 0.29301920551599070613544601311239
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.42
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.837
Order of pole (six term test) = -0.8223
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 0
y[1] (numeric) = 0.29869537350073903855378386723711
absolute error = 0.29869537350073903855378386723711
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.425
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.845
Order of pole (six term test) = -0.8217
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (analytic) = 0
y[1] (numeric) = 0.30436547341290548412603617841879
absolute error = 0.30436547341290548412603617841879
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.431
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.853
Order of pole (six term test) = -0.8211
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 0
y[1] (numeric) = 0.31002956334258164187175406862758
absolute error = 0.31002956334258164187175406862758
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.436
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.861
Order of pole (six term test) = -0.8205
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = 0
y[1] (numeric) = 0.31568770098105424496802644891696
absolute error = 0.31568770098105424496802644891696
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.442
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.868
Order of pole (six term test) = -0.8199
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 0
y[1] (numeric) = 0.32133994362548138215392183747686
absolute error = 0.32133994362548138215392183747686
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.447
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.876
Order of pole (six term test) = -0.8193
TOP MAIN SOLVE Loop
bytes used=24006144, alloc=4455632, time=0.80
x[1] = 0.66
y[1] (analytic) = 0
y[1] (numeric) = 0.32698634818350257888520404269158
absolute error = 0.32698634818350257888520404269158
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.453
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.884
Order of pole (six term test) = -0.8187
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = 0
y[1] (numeric) = 0.33262697117778391378987036272055
absolute error = 0.33262697117778391378987036272055
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.458
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.892
Order of pole (six term test) = -0.8181
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = 0
y[1] (numeric) = 0.33826186875049932101156961581495
absolute error = 0.33826186875049932101156961581495
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.464
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.899
Order of pole (six term test) = -0.8175
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = 0
y[1] (numeric) = 0.34389109666774920468457328278079
absolute error = 0.34389109666774920468457328278079
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.469
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.907
Order of pole (six term test) = -0.8169
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 0
y[1] (numeric) = 0.34951471032391746804304615660381
absolute error = 0.34951471032391746804304615660381
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.474
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.915
Order of pole (six term test) = -0.8164
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (analytic) = 0
y[1] (numeric) = 0.35513276474596803651180948146586
absolute error = 0.35513276474596803651180948146586
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.48
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.923
Order of pole (six term test) = -0.8158
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 0
y[1] (numeric) = 0.36074531459768193153907220309494
absolute error = 0.36074531459768193153907220309494
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.485
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.93
Order of pole (six term test) = -0.8152
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = 0
y[1] (numeric) = 0.36635241418383592989771403719095
absolute error = 0.36635241418383592989771403719095
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.491
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.938
Order of pole (six term test) = -0.8147
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = 0
y[1] (numeric) = 0.3719541174543238216851351223505
absolute error = 0.3719541174543238216851351223505
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.496
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.946
Order of pole (six term test) = -0.8141
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (analytic) = 0
y[1] (numeric) = 0.37755047800822125927742877792644
absolute error = 0.37755047800822125927742877792644
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.502
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.953
Order of pole (six term test) = -0.8136
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 0
y[1] (numeric) = 0.38314154909779516902714699505441
absolute error = 0.38314154909779516902714699505441
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.507
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.961
Order of pole (six term test) = -0.813
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 0
y[1] (numeric) = 0.38872738363245867752112976875867
absolute error = 0.38872738363245867752112976875867
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.513
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.969
Order of pole (six term test) = -0.8125
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = 0
y[1] (numeric) = 0.3943080341826724847221166660382
absolute error = 0.3943080341826724847221166660382
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.518
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.977
Order of pole (six term test) = -0.812
bytes used=28009588, alloc=4455632, time=0.95
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 0
y[1] (numeric) = 0.39988355298379359729193464364837
absolute error = 0.39988355298379359729193464364837
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.524
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.984
Order of pole (six term test) = -0.8114
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (analytic) = 0
y[1] (numeric) = 0.4054539919398723168221529526631
absolute error = 0.4054539919398723168221529526631
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.529
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.992
Order of pole (six term test) = -0.8109
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = 0
y[1] (numeric) = 0.41101940262739835956780303768823
absolute error = 0.41101940262739835956780303768823
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.535
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2
Order of pole (six term test) = -0.8104
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = 0
y[1] (numeric) = 0.41657983629899696657905023106338
absolute error = 0.41657983629899696657905023106338
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.54
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.008
Order of pole (six term test) = -0.8099
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 0
y[1] (numeric) = 0.42213534388707584584291574043743
absolute error = 0.42213534388707584584291574043743
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.546
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.015
Order of pole (six term test) = -0.8094
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (analytic) = 0
y[1] (numeric) = 0.42768597600742377117097969908559
absolute error = 0.42768597600742377117097969908559
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.551
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.023
Order of pole (six term test) = -0.8089
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 0
y[1] (numeric) = 0.43323178296276164608849129203172
absolute error = 0.43323178296276164608849129203172
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.557
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.031
Order of pole (six term test) = -0.8084
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 0
y[1] (numeric) = 0.43877281474624682488484552426931
absolute error = 0.43877281474624682488484552426931
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.562
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.038
Order of pole (six term test) = -0.8079
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 0
y[1] (numeric) = 0.44430912104493146726465507561653
absolute error = 0.44430912104493146726465507561653
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.568
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.046
Order of pole (six term test) = -0.8074
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = 0
y[1] (numeric) = 0.44984075124317568768265774493148
absolute error = 0.44984075124317568768265774493148
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.573
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.054
Order of pole (six term test) = -0.8069
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 0
y[1] (numeric) = 0.45536775442601624544476348189246
absolute error = 0.45536775442601624544476348189246
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.579
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.062
Order of pole (six term test) = -0.8064
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = 0
y[1] (numeric) = 0.46089017938249150700225854587427
absolute error = 0.46089017938249150700225854587427
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.584
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.069
Order of pole (six term test) = -0.806
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = 0
y[1] (numeric) = 0.4664080746089233975474271975165
absolute error = 0.4664080746089233975474271975165
relative error = -1 %
Correct digits = -1
h = 0.01
bytes used=32010260, alloc=4521156, time=1.09
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.59
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.077
Order of pole (six term test) = -0.8055
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 0
y[1] (numeric) = 0.47192148831215704502777414313521
absolute error = 0.47192148831215704502777414313521
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.595
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.085
Order of pole (six term test) = -0.805
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (analytic) = 0
y[1] (numeric) = 0.47743046841275880602404669948257
absolute error = 0.47743046841275880602404669948257
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.601
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.093
Order of pole (six term test) = -0.8046
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 0
y[1] (numeric) = 0.48293506254817334957603101462252
absolute error = 0.48293506254817334957603101462252
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.606
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.1
Order of pole (six term test) = -0.8041
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = 0
y[1] (numeric) = 0.48843531807584046198154371954755
absolute error = 0.48843531807584046198154371954755
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.612
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.108
Order of pole (six term test) = -0.8037
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = 0
y[1] (numeric) = 0.49393128207627222283030846567887
absolute error = 0.49393128207627222283030846567887
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.617
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.116
Order of pole (six term test) = -0.8032
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 0
y[1] (numeric) = 0.499423001356091190057874867945
absolute error = 0.499423001356091190057874867945
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.622
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.123
Order of pole (six term test) = -0.8028
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 0
y[1] (numeric) = 0.50491052245103021960800646401744
absolute error = 0.50491052245103021960800646401744
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.628
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.131
Order of pole (six term test) = -0.8023
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 0
y[1] (numeric) = 0.51039389162889453336785035607535
absolute error = 0.51039389162889453336785035607535
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.633
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.139
Order of pole (six term test) = -0.8019
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 0
y[1] (numeric) = 0.51587315489248663738172811067429
absolute error = 0.51587315489248663738172811067429
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.639
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.147
Order of pole (six term test) = -0.8015
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = 0
y[1] (numeric) = 0.52134835798249468094978039422195
absolute error = 0.52134835798249468094978039422195
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.644
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.154
Order of pole (six term test) = -0.801
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (analytic) = 0
y[1] (numeric) = 0.52681954638034483607037664487638
absolute error = 0.52681954638034483607037664487638
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.65
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.162
Order of pole (six term test) = -0.8006
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 0
y[1] (numeric) = 0.53228676531101826578377431136566
absolute error = 0.53228676531101826578377431136566
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.655
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.17
Order of pole (six term test) = -0.8002
TOP MAIN SOLVE Loop
bytes used=36011316, alloc=4521156, time=1.23
x[1] = 1.04
y[1] (analytic) = 0
y[1] (numeric) = 0.53775005974583323931277085319988
absolute error = 0.53775005974583323931277085319988
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.661
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.177
Order of pole (six term test) = -0.7998
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 0
y[1] (numeric) = 0.54320947440519294146800356364331
absolute error = 0.54320947440519294146800356364331
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.666
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.185
Order of pole (six term test) = -0.7994
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 0
y[1] (numeric) = 0.54866505376129951358525625687168
absolute error = 0.54866505376129951358525625687168
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.672
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.193
Order of pole (six term test) = -0.799
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = 0
y[1] (numeric) = 0.55411684204083485328393260199119
absolute error = 0.55411684204083485328393260199119
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.677
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.201
Order of pole (six term test) = -0.7986
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = 0
y[1] (numeric) = 0.55956488322760869057421855897659
absolute error = 0.55956488322760869057421855897659
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.683
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.208
Order of pole (six term test) = -0.7982
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 0
y[1] (numeric) = 0.56500922106517444829000163178472
absolute error = 0.56500922106517444829000163178472
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.688
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.216
Order of pole (six term test) = -0.7978
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 0
y[1] (numeric) = 0.57044989905941338548011378414486
absolute error = 0.57044989905941338548011378414486
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.694
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.224
Order of pole (six term test) = -0.7974
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (analytic) = 0
y[1] (numeric) = 0.5758869604810875132468350777286
absolute error = 0.5758869604810875132468350777286
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.699
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.231
Order of pole (six term test) = -0.797
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = 0
y[1] (numeric) = 0.58132044836836176357289500338014
absolute error = 0.58132044836836176357289500338014
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.705
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.239
Order of pole (six term test) = -0.7966
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = 0
y[1] (numeric) = 0.58675040552929588292163371783758
absolute error = 0.58675040552929588292163371783758
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.71
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.247
Order of pole (six term test) = -0.7962
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 0
y[1] (numeric) = 0.59217687454430651382486439758973
absolute error = 0.59217687454430651382486439758973
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.716
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.255
Order of pole (six term test) = -0.7959
