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._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007
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> #BEGIN OUTFILE1
> # Begin Function number 3
> display_poles := proc()
> global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ;
> local rad_given;
> if (glob_type_given_pole = 4) then # if number 1
> rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ;
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," ");
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 2;
> if (array_poles[1,1] <> glob_large_float) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," ");
> omniout_str(ALWAYS,"Order of pole (ratio test) Not computed");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 2;
> if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 2;
> if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," ");
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 2
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_large_float, array_pole,
glob_type_given_pole, array_given_rad_poles, array_given_ord_poles,
array_complex_poles, array_poles, array_real_poles, array_x;
if glob_type_given_pole = 4 then
rad_given := sqrt(
expt(array_x[1] - array_given_rad_poles[1, 1], 2.0)
+ expt(array_given_rad_poles[1, 2], 2.0));
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ")
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_poles[1, 1], 4, " ");
omniout_str(ALWAYS, "Order of pole (ratio test) \
Not computed")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if 0. < array_real_poles[1, 1] and
array_real_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_real_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_real_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if 0. < array_complex_poles[1, 1] and
array_complex_poles[1, 1] <> glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_complex_poles[1, 1], 4, " ");
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_complex_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
> # End Function number 3
> # Begin Function number 4
> check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 2
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 2;
> ret;;
> end;
check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
> # End Function number 4
> # Begin Function number 5
> est_size_answer := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local min_size;
> min_size := glob_large_float;
> if (omniabs(array_y[1]) < min_size) then # if number 2
> min_size := omniabs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> if (min_size < 1.0) then # if number 2
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 2;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
min_size := glob_large_float;
if omniabs(array_y[1]) < min_size then
min_size := omniabs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 1.0 then
min_size := 1.0;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
> # End Function number 5
> # Begin Function number 6
> test_suggested_h := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := 0.0;
> no_terms := glob_max_terms;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 2
> max_estimated_step_error := est_tmp;
> fi;# end if 2;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
max_estimated_step_error := 0.;
no_terms := glob_max_terms;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := omniabs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
> # End Function number 6
> # Begin Function number 7
> reached_interval := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local ret;
> if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2
> ret := true;
> else
> ret := false;
> fi;# end if 2;
> return(ret);
> end;
reached_interval := proc()
local ret;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then
ret := true
else ret := false
end if;
return ret
end proc
> # End Function number 7
> # Begin Function number 8
> display_alot := proc(iter)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 2
> if (iter >= 0) then # if number 3
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> analytic_val_y := exact_soln_y(ind_var);
> omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := omniabs(numeric_val - analytic_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (omniabs(analytic_val_y) <> 0.0) then # if number 4
> relerr := abserr*100.0/omniabs(analytic_val_y);
> if (relerr > 0.0000000000000000000000000000000001) then # if number 5
> glob_good_digits := -trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 5;
> else
> relerr := -1.0 ;
> glob_good_digits := -1;
> fi;# end if 4;
> if (glob_iter = 1) then # if number 4
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 4;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 3;
> #BOTTOM DISPLAY ALOT
> fi;# end if 2;
> end;
display_alot := proc(iter)
local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
analytic_val_y := exact_soln_y(ind_var);
omniout_float(ALWAYS, "y[1] (analytic) ", 33,
analytic_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := omniabs(numeric_val - analytic_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if omniabs(analytic_val_y) <> 0. then
relerr := abserr*100.0/omniabs(analytic_val_y);
if 0.1*10^(-33) < relerr then
glob_good_digits := -trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -1
end if;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
> # End Function number 8
> # Begin Function number 9
> adjust_for_pole := proc(h_param)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local hnew, sz2, tmp;
> #TOP ADJUST FOR POLE
> hnew := h_param;
> glob_normmax := glob_small_float;
> if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2
> tmp := omniabs(array_y_higher[1,1]);
> if (tmp < glob_normmax) then # if number 3
> glob_normmax := tmp;
> fi;# end if 3
> fi;# end if 2;
> if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2
> sz2 := array_pole[1]/10.0;
> if (sz2 < hnew) then # if number 3
> omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity.");
> omniout_str(INFO,"Reached Optimal");
> return(hnew);
> fi;# end if 3
> fi;# end if 2;
> if ( not glob_reached_optimal_h) then # if number 2
> glob_reached_optimal_h := true;
> glob_curr_iter_when_opt := glob_current_iter;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> glob_optimal_start := array_x[1];
> fi;# end if 2;
> hnew := sz2;
> ;#END block
> return(hnew);
> #BOTTOM ADJUST FOR POLE
> end;
adjust_for_pole := proc(h_param)
local hnew, sz2, tmp;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
hnew := h_param;
glob_normmax := glob_small_float;
if glob_small_float < omniabs(array_y_higher[1, 1]) then
tmp := omniabs(array_y_higher[1, 1]);
if tmp < glob_normmax then glob_normmax := tmp end if
end if;
if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and
array_pole[1] <> glob_large_float then
sz2 := array_pole[1]/10.0;
if sz2 < hnew then
omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12,
"due to singularity.");
omniout_str(INFO, "Reached Optimal");
return hnew
end if
end if;
if not glob_reached_optimal_h then
glob_reached_optimal_h := true;
glob_curr_iter_when_opt := glob_current_iter;
glob_optimal_clock_start_sec := elapsed_time_seconds();
glob_optimal_start := array_x[1]
end if;
hnew := sz2;
return hnew
end proc
> # End Function number 9
> # Begin Function number 10
> prog_report := proc(x_start,x_end)
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
> glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
> left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1);
> expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec));
> opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr(convfloat(total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr(convfloat(glob_clock_sec));
> if (convfloat(percent_done) < convfloat(100.0)) then # if number 2
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr(convfloat(expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr(convfloat(glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr(convfloat(glob_total_exp_sec));
> fi;# end if 2;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr(convfloat(left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_orig_start_sec);
glob_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_clock_start_sec);
left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec)
- convfloat(clock_sec1);
expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h),
convfloat(clock_sec1) - convfloat(glob_orig_start_sec));
opt_clock_sec :=
convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec);
glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),
convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h),
convfloat(opt_clock_sec));
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(convfloat(x_end), convfloat(x_start),
convfloat(array_x[1]) + convfloat(glob_h));
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(convfloat(total_clock_sec));
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(convfloat(glob_clock_sec));
if convfloat(percent_done) < convfloat(100.0) then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(convfloat(expect_sec));
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(convfloat(glob_optimal_expect_sec));
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(convfloat(glob_total_exp_sec))
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(convfloat(left_sec));
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
> # End Function number 10
> # Begin Function number 11
> check_for_pole := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad;
> #TOP CHECK FOR POLE
> array_pole[1] := glob_large_float;
> array_pole[2] := glob_large_float;
> tmp_rad := glob_large_float;
> prev_tmp_rad := glob_large_float;
> tmp_ratio := glob_large_float;
> rad_c := glob_large_float;
> array_poles[1,1] := glob_large_float;
> array_poles[1,2] := glob_large_float;
> #TOP radius ratio test in Henrici1
> found_sing := 1;
> n := glob_max_terms - 1 - 10;
> cnt := 0;
> while ((cnt < 5) and (found_sing = 1)) do # do number 1
> if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2
> found_sing := 0;
> else
> tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3
> if (tmp_rad < rad_c) then # if number 4
> rad_c := tmp_rad;
> fi;# end if 4;
> elif
> (cnt = 0) then # if number 4
> if (tmp_rad < rad_c) then # if number 5
> rad_c := tmp_rad;
> fi;# end if 5;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5
> fi;# end if 4;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> n := n + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 4
> if (rad_c < array_pole[1]) then # if number 5
> array_pole[1] := rad_c;
> array_poles[1,1] := rad_c;
> fi;# end if 5;
> fi;# end if 4;
> #BOTTOM radius ratio test in Henrici1
> #IN RADII REAL EQ = 1
> #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1
> #Applies to pole of arbitrary r_order on the real axis,
> #Due to Prof. George Corliss.
> n := glob_max_terms;
> m := n - 1 - 1;
> while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1
> m := m - 1;
> od;# end do number 1;
> if (m > 10) then # if number 4
> rm0 := array_y_higher[1,m]/array_y_higher[1,m-1];
> rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2];
> hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1;
> if (omniabs(hdrc) > 0.0) then # if number 5
> rcs := glob_h/hdrc;
> ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc;
> array_real_poles[1,1] := rcs;
> array_real_poles[1,2] := ord_no;
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 5
> else
> array_real_poles[1,1] := glob_large_float;
> array_real_poles[1,2] := glob_large_float;
> fi;# end if 4;
> #BOTTOM RADII REAL EQ = 1
> #TOP RADII COMPLEX EQ = 1
> #Computes radius of convergence for complex conjugate pair of poles.
> #from 6 adjacent Taylor series terms
> #Also computes r_order of poles.
> #Due to Manuel Prieto.
> #With a correction by Dennis J. Darland
> n := glob_max_terms - 1 - 1;
> cnt := 0;
> while ((cnt < 5) and (n >= 10)) do # do number 1
> if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4
> cnt := cnt + 1;
> else
> cnt := 0;
> fi;# end if 4;
> n := n - 1;
> od;# end do number 1;
> m := n + cnt;
> if (m <= 10) then # if number 4
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]);
> rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]);
> rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]);
> rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]);
> rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]);
> nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2;
> nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> else
> if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0;
> if (omniabs(rcs) <> 0.0) then # if number 7
> if (rcs > 0.0) then # if number 8
> rad_c := sqrt(rcs) * omniabs(glob_h);
> else
> rad_c := glob_large_float;
> fi;# end if 8
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 7
> else
> rad_c := glob_large_float;
> ord_no := glob_large_float;
> fi;# end if 6
> fi;# end if 5;
> array_complex_poles[1,1] := rad_c;
> array_complex_poles[1,2] := ord_no;
> fi;# end if 4;
> #BOTTOM RADII COMPLEX EQ = 1
> #START ADJUST ALL SERIES
> if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4
> h_new := array_pole[1] * glob_ratio_of_radius;
> term := 1;
> ratio := 1.0;
> while (term <= glob_max_terms) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / omniabs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 4;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 4
> display_poles();
> fi;# end if 4
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs,
rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test,
tmp_rad, tmp_ratio, prev_tmp_rad;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_pole[1] := glob_large_float;
array_pole[2] := glob_large_float;
tmp_rad := glob_large_float;
prev_tmp_rad := glob_large_float;
tmp_ratio := glob_large_float;
rad_c := glob_large_float;
array_poles[1, 1] := glob_large_float;
array_poles[1, 2] := glob_large_float;
found_sing := 1;
n := glob_max_terms - 11;
cnt := 0;
while cnt < 5 and found_sing = 1 do
if omniabs(array_y_higher[1, n]) = 0. or
omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0
else
tmp_rad := omniabs(
array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif cnt = 0 then
if tmp_rad < rad_c then rad_c := tmp_rad end if
elif 0 < cnt then found_sing := 0
end if
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
n := n + 1
end do;
if found_sing = 1 then
if rad_c < array_pole[1] then
array_pole[1] := rad_c; array_poles[1, 1] := rad_c
end if
end if;
n := glob_max_terms;
m := n - 2;
while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or
omniabs(array_y_higher[1, m - 1]) = 0. or
omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1
end do;
if 10 < m then
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1;
if 0. < omniabs(hdrc) then
rcs := glob_h/hdrc;
ord_no := (
rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc
;
array_real_poles[1, 1] := rcs;
array_real_poles[1, 2] := ord_no
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if
else
array_real_poles[1, 1] := glob_large_float;
array_real_poles[1, 2] := glob_large_float
end if;
n := glob_max_terms - 2;
cnt := 0;
while cnt < 5 and 10 <= n do
if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1
else cnt := 0
end if;
n := n - 1
end do;
m := n + cnt;
if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float
else
rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1];
rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2];
rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3];
rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4];
rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5];
nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1
+ convfloat(m - 3)*rm2;
nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2
+ convfloat(m - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then
rad_c := glob_large_float; ord_no := glob_large_float
else
if omniabs(nr1*dr2 - nr2*dr1) <> 0. then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0;
if omniabs(rcs) <> 0. then
if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h)
else rad_c := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
else rad_c := glob_large_float; ord_no := glob_large_float
end if
end if;
array_complex_poles[1, 1] := rad_c;
array_complex_poles[1, 2] := ord_no
end if;
if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then
h_new := array_pole[1]*glob_ratio_of_radius;
term := 1;
ratio := 1.0;
while term <= glob_max_terms do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/omniabs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
> # End Function number 11
> # Begin Function number 12
> get_norms := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local iii;
> if ( not glob_initial_pass) then # if number 4
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> array_norms[iii] := 0.0;
> iii := iii + 1;
> od;# end do number 1;
> #TOP GET NORMS
> iii := 1;
> while (iii <= glob_max_terms) do # do number 1
> if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5
> array_norms[iii] := omniabs(array_y[iii]);
> fi;# end if 5;
> iii := iii + 1;
> od;# end do number 1
> #BOTTOM GET NORMS
> ;
> fi;# end if 4;
> end;
get_norms := proc()
local iii;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
if not glob_initial_pass then
iii := 1;
while iii <= glob_max_terms do
array_norms[iii] := 0.; iii := iii + 1
end do;
iii := 1;
while iii <= glob_max_terms do
if array_norms[iii] < omniabs(array_y[iii]) then
array_norms[iii] := omniabs(array_y[iii])
end if;
iii := iii + 1
end do
end if
end proc
> # End Function number 12
> # Begin Function number 13
> atomall := proc()
> global
> glob_max_terms,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_html_log,
> glob_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_disp_incr,
> glob_h,
> glob_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_last_good_h,
> glob_look_poles,
> glob_neg_h,
> glob_display_interval,
> glob_next_display,
> glob_dump_analytic,
> glob_abserr,
> glob_relerr,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_curr_iter_when_opt,
> glob_current_iter,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> #END OUTFILE1
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> #emit pre tanh $eq_no = 1
> array_tmp4_a1[1] := sinh(array_tmp3[1]);
> array_tmp4_a2[1] := cosh(array_tmp3[1]);
> array_tmp4[1] := (array_tmp4_a1[1] / array_tmp4_a2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1);
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[2,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0;
> #emit pre tanh $eq_no = 1
> array_tmp4_a1[2] := att(1,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[2] := att(1,array_tmp4_a1,array_tmp3,1);
> array_tmp4[2] := (array_tmp4_a1[2] - ats(2,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2);
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0.0;
> array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre tanh $eq_no = 1
> array_tmp4_a1[3] := att(2,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[3] := att(2,array_tmp4_a1,array_tmp3,1);
> array_tmp4[3] := (array_tmp4_a1[3] - ats(3,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3);
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0.0;
> array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre tanh $eq_no = 1
> array_tmp4_a1[4] := att(3,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[4] := att(3,array_tmp4_a1,array_tmp3,1);
> array_tmp4[4] := (array_tmp4_a1[4] - ats(4,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4);
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0.0;
> array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0;
> #emit pre tanh $eq_no = 1
> array_tmp4_a1[5] := att(4,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[5] := att(4,array_tmp4_a1,array_tmp3,1);
> array_tmp4[5] := (array_tmp4_a1[5] - ats(5,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= glob_max_terms) then # if number 2
> temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5);
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= glob_max_terms) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0.0;
> array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0;
> array_tmp4_a1[kkk] := att(kkk-1 ,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[kkk] := att(kkk-1,array_tmp4_a1,array_tmp3,1);
> array_tmp4[kkk] := (array_tmp4_a1[kkk] - ats(kkk ,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d < glob_max_terms) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while (term >= 1) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := temporary / glob_h * convfp(adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
array_tmp1[1] := array_const_2D0[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4_a1[1] := sinh(array_tmp3[1]);
array_tmp4_a2[1] := cosh(array_tmp3[1]);
array_tmp4[1] := array_tmp4_a1[1]/array_tmp4_a2[1];
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= glob_max_terms then
temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1);
array_y[2] := temporary;
array_y_higher[1, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[2, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_2D0[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0);
array_tmp4_a1[2] := att(1, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[2] := att(1, array_tmp4_a1, array_tmp3, 1);
array_tmp4[2] := (
array_tmp4_a1[2] - ats(2, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= glob_max_terms then
temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2);
array_y[3] := temporary;
array_y_higher[1, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary
end if
end if;
kkk := 3;
array_tmp3[3] := 0.;
array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4_a1[3] := att(2, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[3] := att(2, array_tmp4_a1, array_tmp3, 1);
array_tmp4[3] := (
array_tmp4_a1[3] - ats(3, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= glob_max_terms then
temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3);
array_y[4] := temporary;
array_y_higher[1, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary
end if
end if;
kkk := 4;
array_tmp3[4] := 0.;
array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4_a1[4] := att(3, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[4] := att(3, array_tmp4_a1, array_tmp3, 1);
array_tmp4[4] := (
array_tmp4_a1[4] - ats(4, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= glob_max_terms then
temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4);
array_y[5] := temporary;
array_y_higher[1, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary
end if
end if;
kkk := 5;
array_tmp3[5] := 0.;
array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0)
;
array_tmp4_a1[5] := att(4, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[5] := att(4, array_tmp4_a1, array_tmp3, 1);
array_tmp4[5] := (
array_tmp4_a1[5] - ats(5, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= glob_max_terms then
temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5);
array_y[6] := temporary;
array_y_higher[1, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= glob_max_terms do
array_tmp3[kkk] := 0.;
array_tmp3[kkk] :=
-ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0);
array_tmp4_a1[kkk] := att(kkk - 1, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[kkk] := att(kkk - 1, array_tmp4_a1, array_tmp3, 1);
array_tmp4[kkk] := (
array_tmp4_a1[kkk] - ats(kkk, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[kkk] := array_tmp4[kkk];
order_d := 1;
if kkk + order_d < glob_max_terms then
if not array_y_set_initial[1, kkk + order_d] then
temporary := array_tmp5[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while 1 <= term do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := temporary*convfp(adj2)/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
> # End Function number 13
> #BEGIN ATS LIBRARY BLOCK
> # Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s
", str)
end if
end proc
> # End Function number 2
> # Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
> # End Function number 3
> # Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
> # End Function number 4
> # Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-42.4g %s
", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 5
> # Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then printf("%-30s = %-32d %s
", prelabel, value, postlabel)
else printf("%-30s = %-32d %s
", prelabel, value, postlabel)
end if
end if
end proc
> # End Function number 6
> # Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
> # End Function number 7
> # Begin Function number 8
> dump_series := proc(iolevel,dump_label,series_name,arr_series,numb)
> global glob_iolevel;
> local i;
> if (glob_iolevel >= iolevel) then # if number 0
> i := 1;
> while (i <= numb) do # do number 1
> print(dump_label,series_name
> ,i,arr_series[i]);
> i := i + 1;
> od;# end do number 1
> fi;# end if 0
> end;
dump_series := proc(iolevel, dump_label, series_name, arr_series, numb)
local i;
global glob_iolevel;
if iolevel <= glob_iolevel then
i := 1;
while i <= numb do
print(dump_label, series_name, i, arr_series[i]); i := i + 1
end do
end if
end proc
> # End Function number 8
> # Begin Function number 9
> dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x)
> global glob_iolevel;
> local i,sub,ts_term;
> if (glob_iolevel >= iolevel) then # if number 0
> sub := 1;
> while (sub <= subnum) do # do number 1
> i := 1;
> while (i <= numb) do # do number 2
> print(dump_label,series_name2,sub,i,arr_series2[sub,i]);
> od;# end do number 2;
> sub := sub + 1;
> od;# end do number 1;
> fi;# end if 0;
> end;
dump_series_2 := proc(
iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x)
local i, sub, ts_term;
global glob_iolevel;