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = 0
y[1] (numeric) = 0.59759989776859991928476781280392
absolute error = 0.59759989776859991928476781280392
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.721
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.262
Order of pole (six term test) = -0.7955
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = 0
y[1] (numeric) = 0.60301951733457579660543290375159
absolute error = 0.60301951733457579660543290375159
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.727
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.27
Order of pole (six term test) = -0.7951
TOP MAIN SOLVE Loop
bytes used=40012252, alloc=4521156, time=1.37
x[1] = 1.17
y[1] (analytic) = 0
y[1] (numeric) = 0.60843577515420261923213545433232
absolute error = 0.60843577515420261923213545433232
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.732
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.278
Order of pole (six term test) = -0.7948
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = 0
y[1] (numeric) = 0.61384871292136493730794101017802
absolute error = 0.61384871292136493730794101017802
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.738
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.285
Order of pole (six term test) = -0.7944
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 0
y[1] (numeric) = 0.61925837211418305995366179279409
absolute error = 0.61925837211418305995366179279409
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.743
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.293
Order of pole (six term test) = -0.794
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (analytic) = 0
y[1] (numeric) = 0.62466479399730553473463458692124
absolute error = 0.62466479399730553473463458692124
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.749
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.301
Order of pole (six term test) = -0.7937
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 0
y[1] (numeric) = 0.63006801962417483239236842937904
absolute error = 0.63006801962417483239236842937904
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.754
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.309
Order of pole (six term test) = -0.7933
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = 0
y[1] (numeric) = 0.63546808983926663768709212385878
absolute error = 0.63546808983926663768709212385878
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.759
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.316
Order of pole (six term test) = -0.793
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = 0
y[1] (numeric) = 0.64086504528030314011496747323405
absolute error = 0.64086504528030314011496747323405
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.765
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.324
Order of pole (six term test) = -0.7926
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = 0
y[1] (numeric) = 0.64625892638044071132767758322071
absolute error = 0.64625892638044071132767758322071
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.77
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.332
Order of pole (six term test) = -0.7923
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (analytic) = 0
y[1] (numeric) = 0.65164977337043234928879826294063
absolute error = 0.65164977337043234928879826294063
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.776
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.34
Order of pole (six term test) = -0.792
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = 0
y[1] (numeric) = 0.65703762628076526254745392042456
absolute error = 0.65703762628076526254745392042456
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.781
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.347
Order of pole (six term test) = -0.7916
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = 0
y[1] (numeric) = 0.66242252494377396149197607163832
absolute error = 0.66242252494377396149197607163832
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.787
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.355
Order of pole (six term test) = -0.7913
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = 0
y[1] (numeric) = 0.66780450899572921706143782130104
absolute error = 0.66780450899572921706143782130104
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.792
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.363
Order of pole (six term test) = -0.791
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (analytic) = 0
y[1] (numeric) = 0.67318361787890324113793058074663
absolute error = 0.67318361787890324113793058074663
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.798
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.37
Order of pole (six term test) = -0.7907
TOP MAIN SOLVE Loop
bytes used=44014828, alloc=4521156, time=1.51
x[1] = 1.3
y[1] (analytic) = 0
y[1] (numeric) = 0.67855989084361143671426052349733
absolute error = 0.67855989084361143671426052349733
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.803
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.378
Order of pole (six term test) = -0.7903
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = 0
y[1] (numeric) = 0.68393336695023105992743163269174
absolute error = 0.68393336695023105992743163269174
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.809
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.386
Order of pole (six term test) = -0.79
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = 0
y[1] (numeric) = 0.68930408507119713016498627646673
absolute error = 0.68930408507119713016498627646673
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.814
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.394
Order of pole (six term test) = -0.7897
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = 0
y[1] (numeric) = 0.69467208389297591868620425550978
absolute error = 0.69467208389297591868620425550978
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.82
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.401
Order of pole (six term test) = -0.7894
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (analytic) = 0
y[1] (numeric) = 0.70003740191801634055060082415675
absolute error = 0.70003740191801634055060082415675
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.825
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.409
Order of pole (six term test) = -0.7891
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = 0
y[1] (numeric) = 0.7054000774666795691094672476728
absolute error = 0.7054000774666795691094672476728
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.831
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.417
Order of pole (six term test) = -0.7888
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = 0
y[1] (numeric) = 0.7107601486791471868897862845512
absolute error = 0.7107601486791471868897862845512
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.836
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.424
Order of pole (six term test) = -0.7885
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = 0
y[1] (numeric) = 0.71611765351730818138121817827948
absolute error = 0.71611765351730818138121817827948
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.842
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.432
Order of pole (six term test) = -0.7882
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (analytic) = 0
y[1] (numeric) = 0.72147262976662508902354335614623
absolute error = 0.72147262976662508902354335614623
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.847
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.44
Order of pole (six term test) = -0.7879
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = 0
y[1] (numeric) = 0.72682511503797958558158171487872
absolute error = 0.72682511503797958558158171487872
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.853
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.448
Order of pole (six term test) = -0.7876
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = 0
y[1] (numeric) = 0.73217514676949781608486159703212
absolute error = 0.73217514676949781608486159703212
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.858
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.455
Order of pole (six term test) = -0.7873
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = 0
y[1] (numeric) = 0.73752276222835575259791989577921
absolute error = 0.73752276222835575259791989577921
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.864
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.463
Order of pole (six term test) = -0.787
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = 0
y[1] (numeric) = 0.74286799851256486327187115920847
absolute error = 0.74286799851256486327187115920847
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.869
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.471
Order of pole (six term test) = -0.7868
TOP MAIN SOLVE Loop
bytes used=48016652, alloc=4521156, time=1.65
x[1] = 1.43
y[1] (analytic) = 0
y[1] (numeric) = 0.74821089255273837140663689072559
absolute error = 0.74821089255273837140663689072559
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.875
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.479
Order of pole (six term test) = -0.7865
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 0
y[1] (numeric) = 0.75355148111383837862387948418856
absolute error = 0.75355148111383837862387948418856
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.88
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.486
Order of pole (six term test) = -0.7862
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = 0
y[1] (numeric) = 0.75888980079690412171119412643947
absolute error = 0.75888980079690412171119412643947
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.886
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.494
Order of pole (six term test) = -0.7859
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = 0
y[1] (numeric) = 0.7642258880407616282464835180027
absolute error = 0.7642258880407616282464835180027
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.891
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.502
Order of pole (six term test) = -0.7857
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (analytic) = 0
y[1] (numeric) = 0.769559779123715031745731184715
absolute error = 0.769559779123715031745731184715
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.896
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.51
Order of pole (six term test) = -0.7854
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = 0
y[1] (numeric) = 0.77489151016521980279570468148905
absolute error = 0.77489151016521980279570468148905
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.902
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.517
Order of pole (six term test) = -0.7851
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 0
y[1] (numeric) = 0.78022111712753814843361240698176
absolute error = 0.78022111712753814843361240698176
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.907
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.525
Order of pole (six term test) = -0.7849
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = 0
y[1] (numeric) = 0.78554863581737682791660511588402
absolute error = 0.78554863581737682791660511588402
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.913
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.533
Order of pole (six term test) = -0.7846
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = 0
y[1] (numeric) = 0.79087410188750762898349811169015
absolute error = 0.79087410188750762898349811169015
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.918
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.54
Order of pole (six term test) = -0.7844
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (analytic) = 0
y[1] (numeric) = 0.79619755083837074474747839788793
absolute error = 0.79619755083837074474747839788793
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.924
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.548
Order of pole (six term test) = -0.7841
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = 0
y[1] (numeric) = 0.80151901801966128747018073658573
absolute error = 0.80151901801966128747018073658573
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.929
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.556
Order of pole (six term test) = -0.7839
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = 0
y[1] (numeric) = 0.80683853863189917165273654322496
absolute error = 0.80683853863189917165273654322496
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.935
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.564
Order of pole (six term test) = -0.7836
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = 0
y[1] (numeric) = 0.81215614772798259513662860612714
absolute error = 0.81215614772798259513662860612714
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.94
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.571
Order of pole (six term test) = -0.7834
bytes used=52018224, alloc=4521156, time=1.79
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (analytic) = 0
y[1] (numeric) = 0.81747188021472534323487028879657
absolute error = 0.81747188021472534323487028879657
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.946
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.579
Order of pole (six term test) = -0.7831
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = 0
y[1] (numeric) = 0.82278577085437813731065538617117
absolute error = 0.82278577085437813731065538617117
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.951
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.587
Order of pole (six term test) = -0.7829
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = 0
y[1] (numeric) = 0.82809785426613424568471608592541
absolute error = 0.82809785426613424568471608592541
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.957
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.595
Order of pole (six term test) = -0.7827
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = 0
y[1] (numeric) = 0.83340816492761957128273915393346
absolute error = 0.83340816492761957128273915393346
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.962
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.602
Order of pole (six term test) = -0.7824
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = 0
y[1] (numeric) = 0.83871673717636742702891688020551
absolute error = 0.83871673717636742702891688020551
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.968
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.61
Order of pole (six term test) = -0.7822
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (analytic) = 0
y[1] (numeric) = 0.84402360521127820664967565790212
absolute error = 0.84402360521127820664967565790212
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.973
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.618
Order of pole (six term test) = -0.782
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = 0
y[1] (numeric) = 0.84932880309406415527149039867287
absolute error = 0.84932880309406415527149039867287
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.979
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.626
Order of pole (six term test) = -0.7818
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = 0
y[1] (numeric) = 0.85463236475067944097714841637085
absolute error = 0.85463236475067944097714841637085
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.984
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.633
Order of pole (six term test) = -0.7815
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = 0
y[1] (numeric) = 0.85993432397273572532459421944062
absolute error = 0.85993432397273572532459421944062
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.99
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.641
Order of pole (six term test) = -0.7813
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (analytic) = 0
y[1] (numeric) = 0.86523471441890342773031947251716
absolute error = 0.86523471441890342773031947251716
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.995
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.649
Order of pole (six term test) = -0.7811
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = 0
y[1] (numeric) = 0.8705335696162988755739424017593
absolute error = 0.8705335696162988755739424017593
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.001
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.657
Order of pole (six term test) = -0.7809
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = 0
y[1] (numeric) = 0.87583092296185752889095907839214
absolute error = 0.87583092296185752889095907839214
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.006
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.664
Order of pole (six term test) = -0.7807
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = 0
y[1] (numeric) = 0.88112680772369346558548428739803
absolute error = 0.88112680772369346558548428739803
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.012
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.672
Order of pole (six term test) = -0.7805
bytes used=56020728, alloc=4586680, time=1.93
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = 0
y[1] (numeric) = 0.88642125704244531021299831990701
absolute error = 0.88642125704244531021299831990701
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.017
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.68
Order of pole (six term test) = -0.7803
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (analytic) = 0
y[1] (numeric) = 0.89171430393260878655357083224912
absolute error = 0.89171430393260878655357083224912
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.023
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.688
Order of pole (six term test) = -0.7801
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = 0
y[1] (numeric) = 0.89700598128385607141766257998917
absolute error = 0.89700598128385607141766257998917
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.028
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.695
Order of pole (six term test) = -0.7799
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = 0
y[1] (numeric) = 0.90229632186234212439835425155191
absolute error = 0.90229632186234212439835425155191
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.034
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.703
Order of pole (six term test) = -0.7797
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = 0
y[1] (numeric) = 0.90758535831199816560468723168726
absolute error = 0.90758535831199816560468723168726
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.039
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.711
Order of pole (six term test) = -0.7795
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (analytic) = 0
y[1] (numeric) = 0.91287312315581247077971627214481
absolute error = 0.91287312315581247077971627214481
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.044
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.719
Order of pole (six term test) = -0.7793
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = 0
y[1] (numeric) = 0.91815964879709865062288438467901
absolute error = 0.91815964879709865062288438467901
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.05
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.727
Order of pole (six term test) = -0.7791
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = 0
y[1] (numeric) = 0.92344496752075157859847414692112
absolute error = 0.92344496752075157859847414692112
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.055
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.734
Order of pole (six term test) = -0.7789
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = 0
y[1] (numeric) = 0.92872911149449112901922748744565
absolute error = 0.92872911149449112901922748744565
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.061
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.742
Order of pole (six term test) = -0.7787
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 0
y[1] (numeric) = 0.93401211277009388474583990518477
absolute error = 0.93401211277009388474583990518477
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.066
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.75
Order of pole (six term test) = -0.7786
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (analytic) = 0
y[1] (numeric) = 0.93929400328461297143802799299501
absolute error = 0.93929400328461297143802799299501
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.072
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.758
Order of pole (six term test) = -0.7784
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = 0
y[1] (numeric) = 0.94457481486158617293036455421993
absolute error = 0.94457481486158617293036455421993
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.077
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.765
Order of pole (six term test) = -0.7782
TOP MAIN SOLVE Loop
bytes used=60021420, alloc=4586680, time=2.07
x[1] = 1.81
y[1] (analytic) = 0
y[1] (numeric) = 0.94985457921223247998521694947014
absolute error = 0.94985457921223247998521694947014
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.083
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.773
Order of pole (six term test) = -0.778
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = 0
y[1] (numeric) = 0.9551333279366372223950744550192
absolute error = 0.9551333279366372223950744550192
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.088
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.781
Order of pole (six term test) = -0.7779
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (analytic) = 0
y[1] (numeric) = 0.96041109252492593216649117136289
absolute error = 0.96041109252492593216649117136289
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.094
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.789
Order of pole (six term test) = -0.7777
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = 0
y[1] (numeric) = 0.96568790435842708331700268133603
absolute error = 0.96568790435842708331700268133603
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.099
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.796
Order of pole (six term test) = -0.7775
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = 0
y[1] (numeric) = 0.97096379471082385165391552207742
absolute error = 0.97096379471082385165391552207742
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.105
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.804
Order of pole (six term test) = -0.7774
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = 0
y[1] (numeric) = 0.97623879474929503577905446295871
absolute error = 0.97623879474929503577905446295871
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.11
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.812
Order of pole (six term test) = -0.7772
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = 0
y[1] (numeric) = 0.98151293553564527847563655109743
absolute error = 0.98151293553564527847563655109743
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.116
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.82
Order of pole (six term test) = -0.777
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (analytic) = 0
y[1] (numeric) = 0.98678624802742472558169256928921
absolute error = 0.98678624802742472558169256928921
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.121
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.828
Order of pole (six term test) = -0.7769
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = 0
y[1] (numeric) = 0.99205876307903825743816189854778
absolute error = 0.99205876307903825743816189854778
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.127
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.835
Order of pole (six term test) = -0.7767
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = 0
y[1] (numeric) = 0.99733051144284442601824761422841
absolute error = 0.99733051144284442601824761422841
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.132
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.843
Order of pole (six term test) = -0.7766
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = 0
y[1] (numeric) = 1.0026015237702442288971522785761
absolute error = 1.0026015237702442288971522785761
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.138
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.851
Order of pole (six term test) = -0.7764
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (analytic) = 0
y[1] (numeric) = 1.0078718306127598493072537316516
absolute error = 1.0078718306127598493072537316516
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.143
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.859
Order of pole (six term test) = -0.7763
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (analytic) = 0
y[1] (numeric) = 1.0131414624231034896424713641744
absolute error = 1.0131414624231034896424713641744
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.149
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.867
Order of pole (six term test) = -0.7761
TOP MAIN SOLVE Loop
bytes used=64022416, alloc=4586680, time=2.22
x[1] = 1.94
y[1] (analytic) = 0
y[1] (numeric) = 1.0184104495562364239263783847763
absolute error = 1.0184104495562364239263783847763
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.154
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.874
Order of pole (six term test) = -0.776
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = 0
y[1] (numeric) = 1.0236788222704183929409099914037
absolute error = 1.0236788222704183929409099914037
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.16
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.882
Order of pole (six term test) = -0.7759
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = 0
y[1] (numeric) = 1.0289466107282474639256903169314
absolute error = 1.0289466107282474639256903169314
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.165
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.89
Order of pole (six term test) = -0.7757
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (analytic) = 0
y[1] (numeric) = 1.0342138449976904750014550781631
absolute error = 1.0342138449976904750014550781631
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.171
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.898
Order of pole (six term test) = -0.7756
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = 0
y[1] (numeric) = 1.0394805550531041827441975678686
absolute error = 1.0394805550531041827441975678686
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.176
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.906
Order of pole (six term test) = -0.7754
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = 0
y[1] (numeric) = 1.0447467707762472296389412454337
absolute error = 1.0447467707762472296389412454337
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.181
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.913
Order of pole (six term test) = -0.7753
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 0
y[1] (numeric) = 1.050012521957283046472883351715
absolute error = 1.050012521957283046472883351715
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.187
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.921
Order of pole (six term test) = -0.7752
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (analytic) = 0
y[1] (numeric) = 1.0552778382957738030865134422076
absolute error = 1.0552778382957738030865134422076
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.192
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.929
Order of pole (six term test) = -0.7751
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = 0
y[1] (numeric) = 1.0605427494016655192876530489636
absolute error = 1.0605427494016655192876530489636
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.198
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.937
Order of pole (six term test) = -0.7749
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 0
y[1] (numeric) = 1.0658072847962644461466639169152
absolute error = 1.0658072847962644461466639169152
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.203
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.945
Order of pole (six term test) = -0.7748
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = 0
y[1] (numeric) = 1.0710714739132048263308197315096
absolute error = 1.0710714739132048263308197315096
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.209
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.952
Order of pole (six term test) = -0.7747
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = 0
y[1] (numeric) = 1.0763353460994081406015282566644
absolute error = 1.0763353460994081406015282566644
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.214
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.96
Order of pole (six term test) = -0.7746
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (analytic) = 0
y[1] (numeric) = 1.0815989306160339460892363461146
absolute error = 1.0815989306160339460892363461146
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.22
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.968
Order of pole (six term test) = -0.7745
TOP MAIN SOLVE Loop
bytes used=68023352, alloc=4586680, time=2.36
x[1] = 2.07
y[1] (analytic) = 0
y[1] (numeric) = 1.086862256639422410476968850156
absolute error = 1.086862256639422410476968850156
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.225
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.976
Order of pole (six term test) = -0.7743
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 0
y[1] (numeric) = 1.0921253532620286447640737004359
absolute error = 1.0921253532620286447640737004359
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.231
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.984
Order of pole (six term test) = -0.7742
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = 0
y[1] (numeric) = 1.0973882494933489358464090771959
absolute error = 1.0973882494933489358464090771959
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.236
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.992
Order of pole (six term test) = -0.7741
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (analytic) = 0
y[1] (numeric) = 1.1026509742608389787374639430671
absolute error = 1.1026509742608389787374639430671
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.242
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.999
Order of pole (six term test) = -0.774
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = 0
y[1] (numeric) = 1.1079135564108242068663092704286
absolute error = 1.1079135564108242068663092704286
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.247
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.007
Order of pole (six term test) = -0.7739
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = 0
y[1] (numeric) = 1.1131760247094023175224021860931
absolute error = 1.1131760247094023175224021860931
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.253
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.015
Order of pole (six term test) = -0.7738
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 0
y[1] (numeric) = 1.1184384078433380881736862663606
absolute error = 1.1184384078433380881736862663606
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.258
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.023
Order of pole (six term test) = -0.7737
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 0
y[1] (numeric) = 1.1237007344209505780627344522918
absolute error = 1.1237007344209505780627344522918
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.264
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.031
Order of pole (six term test) = -0.7736
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (analytic) = 0
y[1] (numeric) = 1.1289630329729928081854612844759
absolute error = 1.1289630329729928081854612844759
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.269
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.039
Order of pole (six term test) = -0.7735
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 0
y[1] (numeric) = 1.1342253319535240114777915927495
absolute error = 1.1342253319535240114777915927495
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.275
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.046
Order of pole (six term test) = -0.7734
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = 0
y[1] (numeric) = 1.1394876597407745437772248866639
absolute error = 1.1394876597407745437772248866639
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.28
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.054
Order of pole (six term test) = -0.7733
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 0
y[1] (numeric) = 1.1447500446380035448880980067848
absolute error = 1.1447500446380035448880980067848
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.286
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.062
Order of pole (six term test) = -0.7732
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 0
y[1] (numeric) = 1.1500125148743494378611505213381
absolute error = 1.1500125148743494378611505213381
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.291
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.07
Order of pole (six term test) = -0.7731
TOP MAIN SOLVE Loop
bytes used=72024612, alloc=4586680, time=2.50
x[1] = 2.2
y[1] (analytic) = 0
y[1] (numeric) = 1.1552750986056733533993729886446
absolute error = 1.1552750986056733533993729886446
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.297
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.078
Order of pole (six term test) = -0.7731
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 0
y[1] (numeric) = 1.160537823915395565122710173042
absolute error = 1.160537823915395565122710173042
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.302
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.086
Order of pole (six term test) = -0.773
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 0
y[1] (numeric) = 1.1658007188153250202636495666918
absolute error = 1.1658007188153250202636495666918
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.308
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.094
Order of pole (six term test) = -0.7729
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = 0
y[1] (numeric) = 1.1710638112464820492237072763315
absolute error = 1.1710638112464820492237072763315
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.313
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.101
Order of pole (six term test) = -0.7728
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (analytic) = 0