if iolevel <= glob_iolevel then
sub := 1;
while sub <= subnum do
i := 1;
while i <= numb do print(dump_label, series_name2, sub, i,
arr_series2[sub, i])
end do;
sub := sub + 1
end do
end if
end proc
> # End Function number 9
> # Begin Function number 10
> cs_info := proc(iolevel,str)
> global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h;
> if (glob_iolevel >= iolevel) then # if number 0
> print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h)
> fi;# end if 0;
> end;
cs_info := proc(iolevel, str)
global
glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h;
if iolevel <= glob_iolevel then print("cs_info ", str,
" glob_correct_start_flag = ", glob_correct_start_flag,
"glob_h := ", glob_h, "glob_reached_optimal_h := ",
glob_reached_optimal_h)
end if
end proc
> # End Function number 10
> # Begin Function number 11
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," Unknown");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " Unknown")
end if;
fprintf(fd, " |
")
end proc
> # End Function number 11
> # Begin Function number 12
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := trunc(secs_in / glob_sec_in_year);
> sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year));
> days_int := trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ;
> hours_int := trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod trunc(glob_sec_in_hour));
> minutes_int := trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" Unknown\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := trunc(secs_in/glob_sec_in_year);
sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year);
days_int := trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod trunc(glob_sec_in_day);
hours_int := trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod trunc(glob_sec_in_hour);
minutes_int := trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod trunc(glob_sec_in_minute);
if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\
nutes %d Seconds
", years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\
Seconds
", days_int, hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\
s
", hours_int, minutes_int, sec_int)
elif 0 < minutes_int then printf(" = %d Minutes %d Seconds
", minutes_int, sec_int)
else printf(" = %d Seconds
", sec_int)
end if
else printf(" Unknown
")
end if
end proc
> # End Function number 12
> # Begin Function number 13
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
ret_ats := 0.;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats];
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
> # End Function number 13
> # Begin Function number 14
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global glob_max_terms;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> if (jjj_att <= mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while (iii_att <= mmm_att) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if (lll_att <= glob_max_terms) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / convfp(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global glob_max_terms;
ret_att := 0.;
if jjj_att <= mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att <= mmm_att do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= glob_max_terms then ret_att :=
ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/convfp(mmm_att)
end if;
ret_att
end proc
> # End Function number 14
> # Begin Function number 15
> display_pole_debug := proc(typ,m,radius,order2)
> global ALWAYS,glob_display_flag, glob_large_float, array_pole;
> if (typ = 1) then # if number 6
> omniout_str(ALWAYS,"Real");
> else
> omniout_str(ALWAYS,"Complex");
> fi;# end if 6;
> omniout_int(ALWAYS,"m",4, m ,4," ");
> omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," ");
> omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," ");
> end;
display_pole_debug := proc(typ, m, radius, order2)
global ALWAYS, glob_display_flag, glob_large_float, array_pole;
if typ = 1 then omniout_str(ALWAYS, "Real")
else omniout_str(ALWAYS, "Complex")
end if;
omniout_int(ALWAYS, "m", 4, m, 4, " ");
omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4,
" ");
omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4,
" ")
end proc
> # End Function number 15
> # Begin Function number 16
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
> # End Function number 16
> # Begin Function number 17
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
> # End Function number 17
> # Begin Function number 18
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
> # End Function number 18
> # Begin Function number 19
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float;
> local good_digits;
> fprintf(file,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7
> good_digits := 1-trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float;
fprintf(file, "");
if rel_error <> -1.0 then
if 0.1*10^(-33) < rel_error then
good_digits := 1 - trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
fprintf(file, " | ")
end proc
> # End Function number 19
> # Begin Function number 20
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
> # End Function number 20
> # Begin Function number 21
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
> # End Function number 21
> # Begin Function number 22
> logitem_pole := proc(file,pole)
> fprintf(file,"");
> if (pole = 0) then # if number 6
> fprintf(file,"NA");
> elif
> (pole = 1) then # if number 7
> fprintf(file,"Real");
> elif
> (pole = 2) then # if number 8
> fprintf(file,"Complex");
> elif
> (pole = 4) then # if number 9
> fprintf(file,"Yes");
> else
> fprintf(file,"No");
> fi;# end if 9
> fprintf(file," | ");
> end;
logitem_pole := proc(file, pole)
fprintf(file, "");
if pole = 0 then fprintf(file, "NA")
elif pole = 1 then fprintf(file, "Real")
elif pole = 2 then fprintf(file, "Complex")
elif pole = 4 then fprintf(file, "Yes")
else fprintf(file, "No")
end if;
fprintf(file, " | ")
end proc
> # End Function number 22
> # Begin Function number 23
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
> # End Function number 23
> # Begin Function number 24
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file)
fprintf(file, "
")
end proc
> # End Function number 24
> # Begin Function number 25
> chk_data := proc()
> global glob_max_iter,ALWAYS, glob_max_terms;
> local errflag;
> errflag := false;
> if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9
> omniout_str(ALWAYS,"Illegal max_terms = -- Using 30");
> glob_max_terms := 30;
> fi;# end if 9;
> if (glob_max_iter < 2) then # if number 9
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 9;
> if (errflag) then # if number 9
> quit;
> fi;# end if 9
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, glob_max_terms;
errflag := false;
if glob_max_terms < 15 or 512 < glob_max_terms then
omniout_str(ALWAYS, "Illegal max_terms = -- Using 30");
glob_max_terms := 30
end if;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
> # End Function number 25
> # Begin Function number 26
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 9
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 10
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> fi;# end if 10
> fi;# end if 9;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 0.
end if
end if;
sec_left
end proc
> # End Function number 26
> # Begin Function number 27
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 9
> rrr := (100.0*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 9;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := 100.0*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
> # End Function number 27
> # Begin Function number 28
> factorial_2 := proc(nnn)
> nnn!;
> end;
factorial_2 := proc(nnn) nnn! end proc
> # End Function number 28
> # Begin Function number 29
> factorial_1 := proc(nnn)
> global glob_max_terms,array_fact_1;
> local ret;
> if (nnn <= glob_max_terms) then # if number 9
> if (array_fact_1[nnn] = 0) then # if number 10
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 10;
> else
> ret := factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global glob_max_terms, array_fact_1;
if nnn <= glob_max_terms then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
> # End Function number 29
> # Begin Function number 30
> factorial_3 := proc(mmm,nnn)
> global glob_max_terms,array_fact_2;
> local ret;
> if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9
> if (array_fact_2[mmm,nnn] = 0) then # if number 10
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 10;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 9;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global glob_max_terms, array_fact_2;
if nnn <= glob_max_terms and mmm <= glob_max_terms then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
> # End Function number 30
> # Begin Function number 31
> convfp := proc(mmm)
> (mmm);
> end;
convfp := proc(mmm) mmm end proc
> # End Function number 31
> # Begin Function number 32
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
> # End Function number 32
> # Begin Function number 33
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
> # End Function number 33
> # Begin Function number 34
> omniabs := proc(x)
> abs(x);
> end;
omniabs := proc(x) abs(x) end proc
> # End Function number 34
> # Begin Function number 35
> expt := proc(x,y)
> (x^y);
> end;
expt := proc(x, y) x^y end proc
> # End Function number 35
> # Begin Function number 36
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer);
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := omniabs(desired_abs_gbl_error / estimated_steps);
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer);
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := omniabs(desired_abs_gbl_error/estimated_steps);
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
> # End Function number 36
> #END ATS LIBRARY BLOCK
> #BEGIN USER DEF BLOCK
> #BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(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_2D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_pole,
> array_real_pole,
> array_complex_pole,
> array_1st_rel_error,
> array_last_rel_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_poles,
> array_given_rad_poles,
> array_given_ord_poles,
> array_real_poles,
> array_complex_poles,
> array_fact_2,
> glob_last;
> glob_last;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := INFO;
> glob_max_terms := 30;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_estimated_step_error := 0.0;
> glob_ratio_of_radius := 0.1;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_html_log := true;
> glob_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_sec_in_minute := 60;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_disp_incr := 0.1;
> glob_h := 0.1;
> glob_max_h := 0.1;
> glob_min_h := 0.000001;
> glob_type_given_pole := 0;
> glob_large_float := 9.0e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_neg_h := false;
> glob_display_interval := 0.0;
> glob_next_display := 0.0;
> glob_dump_analytic := false;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_curr_iter_when_opt := 0;
> glob_current_iter := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_max_minutes := 0.0;
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> MAX_UNCHANGED := 10;
> glob_curr_iter_when_opt := 0;
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/tanh_sqrtpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 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_g:= Array(0..(max_terms + 1),[]);
> array_tmp4_a1:= Array(0..(max_terms + 1),[]);
> array_tmp4_a2:= Array(0..(max_terms + 1),[]);
> array_tmp4:= Array(0..(max_terms + 1),[]);
> array_tmp5:= Array(0..(max_terms + 1),[]);
> array_m1:= Array(0..(max_terms + 1),[]);
> array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]);
> array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]);
> array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 4) do # do number 1
> array_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_real_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_complex_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=max_terms) do # do number 1
> term := 1;
> while (term <= max_terms) do # do number 2
> array_fact_2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> #BEGIN ARRAYS DEFINED AND INITIALIZATED
> array_y := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_x := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp3 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4_g := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4_g[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4_a1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4_a2 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp4 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_tmp5 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_1[1] := 1;
> array_const_0D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_0D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_0D0[1] := 0.0;
> array_const_2D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_2D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_2D0[1] := 2.0;
> array_const_3D0 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms + 1) do # do number 1
> array_const_3D0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_const_3D0[1] := 3.0;
> array_m1 := Array(1..(max_terms+1 + 1),[]);
> term := 1;
> while (term <= max_terms) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> array_m1[1] := -1.0;
> #END ARRAYS DEFINED AND INITIALIZATED
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= glob_max_terms) do # do number 1
> jjjf := 0;
> while (jjjf <= glob_max_terms) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Tables
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 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 ) = tanh(sqrt(2.0*x + 3.0));");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 6
> logstart(html_log_file);
> logitem_str(html_log_file,"2013-05-26T05:29:04-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"tanh_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_good_digits(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_max_terms)
> ;
> logitem_float(html_log_file,array_1st_rel_error[1])
> ;
> logitem_float(html_log_file,array_last_rel_error[1])
> ;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,convfloat(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 7
> logitem_time(html_log_file,convfloat(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 7;
> log_revs(html_log_file," 189 | ")
> ;
> logitem_str(html_log_file,"tanh_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"tanh_sqrt maple results")
> ;
> logitem_str(html_log_file,"All Tests - All Languages")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 6;
> if (glob_html_log) then # if number 6
> fclose(html_log_file);
> fi;# end if 6
> ;
> ;;
> fi;# end if 5
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff,
term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii,
temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp,
subiter, est_needed_step_err, estimated_step_error, min_value, est_answer,
best_h, found_h, repeat_it;
global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole,
glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log,
glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec,
glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg,
glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h,
glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float,
glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval,
glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned,
glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start,
glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax,
glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole,
array_real_pole, array_complex_pole, array_1st_rel_error,
array_last_rel_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1, array_tmp4_a2,
array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_poles,
array_given_rad_poles, array_given_ord_poles, array_real_poles,
array_complex_poles, array_fact_2, glob_last;
glob_last;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := INFO;
glob_max_terms := 30;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_estimated_step_error := 0.;
glob_ratio_of_radius := 0.1;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_html_log := true;
glob_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_disp_incr := 0.1;
glob_h := 0.1;
glob_max_h := 0.1;
glob_min_h := 0.1*10^(-5);
glob_type_given_pole := 0;
glob_large_float := 0.90*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_neg_h := false;
glob_display_interval := 0.;
glob_next_display := 0.;
glob_dump_analytic := false;
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_curr_iter_when_opt := 0;
glob_current_iter := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_max_minutes := 0.;
glob_orig_start_sec := elapsed_time_seconds();
MAX_UNCHANGED := 10;
glob_curr_iter_when_opt := 0;
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/tanh_sqrtpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 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_g := Array(0 .. max_terms + 1, []);
array_tmp4_a1 := Array(0 .. max_terms + 1, []);
array_tmp4_a2 := Array(0 .. max_terms + 1, []);
array_tmp4 := Array(0 .. max_terms + 1, []);
array_tmp5 := Array(0 .. max_terms + 1, []);
array_m1 := Array(0 .. max_terms + 1, []);
array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []);
array_poles := Array(0 .. 3, 0 .. 4, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_real_poles := Array(0 .. 3, 0 .. 4, []);
array_complex_poles := Array(0 .. 3, 0 .. 4, []);
array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []);
term := 1;
while term <= max_terms do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 4 do array_pole[term] := 0.; term := term + 1 end do;
term := 1;
while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 4 do array_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 2 do
array_type_complex_pole[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= max_terms do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4_g[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4_a1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4_a2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= max_terms do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do array_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_real_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_complex_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= max_terms do
term := 1;
while term <= max_terms do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
array_y := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1
end do;
array_x := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1
end do;
array_tmp0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1
end do;
array_tmp1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1
end do;
array_tmp2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1
end do;
array_tmp3 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1
end do;
array_tmp4_g := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_g[term] := 0.; term := term + 1
end do;
array_tmp4_a1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_a1[term] := 0.; term := term + 1
end do;
array_tmp4_a2 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_tmp4_a2[term] := 0.; term := term + 1
end do;
array_tmp4 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1
end do;
array_tmp5 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1
end do;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1
end do;
array_const_1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_1[term] := 0.; term := term + 1
end do;
array_const_1[1] := 1;
array_const_0D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_0D0[term] := 0.; term := term + 1
end do;
array_const_0D0[1] := 0.;
array_const_2D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_2D0[term] := 0.; term := term + 1
end do;
array_const_2D0[1] := 2.0;
array_const_3D0 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms + 1 do
array_const_3D0[term] := 0.; term := term + 1
end do;
array_const_3D0[1] := 3.0;
array_m1 := Array(1 .. max_terms + 2, []);
term := 1;
while term <= max_terms do array_m1[term] := 0.; term := term + 1
end do;
array_m1[1] := -1.0;
iiif := 0;
while iiif <= glob_max_terms do
jjjf := 0;
while jjjf <= glob_max_terms do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
x_start := 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 ) = tanh(sqrt(2.0*x + 3.0));");
omniout_int(INFO, "Iterations ", 32,
glob_iter, 4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2013-05-26T05:29:04-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"tanh_sqrt");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_integer(html_log_file, Digits);
logitem_good_digits(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_max_terms);
logitem_float(html_log_file, array_1st_rel_error[1]);
logitem_float(html_log_file, array_last_rel_error[1]);
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, convfloat(glob_clock_sec));
if glob_percent_done < 100.0 then
logitem_time(html_log_file, convfloat(glob_total_exp_sec));
0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 189 | ");
logitem_str(html_log_file, "tanh_sqrt diffeq.mxt");
logitem_str(html_log_file, "tanh_sqrt 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/tanh_sqrtpostode.ode#################
diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 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 = 1.3441454810443660492218885643395e-165
estimated_step_error = 1.3441454810443660492218885643395e-165
best_h = 2.0e-06
opt_iter = 2
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 9.0204050799970995785261903090292e-158
estimated_step_error = 9.0204050799970995785261903090292e-158
best_h = 4.00e-06
opt_iter = 3
bytes used=4000616, alloc=2883056, time=0.28
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 6.0534879570296586772398458897117e-150
estimated_step_error = 6.0534879570296586772398458897117e-150
best_h = 8.000e-06
opt_iter = 4
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 4.0624224096248755985942030517609e-142
estimated_step_error = 4.0624224096248755985942030517609e-142
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 = 2.7262393684489029510297946944593e-134
estimated_step_error = 2.7262393684489029510297946944593e-134
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 = 1.8295400002751677055238188886066e-126
estimated_step_error = 1.8295400002751677055238188886066e-126
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 = 1.2277724112080545945639910186011e-118
estimated_step_error = 1.2277724112080545945639910186011e-118
best_h = 0.000128
opt_iter = 8
bytes used=8001712, alloc=3931440, time=0.56
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 8.2392922070732943093274398802390e-111
estimated_step_error = 8.2392922070732943093274398802390e-111
best_h = 0.000256
opt_iter = 9
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.5290954690868474707224568245584e-103
estimated_step_error = 5.5290954690868474707224568245584e-103
best_h = 0.000512
opt_iter = 10
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.7102448428554323100779449740857e-95
estimated_step_error = 3.7102448428554323100779449740857e-95
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 = 2.4895431165874853931993755416428e-87
estimated_step_error = 2.4895431165874853931993755416428e-87
best_h = 0.002048
opt_iter = 12
bytes used=12002740, alloc=4128012, time=0.86
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.6702210652792571703646141730979e-79
estimated_step_error = 1.6702210652792571703646141730979e-79
best_h = 0.004096
opt_iter = 13
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 1.1202186245625089675705095988165e-71
estimated_step_error = 1.1202186245625089675705095988165e-71
best_h = 0.008192
opt_iter = 14
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 7.5089810409001970284828312911833e-64
estimated_step_error = 7.5089810409001970284828312911833e-64
best_h = 0.016384
opt_iter = 15
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 5.0275840051265146466699765871287e-56
estimated_step_error = 5.0275840051265146466699765871287e-56
best_h = 0.032768
opt_iter = 16
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 3.3584840595164694456205455792571e-48
estimated_step_error = 3.3584840595164694456205455792571e-48
best_h = 0.065536
opt_iter = 17
bytes used=16003520, alloc=4193536, time=1.17
hn_div_ho = 0.5
hn_div_ho_2 = 0.25
hn_div_ho_3 = 0.125
max_estimated_step_error = 2.2333699855337776852240734087567e-40
estimated_step_error = 2.2333699855337776852240734087567e-40
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 = 1.4721022290633497291558764157676e-32
estimated_step_error = 1.4721022290633497291558764157676e-32
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 = 1.806
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 = 2.202
Order of pole (six term test) = -0.4372
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (analytic) = 0
y[1] (numeric) = 0.0094593381004985954826601201816836
absolute error = 0.0094593381004985954826601201816836
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.817
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 = 2.216
Order of pole (six term test) = -0.4326
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (analytic) = 0
y[1] (numeric) = 0.018924508505127767640193031685038
absolute error = 0.018924508505127767640193031685038
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.829
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.23
Order of pole (six term test) = -0.4273
TOP MAIN SOLVE Loop
bytes used=20004976, alloc=4259060, time=1.48
x[1] = 0.13
y[1] (analytic) = 0
y[1] (numeric) = 0.028395432263158646197743615872164
absolute error = 0.028395432263158646197743615872164
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.245
Order of pole (six term test) = -0.4212
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (analytic) = 0
y[1] (numeric) = 0.037872031748748671402376307987138
absolute error = 0.037872031748748671402376307987138
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.851
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.261
Order of pole (six term test) = -0.4141
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (analytic) = 0
y[1] (numeric) = 0.047354230633830724064787478470808
absolute error = 0.047354230633830724064787478470808
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.863
Order 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) = -0.4055
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (analytic) = 0
y[1] (numeric) = 0.056841953861666999718122852049415
absolute error = 0.056841953861666999718122852049415
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.874
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.295
Order of pole (six term test) = -0.3952
TOP MAIN SOLVE Loop
bytes used=24005656, alloc=4324584, time=1.79
x[1] = 0.17
y[1] (analytic) = 0
y[1] (numeric) = 0.066335127621048416388199497381673
absolute error = 0.066335127621048416388199497381673
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 = 2.315
Order of pole (six term test) = -0.3825
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (analytic) = 0
y[1] (numeric) = 0.075833679321120990162842049045725
absolute error = 0.075833679321120990162842049045725
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.897
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.337
Order of pole (six term test) = -0.3664
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (analytic) = 0
y[1] (numeric) = 0.085337537566821232645635838403177
absolute error = 0.085337537566821232645635838403177
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.908
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.362
Order of pole (six term test) = -0.3455
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (analytic) = 0
y[1] (numeric) = 0.094846632134903220561373955674941
absolute error = 0.094846632134903220561373955674941
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.92
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.392
Order of pole (six term test) = -0.317
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (analytic) = 0
y[1] (numeric) = 0.10436089395054056127429279863007
absolute error = 0.10436089395054056127429279863007
relative error = -1 %
Correct digits = -1
h = 0.01
bytes used=28006872, alloc=4324584, time=2.10
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.931
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.431
Order of pole (six term test) = -0.2763
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (analytic) = 0
y[1] (numeric) = 0.11388025506448702976343427646557
absolute error = 0.11388025506448702976343427646557
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.943
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 = 2.485
Order of pole (six term test) = -0.2128
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (analytic) = 0
y[1] (numeric) = 0.12340464863078018360253372766059
absolute error = 0.12340464863078018360253372766059
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.954
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 = 2.57
Order of pole (six term test) = -0.1006
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (analytic) = 0
y[1] (numeric) = 0.13293400888497277360043827278055
absolute error = 0.13293400888497277360043827278055
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.965
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 = 2.741
Order of pole (six term test) = 0.1518
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (analytic) = 0
y[1] (numeric) = 0.14246827112287725981565357397372
absolute error = 0.14246827112287725981565357397372
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.977
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.36
Order of pole (six term test) = 1.243
TOP MAIN SOLVE Loop
bytes used=32007740, alloc=4324584, time=2.41
x[1] = 0.26
y[1] (analytic) = 0
y[1] (numeric) = 0.15200737167980921646859558455708
absolute error = 0.15200737167980921646859558455708
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 1.988
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] = 0.27
y[1] (analytic) = 0
y[1] (numeric) = 0.16155124791031586560294973042079
absolute error = 0.16155124791031586560294973042079
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 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 = 1.689
Order of pole (six term test) = -1.257
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (analytic) = 0
y[1] (numeric) = 0.17109983816837641892272604620079
absolute error = 0.17109983816837641892272604620079
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.011
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 1.993
Order of pole (six term test) = -0.9433
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (analytic) = 0
y[1] (numeric) = 0.18065308178806133074958168002429
absolute error = 0.18065308178806133074958168002429
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 = 2.112
Order of pole (six term test) = -0.8143
TOP MAIN SOLVE Loop
bytes used=36008908, alloc=4390108, time=2.72
x[1] = 0.3
y[1] (analytic) = 0
y[1] (numeric) = 0.19021091906463797316888733656982
absolute error = 0.19021091906463797316888733656982
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 = 2.18
Order of pole (six term test) = -0.7439
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (analytic) = 0
y[1] (numeric) = 0.19977329123611063779532067429614
absolute error = 0.19977329123611063779532067429614
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.045
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.225
Order of pole (six term test) = -0.6996
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (analytic) = 0
y[1] (numeric) = 0.20934014046518314779288039807363
absolute error = 0.20934014046518314779288039807363
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.057
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.259
Order of pole (six term test) = -0.6692
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (analytic) = 0
y[1] (numeric) = 0.21891140982163272940593866350275
absolute error = 0.21891140982163272940593866350275
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.068
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.287
Order of pole (six term test) = -0.6469
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (analytic) = 0
y[1] (numeric) = 0.22848704326508414484690006502808
absolute error = 0.22848704326508414484690006502808
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.08
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 = 2.311
Order of pole (six term test) = -0.63
TOP MAIN SOLVE Loop
bytes used=40009844, alloc=4390108, time=3.04
x[1] = 0.35
y[1] (analytic) = 0
y[1] (numeric) = 0.23806698562817342846695222656459
absolute error = 0.23806698562817342846695222656459
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.091
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 = 2.331
Order of pole (six term test) = -0.6167
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (analytic) = 0
y[1] (numeric) = 0.2476511826000908962103885371528
absolute error = 0.2476511826000908962103885371528
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.103
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.35
Order of pole (six term test) = -0.6059
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (analytic) = 0
y[1] (numeric) = 0.25723958071049341489872284282348
absolute error = 0.25723958071049341489872284282348
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.114
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.367
Order of pole (six term test) = -0.597
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (analytic) = 0
y[1] (numeric) = 0.26683212731377622336563041849995
absolute error = 0.26683212731377622336563041849995
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.125
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.383
Order of pole (six term test) = -0.5896
TOP MAIN SOLVE Loop
bytes used=44010728, alloc=4390108, time=3.35
x[1] = 0.39
y[1] (analytic) = 0
y[1] (numeric) = 0.27642877057369489230469079469626
absolute error = 0.27642877057369489230469079469626
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.137
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.398
Order of pole (six term test) = -0.5832
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (analytic) = 0
y[1] (numeric) = 0.28602945944832829431674378722383
absolute error = 0.28602945944832829431674378722383
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.148
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.413
Order of pole (six term test) = -0.5777
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (analytic) = 0
y[1] (numeric) = 0.29563414367537373045182695827513
absolute error = 0.29563414367537373045182695827513
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 = 2.427
Order of pole (six term test) = -0.573
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (analytic) = 0
y[1] (numeric) = 0.30524277375776562491411800061105
absolute error = 0.30524277375776562491411800061105
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 = 2.44
Order of pole (six term test) = -0.5688
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (analytic) = 0
y[1] (numeric) = 0.31485530094960945590243139181776
absolute error = 0.31485530094960945590243139181776
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.183
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.454
Order of pole (six term test) = -0.5651
TOP MAIN SOLVE Loop
bytes used=48011516, alloc=4390108, time=3.66
x[1] = 0.44
y[1] (analytic) = 0
y[1] (numeric) = 0.32447167724242283814318161780193
absolute error = 0.32447167724242283814318161780193
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.194
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.467
Order of pole (six term test) = -0.5618
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (analytic) = 0
y[1] (numeric) = 0.33409185535167591187184320551523
absolute error = 0.33409185535167591187184320551523
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.206
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 = 2.479
Order of pole (six term test) = -0.5588
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (analytic) = 0
y[1] (numeric) = 0.34371578870362342415299726685656
absolute error = 0.34371578870362342415299726685656
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.217
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 = 2.492
Order of pole (six term test) = -0.5561
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (analytic) = 0
y[1] (numeric) = 0.35334343142242111180459011639801
absolute error = 0.35334343142242111180459011639801
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.228
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 = 2.504
Order of pole (six term test) = -0.5537
TOP MAIN SOLVE Loop
bytes used=52012364, alloc=4390108, time=3.98
x[1] = 0.48
y[1] (analytic) = 0
y[1] (numeric) = 0.36297473831751921110256930561015
absolute error = 0.36297473831751921110256930561015
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.24
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.516
Order of pole (six term test) = -0.5515
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (analytic) = 0
y[1] (numeric) = 0.37260966487132612816873718190928
absolute error = 0.37260966487132612816873718190928
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.251
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.528
Order of pole (six term test) = -0.5495
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (analytic) = 0
y[1] (numeric) = 0.38224816722713550575678583899844
absolute error = 0.38224816722713550575678583899844
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.263
Order 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) = -0.5476
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (analytic) = 0
y[1] (numeric) = 0.39189020217731011730709668204362
absolute error = 0.39189020217731011730709668204362
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.274
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.551
Order of pole (six term test) = -0.5459
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (analytic) = 0
y[1] (numeric) = 0.4015357271517162078873035800369
absolute error = 0.4015357271517162078873035800369
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 = 2.563
Order of pole (six term test) = -0.5443
TOP MAIN SOLVE Loop
bytes used=56013192, alloc=4390108, time=4.29
x[1] = 0.53
y[1] (analytic) = 0
y[1] (numeric) = 0.41118470020640208420988077531185
absolute error = 0.41118470020640208420988077531185
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 = 2.574
Order of pole (six term test) = -0.5428
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (analytic) = 0
y[1] (numeric) = 0.42083708001251493254739472549063
absolute error = 0.42083708001251493254739472549063
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.309
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.586
Order of pole (six term test) = -0.5414
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (analytic) = 0
y[1] (numeric) = 0.43049282584545001426848790485425
absolute error = 0.43049282584545001426848790485425
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.32
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.597
Order of pole (six term test) = -0.5401
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (analytic) = 0
y[1] (numeric) = 0.44015189757422655410216702524936
absolute error = 0.44015189757422655410216702524936
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.332
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 = 2.609
Order of pole (six term test) = -0.5389
TOP MAIN SOLVE Loop
bytes used=60013968, alloc=4390108, time=4.60
x[1] = 0.57
y[1] (analytic) = 0
y[1] (numeric) = 0.44981425565108479630506545859128
absolute error = 0.44981425565108479630506545859128
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.343
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 = 2.62
Order of pole (six term test) = -0.5378
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (analytic) = 0
y[1] (numeric) = 0.45947986110129885884843261808437
absolute error = 0.45947986110129885884843261808437
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.355
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 = 2.631
Order of pole (six term test) = -0.5367
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (analytic) = 0
y[1] (numeric) = 0.46914867551320016574330387868113
absolute error = 0.46914867551320016574330387868113
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.366
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 = 2.642
Order of pole (six term test) = -0.5357
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (analytic) = 0
y[1] (numeric) = 0.47882066102840638286084099671665
absolute error = 0.47882066102840638286084099671665
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.378
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.653
Order of pole (six term test) = -0.5348
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (analytic) = 0
y[1] (numeric) = 0.48849578033225092325033729171599
absolute error = 0.48849578033225092325033729171599
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.389
Order 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) = -0.5339
TOP MAIN SOLVE Loop
bytes used=64014876, alloc=4455632, time=4.92
x[1] = 0.62
y[1] (analytic) = 0
y[1] (numeric) = 0.49817399664440822417321422410108
absolute error = 0.49817399664440822417321422410108
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 = 2.675
Order of pole (six term test) = -0.5331
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (analytic) = 0
y[1] (numeric) = 0.50785527370971013001438229746865
absolute error = 0.50785527370971013001438229746865
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 = 2.686
Order of pole (six term test) = -0.5323
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (analytic) = 0
y[1] (numeric) = 0.51753957578914884305329456010142
absolute error = 0.51753957578914884305329456010142
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.424
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.697
Order of pole (six term test) = -0.5315
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (analytic) = 0
y[1] (numeric) = 0.52722686765106202792065970990518
absolute error = 0.52722686765106202792065970990518
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.435
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.708
Order of pole (six term test) = -0.5308
TOP MAIN SOLVE Loop
bytes used=68015832, alloc=4455632, time=5.23
x[1] = 0.66
y[1] (analytic) = 0
y[1] (numeric) = 0.53691711456249577557221448420373
absolute error = 0.53691711456249577557221448420373
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.447
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 = 2.719
Order of pole (six term test) = -0.5301
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (analytic) = 0
y[1] (numeric) = 0.54661028228074124891187322581841
absolute error = 0.54661028228074124891187322581841
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.458
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 = 2.73
Order of pole (six term test) = -0.5294
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (analytic) = 0
y[1] (numeric) = 0.55630633704504094492148205258085
absolute error = 0.55630633704504094492148205258085
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.469
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 = 2.741
Order of pole (six term test) = -0.5288
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (analytic) = 0
y[1] (numeric) = 0.56600524556846061742684810365333
absolute error = 0.56600524556846061742684810365333
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.481
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 = 2.752
Order of pole (six term test) = -0.5282
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (analytic) = 0
y[1] (numeric) = 0.5757069750299230105684812155902
absolute error = 0.5757069750299230105684812155902
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.492
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 = 2.762
Order of pole (six term test) = -0.5276
TOP MAIN SOLVE Loop
bytes used=72016744, alloc=4455632, time=5.54
x[1] = 0.71
y[1] (analytic) = 0
y[1] (numeric) = 0.58541149306639965576481639750987
absolute error = 0.58541149306639965576481639750987
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.504
Order 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) = -0.5271
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (analytic) = 0
y[1] (numeric) = 0.59511876776525708456546335586711
absolute error = 0.59511876776525708456546335586711
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.515
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.784
Order of pole (six term test) = -0.5266
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (analytic) = 0
y[1] (numeric) = 0.60482876765675390639796273829035
absolute error = 0.60482876765675390639796273829035
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 = 2.795
Order of pole (six term test) = -0.5261
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (analytic) = 0
y[1] (numeric) = 0.61454146170668529391532739044028
absolute error = 0.61454146170668529391532739044028
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 = 2.805
Order of pole (six term test) = -0.5256
TOP MAIN SOLVE Loop
bytes used=76017524, alloc=4455632, time=5.86
x[1] = 0.75
y[1] (analytic) = 0
y[1] (numeric) = 0.62425681930917150955118841504449
absolute error = 0.62425681930917150955118841504449
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.55
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.816
Order of pole (six term test) = -0.5251
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (analytic) = 0
y[1] (numeric) = 0.63397481027958719507885521052329
absolute error = 0.63397481027958719507885521052329
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.561
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.827
Order of pole (six term test) = -0.5247
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (analytic) = 0
y[1] (numeric) = 0.64369540484762823154072042458552
absolute error = 0.64369540484762823154072042458552
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.573
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 = 2.838
Order of pole (six term test) = -0.5242
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (analytic) = 0
y[1] (numeric) = 0.65341857365051305995250401171891
absolute error = 0.65341857365051305995250401171891
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.584
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 = 2.848
Order of pole (six term test) = -0.5238
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (analytic) = 0
y[1] (numeric) = 0.66314428772631543377690774150833
absolute error = 0.66314428772631543377690774150833
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.596
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 = 2.859
Order of pole (six term test) = -0.5234
TOP MAIN SOLVE Loop
bytes used=80018832, alloc=4455632, time=6.17
x[1] = 0.8
y[1] (analytic) = 0
y[1] (numeric) = 0.67287251850742565238431065441871
absolute error = 0.67287251850742565238431065441871
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.607
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 = 2.87
Order of pole (six term test) = -0.523
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (analytic) = 0
y[1] (numeric) = 0.68260323781413740065216733116174
absolute error = 0.68260323781413740065216733116174
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.619
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.88
Order of pole (six term test) = -0.5227
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (analytic) = 0
y[1] (numeric) = 0.69233641784835739357490761900255
absolute error = 0.69233641784835739357490761900255
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 = 2.891
Order of pole (six term test) = -0.5223
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (analytic) = 0
y[1] (numeric) = 0.70207203118743509633477024091084
absolute error = 0.70207203118743509633477024091084
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 = 2.901
Order of pole (six term test) = -0.522
TOP MAIN SOLVE Loop
bytes used=84019716, alloc=4455632, time=6.49
x[1] = 0.84
y[1] (analytic) = 0
y[1] (numeric) = 0.71181005077810985979089384848292
absolute error = 0.71181005077810985979089384848292
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.654
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.912
Order of pole (six term test) = -0.5217
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (analytic) = 0
y[1] (numeric) = 0.72155044993057287884637214031855
absolute error = 0.72155044993057287884637214031855
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.665
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.923
Order of pole (six term test) = -0.5213
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (analytic) = 0
y[1] (numeric) = 0.73129320231264144671566429961438
absolute error = 0.73129320231264144671566429961438
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.677
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 = 2.933
Order of pole (six term test) = -0.521
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (analytic) = 0
y[1] (numeric) = 0.74103828194404304180021936319238
absolute error = 0.74103828194404304180021936319238
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.688
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 = 2.944
Order of pole (six term test) = -0.5207
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (analytic) = 0
y[1] (numeric) = 0.75078566319080684574866812136545
absolute error = 0.75078566319080684574866812136545
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.7
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 = 2.955
Order of pole (six term test) = -0.5204
bytes used=88021980, alloc=4455632, time=6.80
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (analytic) = 0
y[1] (numeric) = 0.76053532075976035138755565102848
absolute error = 0.76053532075976035138755565102848
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.711
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 = 2.965
Order of pole (six term test) = -0.5202
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (analytic) = 0
y[1] (numeric) = 0.77028722969312877761536490077257
absolute error = 0.77028722969312877761536490077257
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.723
Order 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) = -0.5199
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (analytic) = 0
y[1] (numeric) = 0.78004136536323506511056737814094
absolute error = 0.78004136536323506511056737814094
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.734
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 2.986
Order of pole (six term test) = -0.5196
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (analytic) = 0
y[1] (numeric) = 0.78979770346729828186577597157098
absolute error = 0.78979770346729828186577597157098
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 = 2.997
Order of pole (six term test) = -0.5194
TOP MAIN SOLVE Loop