y[1] (numeric) = 1.1763271290799143362969926419777
absolute error = 1.1763271290799143362969926419777
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.319
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.109
Order of pole (six term test) = -0.7727
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 0
y[1] (numeric) = 1.18159070011750623276106087836
absolute error = 1.18159070011750623276106087836
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.324
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.117
Order of pole (six term test) = -0.7727
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 0
y[1] (numeric) = 1.186854552092781492446827283741
absolute error = 1.186854552092781492446827283741
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.329
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.125
Order of pole (six term test) = -0.7726
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = 0
y[1] (numeric) = 1.1921187126716995088281014070801
absolute error = 1.1921187126716995088281014070801
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.335
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.133
Order of pole (six term test) = -0.7725
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = 0
y[1] (numeric) = 1.1973832094534451316169956657351
absolute error = 1.1973832094534451316169956657351
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.34
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.141
Order of pole (six term test) = -0.7724
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 0
y[1] (numeric) = 1.2026480699712121398137671805724
absolute error = 1.2026480699712121398137671805724
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.346
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.149
Order of pole (six term test) = -0.7724
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 0
y[1] (numeric) = 1.2079133216929804471382670773362
absolute error = 1.2079133216929804471382670773362
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.351
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.156
Order of pole (six term test) = -0.7723
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 0
y[1] (numeric) = 1.2131789920222871147648072045124
absolute error = 1.2131789920222871147648072045124
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.357
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.164
Order of pole (six term test) = -0.7722
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = 0
y[1] (numeric) = 1.2184451082989912452926249952798
absolute error = 1.2184451082989912452926249952798
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.362
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.172
Order of pole (six term test) = -0.7722
TOP MAIN SOLVE Loop
bytes used=76025512, alloc=4586680, time=2.64
x[1] = 2.33
y[1] (analytic) = 0
y[1] (numeric) = 1.2237116978000328309099536250568
absolute error = 1.2237116978000328309099536250568
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.368
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.18
Order of pole (six term test) = -0.7721
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = 0
y[1] (numeric) = 1.2289787877401856277507128439637
absolute error = 1.2289787877401856277507128439637
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.373
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.188
Order of pole (six term test) = -0.7721
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 0
y[1] (numeric) = 1.2342464052728041274987575152018
absolute error = 1.2342464052728041274987575152018
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.379
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.196
Order of pole (six term test) = -0.772
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 0
y[1] (numeric) = 1.2395145774905646963651929273813
absolute error = 1.2395145774905646963651929273813
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.384
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.204
Order of pole (six term test) = -0.7719
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = 0
y[1] (numeric) = 1.2447833314262009506492305560962
absolute error = 1.2447833314262009506492305560962
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.39
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.212
Order of pole (six term test) = -0.7719
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (analytic) = 0
y[1] (numeric) = 1.2500526940532334371921624205255
absolute error = 1.2500526940532334371921624205255
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.395
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.22
Order of pole (six term test) = -0.7718
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = 0
y[1] (numeric) = 1.2553226922866936861470288031799
absolute error = 1.2553226922866936861470288031799
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.401
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.227
Order of pole (six term test) = -0.7718
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 0
y[1] (numeric) = 1.2605933529838427026132000496607
absolute error = 1.2605933529838427026132000496607
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.406
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.235
Order of pole (six term test) = -0.7718
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 0
y[1] (numeric) = 1.2658647029448839628251503938186
absolute error = 1.2658647029448839628251503938186
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.412
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.243
Order of pole (six term test) = -0.7717
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (analytic) = 0
y[1] (numeric) = 1.2711367689136709797379368896878
absolute error = 1.2711367689136709797379368896878
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.417
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.251
Order of pole (six term test) = -0.7717
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = 0
y[1] (numeric) = 1.2764095775784095020180807750441
absolute error = 1.2764095775784095020180807750441
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.423
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.259
Order of pole (six term test) = -0.7716
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = 0
y[1] (numeric) = 1.2816831555723544096274576152062
absolute error = 1.2816831555723544096274576152062
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.428
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.267
Order of pole (six term test) = -0.7716
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = 0
y[1] (numeric) = 1.286957529474501368379216428226
absolute error = 1.286957529474501368379216428226
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.434
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.275
Order of pole (six term test) = -0.7715
TOP MAIN SOLVE Loop
bytes used=80026720, alloc=4586680, time=2.78
x[1] = 2.46
y[1] (analytic) = 0
y[1] (numeric) = 1.2922327258102733050484510031562
absolute error = 1.2922327258102733050484510031562
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.439
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.283
Order of pole (six term test) = -0.7715
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (analytic) = 0
y[1] (numeric) = 1.2975087710522017638361273091522
absolute error = 1.2975087710522017638361273091522
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.445
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.291
Order of pole (six term test) = -0.7715
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 0
y[1] (numeric) = 1.3027856916206032042124218701493
absolute error = 1.3027856916206032042124218701493
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.45
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.299
Order of pole (six term test) = -0.7714
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 0
y[1] (numeric) = 1.308063513884250299404943872796
absolute error = 1.308063513884250299404943872796
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.456
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.307
Order of pole (six term test) = -0.7714
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 0
y[1] (numeric) = 1.3133422641610382940480991328072
absolute error = 1.3133422641610382940480991328072
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.461
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.315
Order of pole (six term test) = -0.7714
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (analytic) = 0
y[1] (numeric) = 1.3186219687186464787719112549454
absolute error = 1.3186219687186464787719112549454
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.466
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.322
Order of pole (six term test) = -0.7714
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 0
y[1] (numeric) = 1.3239026537751948387817525297986
absolute error = 1.3239026537751948387817525297986
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.472
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.33
Order of pole (six term test) = -0.7713
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = 0
y[1] (numeric) = 1.3291843454998959327644661389189
absolute error = 1.3291843454998959327644661389189
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.477
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.338
Order of pole (six term test) = -0.7713
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 0
y[1] (numeric) = 1.3344670700137020577510975100955
absolute error = 1.3344670700137020577510975100955
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.483
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.346
Order of pole (six term test) = -0.7713
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = 0
y[1] (numeric) = 1.3397508533899477548717151203578
absolute error = 1.3397508533899477548717151203578
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.488
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.354
Order of pole (six term test) = -0.7713
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (analytic) = 0
y[1] (numeric) = 1.3450357216549877102534120772681
absolute error = 1.3450357216549877102534120772681
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.494
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.362
Order of pole (six term test) = -0.7713
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 0
y[1] (numeric) = 1.3503217007888301046383651855277
absolute error = 1.3503217007888301046383651855277
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.499
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.37
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = 0
y[1] (numeric) = 1.3556088167257654646346169958164
absolute error = 1.3556088167257654646346169958164
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.505
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.378
Order of pole (six term test) = -0.7712
bytes used=84028384, alloc=4586680, time=2.93
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = 0
y[1] (numeric) = 1.3608970953549910678578708400643
absolute error = 1.3608970953549910678578708400643
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.51
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.386
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (analytic) = 0
y[1] (numeric) = 1.3661865625212309535778845520185
absolute error = 1.3661865625212309535778845520185
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.516
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.394
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = 0
y[1] (numeric) = 1.3714772440253515898478540236734
absolute error = 1.3714772440253515898478540236734
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.521
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.402
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 0
y[1] (numeric) = 1.3767691656249732474693345613512
absolute error = 1.3767691656249732474693345613512
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.527
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.41
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = 0
y[1] (numeric) = 1.3820623530350771305286007558486
absolute error = 1.3820623530350771305286007558486
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.532
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.418
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = 0
y[1] (numeric) = 1.3873568319286083126327417545517
absolute error = 1.3873568319286083126327417545517
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.538
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.426
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (analytic) = 0
y[1] (numeric) = 1.3926526279370745273750787542421
absolute error = 1.3926526279370745273750787542421
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.543
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.434
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 0
y[1] (numeric) = 1.3979497666511408609695283458993
absolute error = 1.3979497666511408609695283458993
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.549
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.442
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 0
y[1] (numeric) = 1.4032482736212203944121748937602
absolute error = 1.4032482736212203944121748937602
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.554
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.45
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 0
y[1] (numeric) = 1.4085481743580608419554159525845
absolute error = 1.4085481743580608419554159525845
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.56
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.458
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (analytic) = 0
y[1] (numeric) = 1.4138494943333272321154679724495
absolute error = 1.4138494943333272321154679724495
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.565
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.466
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = 0
y[1] (numeric) = 1.419152258980180676877628929097
absolute error = 1.419152258980180676877628929097
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.571
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.474
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = 0
y[1] (numeric) = 1.4244564936938532742153562835348
absolute error = 1.4244564936938532742153562835348
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.576
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.482
Order of pole (six term test) = -0.7712
bytes used=88029624, alloc=4586680, time=3.06
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = 0
y[1] (numeric) = 1.4297622238322191884988015134019
absolute error = 1.4297622238322191884988015134019
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.582
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.49
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 0
y[1] (numeric) = 1.4350694747163619528358174788901
absolute error = 1.4350694747163619528358174788901
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.587
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.498
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (analytic) = 0
y[1] (numeric) = 1.4403782716311380368634955590827
absolute error = 1.4403782716311380368634955590827
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.593
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.506
Order of pole (six term test) = -0.7712
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = 0
y[1] (numeric) = 1.445688639825736722990871606625
absolute error = 1.445688639825736722990871606625
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.598
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.514
Order of pole (six term test) = -0.7713
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = 0
y[1] (numeric) = 1.4510006045142363335834413737432
absolute error = 1.4510006045142363335834413737432
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.604
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.522
Order of pole (six term test) = -0.7713
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = 0
y[1] (numeric) = 1.4563141908761568510774274367357
absolute error = 1.4563141908761568510774274367357
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.609
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.53
Order of pole (six term test) = -0.7713
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = 0
y[1] (numeric) = 1.4616294240570089725162232420815
absolute error = 1.4616294240570089725162232420815
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.614
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.538
Order of pole (six term test) = -0.7713
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = 0
y[1] (numeric) = 1.4669463291688396395129903011744
absolute error = 1.4669463291688396395129903011744
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.62
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.546
Order of pole (six term test) = -0.7713
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = 0
y[1] (numeric) = 1.47226493129077408416188844836
absolute error = 1.47226493129077408416188844836
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.625
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.554
Order of pole (six term test) = -0.7714
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = 0