bytes used=92022660, alloc=4455632, time=7.13
x[1] = 0.93
y[1] (analytic) = 0
y[1] (numeric) = 0.79955622002232832117508087377279
absolute error = 0.79955622002232832117508087377279
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 = 3.007
Order of pole (six term test) = -0.5192
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (analytic) = 0
y[1] (numeric) = 0.80931689136011482681887550640978
absolute error = 0.80931689136011482681887550640978
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.769
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.018
Order of pole (six term test) = -0.5189
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (analytic) = 0
y[1] (numeric) = 0.81907969412230833085678565131263
absolute error = 0.81907969412230833085678565131263
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.78
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.029
Order of pole (six term test) = -0.5187
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (analytic) = 0
y[1] (numeric) = 0.82884460525559163869993438645545
absolute error = 0.82884460525559163869993438645545
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.792
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 = 3.039
Order of pole (six term test) = -0.5185
TOP MAIN SOLVE Loop
x[1] = 0.97
y[1] (analytic) = 0
y[1] (numeric) = 0.83861160200693954403237524628494
absolute error = 0.83861160200693954403237524628494
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.803
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 = 3.05
Order of pole (six term test) = -0.5183
bytes used=96027836, alloc=4455632, time=7.44
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (analytic) = 0
y[1] (numeric) = 0.84838066191896500273026791747588
absolute error = 0.84838066191896500273026791747588
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.815
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 = 3.06
Order of pole (six term test) = -0.5181
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (analytic) = 0
y[1] (numeric) = 0.85815176282534994022696787232501
absolute error = 0.85815176282534994022696787232501
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.826
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 = 3.071
Order of pole (six term test) = -0.5179
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (analytic) = 0
y[1] (numeric) = 0.86792488284635891083197306080736
absolute error = 0.86792488284635891083197306080736
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.838
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.081
Order of pole (six term test) = -0.5177
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (analytic) = 0
y[1] (numeric) = 0.87770000038443387036959539728858
absolute error = 0.87770000038443387036959539728858
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.849
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.092
Order of pole (six term test) = -0.5175
TOP MAIN SOLVE Loop
bytes used=100028644, alloc=4455632, time=7.75
x[1] = 1.02
y[1] (analytic) = 0
y[1] (numeric) = 0.88747709411986836519598977333318
absolute error = 0.88747709411986836519598977333318
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 = 3.102
Order of pole (six term test) = -0.5174
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (analytic) = 0
y[1] (numeric) = 0.89725614300655948121622370999137
absolute error = 0.89725614300655948121622370999137
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 = 3.113
Order of pole (six term test) = -0.5172
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (analytic) = 0
y[1] (numeric) = 0.90703712626783593599065538790119
absolute error = 0.90703712626783593599065538790119
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.884
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.123
Order of pole (six term test) = -0.5171
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (analytic) = 0
y[1] (numeric) = 0.91682002339236073542510380818754
absolute error = 0.91682002339236073542510380818754
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.895
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.134
Order of pole (six term test) = -0.5169
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (analytic) = 0
y[1] (numeric) = 0.92660481413010685391413031260164
absolute error = 0.92660481413010685391413031260164
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.907
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 = 3.144
Order of pole (six term test) = -0.5168
bytes used=104030612, alloc=4455632, time=8.07
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (analytic) = 0
y[1] (numeric) = 0.93639147848840443318212553179931
absolute error = 0.93639147848840443318212553179931
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.918
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 = 3.155
Order of pole (six term test) = -0.5166
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (analytic) = 0
y[1] (numeric) = 0.94617999672805803047270103217014
absolute error = 0.94617999672805803047270103217014
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.93
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.165
Order of pole (six term test) = -0.5165
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (analytic) = 0
y[1] (numeric) = 0.95597034935953248120202026353444
absolute error = 0.95597034935953248120202026353444
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.942
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.176
Order of pole (six term test) = -0.5164
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (analytic) = 0
y[1] (numeric) = 0.96576251713920597474411358771586
absolute error = 0.96576251713920597474411358771586
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.953
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.186
Order of pole (six term test) = -0.5163
TOP MAIN SOLVE Loop
bytes used=108031416, alloc=4521156, time=8.39
x[1] = 1.11
y[1] (analytic) = 0
y[1] (numeric) = 0.97555648106568897468293158276567
absolute error = 0.97555648106568897468293158276567
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 = 3.197
Order of pole (six term test) = -0.5162
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (analytic) = 0
y[1] (numeric) = 0.98535222237620764667303688607237
absolute error = 0.98535222237620764667303688607237
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 = 3.207
Order of pole (six term test) = -0.5161
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (analytic) = 0
y[1] (numeric) = 0.99514972254305048802370003228761
absolute error = 0.99514972254305048802370003228761
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.988
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.218
Order of pole (six term test) = -0.516
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (analytic) = 0
y[1] (numeric) = 1.0049489632700768832842073480775
absolute error = 1.0049489632700768832842073480775
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 2.999
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.228
Order of pole (six term test) = -0.5159
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (analytic) = 0
y[1] (numeric) = 1.0147499264892863394850726477601
absolute error = 1.0147499264892863394850726477601
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.011
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.239
Order of pole (six term test) = -0.5158
bytes used=112033800, alloc=4521156, time=8.70
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (analytic) = 0
y[1] (numeric) = 1.0245525943574471833034666647296
absolute error = 1.0245525943574471833034666647296
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.022
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.249
Order of pole (six term test) = -0.5157
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (analytic) = 0
y[1] (numeric) = 1.0343569492527835302936973441727
absolute error = 1.0343569492527835302936973441727
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.034
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 = 3.26
Order of pole (six term test) = -0.5156
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (analytic) = 0
y[1] (numeric) = 1.0441629737717193634764360882757
absolute error = 1.0441629737717193634764360882757
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.045
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.27
Order of pole (six term test) = -0.5156
TOP MAIN SOLVE Loop
x[1] = 1.19
y[1] (analytic) = 0
y[1] (numeric) = 1.0539706507256785850343480548076
absolute error = 1.0539706507256785850343480548076
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.057
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.281
Order of pole (six term test) = -0.5155
TOP MAIN SOLVE Loop
bytes used=116034856, alloc=4521156, time=9.02
x[1] = 1.2
y[1] (analytic) = 0
y[1] (numeric) = 1.0637799631379399306369436613221
absolute error = 1.0637799631379399306369436613221
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.068
Order 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) = -0.5155
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (analytic) = 0
y[1] (numeric) = 1.0735908942405456610332785686242
absolute error = 1.0735908942405456610332785686242
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 = 3.301
Order of pole (six term test) = -0.5154
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (analytic) = 0
y[1] (numeric) = 1.0834034274712629700264280754662
absolute error = 1.0834034274712629700264280754662
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 = 3.312
Order of pole (six term test) = -0.5154
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (analytic) = 0
y[1] (numeric) = 1.0932175464705970717966905078279
absolute error = 1.0932175464705970717966905078279
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.103
Order 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) = -0.5153
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (analytic) = 0
y[1] (numeric) = 1.1030332350788549537888990055612
absolute error = 1.1030332350788549537888990055612
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.114
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.333
Order of pole (six term test) = -0.5153
TOP MAIN SOLVE Loop
bytes used=120035752, alloc=4521156, time=9.33
x[1] = 1.25
y[1] (analytic) = 0
y[1] (numeric) = 1.1128504773332588040401529325035
absolute error = 1.1128504773332588040401529325035
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.126
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.343
Order of pole (six term test) = -0.5153
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (analytic) = 0
y[1] (numeric) = 1.1226692574651081439142936474008
absolute error = 1.1226692574651081439142936474008
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.137
Order 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) = -0.5153
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (analytic) = 0
y[1] (numeric) = 1.1324895598969897187446015676407
absolute error = 1.1324895598969897187446015676407
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.149
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 = 3.364
Order of pole (six term test) = -0.5152
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (analytic) = 0
y[1] (numeric) = 1.1423113692400342198820394120326
absolute error = 1.1423113692400342198820394120326
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.161
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.375
Order of pole (six term test) = -0.5152
TOP MAIN SOLVE Loop
bytes used=124036732, alloc=4521156, time=9.64
x[1] = 1.29
y[1] (analytic) = 0
y[1] (numeric) = 1.1521346702912189321179844827172
absolute error = 1.1521346702912189321179844827172
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.172
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.385
Order of pole (six term test) = -0.5152
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (analytic) = 0
y[1] (numeric) = 1.1619594480307154204123887481079
absolute error = 1.1619594480307154204123887481079
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.184
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 = 3.396
Order of pole (six term test) = -0.5152
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (analytic) = 0
y[1] (numeric) = 1.1717856876192813893248367267776
absolute error = 1.1717856876192813893248367267776
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.195
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 = 3.406
Order of pole (six term test) = -0.5153
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (analytic) = 0
y[1] (numeric) = 1.1816133743956958675307599178874
absolute error = 1.1816133743956958675307599178874
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 = 3.416
Order of pole (six term test) = -0.5153
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (analytic) = 0
y[1] (numeric) = 1.1914424938742368883214144107534
absolute error = 1.1914424938742368883214144107534
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.218
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.427
Order of pole (six term test) = -0.5153
TOP MAIN SOLVE Loop
bytes used=128037640, alloc=4521156, time=9.96
x[1] = 1.34
y[1] (analytic) = 0
y[1] (numeric) = 1.2012730317422008550470305874214
absolute error = 1.2012730317422008550470305874214
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.23
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.437
Order of pole (six term test) = -0.5153
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (analytic) = 0
y[1] (numeric) = 1.2111049738574627980803030168932
absolute error = 1.2111049738574627980803030168932
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.241
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.448
Order of pole (six term test) = -0.5154
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (analytic) = 0
y[1] (numeric) = 1.2209383062460767470642276310155
absolute error = 1.2209383062460767470642276310155
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.253
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 = 3.458
Order of pole (six term test) = -0.5154
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (analytic) = 0
y[1] (numeric) = 1.2307730150999154589759680249779
absolute error = 1.2307730150999154589759680249779
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.264
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 = 3.469
Order of pole (six term test) = -0.5154
TOP MAIN SOLVE Loop
bytes used=132038656, alloc=4521156, time=10.28
x[1] = 1.38
y[1] (analytic) = 0
y[1] (numeric) = 1.2406090867743487588983444441873
absolute error = 1.2406090867743487588983444441873
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.276
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.479
Order of pole (six term test) = -0.5155
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (analytic) = 0
y[1] (numeric) = 1.2504465077859597663537459127207
absolute error = 1.2504465077859597663537459127207
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.287
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.489
Order of pole (six term test) = -0.5156
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (analytic) = 0
y[1] (numeric) = 1.2602852648102982956324945698509
absolute error = 1.2602852648102982956324945698509
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.299
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 = 3.5
Order of pole (six term test) = -0.5156
TOP MAIN SOLVE Loop
x[1] = 1.41
y[1] (analytic) = 0
y[1] (numeric) = 1.2701253446796707337493474098215
absolute error = 1.2701253446796707337493474098215
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.31
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 = 3.51
Order of pole (six term test) = -0.5157
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (analytic) = 0
y[1] (numeric) = 1.2799667343809657144979998513758
absolute error = 1.2799667343809657144979998513758
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 = 3.521
Order of pole (six term test) = -0.5158
TOP MAIN SOLVE Loop
bytes used=136039648, alloc=4521156, time=10.59
x[1] = 1.43
y[1] (analytic) = 0
y[1] (numeric) = 1.2898094210535149215539534208783
absolute error = 1.2898094210535149215539534208783
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 = 3.531
Order of pole (six term test) = -0.5159
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (analytic) = 0
y[1] (numeric) = 1.2996533919869883677104315676126
absolute error = 1.2996533919869883677104315676126
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.345
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.542
Order of pole (six term test) = -0.5159
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (analytic) = 0
y[1] (numeric) = 1.3094986346193235111293976630234
absolute error = 1.3094986346193235111293976630234
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.356
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.552
Order of pole (six term test) = -0.516
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (analytic) = 0
y[1] (numeric) = 1.319345136534687582959100264573
absolute error = 1.319345136534687582959100264573
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.368
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 = 3.562
Order of pole (six term test) = -0.5162
TOP MAIN SOLVE Loop
bytes used=140041152, alloc=4521156, time=10.91
x[1] = 1.47
y[1] (analytic) = 0
y[1] (numeric) = 1.3291928854614725138196325076093
absolute error = 1.3291928854614725138196325076093
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.379
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 = 3.573
Order of pole (six term test) = -0.5163
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (analytic) = 0
y[1] (numeric) = 1.3390418692703218594971803189922
absolute error = 1.3390418692703218594971803189922
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.391
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.583
Order of pole (six term test) = -0.5164
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (analytic) = 0
y[1] (numeric) = 1.3488920759721891387241370307101
absolute error = 1.3488920759721891387241370307101
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.402
Order 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) = -0.5165
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (analytic) = 0
y[1] (numeric) = 1.3587434937164270081640305200396
absolute error = 1.3587434937164270081640305200396
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.414
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 = 3.604
Order of pole (six term test) = -0.5166
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (analytic) = 0
y[1] (numeric) = 1.3685961107889067116749630427342
absolute error = 1.3685961107889067116749630427342
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.425
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 = 3.615
Order of pole (six term test) = -0.5168
TOP MAIN SOLVE Loop
bytes used=144041820, alloc=4521156, time=11.23
x[1] = 1.52
y[1] (analytic) = 0
y[1] (numeric) = 1.3784499156101672526004998527908
absolute error = 1.3784499156101672526004998527908
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 = 3.625
Order of pole (six term test) = -0.5169
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (analytic) = 0
y[1] (numeric) = 1.3883048967335937492399405742862
absolute error = 1.3883048967335937492399405742862
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 = 3.635
Order of pole (six term test) = -0.5171
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (analytic) = 0
y[1] (numeric) = 1.3981610428436244447877376765368
absolute error = 1.3981610428436244447877376765368
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.46
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.646
Order of pole (six term test) = -0.5172
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (analytic) = 0
y[1] (numeric) = 1.4080183427539858539113569960737
absolute error = 1.4080183427539858539113569960737
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.471
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.656
Order of pole (six term test) = -0.5174
TOP MAIN SOLVE Loop
bytes used=148043104, alloc=4521156, time=11.54
x[1] = 1.56
y[1] (analytic) = 0
y[1] (numeric) = 1.4178767854059555387647772490946
absolute error = 1.4178767854059555387647772490946
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.483
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 = 3.667
Order of pole (six term test) = -0.5176
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (analytic) = 0
y[1] (numeric) = 1.4277363598666520176175797624253
absolute error = 1.4277363598666520176175797624253
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.494
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 = 3.677
Order of pole (six term test) = -0.5177
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (analytic) = 0
y[1] (numeric) = 1.437597055327351319423482725791
absolute error = 1.437597055327351319423482725791
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.506
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.687
Order of pole (six term test) = -0.5179
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (analytic) = 0
y[1] (numeric) = 1.4474588611018297075633440215725
absolute error = 1.4474588611018297075633440215725
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.517
Order 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) = -0.5181
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (analytic) = 0
y[1] (numeric) = 1.4573217666247321056820379468978
absolute error = 1.4573217666247321056820379468978
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.529
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 = 3.708
Order of pole (six term test) = -0.5183
TOP MAIN SOLVE Loop
bytes used=152044112, alloc=4521156, time=11.86
x[1] = 1.61
y[1] (analytic) = 0
y[1] (numeric) = 1.4671857614499657680019810402239
absolute error = 1.4671857614499657680019810402239
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.54
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 = 3.719
Order of pole (six term test) = -0.5185
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (analytic) = 0
y[1] (numeric) = 1.4770508352491187457440553871414
absolute error = 1.4770508352491187457440553871414
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 = 3.729
Order of pole (six term test) = -0.5187
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (analytic) = 0
y[1] (numeric) = 1.4869169778099027103247113398399
absolute error = 1.4869169778099027103247113398399
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 = 3.74
Order of pole (six term test) = -0.5189
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (analytic) = 0
y[1] (numeric) = 1.4967841790346197028314300220635
absolute error = 1.4967841790346197028314300220635
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.575
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.75
Order of pole (six term test) = -0.5192
TOP MAIN SOLVE Loop
bytes used=156045092, alloc=4521156, time=12.17
x[1] = 1.65
y[1] (analytic) = 0
y[1] (numeric) = 1.5066524289386523879126458169135
absolute error = 1.5066524289386523879126458169135
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.586
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.76
Order of pole (six term test) = -0.5194
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (analytic) = 0
y[1] (numeric) = 1.516521717648977398657683313669
absolute error = 1.516521717648977398657683313669
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.598
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 = 3.771
Order of pole (six term test) = -0.5197
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (analytic) = 0
y[1] (numeric) = 1.5263920354027013672921259158465
absolute error = 1.5263920354027013672921259158465
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.609
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 = 3.781
Order of pole (six term test) = -0.5199
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (analytic) = 0
y[1] (numeric) = 1.536263372545619244579043637507
absolute error = 1.536263372545619244579043637507
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.621
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.792
Order of pole (six term test) = -0.5202
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (analytic) = 0
y[1] (numeric) = 1.5461357195307945187012739361634
absolute error = 1.5461357195307945187012739361634
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.632
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.802
Order of pole (six term test) = -0.5204
TOP MAIN SOLVE Loop
bytes used=160045916, alloc=4521156, time=12.49
x[1] = 1.7
y[1] (analytic) = 0
y[1] (numeric) = 1.5560090669171609521089533463316
absolute error = 1.5560090669171609521089533463316
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.644
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 = 3.812
Order of pole (six term test) = -0.5207
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (analytic) = 0
y[1] (numeric) = 1.5658834053681454623540978090601
absolute error = 1.5658834053681454623540978090601
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.655
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 = 3.823
Order of pole (six term test) = -0.521
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (analytic) = 0
y[1] (numeric) = 1.5757587256503117803044652823162
absolute error = 1.5757587256503117803044652823162
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 = 3.833
Order of pole (six term test) = -0.5213
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (analytic) = 0
y[1] (numeric) = 1.5856350186320245263363291057308
absolute error = 1.5856350186320245263363291057308
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 = 3.844
Order of pole (six term test) = -0.5216
TOP MAIN SOLVE Loop
bytes used=164047532, alloc=4521156, time=12.80
x[1] = 1.74
y[1] (analytic) = 0
y[1] (numeric) = 1.595512275282133352154156079988
absolute error = 1.595512275282133352154156079988
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.69
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.854
Order of pole (six term test) = -0.5219
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (analytic) = 0
y[1] (numeric) = 1.6053904866686768027784218107169
absolute error = 1.6053904866686768027784218107169
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.701
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.864
Order of pole (six term test) = -0.5222
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (analytic) = 0
y[1] (numeric) = 1.6152696439576055599847044079647
absolute error = 1.6152696439576055599847044079647
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.713
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 = 3.875
Order of pole (six term test) = -0.5225
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (analytic) = 0
y[1] (numeric) = 1.6251497384115247350714704520594
absolute error = 1.6251497384115247350714704520594
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.724
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 = 3.885
Order of pole (six term test) = -0.5228
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (analytic) = 0
y[1] (numeric) = 1.6350307613884548852841990723315
absolute error = 1.6350307613884548852841990723315
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.735
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 = 3.896
Order of pole (six term test) = -0.5232
TOP MAIN SOLVE Loop
bytes used=168048780, alloc=4521156, time=13.12
x[1] = 1.79
y[1] (analytic) = 0
y[1] (numeric) = 1.6449127043406114345331793196886
absolute error = 1.6449127043406114345331793196886
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.747
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.906
Order of pole (six term test) = -0.5235
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (analytic) = 0
y[1] (numeric) = 1.654795558813202185214867316495
absolute error = 1.654795558813202185214867316495
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.758
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.916
Order of pole (six term test) = -0.5239
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (analytic) = 0
y[1] (numeric) = 1.6646793164432426139854165425218
absolute error = 1.6646793164432426139854165425218
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.77
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 = 3.927
Order of pole (six term test) = -0.5242
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (analytic) = 0
y[1] (numeric) = 1.6745639689583886502431223665296
absolute error = 1.6745639689583886502431223665296
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.781
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 = 3.937
Order of pole (six term test) = -0.5246
TOP MAIN SOLVE Loop
bytes used=172049740, alloc=4521156, time=13.44
x[1] = 1.83
y[1] (analytic) = 0
y[1] (numeric) = 1.6844495081757866418571901367256
absolute error = 1.6844495081757866418571901367256
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 = 3.948
Order of pole (six term test) = -0.525
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (analytic) = 0
y[1] (numeric) = 1.6943359260009402183365011473086
absolute error = 1.6943359260009402183365011473086
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 = 3.958
Order of pole (six term test) = -0.5253
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (analytic) = 0
y[1] (numeric) = 1.7042232144265937671668881361422
absolute error = 1.7042232144265937671668881361422
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.816
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.968
Order of pole (six term test) = -0.5257
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (analytic) = 0
y[1] (numeric) = 1.714111365531632244461738699845
absolute error = 1.714111365531632244461738699845
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.827
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 3.979
Order of pole (six term test) = -0.5261
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (analytic) = 0
y[1] (numeric) = 1.7240003714799970463713419889124
absolute error = 1.7240003714799970463713419889124
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.839
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 = 3.989
Order of pole (six term test) = -0.5265
TOP MAIN SOLVE Loop
bytes used=176050744, alloc=4521156, time=13.76
x[1] = 1.88
y[1] (analytic) = 0
y[1] (numeric) = 1.7338902245196176728840281055415
absolute error = 1.7338902245196176728840281055415
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.85
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 = 4
Order of pole (six term test) = -0.527
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (analytic) = 0
y[1] (numeric) = 1.7437809169813589207294957223611
absolute error = 1.7437809169813589207294957223611
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.861
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 = 4.01
Order of pole (six term test) = -0.5274
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (analytic) = 0
y[1] (numeric) = 1.7536724412779833470643866957529
absolute error = 1.7536724412779833470643866957529
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.873
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.02
Order of pole (six term test) = -0.5278
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (analytic) = 0
y[1] (numeric) = 1.7635647899031287504846841555408
absolute error = 1.7635647899031287504846841555408
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.884
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.031
Order of pole (six term test) = -0.5283
TOP MAIN SOLVE Loop
bytes used=180051572, alloc=4521156, time=14.08
x[1] = 1.92
y[1] (analytic) = 0
y[1] (numeric) = 1.7734579554303004206713541077481
absolute error = 1.7734579554303004206713541077481
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.896
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 = 4.041
Order of pole (six term test) = -0.5287
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (analytic) = 0
y[1] (numeric) = 1.7833519305118779126372273581047
absolute error = 1.7833519305118779126372273581047
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.907
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 = 4.052
Order of pole (six term test) = -0.5292
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (analytic) = 0
y[1] (numeric) = 1.7932467078781361061067737107619
absolute error = 1.7932467078781361061067737107619
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.919
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.062
Order of pole (six term test) = -0.5297
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (analytic) = 0
y[1] (numeric) = 1.8031422803362803150284386289666
absolute error = 1.8031422803362803150284386289666
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.93
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.072
Order of pole (six term test) = -0.5301
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (analytic) = 0
y[1] (numeric) = 1.8130386407694952165938198273431
absolute error = 1.8130386407694952165938198273431
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.941
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.083
Order of pole (six term test) = -0.5306
TOP MAIN SOLVE Loop
bytes used=184052840, alloc=4521156, time=14.40
x[1] = 1.97
y[1] (analytic) = 0
y[1] (numeric) = 1.8229357821360073734213264723789
absolute error = 1.8229357821360073734213264723789
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.953
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.093
Order of pole (six term test) = -0.5311
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (analytic) = 0
y[1] (numeric) = 1.8328336974681611267562001829739
absolute error = 1.8328336974681611267562001829739
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.964
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.103
Order of pole (six term test) = -0.5316
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (analytic) = 0
y[1] (numeric) = 1.842732379871507642645944295065
absolute error = 1.842732379871507642645944295065
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.976
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 = 4.114
Order of pole (six term test) = -0.5322
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (analytic) = 0
y[1] (numeric) = 1.8526318225239068970723129024668
absolute error = 1.8526318225239068970723129024668
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.987
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 = 4.124
Order of pole (six term test) = -0.5327
TOP MAIN SOLVE Loop
bytes used=188053656, alloc=4521156, time=14.71
x[1] = 2.01
y[1] (analytic) = 0
y[1] (numeric) = 1.8625320186746423899600100602514
absolute error = 1.8625320186746423899600100602514
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 3.998
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 = 4.135
Order of pole (six term test) = -0.5332
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (analytic) = 0
y[1] (numeric) = 1.8724329616435483818400487344794
absolute error = 1.8724329616435483818400487344794
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.01
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.145
Order of pole (six term test) = -0.5338
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (analytic) = 0
y[1] (numeric) = 1.8823346448201494507241769207718
absolute error = 1.8823346448201494507241769207718
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.021
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.155
Order of pole (six term test) = -0.5343
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (analytic) = 0
y[1] (numeric) = 1.8922370616628121704477063045975
absolute error = 1.8922370616628121704477063045975
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.033
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.166
Order of pole (six term test) = -0.5349
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (analytic) = 0
y[1] (numeric) = 1.9021402056979087153632428133803
absolute error = 1.9021402056979087153632428133803
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.044
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 = 4.176
Order of pole (six term test) = -0.5355
TOP MAIN SOLVE Loop
bytes used=192054472, alloc=4521156, time=15.03
x[1] = 2.06
y[1] (analytic) = 0
y[1] (numeric) = 1.9120440705189921998189400276172
absolute error = 1.9120440705189921998189400276172
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.055
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 = 4.187
Order of pole (six term test) = -0.5361
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (analytic) = 0
y[1] (numeric) = 1.9219486497859835643336542017604
absolute error = 1.9219486497859835643336542017604
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.067
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.197
Order of pole (six term test) = -0.5366
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (analytic) = 0
y[1] (numeric) = 1.9318539372243698237894102153662
absolute error = 1.9318539372243698237894102153662
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.078
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.207
Order of pole (six term test) = -0.5372
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (analytic) = 0
y[1] (numeric) = 1.9417599266244134963004869881377
absolute error = 1.9417599266244134963004869881377
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.09
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.218
Order of pole (six term test) = -0.5379
TOP MAIN SOLVE Loop
bytes used=196055564, alloc=4521156, time=15.35
x[1] = 2.1
y[1] (analytic) = 0
y[1] (numeric) = 1.9516666118403730346897549540367
absolute error = 1.9516666118403730346897549540367
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.101
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.228
Order of pole (six term test) = -0.5385
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (analytic) = 0
y[1] (numeric) = 1.9615739867897340857081647300476
absolute error = 1.9615739867897340857081647300476
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.112
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.238
Order of pole (six term test) = -0.5391
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (analytic) = 0
y[1] (numeric) = 1.9714820454524514052739752359584
absolute error = 1.9714820454524514052739752359584
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.124
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 = 4.249
Order of pole (six term test) = -0.5398
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (analytic) = 0
y[1] (numeric) = 1.9813907818702012610858648101341
absolute error = 1.9813907818702012610858648101341
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.135
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 = 4.259
Order of pole (six term test) = -0.5404
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (analytic) = 0
y[1] (numeric) = 1.991300190145644156979898381147
absolute error = 1.991300190145644156979898381147
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.147
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.27
Order of pole (six term test) = -0.5411
TOP MAIN SOLVE Loop
bytes used=200057120, alloc=4521156, time=15.67
x[1] = 2.15
y[1] (analytic) = 0
y[1] (numeric) = 2.0012102644416977163558009818894
absolute error = 2.0012102644416977163558009818894
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.158
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.28
Order of pole (six term test) = -0.5417
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (analytic) = 0
y[1] (numeric) = 2.0111209989808195648944526723583
absolute error = 2.0111209989808195648944526723583
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.169
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.29
Order of pole (six term test) = -0.5424
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (analytic) = 0
y[1] (numeric) = 2.0210323880443000556272793670455
absolute error = 2.0210323880443000556272793670455
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.181
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 = 4.301
Order of pole (six term test) = -0.5431
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (analytic) = 0
y[1] (numeric) = 2.0309444259715646822005433714902
absolute error = 2.0309444259715646822005433714902
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.192
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 = 4.311
Order of pole (six term test) = -0.5438
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (analytic) = 0
y[1] (numeric) = 2.0408571071594860289046808295383
absolute error = 2.0408571071594860289046808295383
relative error = -1 %
Correct digits = -1
h = 0.01
bytes used=204058308, alloc=4521156, time=15.98
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.203
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 = 4.322
Order of pole (six term test) = -0.5445
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (analytic) = 0
y[1] (numeric) = 2.0507704260617051087120047833663
absolute error = 2.0507704260617051087120047833663
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.215
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.332
Order of pole (six term test) = -0.5453
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (analytic) = 0
y[1] (numeric) = 2.0606843771879619431864767742034
absolute error = 2.0606843771879619431864767742034
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.226
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.342
Order of pole (six term test) = -0.546
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (analytic) = 0
y[1] (numeric) = 2.0705989551034352406980028694012
absolute error = 2.0705989551034352406980028694012
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.237
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.353
Order of pole (six term test) = -0.5467
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (analytic) = 0
y[1] (numeric) = 2.0805141544280910318919598377317
absolute error = 2.0805141544280910318919598377317
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.249
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.363
Order of pole (six term test) = -0.5475
TOP MAIN SOLVE Loop
bytes used=208059380, alloc=4521156, time=16.30
x[1] = 2.24
y[1] (analytic) = 0
y[1] (numeric) = 2.090429969836040123833504930294
absolute error = 2.090429969836040123833504930294
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.26
Order 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) = -0.5483
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (analytic) = 0
y[1] (numeric) = 2.1003463960549042366667429669167
absolute error = 2.1003463960549042366667429669167
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.272
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 = 4.384
Order of pole (six term test) = -0.549
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (analytic) = 0
y[1] (numeric) = 2.1102634278651906890020660646919
absolute error = 2.1102634278651906890020660646919
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.283
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 = 4.394
Order of pole (six term test) = -0.5498
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (analytic) = 0
y[1] (numeric) = 2.1201810600996755005719682158104
absolute error = 2.1201810600996755005719682158104
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.294
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 = 4.404
Order of pole (six term test) = -0.5506
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (analytic) = 0
y[1] (numeric) = 2.130099287642794782977368471723
absolute error = 2.130099287642794782977368471723
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.306
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.415
Order of pole (six term test) = -0.5514
bytes used=212060756, alloc=4521156, time=16.61
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (analytic) = 0
y[1] (numeric) = 2.1400181054300442915839284065133
absolute error = 2.1400181054300442915839284065133
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.317
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.425
Order of pole (six term test) = -0.5522
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (analytic) = 0
y[1] (numeric) = 2.1499375084473870138219743592397
absolute error = 2.1499375084473870138219743592397
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.328
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.436
Order of pole (six term test) = -0.5531
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (analytic) = 0
y[1] (numeric) = 2.1598574917306686712953626960059
absolute error = 2.1598574917306686712953626960059
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.34
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 = 4.446
Order of pole (six term test) = -0.5539
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (analytic) = 0
y[1] (numeric) = 2.169778050365041015214865031755
absolute error = 2.169778050365041015214865031755
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.351
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 = 4.456
Order of pole (six term test) = -0.5547
TOP MAIN SOLVE Loop
bytes used=216061788, alloc=4521156, time=16.93
x[1] = 2.33
y[1] (analytic) = 0
y[1] (numeric) = 2.1796991794843927967412866608612
absolute error = 2.1796991794843927967412866608612
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.362
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 = 4.467
Order of pole (six term test) = -0.5556
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (analytic) = 0
y[1] (numeric) = 2.1896208742707882958534311742777
absolute error = 2.1896208742707882958534311742777
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.374
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.477
Order of pole (six term test) = -0.5565
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (analytic) = 0
y[1] (numeric) = 2.1995431299539132943470328924389
absolute error = 2.1995431299539132943470328924389
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.385
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.487
Order of pole (six term test) = -0.5574
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (analytic) = 0
y[1] (numeric) = 2.2094659418105283805237220341877
absolute error = 2.2094659418105283805237220341877
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.396
Order 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) = -0.5583
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (analytic) = 0
y[1] (numeric) = 2.2193893051639294750447719091272
absolute error = 2.2193893051639294750447719091272
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.407
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.508
Order of pole (six term test) = -0.5592
TOP MAIN SOLVE Loop
bytes used=220062832, alloc=4521156, time=17.25
x[1] = 2.38
y[1] (analytic) = 0
y[1] (numeric) = 2.2293132153834154693035905117604
absolute error = 2.2293132153834154693035905117604
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.419
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.519
Order of pole (six term test) = -0.5601
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (analytic) = 0
y[1] (numeric) = 2.2392376678837628695144300478953
absolute error = 2.2392376678837628695144300478953
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.43
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.529
Order of pole (six term test) = -0.561
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (analytic) = 0
y[1] (numeric) = 2.2491626581247073415233486288436
absolute error = 2.2491626581247073415233486288436
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.441
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.539
Order of pole (six term test) = -0.5619
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (analytic) = 0
y[1] (numeric) = 2.2590881816104320531218027253603
absolute error = 2.2590881816104320531218027253603
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.453
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 = 4.55
Order of pole (six term test) = -0.5629
TOP MAIN SOLVE Loop
bytes used=224063632, alloc=4521156, time=17.57
x[1] = 2.42
y[1] (analytic) = 0
y[1] (numeric) = 2.2690142338890627123840941257992
absolute error = 2.2690142338890627123840941257992
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.464
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 = 4.56
Order of pole (six term test) = -0.5638
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (analytic) = 0
y[1] (numeric) = 2.2789408105521692022579417103119
absolute error = 2.2789408105521692022579417103119
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.475
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 = 4.57
Order of pole (six term test) = -0.5648
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (analytic) = 0
y[1] (numeric) = 2.2888679072342737133133808436781
absolute error = 2.2888679072342737133133808436781
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.487
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.581
Order of pole (six term test) = -0.5658
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (analytic) = 0
y[1] (numeric) = 2.2987955196123652781996804065502
absolute error = 2.2987955196123652781996804065502
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.498
Order 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) = -0.5668
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (analytic) = 0
y[1] (numeric) = 2.3087236434054206129736629195099
absolute error = 2.3087236434054206129736629195099
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.509
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.601
Order of pole (six term test) = -0.5678
TOP MAIN SOLVE Loop
bytes used=228064496, alloc=4521156, time=17.88
x[1] = 2.47
y[1] (analytic) = 0
y[1] (numeric) = 2.3186522743739311720463554281373
absolute error = 2.3186522743739311720463554281373
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.52
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.612
Order of pole (six term test) = -0.5688
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (analytic) = 0
y[1] (numeric) = 2.3285814083194363250489118152737
absolute error = 2.3285814083194363250489118152737
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.532
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 = 4.622
Order of pole (six term test) = -0.5698
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (analytic) = 0
y[1] (numeric) = 2.3385110410840625654438407993632
absolute error = 2.3385110410840625654438407993632
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.543
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 = 4.632
Order of pole (six term test) = -0.5708
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (analytic) = 0
y[1] (numeric) = 2.348441168550068662204344033852
absolute error = 2.348441168550068662204344033852
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.554
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 = 4.643
Order of pole (six term test) = -0.5719
TOP MAIN SOLVE Loop
bytes used=232066024, alloc=4521156, time=18.20
x[1] = 2.51