y[1] (numeric) = 1.4775852554695544309457651724337
absolute error = 1.4775852554695544309457651724337
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.631
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.562
Order of pole (six term test) = -0.7714
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = 0
y[1] (numeric) = 1.4829073267200748942202090659994
absolute error = 1.4829073267200748942202090659994
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.636
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.57
Order of pole (six term test) = -0.7714
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (analytic) = 0
y[1] (numeric) = 1.4882311700259136103925771078135
absolute error = 1.4882311700259136103925771078135
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.642
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.578
Order of pole (six term test) = -0.7714
TOP MAIN SOLVE Loop
bytes used=92030352, alloc=4586680, time=3.20
x[1] = 2.84
y[1] (analytic) = 0
y[1] (numeric) = 1.4935568103398611434598304256552
absolute error = 1.4935568103398611434598304256552
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.647
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.586
Order of pole (six term test) = -0.7715
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = 0
y[1] (numeric) = 1.4988842725844457021206548956227
absolute error = 1.4988842725844457021206548956227
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.653
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.594
Order of pole (six term test) = -0.7715
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = 0
y[1] (numeric) = 1.5042135816524551062352997837857
absolute error = 1.5042135816524551062352997837857
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.658
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.602
Order of pole (six term test) = -0.7715
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = 0
y[1] (numeric) = 1.5095447624074555399707398082549
absolute error = 1.5095447624074555399707398082549
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.664
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.61
Order of pole (six term test) = -0.7716
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (analytic) = 0
y[1] (numeric) = 1.5148778396843071285390554531405
absolute error = 1.5148778396843071285390554531405
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.669
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.618
Order of pole (six term test) = -0.7716
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = 0
y[1] (numeric) = 1.5202128382896763750132368033135
absolute error = 1.5202128382896763750132368033135
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.675
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.626
Order of pole (six term test) = -0.7716
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = 0
y[1] (numeric) = 1.5255497830025454932868530022748
absolute error = 1.5255497830025454932868530022748
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.68
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.634
Order of pole (six term test) = -0.7717
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = 0
y[1] (numeric) = 1.5308886985747186728320997521941
absolute error = 1.5308886985747186728320997521941
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.686
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.642
Order of pole (six term test) = -0.7717
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (analytic) = 0
y[1] (numeric) = 1.5362296097313253105045498052959
absolute error = 1.5362296097313253105045498052959
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.691
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.65
Order of pole (six term test) = -0.7718
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = 0
y[1] (numeric) = 1.5415725411713202442423964795806
absolute error = 1.5415725411713202442423964795806
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.697
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.658
Order of pole (six term test) = -0.7718
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = 0
y[1] (numeric) = 1.5469175175679810231130097885443
absolute error = 1.5469175175679810231130097885443
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.702
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.666
Order of pole (six term test) = -0.7719
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = 0
y[1] (numeric) = 1.5522645635694022477701322712484
absolute error = 1.5522645635694022477701322712484
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.708
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.674
Order of pole (six term test) = -0.7719
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = 0
y[1] (numeric) = 1.5576137037989870150009420307339
absolute error = 1.5576137037989870150009420307339
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.713
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.682
Order of pole (six term test) = -0.772
TOP MAIN SOLVE Loop
bytes used=96032132, alloc=4652204, time=3.35
x[1] = 2.97
y[1] (analytic) = 0
y[1] (numeric) = 1.5629649628559354996634203085924
absolute error = 1.5629649628559354996634203085924
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.719
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.69
Order of pole (six term test) = -0.772
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = 0
y[1] (numeric) = 1.5683183653157307069408980740642
absolute error = 1.5683183653157307069408980740642
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.724
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.698
Order of pole (six term test) = -0.7721
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = 0
y[1] (numeric) = 1.5736739357306214274722399509888
absolute error = 1.5736739357306214274722399509888
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.73
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.707
Order of pole (six term test) = -0.7721
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (analytic) = 0
y[1] (numeric) = 1.5790316986301024275527751123346
absolute error = 1.5790316986301024275527751123346
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.735
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.715
Order of pole (six term test) = -0.7722
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (analytic) = 0
y[1] (numeric) = 1.5843916785213919062427256832332
absolute error = 1.5843916785213919062427256832332
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.741
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.723
Order of pole (six term test) = -0.7722
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = 0
y[1] (numeric) = 1.5897538998899062508664372025824
absolute error = 1.5897538998899062508664372025824
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.746
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.731
Order of pole (six term test) = -0.7723
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = 0
y[1] (numeric) = 1.5951183871997321220371076173417
absolute error = 1.5951183871997321220371076173417
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.752
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.739
Order of pole (six term test) = -0.7724
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = 0
y[1] (numeric) = 1.6004851648940958989978672380214
absolute error = 1.6004851648940958989978672380214
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.757
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.747
Order of pole (six term test) = -0.7724
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = 0
y[1] (numeric) = 1.605854257395830515730909457535
absolute error = 1.605854257395830515730909457535
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.762
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.755
Order of pole (six term test) = -0.7725
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (analytic) = 0
y[1] (numeric) = 1.6112256891078397179518394667203
absolute error = 1.6112256891078397179518394667203
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.768
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.763
Order of pole (six term test) = -0.7725
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = 0
y[1] (numeric) = 1.6165994844135597707764255520059
absolute error = 1.6165994844135597707764255520059
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.773
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.771
Order of pole (six term test) = -0.7726
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = 0
y[1] (numeric) = 1.6219756676774186465214358995171
absolute error = 1.6219756676774186465214358995171
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.779
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.779
Order of pole (six term test) = -0.7727
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = 0
y[1] (numeric) = 1.6273542632452927217801554002093
absolute error = 1.6273542632452927217801554002093
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.784
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.787
Order of pole (six term test) = -0.7727
TOP MAIN SOLVE Loop
bytes used=100033220, alloc=4652204, time=3.49
x[1] = 3.1
y[1] (analytic) = 0
y[1] (numeric) = 1.6327352954449610125964351540452
absolute error = 1.6327352954449610125964351540452
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.79
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.796
Order of pole (six term test) = -0.7728
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = 0
y[1] (numeric) = 1.638118788586556976248666744412
absolute error = 1.638118788586556976248666744412
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.795
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.804
Order of pole (six term test) = -0.7729
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = 0
y[1] (numeric) = 1.643504766963017907846829547008
absolute error = 1.643504766963017907846829547008
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.801
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.812
Order of pole (six term test) = -0.773
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = 0
y[1] (numeric) = 1.6488932548505319596416690929366
absolute error = 1.6488932548505319596416690929366
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.806
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.82
Order of pole (six term test) = -0.773
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = 0
y[1] (numeric) = 1.6542842765089828106450656382773
absolute error = 1.6542842765089828106450656382773
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.812
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.828
Order of pole (six term test) = -0.7731
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (analytic) = 0
y[1] (numeric) = 1.6596778561823920138646834683298
absolute error = 1.6596778561823920138646834683298
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.817
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.836
Order of pole (six term test) = -0.7732
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = 0
y[1] (numeric) = 1.6650740180993590481639929824931
absolute error = 1.6650740180993590481639929824931
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.823
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.844
Order of pole (six term test) = -0.7733
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = 0
y[1] (numeric) = 1.6704727864734991014706701765797
absolute error = 1.6704727864734991014706701765797
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.828
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.852
Order of pole (six term test) = -0.7734
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = 0
y[1] (numeric) = 1.6758741855038786117721436683556
absolute error = 1.6758741855038786117721436683556
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.834
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.861
Order of pole (six term test) = -0.7734
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (analytic) = 0
y[1] (numeric) = 1.6812782393754485920566207796734
absolute error = 1.6812782393754485920566207796734
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.839
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.869
Order of pole (six term test) = -0.7735
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = 0
y[1] (numeric) = 1.6866849722594757650812252323254
absolute error = 1.6866849722594757650812252323254
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.845
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.877
Order of pole (six term test) = -0.7736
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = 0
y[1] (numeric) = 1.6920944083139715335758645117251
absolute error = 1.6920944083139715335758645117251
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.85
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.885
Order of pole (six term test) = -0.7737
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = 0
y[1] (numeric) = 1.6975065716841188112220606017432
absolute error = 1.6975065716841188112220606017432
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.856
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.893
Order of pole (six term test) = -0.7738
TOP MAIN SOLVE Loop
bytes used=104034392, alloc=4652204, time=3.63
x[1] = 3.23
y[1] (analytic) = 0
y[1] (numeric) = 1.7029214865026967394801701994636
absolute error = 1.7029214865026967394801701994636
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.861
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.901
Order of pole (six term test) = -0.7739
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (analytic) = 0
y[1] (numeric) = 1.7083391768905033150761371724872
absolute error = 1.7083391768905033150761371724872
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.867
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.91
Order of pole (six term test) = -0.774
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = 0
y[1] (numeric) = 1.713759666956775952700109287779
absolute error = 1.713759666956775952700109287779
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.872
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.918
Order of pole (six term test) = -0.7741
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = 0
y[1] (numeric) = 1.7191829807996100072138623398372
absolute error = 1.7191829807996100072138623398372
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.878
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.926
Order of pole (six term test) = -0.7742
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = 0
y[1] (numeric) = 1.7246091425063752794119577971792
absolute error = 1.7246091425063752794119577971792
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.883
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.934
Order of pole (six term test) = -0.7743
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = 0
y[1] (numeric) = 1.7300381761541305291328658545424
absolute error = 1.7300381761541305291328658545424
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.889
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.942
Order of pole (six term test) = -0.7744
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = 0
y[1] (numeric) = 1.7354701058100360192708660181627
absolute error = 1.7354701058100360192708660181627
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.894
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.95
Order of pole (six term test) = -0.7745
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = 0
y[1] (numeric) = 1.7409049555317641139973445522612
absolute error = 1.7409049555317641139973445522612
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.9
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.959
Order of pole (six term test) = -0.7746
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = 0
y[1] (numeric) = 1.74634274936790795426109554604
absolute error = 1.74634274936790795426109554604
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.905
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.967
Order of pole (six term test) = -0.7747
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = 0
y[1] (numeric) = 1.7517835113583882334013540578509
absolute error = 1.7517835113583882334013540578509
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.91
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.975
Order of pole (six term test) = -0.7748
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (analytic) = 0
y[1] (numeric) = 1.7572272655348580954745005447906
absolute error = 1.7572272655348580954745005447906
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.916
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.983
Order of pole (six term test) = -0.7749
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = 0
y[1] (numeric) = 1.7626740359211061786656311184863
absolute error = 1.7626740359211061786656311184863
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.921
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.991
Order of pole (six term test) = -0.775
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = 0
y[1] (numeric) = 1.768123846533457825929444333208
absolute error = 1.768123846533457825929444333208
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.927
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4
Order of pole (six term test) = -0.7751
TOP MAIN SOLVE Loop
bytes used=108035464, alloc=4652204, time=3.77