y[1] (analytic) = 0
y[1] (numeric) = 2.3583717866393966673535979119389
absolute error = 2.3583717866393966673535979119389
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.566
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.653
Order of pole (six term test) = -0.5729
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (analytic) = 0
y[1] (numeric) = 2.3683028913132286935976702083368
absolute error = 2.3683028913132286935976702083368
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.577
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.663
Order of pole (six term test) = -0.574
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (analytic) = 0
y[1] (numeric) = 2.3782344785715493777010050197882
absolute error = 2.3782344785715493777010050197882
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.588
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.674
Order of pole (six term test) = -0.5751
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (analytic) = 0
y[1] (numeric) = 2.3881665444527139466425805395772
absolute error = 2.3881665444527139466425805395772
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.599
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.684
Order of pole (six term test) = -0.5762
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (analytic) = 0
y[1] (numeric) = 2.3980990850330218049544757426029
absolute error = 2.3980990850330218049544757426029
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.611
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.695
Order of pole (six term test) = -0.5772
TOP MAIN SOLVE Loop
bytes used=236066820, alloc=4521156, time=18.51
x[1] = 2.56
y[1] (analytic) = 0
y[1] (numeric) = 2.4080320964262955629831938743774
absolute error = 2.4080320964262955629831938743774
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.622
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 = 4.705
Order of pole (six term test) = -0.5784
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (analytic) = 0
y[1] (numeric) = 2.4179655747834654271281909120001
absolute error = 2.4179655747834654271281909120001
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.633
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 = 4.715
Order of pole (six term test) = -0.5795
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (analytic) = 0
y[1] (numeric) = 2.4278995162921588744021427387288
absolute error = 2.4278995162921588744021427387288
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.644
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 = 4.726
Order of pole (six term test) = -0.5806
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (analytic) = 0
y[1] (numeric) = 2.4378339171762955349240414220511
absolute error = 2.4378339171762955349240414220511
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.656
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 = 4.736
Order of pole (six term test) = -0.5818
TOP MAIN SOLVE Loop
bytes used=240067824, alloc=4521156, time=18.83
x[1] = 2.6
y[1] (analytic) = 0
y[1] (numeric) = 2.4477687736956872071997136878196
absolute error = 2.4477687736956872071997136878196
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.667
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 = 4.746
Order of pole (six term test) = -0.5829
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (analytic) = 0
y[1] (numeric) = 2.4577040821456429322652678854184
absolute error = 2.4577040821456429322652678854184
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.678
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 = 4.757
Order of pole (six term test) = -0.5841
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (analytic) = 0
y[1] (numeric) = 2.4676398388565790539677536071431
absolute error = 2.4676398388565790539677536071431
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.689
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 = 4.767
Order of pole (six term test) = -0.5852
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (analytic) = 0
y[1] (numeric) = 2.4775760401936341938344047940514
absolute error = 2.4775760401936341938344047940514
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.7
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 = 4.777
Order of pole (six term test) = -0.5864
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (analytic) = 0
y[1] (numeric) = 2.4875126825562890701376669763056
absolute error = 2.4875126825562890701376669763056
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.712
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.788
Order of pole (six term test) = -0.5876
TOP MAIN SOLVE Loop
bytes used=244068792, alloc=4586680, time=19.15
x[1] = 2.65
y[1] (analytic) = 0
y[1] (numeric) = 2.4974497623779910918982070505369
absolute error = 2.4974497623779910918982070505369
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.723
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.798
Order of pole (six term test) = -0.5888
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (analytic) = 0
y[1] (numeric) = 2.5073872761257836596826851576359
absolute error = 2.5073872761257836596826851576359
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.734
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.808
Order of pole (six term test) = -0.59
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (analytic) = 0
y[1] (numeric) = 2.5173252202999401061476391581097
absolute error = 2.5173252202999401061476391581097
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.745
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.819
Order of pole (six term test) = -0.5913
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (analytic) = 0
y[1] (numeric) = 2.5272635914336022103557903917093
absolute error = 2.5272635914336022103557903917093
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.757
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 = 4.829
Order of pole (six term test) = -0.5925
TOP MAIN SOLVE Loop
bytes used=248069772, alloc=4586680, time=19.46
x[1] = 2.69
y[1] (analytic) = 0
y[1] (numeric) = 2.5372023860924232209468136647
absolute error = 2.5372023860924232209468136647
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.768
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 = 4.839
Order of pole (six term test) = -0.5938
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (analytic) = 0
y[1] (numeric) = 2.5471416008742153242815050779763
absolute error = 2.5471416008742153242815050779763
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.779
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 = 4.85
Order of pole (six term test) = -0.595
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (analytic) = 0
y[1] (numeric) = 2.5570812324086014946967004741106
absolute error = 2.5570812324086014946967004741106
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.79
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 = 4.86
Order of pole (six term test) = -0.5963
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (analytic) = 0
y[1] (numeric) = 2.5670212773566716650086089550159
absolute error = 2.5670212773566716650086089550159
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.801
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 = 4.87
Order of pole (six term test) = -0.5976
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (analytic) = 0
y[1] (numeric) = 2.5769617324106431563847862404778
absolute error = 2.5769617324106431563847862404778
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.813
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.881
Order of pole (six term test) = -0.5989
TOP MAIN SOLVE Loop
bytes used=252070716, alloc=4586680, time=19.64
x[1] = 2.74
y[1] (analytic) = 0
y[1] (numeric) = 2.5869025942935253076701300462303
absolute error = 2.5869025942935253076701300462303
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.824
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.891
Order of pole (six term test) = -0.6002
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (analytic) = 0
y[1] (numeric) = 2.596843859758788245200375093197
absolute error = 2.596843859758788245200375093197
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.835
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.901
Order of pole (six term test) = -0.6015
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (analytic) = 0
y[1] (numeric) = 2.606785525590035735067932418038
absolute error = 2.606785525590035735067932418038
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.846
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.912
Order of pole (six term test) = -0.6028
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (analytic) = 0
y[1] (numeric) = 2.6167275886006820607198827787648
absolute error = 2.6167275886006820607198827787648
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.857
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.922
Order of pole (six term test) = -0.6041
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (analytic) = 0
y[1] (numeric) = 2.6266700456336328696668165835754
absolute error = 2.6266700456336328696668165835754
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.869
Order of pole (ratio test) Not computed
bytes used=256071724, alloc=4586680, time=19.77
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) = -0.6055
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (analytic) = 0
y[1] (numeric) = 2.6366128935609699339643255314998
absolute error = 2.6366128935609699339643255314998
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.88
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 = 4.942
Order of pole (six term test) = -0.6068
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (analytic) = 0
y[1] (numeric) = 2.6465561292836397699965999840971
absolute error = 2.6465561292836397699965999840971
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.891
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 = 4.953
Order of pole (six term test) = -0.6082
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (analytic) = 0
y[1] (numeric) = 2.6564997497311460639440704166436
absolute error = 2.6564997497311460639440704166436
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.902
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 = 4.963
Order of pole (six term test) = -0.6096
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (analytic) = 0
y[1] (numeric) = 2.6664437518612458501546441888344
absolute error = 2.6664437518612458501546441888344
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.913
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 = 4.973
Order of pole (six term test) = -0.611
TOP MAIN SOLVE Loop
bytes used=260072496, alloc=4586680, time=19.90
x[1] = 2.83
y[1] (analytic) = 0
y[1] (numeric) = 2.6763881326596493904611171758946
absolute error = 2.6763881326596493904611171758946
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.924
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 = 4.984
Order of pole (six term test) = -0.6124
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (analytic) = 0
y[1] (numeric) = 2.6863328891397237032960642849197
absolute error = 2.6863328891397237032960642849197
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.936
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 4.994
Order of pole (six term test) = -0.6138
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (analytic) = 0
y[1] (numeric) = 2.6962780183421996922502083891256
absolute error = 2.6962780183421996922502083891256
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.947
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.004
Order of pole (six term test) = -0.6152
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (analytic) = 0
y[1] (numeric) = 2.7062235173348828245012027891654
absolute error = 2.7062235173348828245012027891654
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.958
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.015
Order of pole (six term test) = -0.6166
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (analytic) = 0
y[1] (numeric) = 2.7161693832123673103072013375566
absolute error = 2.7161693832123673103072013375566
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.969
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.025
Order of pole (six term test) = -0.6181
TOP MAIN SOLVE Loop
bytes used=264073552, alloc=4586680, time=20.04
x[1] = 2.88
y[1] (analytic) = 0
y[1] (numeric) = 2.7261156130957537355137906884326
absolute error = 2.7261156130957537355137906884326
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.98
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.035
Order of pole (six term test) = -0.6195
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (analytic) = 0
y[1] (numeric) = 2.7360622041323700997640732029708
absolute error = 2.7360622041323700997640732029708
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 4.991
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.046
Order of pole (six term test) = -0.621
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (analytic) = 0
y[1] (numeric) = 2.7460091534954962138301640110533
absolute error = 2.7460091534954962138301640110533
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.003
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.056
Order of pole (six term test) = -0.6224
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (analytic) = 0
y[1] (numeric) = 2.7559564583840914102003436000125
absolute error = 2.7559564583840914102003436000125
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.014
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.066
Order of pole (six term test) = -0.6239
TOP MAIN SOLVE Loop
bytes used=268074612, alloc=4586680, time=20.17
x[1] = 2.92
y[1] (analytic) = 0
y[1] (numeric) = 2.7659041160225255217598250252138
absolute error = 2.7659041160225255217598250252138
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.025
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.076
Order of pole (six term test) = -0.6254
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (analytic) = 0
y[1] (numeric) = 2.775852123660313084094784438366
absolute error = 2.775852123660313084094784438366
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.036
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.087
Order of pole (six term test) = -0.6269
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (analytic) = 0
y[1] (numeric) = 2.7858004785718507176291923134055
absolute error = 2.7858004785718507176291923134055
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.047
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.097
Order of pole (six term test) = -0.6284
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (analytic) = 0
y[1] (numeric) = 2.7957491780561576464722930131759
absolute error = 2.7957491780561576464722930131759
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.058
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.107
Order of pole (six term test) = -0.6299
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (analytic) = 0
y[1] (numeric) = 2.8056982194366193115115300769259
absolute error = 2.8056982194366193115115300769259
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.069
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 = 5.118
Order of pole (six term test) = -0.6314
TOP MAIN SOLVE Loop
bytes used=272075784, alloc=4586680, time=20.31
x[1] = 2.97
y[1] (analytic) = 0
y[1] (numeric) = 2.8156476000607340359315172140847
absolute error = 2.8156476000607340359315172140847
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.08
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 = 5.128
Order of pole (six term test) = -0.6329
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (analytic) = 0
y[1] (numeric) = 2.8255973172998627019745194615161
absolute error = 2.8255973172998627019745194615161
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.092
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.138
Order of pole (six term test) = -0.6345
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (analytic) = 0
y[1] (numeric) = 2.8355473685489813983820399983915
absolute error = 2.8355473685489813983820399983915
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.103
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.149
Order of pole (six term test) = -0.636
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (analytic) = 0
y[1] (numeric) = 2.8454977512264369985707062114743
absolute error = 2.8454977512264369985707062114743
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.114
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.159
Order of pole (six term test) = -0.6376
TOP MAIN SOLVE Loop
bytes used=276076728, alloc=4586680, time=20.44
x[1] = 3.01
y[1] (analytic) = 0
y[1] (numeric) = 2.8554484627737056301989101521363
absolute error = 2.8554484627737056301989101521363
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.125
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.169
Order of pole (six term test) = -0.6392
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (analytic) = 0
y[1] (numeric) = 2.8653995006551539973737758963923
absolute error = 2.8653995006551539973737758963923
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.136
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.179
Order of pole (six term test) = -0.6407
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (analytic) = 0
y[1] (numeric) = 2.8753508623578035173311879551498
absolute error = 2.8753508623578035173311879551498
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.147
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.19
Order of pole (six term test) = -0.6423
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (analytic) = 0
y[1] (numeric) = 2.8853025453910972339950053885381
absolute error = 2.8853025453910972339950053885381
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.158
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.2
Order of pole (six term test) = -0.6439
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (analytic) = 0
y[1] (numeric) = 2.8952545472866694713853865059938
absolute error = 2.8952545472866694713853865059938
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.169
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.21
Order of pole (six term test) = -0.6455
TOP MAIN SOLVE Loop
bytes used=280077680, alloc=4586680, time=20.58
x[1] = 3.06
y[1] (analytic) = 0
y[1] (numeric) = 2.9052068655981181904005361619187
absolute error = 2.9052068655981181904005361619187
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.18
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.221
Order of pole (six term test) = -0.6471
TOP MAIN SOLVE Loop
x[1] = 3.07
y[1] (analytic) = 0
y[1] (numeric) = 2.9151594979007800130413352743687
absolute error = 2.9151594979007800130413352743687
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.192
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 = 5.231
Order of pole (six term test) = -0.6487
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (analytic) = 0
y[1] (numeric) = 2.9251124417915078786843903798294
absolute error = 2.9251124417915078786843903798294
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.203
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 = 5.241
Order of pole (six term test) = -0.6504
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (analytic) = 0
y[1] (numeric) = 2.9350656948884512975362164357852
absolute error = 2.9350656948884512975362164357852
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.214
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 = 5.251
Order of pole (six term test) = -0.652
TOP MAIN SOLVE Loop
bytes used=284078872, alloc=4586680, time=20.71
x[1] = 3.1
y[1] (analytic) = 0
y[1] (numeric) = 2.9450192548308391669197019817496
absolute error = 2.9450192548308391669197019817496
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.225
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 = 5.262
Order of pole (six term test) = -0.6536
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (analytic) = 0
y[1] (numeric) = 2.9549731192787651165538621718471
absolute error = 2.9549731192787651165538621718471
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.236
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 = 5.272
Order of pole (six term test) = -0.6553
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (analytic) = 0
y[1] (numeric) = 2.9649272859129753494893188889352
absolute error = 2.9649272859129753494893188889352
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.247
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 = 5.282
Order of pole (six term test) = -0.6569
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (analytic) = 0
y[1] (numeric) = 2.9748817524346589458551117907616
absolute error = 2.9748817524346589458551117907616
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.258
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 = 5.292
Order of pole (six term test) = -0.6586
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (analytic) = 0
y[1] (numeric) = 2.9848365165652405970574902986151
absolute error = 2.9848365165652405970574902986151
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.269
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 = 5.303
Order of pole (six term test) = -0.6603
TOP MAIN SOLVE Loop
bytes used=288079860, alloc=4586680, time=20.84
x[1] = 3.15
y[1] (analytic) = 0
y[1] (numeric) = 2.9947915760461757385484117878977
absolute error = 2.9947915760461757385484117878977
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.28
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 = 5.313
Order of pole (six term test) = -0.6619
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (analytic) = 0
y[1] (numeric) = 3.0047469286387480497507202066455
absolute error = 3.0047469286387480497507202066455
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.291
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 = 5.323
Order of pole (six term test) = -0.6636
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (analytic) = 0
y[1] (numeric) = 3.0147025721238692901885437838192
absolute error = 3.0147025721238692901885437838192
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.302
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 = 5.333
Order of pole (six term test) = -0.6653
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (analytic) = 0
y[1] (numeric) = 3.0246585043018814413254693310287
absolute error = 3.0246585043018814413254693310287
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.313
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 = 5.344
Order of pole (six term test) = -0.667
TOP MAIN SOLVE Loop
bytes used=292080748, alloc=4586680, time=20.98
x[1] = 3.19
y[1] (analytic) = 0
y[1] (numeric) = 3.0346147229923611240596600722681
absolute error = 3.0346147229923611240596600722681
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.324
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 = 5.354
Order of pole (six term test) = -0.6687
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (analytic) = 0
y[1] (numeric) = 3.0445712260339262622644174448743
absolute error = 3.0445712260339262622644174448743
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.335
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 = 5.364
Order of pole (six term test) = -0.6704
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (analytic) = 0
y[1] (numeric) = 3.0545280112840449631948757536427
absolute error = 3.0545280112840449631948757536427
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.346
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 = 5.374
Order of pole (six term test) = -0.6722
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (analytic) = 0
y[1] (numeric) = 3.0644850766188465860066902016057
absolute error = 3.0644850766188465860066902016057
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.357
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 = 5.385
Order of pole (six term test) = -0.6739
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (analytic) = 0
y[1] (numeric) = 3.0744424199329349700508594139835
absolute error = 3.0744424199329349700508594139835
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.369
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.395
Order of pole (six term test) = -0.6756
TOP MAIN SOLVE Loop
bytes used=296081704, alloc=4586680, time=21.11
x[1] = 3.24
y[1] (analytic) = 0
y[1] (numeric) = 3.0844000391392037950203363947351
absolute error = 3.0844000391392037950203363947351
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.38
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.405
Order of pole (six term test) = -0.6773
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (analytic) = 0
y[1] (numeric) = 3.0943579321686540454289477692199
absolute error = 3.0943579321686540454289477692199
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.391
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.415
Order of pole (six term test) = -0.6791
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (analytic) = 0
y[1] (numeric) = 3.104316096970213552301478667346
absolute error = 3.104316096970213552301478667346
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.402
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.426
Order of pole (six term test) = -0.6808
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (analytic) = 0
y[1] (numeric) = 3.1142745315105585853457058696693
absolute error = 3.1142745315105585853457058696693
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.413
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.436
Order of pole (six term test) = -0.6826
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (analytic) = 0
y[1] (numeric) = 3.1242332337739374692627887887214
absolute error = 3.1242332337739374692627887887214
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.424