x[1] = 3.36
y[1] (analytic) = 0
y[1] (numeric) = 1.7735767213811744847811091748165
absolute error = 1.7735767213811744847811091748165
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.932
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.008
Order of pole (six term test) = -0.7752
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = 0
y[1] (numeric) = 1.7790326844668513179369083419016
absolute error = 1.7790326844668513179369083419016
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.938
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.016
Order of pole (six term test) = -0.7753
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (analytic) = 0
y[1] (numeric) = 1.7844917597868130462864541440238
absolute error = 1.7844917597868130462864541440238
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.943
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.024
Order of pole (six term test) = -0.7754
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = 0
y[1] (numeric) = 1.7899539713315080454631104109204
absolute error = 1.7899539713315080454631104109204
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.949
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.032
Order of pole (six term test) = -0.7755
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = 0
y[1] (numeric) = 1.7954193430859007170668823978887
absolute error = 1.7954193430859007170668823978887
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.954
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.041
Order of pole (six term test) = -0.7756
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = 0
y[1] (numeric) = 1.8008878990298621553844181238392
absolute error = 1.8008878990298621553844181238392
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.96
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.049
Order of pole (six term test) = -0.7758
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (analytic) = 0
y[1] (numeric) = 1.8063596631385591302438598661135
absolute error = 1.8063596631385591302438598661135
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.965
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.057
Order of pole (six term test) = -0.7759
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = 0
y[1] (numeric) = 1.811834659382841406438055263984
absolute error = 1.811834659382841406438055263984
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.971
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.065
Order of pole (six term test) = -0.776
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = 0
y[1] (numeric) = 1.8173129117296274199480458710194
absolute error = 1.8173129117296274199480458710194
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.976
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.074
Order of pole (six term test) = -0.7761
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = 0
y[1] (numeric) = 1.822794444142288330999759870822
absolute error = 1.822794444142288330999759870822
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.982
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.082
Order of pole (six term test) = -0.7762
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = 0
y[1] (numeric) = 1.828279280581030473790408451284
absolute error = 1.828279280581030473790408451284
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.987
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.09
Order of pole (six term test) = -0.7764
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (analytic) = 0
y[1] (numeric) = 1.8337674450032762225271860238684
absolute error = 1.8337674450032762225271860238684
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.993
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.098
Order of pole (six term test) = -0.7765
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = 0
y[1] (numeric) = 1.8392589613640432932294676547055
absolute error = 1.8392589613640432932294676547055
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.998
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.107
Order of pole (six term test) = -0.7766
TOP MAIN SOLVE Loop
bytes used=112037040, alloc=4652204, time=3.92
x[1] = 3.49
y[1] (analytic) = 0
y[1] (numeric) = 1.8447538536163225005567478854165
absolute error = 1.8447538536163225005567478854165
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.004
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.115
Order of pole (six term test) = -0.7767
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = 0
y[1] (numeric) = 1.8502521457114539887380392592184
absolute error = 1.8502521457114539887380392592184
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.009
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.123
Order of pole (six term test) = -0.7769
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (analytic) = 0
y[1] (numeric) = 1.8557538615995019554943125717623
absolute error = 1.8557538615995019554943125717623
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.015
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.131
Order of pole (six term test) = -0.777
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = 0
y[1] (numeric) = 1.8612590252296278876637809105554
absolute error = 1.8612590252296278876637809105554
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.02
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.14
Order of pole (six term test) = -0.7771
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = 0
y[1] (numeric) = 1.8667676605504623270603732311105
absolute error = 1.8667676605504623270603732311105
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.026
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.148
Order of pole (six term test) = -0.7772
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = 0
y[1] (numeric) = 1.8722797915104751849185783575257
absolute error = 1.8722797915104751849185783575257
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.031
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.156
Order of pole (six term test) = -0.7774
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = 0
y[1] (numeric) = 1.8777954420583446231029352123761
absolute error = 1.8777954420583446231029352123761
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.037
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.164
Order of pole (six term test) = -0.7775
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (analytic) = 0
y[1] (numeric) = 1.8833146361433245200877685960922
absolute error = 1.8833146361433245200877685960922
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.042
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.173
Order of pole (six term test) = -0.7776
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = 0
y[1] (numeric) = 1.8888373977156105395422912594009
absolute error = 1.8888373977156105395422912594009
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.048
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.181
Order of pole (six term test) = -0.7778
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = 0
y[1] (numeric) = 1.8943637507267048191878821349114
absolute error = 1.8943637507267048191878821349114
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.053
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.189
Order of pole (six term test) = -0.7779
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = 0
y[1] (numeric) = 1.8998937191297792974281776791945
absolute error = 1.8998937191297792974281776791945
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.059
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.198
Order of pole (six term test) = -0.7781
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (analytic) = 0
y[1] (numeric) = 1.9054273268800376950885490529026
absolute error = 1.9054273268800376950885490529026
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.064
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.206
Order of pole (six term test) = -0.7782
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = 0
y[1] (numeric) = 1.9109645979350761694395535182514
absolute error = 1.9109645979350761694395535182514
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.069
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.214
Order of pole (six term test) = -0.7783
TOP MAIN SOLVE Loop
bytes used=116037996, alloc=4652204, time=4.06
x[1] = 3.62
y[1] (analytic) = 0
y[1] (numeric) = 1.9165055562552426575190155937973
absolute error = 1.9165055562552426575190155937973
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.075
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.222
Order of pole (six term test) = -0.7785
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = 0
y[1] (numeric) = 1.9220502258039949256094842500809
absolute error = 1.9220502258039949256094842500809
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.08
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.231
Order of pole (six term test) = -0.7786
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = 0
y[1] (numeric) = 1.9275986305482573415718992638653
absolute error = 1.9275986305482573415718992638653
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.086
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.239
Order of pole (six term test) = -0.7788
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (analytic) = 0
y[1] (numeric) = 1.9331507944587763865823557068127
absolute error = 1.9331507944587763865823557068127
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.091
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.247
Order of pole (six term test) = -0.7789
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = 0
y[1] (numeric) = 1.9387067415104749226668537785598
absolute error = 1.9387067415104749226668537785598
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.097
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.256
Order of pole (six term test) = -0.7791
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = 0
y[1] (numeric) = 1.944266495682805232278835567801
absolute error = 1.944266495682805232278835567801
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.102
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.264
Order of pole (six term test) = -0.7792
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = 0
y[1] (numeric) = 1.9498300809601008460161150061682
absolute error = 1.9498300809601008460161150061682
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.108
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.272
Order of pole (six term test) = -0.7794
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = 0
y[1] (numeric) = 1.9553975213319271744274768339795
absolute error = 1.9553975213319271744274768339795
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.113
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.281
Order of pole (six term test) = -0.7795
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (analytic) = 0
y[1] (numeric) = 1.960968840793430959714729780727
absolute error = 1.960968840793430959714729780727
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.119
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.289
Order of pole (six term test) = -0.7797
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = 0
y[1] (numeric) = 1.9665440633456885629933237170961
absolute error = 1.9665440633456885629933237170961
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.124
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.297
Order of pole (six term test) = -0.7798
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = 0
y[1] (numeric) = 1.9721232129960531026337559776601
absolute error = 1.9721232129960531026337559776601
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.13
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.306
Order of pole (six term test) = -0.78
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = 0
y[1] (numeric) = 1.9777063137585004590668744738098
absolute error = 1.9777063137585004590668744738098
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.135
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.314
Order of pole (six term test) = -0.7801
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (analytic) = 0
y[1] (numeric) = 1.9832933896539741612988110696235
absolute error = 1.9832933896539741612988110696235
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.141
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.322
Order of pole (six term test) = -0.7803
TOP MAIN SOLVE Loop
bytes used=120038912, alloc=4652204, time=4.20
x[1] = 3.75
y[1] (analytic) = 0
y[1] (numeric) = 1.9888844647107291702456247928593
absolute error = 1.9888844647107291702456247928593
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.146
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.331
Order of pole (six term test) = -0.7805
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = 0
y[1] (numeric) = 1.9944795629646745738637779655035
absolute error = 1.9944795629646745738637779655035
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.152
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.339
Order of pole (six term test) = -0.7806
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = 0
y[1] (numeric) = 2.0000787084597152089202867767593
absolute error = 2.0000787084597152089202867767593
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.157
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.347
Order of pole (six term test) = -0.7808
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = 0
y[1] (numeric) = 2.005681925248092224115759040544
absolute error = 2.005681925248092224115759040544
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.163
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.356
Order of pole (six term test) = -0.7809
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (analytic) = 0
y[1] (numeric) = 2.0112892373907225991445340694799
absolute error = 2.0112892373907225991445340694799
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.168
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.364
Order of pole (six term test) = -0.7811
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = 0
y[1] (numeric) = 2.0169006689575376341487512778172
absolute error = 2.0169006689575376341487512778172
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.174
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.373
Order of pole (six term test) = -0.7813
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = 0
y[1] (numeric) = 2.0225162440278204238973741408828
absolute error = 2.0225162440278204238973741408828
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.179
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.381
Order of pole (six term test) = -0.7814
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = 0
y[1] (numeric) = 2.0281359866905423308969636515959
absolute error = 2.0281359866905423308969636515959
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.185
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.389
Order of pole (six term test) = -0.7816
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (analytic) = 0
y[1] (numeric) = 2.0337599210446984715183099020762
absolute error = 2.0337599210446984715183099020762
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.19
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.398
Order of pole (six term test) = -0.7818
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = 0
y[1] (numeric) = 2.0393880711996422291018716655689
absolute error = 2.0393880711996422291018716655689
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.196
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.406
Order of pole (six term test) = -0.7819
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = 0
y[1] (numeric) = 2.0450204612754188078853219493551
absolute error = 2.0450204612754188078853219493551
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.201
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.414
Order of pole (six term test) = -0.7821
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = 0
y[1] (numeric) = 2.0506571154030978414783328198407
absolute error = 2.0506571154030978414783328198407
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.207
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.423
Order of pole (six term test) = -0.7823
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = 0
y[1] (numeric) = 2.0562980577251050694930360468837
absolute error = 2.0562980577251050694930360468837
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.212
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.431
Order of pole (six term test) = -0.7825
TOP MAIN SOLVE Loop
bytes used=124040804, alloc=4652204, time=4.34
x[1] = 3.88
y[1] (analytic) = 0
y[1] (numeric) = 2.0619433123955530958233482444464
absolute error = 2.0619433123955530958233482444464
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.217
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.44
Order of pole (six term test) = -0.7826
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = 0
y[1] (numeric) = 2.0675929035805712419525314514981
absolute error = 2.0675929035805712419525314514981
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.223
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.448
Order of pole (six term test) = -0.7828
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = 0
y[1] (numeric) = 2.0732468554586345085559540325673
absolute error = 2.0732468554586345085559540325673
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.228
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.456
Order of pole (six term test) = -0.783