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.446
Order of pole (six term test) = -0.6843
bytes used=300082932, alloc=4586680, time=21.24
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (analytic) = 0
y[1] (numeric) = 3.1341922017619961982318681860971
absolute error = 3.1341922017619961982318681860971
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.435
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.456
Order of pole (six term test) = -0.6861
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (analytic) = 0
y[1] (numeric) = 3.1441514334936060229780857584629
absolute error = 3.1441514334936060229780857584629
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.446
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.467
Order of pole (six term test) = -0.6879
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (analytic) = 0
y[1] (numeric) = 3.1541109270046929852006312637574
absolute error = 3.1541109270046929852006312637574
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.457
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.477
Order of pole (six term test) = -0.6897
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (analytic) = 0
y[1] (numeric) = 3.1640706803480693744989530236102
absolute error = 3.1640706803480693744989530236102
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.468
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.487
Order of pole (six term test) = -0.6914
TOP MAIN SOLVE Loop
bytes used=304083712, alloc=4586680, time=21.38
x[1] = 3.33
y[1] (analytic) = 0
y[1] (numeric) = 3.1740306915932670832910357144929
absolute error = 3.1740306915932670832910357144929
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.479
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.497
Order of pole (six term test) = -0.6932
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (analytic) = 0
y[1] (numeric) = 3.183990958826372835567757640195
absolute error = 3.183990958826372835567757640195
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.508
Order of pole (six term test) = -0.695
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (analytic) = 0
y[1] (numeric) = 3.1939514801498652656718875024321
absolute error = 3.1939514801498652656718875024321
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.501
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.518
Order of pole (six term test) = -0.6968
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (analytic) = 0
y[1] (numeric) = 3.2039122536824538236293654848623
absolute error = 3.2039122536824538236293654848623
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.512
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.528
Order of pole (six term test) = -0.6986
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (analytic) = 0
y[1] (numeric) = 3.2138732775589194838942307982515
absolute error = 3.2138732775589194838942307982515
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.523
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.538
Order of pole (six term test) = -0.7004
TOP MAIN SOLVE Loop
bytes used=308084700, alloc=4586680, time=21.51
x[1] = 3.38
y[1] (analytic) = 0
y[1] (numeric) = 3.2238345499299572346970014294017
absolute error = 3.2238345499299572346970014294017
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.534
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.548
Order of pole (six term test) = -0.7022
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (analytic) = 0
y[1] (numeric) = 3.2337960689620203255095736290737
absolute error = 3.2337960689620203255095736290737
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.545
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.559
Order of pole (six term test) = -0.704
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (analytic) = 0
y[1] (numeric) = 3.2437578328371662504578788440711
absolute error = 3.2437578328371662504578788440711
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.556
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.569
Order of pole (six term test) = -0.7058
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (analytic) = 0
y[1] (numeric) = 3.2537198397529044458267028062403
absolute error = 3.2537198397529044458267028062403
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.567
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.579
Order of pole (six term test) = -0.7076
TOP MAIN SOLVE Loop
bytes used=312085748, alloc=4586680, time=21.64
x[1] = 3.42
y[1] (analytic) = 0
y[1] (numeric) = 3.2636820879220456801093221131513
absolute error = 3.2636820879220456801093221131513
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.578
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.589
Order of pole (six term test) = -0.7094
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (analytic) = 0
y[1] (numeric) = 3.2736445755725531153580329997506
absolute error = 3.2736445755725531153580329997506
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.589
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.599
Order of pole (six term test) = -0.7113
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (analytic) = 0
y[1] (numeric) = 3.2836073009473950188903186208236
absolute error = 3.2836073009473950188903186208236
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.6
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.61
Order of pole (six term test) = -0.7131
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (analytic) = 0
y[1] (numeric) = 3.2935702623043991046994069729376
absolute error = 3.2935702623043991046994069729376
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.611
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.62
Order of pole (six term test) = -0.7149
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (analytic) = 0
y[1] (numeric) = 3.3035334579161084842073919652586
absolute error = 3.3035334579161084842073919652586
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.622
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 = 5.63
Order of pole (six term test) = -0.7167
TOP MAIN SOLVE Loop
bytes used=316086984, alloc=4586680, time=21.78
x[1] = 3.47
y[1] (analytic) = 0
y[1] (numeric) = 3.3134968860696392062840039680624
absolute error = 3.3134968860696392062840039680624
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.633
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 = 5.64
Order of pole (six term test) = -0.7186
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (analytic) = 0
y[1] (numeric) = 3.3234605450665393667346008070632
absolute error = 3.3234605450665393667346008070632
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.644
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 = 5.651
Order of pole (six term test) = -0.7204
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (analytic) = 0
y[1] (numeric) = 3.3334244332226497677370815568574
absolute error = 3.3334244332226497677370815568574
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.654
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.661
Order of pole (six term test) = -0.7222
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (analytic) = 0
y[1] (numeric) = 3.3433885488679661079792781184255
absolute error = 3.3433885488679661079792781184255
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.665
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.671
Order of pole (six term test) = -0.7241
TOP MAIN SOLVE Loop
bytes used=320087900, alloc=4586680, time=21.91
x[1] = 3.51
y[1] (analytic) = 0
y[1] (numeric) = 3.3533528903465026845160265480854
absolute error = 3.3533528903465026845160265480854
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.676
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.681
Order of pole (six term test) = -0.7259
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (analytic) = 0
y[1] (numeric) = 3.3633174560161575876286331750861
absolute error = 3.3633174560161575876286331750861
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.687
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.691
Order of pole (six term test) = -0.7277
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (analytic) = 0
y[1] (numeric) = 3.3732822442485793702289000987859
absolute error = 3.3732822442485793702289000987859
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.698
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.701
Order of pole (six term test) = -0.7296
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (analytic) = 0
y[1] (numeric) = 3.3832472534290351736053297779741
absolute error = 3.3832472534290351736053297779741
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.709
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.712
Order of pole (six term test) = -0.7314
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (analytic) = 0
y[1] (numeric) = 3.3932124819562802915606569122368
absolute error = 3.3932124819562802915606569122368
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.72
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.722
Order of pole (six term test) = -0.7332
TOP MAIN SOLVE Loop
bytes used=324089244, alloc=4586680, time=22.05
x[1] = 3.56
y[1] (analytic) = 0
y[1] (numeric) = 3.403177928242429155237524206165
absolute error = 3.403177928242429155237524206165
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.731
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.732
Order of pole (six term test) = -0.7351
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (analytic) = 0
y[1] (numeric) = 3.4131435907128277211729922049991
absolute error = 3.4131435907128277211729922049991
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.742
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.742
Order of pole (six term test) = -0.7369
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (analytic) = 0
y[1] (numeric) = 3.4231094678059272453627162887134
absolute error = 3.4231094678059272453627162887134
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.753
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.752
Order of pole (six term test) = -0.7388
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (analytic) = 0
y[1] (numeric) = 3.4330755579731594263520990190868
absolute error = 3.4330755579731594263520990190868
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.764
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.763
Order of pole (six term test) = -0.7406
TOP MAIN SOLVE Loop
bytes used=328090212, alloc=4586680, time=22.18
x[1] = 3.6
y[1] (analytic) = 0
y[1] (numeric) = 3.4430418596788129006045950981195
absolute error = 3.4430418596788129006045950981195
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.775
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.773
Order of pole (six term test) = -0.7424
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (analytic) = 0
y[1] (numeric) = 3.4530083713999110736266698253509
absolute error = 3.4530083713999110736266698253509
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.786
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.783
Order of pole (six term test) = -0.7443
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (analytic) = 0
y[1] (numeric) = 3.4629750916260912705547496300918
absolute error = 3.4629750916260912705547496300918
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.797
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.793
Order of pole (six term test) = -0.7461
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (analytic) = 0
y[1] (numeric) = 3.4729420188594851901319134033079
absolute error = 3.4729420188594851901319134033079
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.808
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.803
Order of pole (six term test) = -0.748
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (analytic) = 0
y[1] (numeric) = 3.4829091516146006462211132928329
absolute error = 3.4829091516146006462211132928329
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.819
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.813
Order of pole (six term test) = -0.7498
TOP MAIN SOLVE Loop
bytes used=332091280, alloc=4586680, time=22.31
x[1] = 3.65
y[1] (analytic) = 0
y[1] (numeric) = 3.4928764884182045812174396350197
absolute error = 3.4928764884182045812174396350197
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.829
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.824
Order of pole (six term test) = -0.7516
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (analytic) = 0
y[1] (numeric) = 3.5028440278092073359344120273741
absolute error = 3.5028440278092073359344120273741
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.84
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.834
Order of pole (six term test) = -0.7535
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (analytic) = 0
y[1] (numeric) = 3.512811768338548160748541443353
absolute error = 3.512811768338548160748541443353
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.851
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.844
Order of pole (six term test) = -0.7553
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (analytic) = 0
y[1] (numeric) = 3.5227797085690819529925200072671
absolute error = 3.5227797085690819529925200072671
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.862
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.854
Order of pole (six term test) = -0.7571
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (analytic) = 0
y[1] (numeric) = 3.5327478470754672057904078703187
absolute error = 3.5327478470754672057904078703187
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.873
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.864
Order of pole (six term test) = -0.759
TOP MAIN SOLVE Loop
bytes used=336092284, alloc=4586680, time=22.45
x[1] = 3.7
y[1] (analytic) = 0
y[1] (numeric) = 3.542716182444055153728151894906
absolute error = 3.542716182444055153728151894906
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.884
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.874
Order of pole (six term test) = -0.7608
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (analytic) = 0
y[1] (numeric) = 3.5526847132727801009497389693544
absolute error = 3.5526847132727801009497389693544
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.895
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.885
Order of pole (six term test) = -0.7626
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (analytic) = 0
y[1] (numeric) = 3.5626534381710509174633072326735
absolute error = 3.5626534381710509174633072326735
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.906
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.895
Order of pole (six term test) = -0.7644
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (analytic) = 0
y[1] (numeric) = 3.5726223557596436896326598878362
absolute error = 3.5726223557596436896326598878362
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.917
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.905
Order of pole (six term test) = -0.7662
TOP MAIN SOLVE Loop
bytes used=340093088, alloc=4586680, time=22.58
x[1] = 3.74
y[1] (analytic) = 0
y[1] (numeric) = 3.5825914646705955110178963446012
absolute error = 3.5825914646705955110178963446012
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.928
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 5.915
Order of pole (six term test) = -0.7681
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (analytic) = 0
y[1] (numeric) = 3.5925607635470993999143410215692
absolute error = 3.5925607635470993999143410215692
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.938
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 = 5.925
Order of pole (six term test) = -0.7699
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (analytic) = 0
y[1] (numeric) = 3.6025302510434003301216572716764
absolute error = 3.6025302510434003301216572716764
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.949
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 = 5.935
Order of pole (six term test) = -0.7717
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (analytic) = 0
y[1] (numeric) = 3.612499925824692361655027769054
absolute error = 3.612499925824692361655027769054
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.96
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 = 5.945
Order of pole (six term test) = -0.7735
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (analytic) = 0
y[1] (numeric) = 3.6224697865670168582876076913005
absolute error = 3.6224697865670168582876076913005
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.971
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 = 5.956
Order of pole (six term test) = -0.7753
TOP MAIN SOLVE Loop
bytes used=344093968, alloc=4586680, time=22.71
x[1] = 3.79
y[1] (analytic) = 0
y[1] (numeric) = 3.6324398319571617789881567385103
absolute error = 3.6324398319571617789881567385103
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.982
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 = 5.966
Order of pole (six term test) = -0.7771
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (analytic) = 0
y[1] (numeric) = 3.6424100606925620304898732587318
absolute error = 3.6424100606925620304898732587318
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 5.993
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 = 5.976
Order of pole (six term test) = -0.7789
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (analytic) = 0
y[1] (numeric) = 3.652380471481200868396030544951
absolute error = 3.652380471481200868396030544951
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.004
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 = 5.986
Order of pole (six term test) = -0.7807
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (analytic) = 0
y[1] (numeric) = 3.6623510630415123343950930283071
absolute error = 3.6623510630415123343950930283071
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.015
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 = 5.996
Order of pole (six term test) = -0.7824
TOP MAIN SOLVE Loop
bytes used=348094956, alloc=4586680, time=22.85
x[1] = 3.83
y[1] (analytic) = 0
y[1] (numeric) = 3.6723218341022847173226091786643
absolute error = 3.6723218341022847173226091786643
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.025
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.006
Order of pole (six term test) = -0.7842
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (analytic) = 0
y[1] (numeric) = 3.6822927834025650259693782792635
absolute error = 3.6822927834025650259693782792635
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.036
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.016
Order of pole (six term test) = -0.786
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (analytic) = 0
y[1] (numeric) = 3.6922639096915644616952090029652
absolute error = 3.6922639096915644616952090029652
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.047
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.026
Order of pole (six term test) = -0.7878
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (analytic) = 0
y[1] (numeric) = 3.7022352117285648790650673268652
absolute error = 3.7022352117285648790650673268652
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.058
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.037
Order of pole (six term test) = -0.7895
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (analytic) = 0
y[1] (numeric) = 3.7122066882828262228795875436838
absolute error = 3.7122066882828262228795875436838
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.069
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 = 6.047
Order of pole (six term test) = -0.7913
TOP MAIN SOLVE Loop
bytes used=352095980, alloc=4586680, time=22.98
x[1] = 3.88
y[1] (analytic) = 0
y[1] (numeric) = 3.722178338133494930124830059849
absolute error = 3.722178338133494930124830059849
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.08
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 = 6.057
Order of pole (six term test) = -0.793
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (analytic) = 0
y[1] (numeric) = 3.7321501600695132855168497555791
absolute error = 3.7321501600695132855168497555791
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.09
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.067
Order of pole (six term test) = -0.7948
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (analytic) = 0
y[1] (numeric) = 3.7421221528895297194651247244623
absolute error = 3.7421221528895297194651247244623
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.101
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.077
Order of pole (six term test) = -0.7965
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (analytic) = 0
y[1] (numeric) = 3.75209431540181003742522238318
absolute error = 3.75209431540181003742522238318
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.112
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.087
Order of pole (six term test) = -0.7982
TOP MAIN SOLVE Loop
bytes used=356097088, alloc=4586680, time=23.12
x[1] = 3.92
y[1] (analytic) = 0
y[1] (numeric) = 3.7620666464241495697552828035116
absolute error = 3.7620666464241495697552828035116
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.123
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.097
Order of pole (six term test) = -0.8
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (analytic) = 0
y[1] (numeric) = 3.7720391447837862313330116209447
absolute error = 3.7720391447837862313330116209447
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.134
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.107
Order of pole (six term test) = -0.8017
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (analytic) = 0
y[1] (numeric) = 3.7820118093173144803299303759696
absolute error = 3.7820118093173144803299303759696
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.145
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.118
Order of pole (six term test) = -0.8034
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (analytic) = 0
y[1] (numeric) = 3.7919846388706001656776634220903
absolute error = 3.7919846388706001656776634220903
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.155
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.128
Order of pole (six term test) = -0.8051
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (analytic) = 0
y[1] (numeric) = 3.8019576322986962528970797942104
absolute error = 3.8019576322986962528970797942104
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.166
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.138
Order of pole (six term test) = -0.8068
TOP MAIN SOLVE Loop
bytes used=360098468, alloc=4586680, time=23.25
x[1] = 3.97
y[1] (analytic) = 0
y[1] (numeric) = 3.8119307884657594180951873174597
absolute error = 3.8119307884657594180951873174597
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.177
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.148
Order of pole (six term test) = -0.8085
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (analytic) = 0
y[1] (numeric) = 3.8219041062449675000668258450745
absolute error = 3.8219041062449675000668258450745
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.188
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.158
Order of pole (six term test) = -0.8102
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (analytic) = 0
y[1] (numeric) = 3.8318775845184378005684574006174
absolute error = 3.8318775845184378005684574006174
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.199
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.168
Order of pole (six term test) = -0.8118
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (analytic) = 0
y[1] (numeric) = 3.8418512221771462229597331914004
absolute error = 3.8418512221771462229597331914004
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.21
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.178
Order of pole (six term test) = -0.8135
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (analytic) = 0
y[1] (numeric) = 3.8518250181208472395350604640074
absolute error = 3.8518250181208472395350604640074
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.22
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 = 6.188
Order of pole (six term test) = -0.8151
TOP MAIN SOLVE Loop
bytes used=364099588, alloc=4586680, time=23.39
x[1] = 4.02
y[1] (analytic) = 0
y[1] (numeric) = 3.8617989712579946779921249873506
absolute error = 3.8617989712579946779921249873506
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.231
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 = 6.198
Order of pole (six term test) = -0.8168
TOP MAIN SOLVE Loop
x[1] = 4.03
y[1] (analytic) = 0
y[1] (numeric) = 3.8717730805056633176072760718993
absolute error = 3.8717730805056633176072760718993
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.242
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 = 6.208
Order of pole (six term test) = -0.8184
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (analytic) = 0
y[1] (numeric) = 3.8817473447894712858088784731681
absolute error = 3.8817473447894712858088784731681
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.253
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 = 6.219
Order of pole (six term test) = -0.8201
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (analytic) = 0
y[1] (numeric) = 3.8917217630435032459592068094793
absolute error = 3.8917217630435032459592068094793
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.264
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 = 6.229
Order of pole (six term test) = -0.8217
TOP MAIN SOLVE Loop
bytes used=368100432, alloc=4586680, time=23.52
x[1] = 4.06
y[1] (analytic) = 0
y[1] (numeric) = 3.9016963342102343672732303022563