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = 0
y[1] (numeric) = 2.0789051922208916585550041878693
absolute error = 2.0789051922208916585550041878693
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.234
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.465
Order of pole (six term test) = -0.7832
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (analytic) = 0
y[1] (numeric) = 2.0845679380714924346684713250312
absolute error = 2.0845679380714924346684713250312
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.239
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.473
Order of pole (six term test) = -0.7833
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = 0
y[1] (numeric) = 2.0902351172279139243994314003229
absolute error = 2.0902351172279139243994314003229
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.245
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.482
Order of pole (six term test) = -0.7835
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = 0
y[1] (numeric) = 2.0959067539212860852887336905532
absolute error = 2.0959067539212860852887336905532
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.25
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.49
Order of pole (six term test) = -0.7837
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = 0
y[1] (numeric) = 2.1015828723967164431605711680871
absolute error = 2.1015828723967164431605711680871
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.256
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.498
Order of pole (six term test) = -0.7839
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = 0
y[1] (numeric) = 2.1072634969136139759813078344069
absolute error = 2.1072634969136139759813078344069
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.261
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.507
Order of pole (six term test) = -0.7841
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (analytic) = 0
y[1] (numeric) = 2.1129486517460121958497173847148
absolute error = 2.1129486517460121958497173847148
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.267
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.515
Order of pole (six term test) = -0.7842
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = 0
y[1] (numeric) = 2.1186383611828914415350420345052
absolute error = 2.1186383611828914415350420345052
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.272
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.524
Order of pole (six term test) = -0.7844
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = 0
y[1] (numeric) = 2.1243326495285003938787920869072
absolute error = 2.1243326495285003938787920869072
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.278
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.532
Order of pole (six term test) = -0.7846
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = 0
y[1] (numeric) = 2.1300315411026768262769599419524
absolute error = 2.1300315411026768262769599419524
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.283
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.541
Order of pole (six term test) = -0.7848
TOP MAIN SOLVE Loop
bytes used=128043760, alloc=4652204, time=4.49
x[1] = 4.01
y[1] (analytic) = 0
y[1] (numeric) = 2.1357350602411676023613010639382
absolute error = 2.1357350602411676023613010639382
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.289
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.549
Order of pole (six term test) = -0.785
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (analytic) = 0
y[1] (numeric) = 2.141443231295947932901523478301
absolute error = 2.141443231295947932901523478301
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.294
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.557
Order of pole (six term test) = -0.7852
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = 0
y[1] (numeric) = 2.1471560786355399038546114381495
absolute error = 2.1471560786355399038546114381495
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.3
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.566
Order of pole (six term test) = -0.7854
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = 0
y[1] (numeric) = 2.1528736266453302873930729781997
absolute error = 2.1528736266453302873930729781997
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.305
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.574
Order of pole (six term test) = -0.7856
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = 0
y[1] (numeric) = 2.1585958997278876476506303741765
absolute error = 2.1585958997278876476506303741765
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.311
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.583
Order of pole (six term test) = -0.7857
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (analytic) = 0
y[1] (numeric) = 2.1643229223032787528317524777308
absolute error = 2.1643229223032787528317524777308
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.316
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.591
Order of pole (six term test) = -0.7859
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = 0
y[1] (numeric) = 2.170054718809384305240444141098
absolute error = 2.170054718809384305240444141098
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.322
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.6
Order of pole (six term test) = -0.7861
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = 0
y[1] (numeric) = 2.1757913137022140006938463308635
absolute error = 2.1757913137022140006938463308635
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.327
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.608
Order of pole (six term test) = -0.7863
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = 0
y[1] (numeric) = 2.1815327314562209286974471100031
absolute error = 2.1815327314562209286974471100031
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.333
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.617
Order of pole (six term test) = -0.7865
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = 0
y[1] (numeric) = 2.1872789965646153246710446972056
absolute error = 2.1872789965646153246710446972056
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.338
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.625
Order of pole (six term test) = -0.7867
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (analytic) = 0
y[1] (numeric) = 2.1930301335396776854280257462127
absolute error = 2.1930301335396776854280257462127
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.344
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.634
Order of pole (six term test) = -0.7869
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = 0
y[1] (numeric) = 2.1987861669130712590250114747197
absolute error = 2.1987861669130712590250114747197
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.349
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.642
Order of pole (six term test) = -0.7871
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = 0
y[1] (numeric) = 2.2045471212361539200144681537173
absolute error = 2.2045471212361539200144681537173
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.355
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.651
Order of pole (six term test) = -0.7873
TOP MAIN SOLVE Loop
bytes used=132044632, alloc=4652204, time=4.63
x[1] = 4.14
y[1] (analytic) = 0
y[1] (numeric) = 2.2103130210802894410494637746809
absolute error = 2.2103130210802894410494637746809
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.36
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.659
Order of pole (six term test) = -0.7875
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (analytic) = 0
y[1] (numeric) = 2.2160838910371581717073666606466
absolute error = 2.2160838910371581717073666606466
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.366
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.668
Order of pole (six term test) = -0.7877
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = 0
y[1] (numeric) = 2.2218597557190671353179117781731
absolute error = 2.2218597557190671353179117781731
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.371
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.676
Order of pole (six term test) = -0.7879
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = 0
y[1] (numeric) = 2.2276406397592595545006941211425
absolute error = 2.2276406397592595545006941211425
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.376
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.685
Order of pole (six term test) = -0.7881
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = 0
y[1] (numeric) = 2.2334265678122238160377735325806
absolute error = 2.2334265678122238160377735325806
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.382
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.693
Order of pole (six term test) = -0.7883
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = 0
y[1] (numeric) = 2.2392175645540018856286796402855
absolute error = 2.2392175645540018856286796402855
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.387
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.702
Order of pole (six term test) = -0.7885
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (analytic) = 0
y[1] (numeric) = 2.2450136546824971829976773112656
absolute error = 2.2450136546824971829976773112656
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.393
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.71
Order of pole (six term test) = -0.7887
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (analytic) = 0
y[1] (numeric) = 2.2508148629177819277466804534386
absolute error = 2.2508148629177819277466804534386
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.398
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.718
Order of pole (six term test) = -0.7889
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = 0
y[1] (numeric) = 2.256621214002403966271673552157
absolute error = 2.256621214002403966271673552157
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.404
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.727
Order of pole (six term test) = -0.7891
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = 0
y[1] (numeric) = 2.2624327327016930899859046295209
absolute error = 2.2624327327016930899859046295209
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.409
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.736
Order of pole (six term test) = -0.7893
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (analytic) = 0
y[1] (numeric) = 2.2682494438040668550194391233759
absolute error = 2.2682494438040668550194391233759
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.415
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.744
Order of pole (six term test) = -0.7895
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = 0
y[1] (numeric) = 2.2740713721213359134919004267843
absolute error = 2.2740713721213359134919004267843
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.42
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.753
Order of pole (six term test) = -0.7897
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = 0
y[1] (numeric) = 2.2798985424890088663833585906805
absolute error = 2.2798985424890088663833585906805
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.426
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.761
Order of pole (six term test) = -0.7899
TOP MAIN SOLVE Loop
bytes used=136045664, alloc=4652204, time=4.77
x[1] = 4.27
y[1] (analytic) = 0
y[1] (numeric) = 2.2857309797665966479573532097385
absolute error = 2.2857309797665966479573532097385
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.431
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.77
Order of pole (six term test) = -0.7901
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = 0
y[1] (numeric) = 2.2915687088379164516199391734153
absolute error = 2.2915687088379164516199391734153
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.437
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.778
Order of pole (six term test) = -0.7904
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (analytic) = 0
y[1] (numeric) = 2.297411754611395207029414309487
absolute error = 2.297411754611395207029414309487
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.442
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.787
Order of pole (six term test) = -0.7906
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = 0
y[1] (numeric) = 2.303260142020372618203015662185
absolute error = 2.303260142020372618203015662185
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.448
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.795
Order of pole (six term test) = -0.7908
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = 0
y[1] (numeric) = 2.3091138960234037722993460623127
absolute error = 2.3091138960234037722993460623127
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.453
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.804
Order of pole (six term test) = -0.791
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = 0
y[1] (numeric) = 2.314973041604561328688604736265
absolute error = 2.314973041604561328688604736265
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.459
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.812
Order of pole (six term test) = -0.7912
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = 0
y[1] (numeric) = 2.3208376037737372978568350790809
absolute error = 2.3208376037737372978568350790809
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.464
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.821
Order of pole (six term test) = -0.7914
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (analytic) = 0
y[1] (numeric) = 2.3267076075669444196253596363688
absolute error = 2.3267076075669444196253596363688
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.47
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.829
Order of pole (six term test) = -0.7916
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = 0
y[1] (numeric) = 2.3325830780466171501023371903143
absolute error = 2.3325830780466171501023371903143
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.475
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.838
Order of pole (six term test) = -0.7918
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = 0
y[1] (numeric) = 2.3384640403019122667199401494477
absolute error = 2.3384640403019122667199401494477
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.481
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.846
Order of pole (six term test) = -0.792
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = 0
y[1] (numeric) = 2.3443505194490091006480028560524
absolute error = 2.3443505194490091006480028560524
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.486
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.855
Order of pole (six term test) = -0.7923
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (analytic) = 0
y[1] (numeric) = 2.3502425406314094058131237349049
absolute error = 2.3502425406314094058131237349049
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.492
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.863
Order of pole (six term test) = -0.7925
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = 0
y[1] (numeric) = 2.3561401290202368736911073265529
absolute error = 2.3561401290202368736911073265529
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.497
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.872
Order of pole (six term test) = -0.7927
TOP MAIN SOLVE Loop
bytes used=140046600, alloc=4652204, time=4.91
x[1] = 4.4
y[1] (analytic) = 0
y[1] (numeric) = 2.3620433098145363029802972179747
absolute error = 2.3620433098145363029802972179747
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.503
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.88
Order of pole (six term test) = -0.7929
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = 0
y[1] (numeric) = 2.3679521082415724332037688680277
absolute error = 2.3679521082415724332037688680277
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.508
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.889
Order of pole (six term test) = -0.7931
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = 0
y[1] (numeric) = 2.3738665495571284512295136119221
absolute error = 2.3738665495571284512295136119221
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.514
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.898
Order of pole (six term test) = -0.7933
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (analytic) = 0
y[1] (numeric) = 2.3797866590458041796396431260614
absolute error = 2.3797866590458041796396431260614
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.519
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.906
Order of pole (six term test) = -0.7935
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = 0
y[1] (numeric) = 2.3857124620213139558222688688589
absolute error = 2.3857124620213139558222688688589
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.525
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.915
Order of pole (six term test) = -0.7938
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = 0
y[1] (numeric) = 2.391643983826784210603055128536
absolute error = 2.391643983826784210603055128536
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.53
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.923
Order of pole (six term test) = -0.794
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = 0
y[1] (numeric) = 2.3975812498350507551774990647405
absolute error = 2.3975812498350507551774990647405
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.535
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.932
Order of pole (six term test) = -0.7942
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (analytic) = 0
y[1] (numeric) = 2.4035242854489557850497483999967
absolute error = 2.4035242854489557850497483999967
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.541
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.94
Order of pole (six term test) = -0.7944
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = 0
y[1] (numeric) = 2.409473116101644609629219184346
absolute error = 2.409473116101644609629219184346
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.546
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.949
Order of pole (six term test) = -0.7946
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = 0
y[1] (numeric) = 2.4154277672568621160824144171226
absolute error = 2.4154277672568621160824144171226
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.552
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.957
Order of pole (six term test) = -0.7949
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = 0
y[1] (numeric) = 2.4213882644092489759841614673148
absolute error = 2.4213882644092489759841614673148
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.557
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.966
Order of pole (six term test) = -0.7951
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = 0
y[1] (numeric) = 2.4273546330846376032599744990584
absolute error = 2.4273546330846376032599744990584
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.563
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.974
Order of pole (six term test) = -0.7953
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (analytic) = 0
y[1] (numeric) = 2.433326898840347871859399897573
absolute error = 2.433326898840347871859399897573
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.568
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.983
Order of pole (six term test) = -0.7955
TOP MAIN SOLVE Loop
bytes used=144048116, alloc=4652204, time=5.06
x[1] = 4.53
y[1] (analytic) = 0
y[1] (numeric) = 2.4393050872654826015490105232055
absolute error = 2.4393050872654826015490105232055
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.574
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.992
Order of pole (six term test) = -0.7957
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = 0
y[1] (numeric) = 2.4452892239812228201631711194298
absolute error = 2.4452892239812228201631711194298
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.579
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5
Order of pole (six term test) = -0.7959
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = 0
y[1] (numeric) = 2.4512793346411228106007950876955
absolute error = 2.4512793346411228106007950876955
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.585
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.009
Order of pole (six term test) = -0.7962
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = 0
y[1] (numeric) = 2.4572754449314049508070449402843
absolute error = 2.4572754449314049508070449402843
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.59
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.017
Order of pole (six term test) = -0.7964
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = 0
y[1] (numeric) = 2.4632775805712543549302879720197
absolute error = 2.4632775805712543549302879720197
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.596
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.026
Order of pole (six term test) = -0.7966
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = 0
y[1] (numeric) = 2.4692857673131133237965980694204
absolute error = 2.4692857673131133237965980694204
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.601
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.034
Order of pole (six term test) = -0.7968
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = 0
y[1] (numeric) = 2.4753000309429756127966872133145
absolute error = 2.4753000309429756127966872133145
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.607
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.043
Order of pole (six term test) = -0.797
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = 0
y[1] (numeric) = 2.4813203972806805252333493332894
absolute error = 2.4813203972806805252333493332894
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.612
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.051
Order of pole (six term test) = -0.7973
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (analytic) = 0
y[1] (numeric) = 2.4873468921802068391312980371332
absolute error = 2.4873468921802068391312980371332
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.618
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.06
Order of pole (six term test) = -0.7975
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = 0
y[1] (numeric) = 2.4933795415299665754656717540168
absolute error = 2.4933795415299665754656717540168
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.623
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.069
Order of pole (six term test) = -0.7977
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = 0
y[1] (numeric) = 2.4994183712530986157204584745346
absolute error = 2.4994183712530986157204584745346
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.629
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.077
Order of pole (six term test) = -0.7979
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = 0
y[1] (numeric) = 2.505463407307762176643651110113
absolute error = 2.505463407307762176643651110113
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.634
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.086
Order of pole (six term test) = -0.7981
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = 0
y[1] (numeric) = 2.5115146756874301500220771819257
absolute error = 2.5115146756874301500220771819257
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.64
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.094
Order of pole (six term test) = -0.7984
TOP MAIN SOLVE Loop
bytes used=148048884, alloc=4652204, time=5.20
x[1] = 4.66
y[1] (analytic) = 0
y[1] (numeric) = 2.5175722024211823152555468242922
absolute error = 2.5175722024211823152555468242922
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.645
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.103
Order of pole (six term test) = -0.7986
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = 0
y[1] (numeric) = 2.5236360135739984324672247730179
absolute error = 2.5236360135739984324672247730179
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.651
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.111
Order of pole (six term test) = -0.7988
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = 0
y[1] (numeric) = 2.5297061352470512238449490119793
absolute error = 2.5297061352470512238449490119793
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.656
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.12
Order of pole (six term test) = -0.799
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = 0
y[1] (numeric) = 2.5357825935779992508665850602372
absolute error = 2.5357825935779992508665850602372
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.662
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.128
Order of pole (six term test) = -0.7992
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (analytic) = 0
y[1] (numeric) = 2.5418654147412796950214145667435
absolute error = 2.5418654147412796950214145667435
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.667
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.137
Order of pole (six term test) = -0.7995
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = 0
y[1] (numeric) = 2.547954624948401049599004089665
absolute error = 2.547954624948401049599004089665
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.673
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.146
Order of pole (six term test) = -0.7997
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = 0
y[1] (numeric) = 2.5540502504482357300769789004432
absolute error = 2.5540502504482357300769789004432
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.678
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.154
Order of pole (six term test) = -0.7999
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = 0
y[1] (numeric) = 2.5601523175273126105996316743421
absolute error = 2.5601523175273126105996316743421
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.684
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.163
Order of pole (six term test) = -0.8001
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = 0
y[1] (numeric) = 2.5662608525101094940003213911507
absolute error = 2.5662608525101094940003213911507
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.689
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.171
Order of pole (six term test) = -0.8003
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (analytic) = 0
y[1] (numeric) = 2.5723758817593455227821581288977
absolute error = 2.5723758817593455227821581288977
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.694
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.18
Order of pole (six term test) = -0.8005
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = 0
y[1] (numeric) = 2.5784974316762735384335192210662
absolute error = 2.5784974316762735384335192210662
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.7
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.188
Order of pole (six term test) = -0.8008
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = 0
y[1] (numeric) = 2.584625528700972396417496068156
absolute error = 2.584625528700972396417496068156
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.705
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.197
Order of pole (six term test) = -0.801
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = 0
y[1] (numeric) = 2.590760199312639244137423423891
absolute error = 2.590760199312639244137423423891
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.711
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.205
Order of pole (six term test) = -0.8012
TOP MAIN SOLVE Loop
bytes used=152051872, alloc=4652204, time=5.34
x[1] = 4.79
y[1] (analytic) = 0
y[1] (numeric) = 2.5969014700298817691441889623305
absolute error = 2.5969014700298817691441889623305
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.716
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.214
Order of pole (six term test) = -0.8014
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = 0
y[1] (numeric) = 2.6030493674110104248150551920822
absolute error = 2.6030493674110104248150551920822
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.722
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.222
Order of pole (six term test) = -0.8016
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = 0
y[1] (numeric) = 2.6092039180543306406982432042529
absolute error = 2.6092039180543306406982432042529
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.727
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.231
Order of pole (six term test) = -0.8018
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = 0
y[1] (numeric) = 2.615365148598435024682523276315
absolute error = 2.615365148598435024682523276315
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.733
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.24
Order of pole (six term test) = -0.802
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = 0
y[1] (numeric) = 2.6215330857224955641165260264368
absolute error = 2.6215330857224955641165260264368
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.738
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.248
Order of pole (six term test) = -0.8022
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (analytic) = 0
y[1] (numeric) = 2.627707756146555832968424709916
absolute error = 2.627707756146555832968424709916
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.744
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.257
Order of pole (six term test) = -0.8025
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = 0
y[1] (numeric) = 2.6338891866318232120830395243148
absolute error = 2.6338891866318232120830395243148
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.749
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.265
Order of pole (six term test) = -0.8027
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = 0
y[1] (numeric) = 2.640077403980961129560273660186
absolute error = 2.640077403980961129560273660186
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.755
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.274
Order of pole (six term test) = -0.8029
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = 0
y[1] (numeric) = 2.646272435038381328246103580801
absolute error = 2.646272435038381328246103580801
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.76
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.282
Order of pole (six term test) = -0.8031
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = 0
y[1] (numeric) = 2.6524743066905361672951079804744
absolute error = 2.6524743066905361672951079804744
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.766
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.291
Order of pole (six term test) = -0.8033
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (analytic) = 0
y[1] (numeric) = 2.6586830458662109647317264620251
absolute error = 2.6586830458662109647317264620251
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.771
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.299
Order of pole (six term test) = -0.8035
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = 0
y[1] (numeric) = 2.6648986795368163879060856555193
absolute error = 2.6648986795368163879060856555193
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.777
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.308
Order of pole (six term test) = -0.8037
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = 0
y[1] (numeric) = 2.6711212347166808987093127985763
absolute error = 2.6711212347166808987093127985763
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.782
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.316
Order of pole (six term test) = -0.8039
TOP MAIN SOLVE Loop
bytes used=156052692, alloc=4652204, time=5.49
x[1] = 4.92
y[1] (analytic) = 0
y[1] (numeric) = 2.6773507384633432603827702981538
absolute error = 2.6773507384633432603827702981538
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.788
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.325
Order of pole (six term test) = -0.8041
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (analytic) = 0
y[1] (numeric) = 2.6835872178778451127255851381681
absolute error = 2.6835872178778451127255851381681
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.793
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.333
Order of pole (six term test) = -0.8043
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = 0
y[1] (numeric) = 2.6898307001050236224752098873177
absolute error = 2.6898307001050236224752098873177
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.799
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.342
Order of pole (six term test) = -0.8045
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = 0
y[1] (numeric) = 2.6960812123338042156065332545541
absolute error = 2.6960812123338042156065332545541
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.804
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.35
Order of pole (six term test) = -0.8047
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = 0
y[1] (numeric) = 2.702338781797493398266253449184
absolute error = 2.702338781797493398266253449184
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.81
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.359
Order of pole (six term test) = -0.8049
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = 0
y[1] (numeric) = 2.708603435774071673030832897127
absolute error = 2.708603435774071673030832897127
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.815
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.367
Order of pole (six term test) = -0.8051
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (analytic) = 0
y[1] (numeric) = 2.7148752015864865571483640673378
absolute error = 2.7148752015864865571483640673378
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.821
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.376
Order of pole (six term test) = -0.8053
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = 0
y[1] (numeric) = 2.7211541066029457093970892493888
absolute error = 2.7211541066029457093970892493888
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.826
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.384
Order of pole (six term test) = -0.8055
Finished!
diff ( y , x , 1 ) = expt((0.1 * x + 0.2) , (0.2 * x + 0.3));
Iterations = 490
Total Elapsed Time = 5 Seconds
Elapsed Time(since restart) = 5 Seconds
Time to Timeout = 2 Minutes 54 Seconds
Percent Done = 100.2 %
> quit
bytes used=158481356, alloc=4652204, time=5.57