absolute error = 3.9016963342102343672732303022563
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.274
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.239
Order of pole (six term test) = -0.8233
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (analytic) = 0
y[1] (numeric) = 3.9116710572404550679187353119336
absolute error = 3.9116710572404550679187353119336
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.285
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.249
Order of pole (six term test) = -0.8249
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (analytic) = 0
y[1] (numeric) = 3.9216459310931965224566864293244
absolute error = 3.9216459310931965224566864293244
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.296
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.259
Order of pole (six term test) = -0.8265
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (analytic) = 0
y[1] (numeric) = 3.9316209547356569248935594798218
absolute error = 3.9316209547356569248935594798218
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.307
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.269
Order of pole (six term test) = -0.8281
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (analytic) = 0
y[1] (numeric) = 3.9415961271431284987286169567986
absolute error = 3.9415961271431284987286169567986
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.318
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.279
Order of pole (six term test) = -0.8296
TOP MAIN SOLVE Loop
bytes used=372101324, alloc=4586680, time=23.66
x[1] = 4.11
y[1] (analytic) = 0
y[1] (numeric) = 3.9515714472989252454887629416168
absolute error = 3.9515714472989252454887629416168
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.328
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.289
Order of pole (six term test) = -0.8312
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (analytic) = 0
y[1] (numeric) = 3.9615469141943114233517348892621
absolute error = 3.9615469141943114233517348892621
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.339
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.299
Order of pole (six term test) = -0.8328
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (analytic) = 0
y[1] (numeric) = 3.9715225268284307475649877449733
absolute error = 3.9715225268284307475649877449733
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.35
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.309
Order of pole (six term test) = -0.8343
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (analytic) = 0
y[1] (numeric) = 3.9814982842082363044727252858824
absolute error = 3.9814982842082363044727252858824
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.361
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.319
Order of pole (six term test) = -0.8358
TOP MAIN SOLVE Loop
bytes used=376102504, alloc=4586680, time=23.79
x[1] = 4.15
y[1] (analytic) = 0
y[1] (numeric) = 3.9914741853484211710671575309832
absolute error = 3.9914741853484211710671575309832
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.371
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 = 6.329
Order of pole (six term test) = -0.8373
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (analytic) = 0
y[1] (numeric) = 4.0014502292713497320822343192492
absolute error = 4.0014502292713497320822343192492
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.382
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 = 6.34
Order of pole (six term test) = -0.8389
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (analytic) = 0
y[1] (numeric) = 4.011426415006989686748846121351
absolute error = 4.011426415006989686748846121351
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.393
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 = 6.35
Order of pole (six term test) = -0.8404
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (analytic) = 0
y[1] (numeric) = 4.0214027415928447374298158495147
absolute error = 4.0214027415928447374298158495147
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.404
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 = 6.36
Order of pole (six term test) = -0.8418
TOP MAIN SOLVE Loop
x[1] = 4.19
y[1] (analytic) = 0
y[1] (numeric) = 4.031379208073887952450951516318
absolute error = 4.031379208073887952450951516318
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.415
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 = 6.37
Order of pole (six term test) = -0.8433
TOP MAIN SOLVE Loop
bytes used=380103864, alloc=4586680, time=23.92
x[1] = 4.2
y[1] (analytic) = 0
y[1] (numeric) = 4.0413558135024957955410103564398
absolute error = 4.0413558135024957955410103564398
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.425
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 = 6.38
Order of pole (six term test) = -0.8448
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (analytic) = 0
y[1] (numeric) = 4.0513325569383828143886613981396
absolute error = 4.0513325569383828143886613981396
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.436
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 = 6.39
Order of pole (six term test) = -0.8462
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (analytic) = 0
y[1] (numeric) = 4.061309437448536980918446035397
absolute error = 4.061309437448536980918446035397
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.447
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 = 6.4
Order of pole (six term test) = -0.8477
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (analytic) = 0
y[1] (numeric) = 4.0712864541071556759803451446961
absolute error = 4.0712864541071556759803451446961
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.458
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 = 6.41
Order of pole (six term test) = -0.8491
TOP MAIN SOLVE Loop
bytes used=384104668, alloc=4586680, time=24.06
x[1] = 4.24
y[1] (analytic) = 0
y[1] (numeric) = 4.0812636059955823112388866118272
absolute error = 4.0812636059955823112388866118272
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.468
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.42
Order of pole (six term test) = -0.8505
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (analytic) = 0
y[1] (numeric) = 4.0912408922022435811377883512894
absolute error = 4.0912408922022435811377883512894
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.479
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.43
Order of pole (six term test) = -0.8519
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (analytic) = 0
y[1] (numeric) = 4.1012183118225873379049482554605
absolute error = 4.1012183118225873379049482554605
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.49
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.44
Order of pole (six term test) = -0.8533
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (analytic) = 0
y[1] (numeric) = 4.1111958639590210826501829241937
absolute error = 4.1111958639590210826501829241937
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.501
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.45
Order of pole (six term test) = -0.8547
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (analytic) = 0
y[1] (numeric) = 4.121173547720851065694500105167
absolute error = 4.121173547720851065694500105167
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.511
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.46
Order of pole (six term test) = -0.8561
TOP MAIN SOLVE Loop
bytes used=388106256, alloc=4586680, time=24.19
x[1] = 4.29
y[1] (analytic) = 0
y[1] (numeric) = 4.1311513622242219893548838198631
absolute error = 4.1311513622242219893548838198631
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.522
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.47
Order of pole (six term test) = -0.8574
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (analytic) = 0
y[1] (numeric) = 4.1411293065920573064925941551582
absolute error = 4.1411293065920573064925941551582
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.533
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.48
Order of pole (six term test) = -0.8588
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (analytic) = 0
y[1] (numeric) = 4.1511073799540001082158533642643
absolute error = 4.1511073799540001082158533642643
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.544
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.491
Order of pole (six term test) = -0.8601
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (analytic) = 0
y[1] (numeric) = 4.1610855814463545942095236490792
absolute error = 4.1610855814463545942095236490792
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.554
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 = 6.501
Order of pole (six term test) = -0.8614
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (analytic) = 0
y[1] (numeric) = 4.1710639102120281192449969077482
absolute error = 4.1710639102120281192449969077482
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.565
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 = 6.511
Order of pole (six term test) = -0.8627
TOP MAIN SOLVE Loop
bytes used=392107056, alloc=4586680, time=24.32
x[1] = 4.34
y[1] (analytic) = 0
y[1] (numeric) = 4.1810423654004738095030296634867
absolute error = 4.1810423654004738095030296634867
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.576
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 = 6.521
Order of pole (six term test) = -0.864
TOP MAIN SOLVE Loop
x[1] = 4.35
y[1] (analytic) = 0
y[1] (numeric) = 4.191020946167633742420683903703
absolute error = 4.191020946167633742420683903703
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.586
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.531
Order of pole (six term test) = -0.8653
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (analytic) = 0
y[1] (numeric) = 4.2009996516758826838508929405762
absolute error = 4.2009996516758826838508929405762
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.597
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.541
Order of pole (six term test) = -0.8665
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (analytic) = 0
y[1] (numeric) = 4.2109784810939723763994766768675
absolute error = 4.2109784810939723763994766768675
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.608
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.551
Order of pole (six term test) = -0.8678
TOP MAIN SOLVE Loop
bytes used=396108064, alloc=4586680, time=24.46
x[1] = 4.38
y[1] (analytic) = 0
y[1] (numeric) = 4.220957433596976372879698582974
absolute error = 4.220957433596976372879698582974
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.619
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.561
Order of pole (six term test) = -0.869
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (analytic) = 0
y[1] (numeric) = 4.230936508366235408898702764595
absolute error = 4.230936508366235408898702764595
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.629
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 = 6.571
Order of pole (six term test) = -0.8702
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (analytic) = 0
y[1] (numeric) = 4.2409157045893033086634089733538
absolute error = 4.2409157045893033086634089733538
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.64
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 = 6.581
Order of pole (six term test) = -0.8714
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (analytic) = 0
y[1] (numeric) = 4.2508950214598934181656912852548
absolute error = 4.2508950214598934181656912852548
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.651
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 = 6.591
Order of pole (six term test) = -0.8726
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (analytic) = 0
y[1] (numeric) = 4.2608744581778255599779371997578
absolute error = 4.2608744581778255599779371997578
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.661
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 = 6.601
Order of pole (six term test) = -0.8738
TOP MAIN SOLVE Loop
bytes used=400109048, alloc=4586680, time=24.60
x[1] = 4.43
y[1] (analytic) = 0
y[1] (numeric) = 4.2708540139489735039603926115089
absolute error = 4.2708540139489735039603926115089
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.672
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 = 6.611
Order of pole (six term test) = -0.875
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (analytic) = 0
y[1] (numeric) = 4.2808336879852129482510587577599
absolute error = 4.2808336879852129482510587577599
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.683
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 = 6.621
Order of pole (six term test) = -0.8761
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (analytic) = 0
y[1] (numeric) = 4.2908134795043700049773338961908
absolute error = 4.2908134795043700049773338961908
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.693
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.631
Order of pole (six term test) = -0.8773
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (analytic) = 0
y[1] (numeric) = 4.3007933877301701851960989418007
absolute error = 4.3007933877301701851960989418007
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.704
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.641
Order of pole (six term test) = -0.8784
TOP MAIN SOLVE Loop
bytes used=404109916, alloc=4586680, time=24.73
x[1] = 4.47
y[1] (analytic) = 0
y[1] (numeric) = 4.3107734118921878776355461859611
absolute error = 4.3107734118921878776355461859611
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.715
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.651
Order of pole (six term test) = -0.8795
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (analytic) = 0
y[1] (numeric) = 4.3207535512257963158777569143873
absolute error = 4.3207535512257963158777569143873
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.726
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.661
Order of pole (six term test) = -0.8806
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (analytic) = 0
y[1] (numeric) = 4.3307338049721180286858603968326
absolute error = 4.3307338049721180286858603968326
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.736
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.671
Order of pole (six term test) = -0.8816
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (analytic) = 0
y[1] (numeric) = 4.340714172377975768243566291059
absolute error = 4.340714172377975768243566291059
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.747
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.681
Order of pole (six term test) = -0.8827
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (analytic) = 0
y[1] (numeric) = 4.3506946526958439111379677302719
absolute error = 4.3506946526958439111379677302719
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.758
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.692
Order of pole (six term test) = -0.8838
TOP MAIN SOLVE Loop
bytes used=408110700, alloc=4586680, time=24.87
x[1] = 4.52
y[1] (analytic) = 0
y[1] (numeric) = 4.360675245183800326978775785411
absolute error = 4.360675245183800326978775785411
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.768
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 = 6.702
Order of pole (six term test) = -0.8848
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (analytic) = 0
y[1] (numeric) = 4.3706559491054787096085799492046
absolute error = 4.3706559491054787096085799492046
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.779
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 = 6.712
Order of pole (six term test) = -0.8858
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (analytic) = 0
y[1] (numeric) = 4.3806367637300213659193459180303
absolute error = 4.3806367637300213659193459180303
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.79
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 = 6.722
Order of pole (six term test) = -0.8868
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (analytic) = 0
y[1] (numeric) = 4.3906176883320324573501731966669
absolute error = 4.3906176883320324573501731966669
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.8
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.732
Order of pole (six term test) = -0.8878
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (analytic) = 0
y[1] (numeric) = 4.400598722191531689200352675622
absolute error = 4.400598722191531689200352675622
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.811
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.742
Order of pole (six term test) = -0.8888
bytes used=412111804, alloc=4586680, time=25.00
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (analytic) = 0
y[1] (numeric) = 4.4105798645939084429499998991768
absolute error = 4.4105798645939084429499998991768
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.822
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.752
Order of pole (six term test) = -0.8897
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (analytic) = 0
y[1] (numeric) = 4.4205611148298763468380046388126
absolute error = 4.4205611148298763468380046388126
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.832
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.762
Order of pole (six term test) = -0.8907
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (analytic) = 0
y[1] (numeric) = 4.4305424721954282800037428145447
absolute error = 4.4305424721954282800037428145447
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.843
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.772
Order of pole (six term test) = -0.8916
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (analytic) = 0
y[1] (numeric) = 4.4405239359917918055549537913825
absolute error = 4.4405239359917918055549537913825
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.854
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.782
Order of pole (six term test) = -0.8925
TOP MAIN SOLVE Loop
bytes used=416112884, alloc=4586680, time=25.14
x[1] = 4.61
y[1] (analytic) = 0
y[1] (numeric) = 4.4505055055253850279794054703944
absolute error = 4.4505055055253850279794054703944
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.864
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 = 6.792
Order of pole (six term test) = -0.8934
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (analytic) = 0
y[1] (numeric) = 4.4604871801077728703724620727035
absolute error = 4.4604871801077728703724620727035
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.875
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 = 6.802
Order of pole (six term test) = -0.8943
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (analytic) = 0
y[1] (numeric) = 4.4704689590556237670064455904091
absolute error = 4.4704689590556237670064455904091
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.886
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 = 6.812
Order of pole (six term test) = -0.8951
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (analytic) = 0
y[1] (numeric) = 4.4804508416906667668207518952674
absolute error = 4.4804508416906667668207518952674
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.896
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 = 6.822
Order of pole (six term test) = -0.896
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (analytic) = 0
y[1] (numeric) = 4.4904328273396490434640566352799
absolute error = 4.4904328273396490434640566352799
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.907
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 = 6.832
Order of pole (six term test) = -0.8968
TOP MAIN SOLVE Loop
bytes used=420113884, alloc=4586680, time=25.27
x[1] = 4.66
y[1] (analytic) = 0
y[1] (numeric) = 4.5004149153342938075716343321847
absolute error = 4.5004149153342938075716343321847
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.918
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 = 6.842
Order of pole (six term test) = -0.8976
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (analytic) = 0
y[1] (numeric) = 4.5103971050112586170118263827609
absolute error = 4.5103971050112586170118263827609
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.928
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.852
Order of pole (six term test) = -0.8984
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (analytic) = 0
y[1] (numeric) = 4.5203793957120940808860396725444
absolute error = 4.5203793957120940808860396725444
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.939
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.862
Order of pole (six term test) = -0.8992
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (analytic) = 0
y[1] (numeric) = 4.5303617867832029531163467885412
absolute error = 4.5303617867832029531163467885412
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.95
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.872
Order of pole (six term test) = -0.9
TOP MAIN SOLVE Loop
bytes used=424114828, alloc=4586680, time=25.41
x[1] = 4.7
y[1] (analytic) = 0
y[1] (numeric) = 4.5403442775757996115038007747157
absolute error = 4.5403442775757996115038007747157
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.96
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 = 6.882
Order of pole (six term test) = -0.9007
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (analytic) = 0
y[1] (numeric) = 4.5503268674458699181889812702954
absolute error = 4.5503268674458699181889812702954
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.971
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 = 6.892
Order of pole (six term test) = -0.9014
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (analytic) = 0
y[1] (numeric) = 4.5603095557541314574940638215514
absolute error = 4.5603095557541314574940638215514
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.981
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.902
Order of pole (six term test) = -0.9022
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (analytic) = 0
y[1] (numeric) = 4.5702923418659941471728591358653
absolute error = 4.5702923418659941471728591358653
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 6.992
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.912
Order of pole (six term test) = -0.9029
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (analytic) = 0
y[1] (numeric) = 4.5802752251515212191418128860443
absolute error = 4.5802752251515212191418128860443
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.003
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.922
Order of pole (six term test) = -0.9036
TOP MAIN SOLVE Loop
bytes used=428115744, alloc=4586680, time=25.54
x[1] = 4.75
y[1] (analytic) = 0
y[1] (numeric) = 4.5902582049853905658108980691059
absolute error = 4.5902582049853905658108980691059
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.013
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.932
Order of pole (six term test) = -0.9042
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (analytic) = 0
y[1] (numeric) = 4.6002412807468564481786794382094
absolute error = 4.6002412807468564481786794382094
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.024
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.942
Order of pole (six term test) = -0.9049
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (analytic) = 0
y[1] (numeric) = 4.6102244518197115619005915873805
absolute error = 4.6102244518197115619005915873805
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.035
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.952
Order of pole (six term test) = -0.9055
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (analytic) = 0
y[1] (numeric) = 4.6202077175922494575836571739625
absolute error = 4.6202077175922494575836571739625
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.045
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.963
Order of pole (six term test) = -0.9062
TOP MAIN SOLVE Loop
bytes used=432116684, alloc=4586680, time=25.68
x[1] = 4.79
y[1] (analytic) = 0
y[1] (numeric) = 4.6301910774572273116044876827995
absolute error = 4.6301910774572273116044876827995
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.056
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 6.973
Order of pole (six term test) = -0.9068
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (analytic) = 0
y[1] (numeric) = 4.6401745308118290437904641123082
absolute error = 4.6401745308118290437904641123082
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.066
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 = 6.983
Order of pole (six term test) = -0.9074
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (analytic) = 0
y[1] (numeric) = 4.6501580770576287783464969150546
absolute error = 4.6501580770576287783464969150546
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.077
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 = 6.993
Order of pole (six term test) = -0.9079
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (analytic) = 0
y[1] (numeric) = 4.6601417156005546444517212514655
absolute error = 4.6601417156005546444517212514655
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.088
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 = 7.003
Order of pole (six term test) = -0.9085
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (analytic) = 0
y[1] (numeric) = 4.6701254458508529129919027921701
absolute error = 4.6701254458508529129919027921701
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.098
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.013
Order of pole (six term test) = -0.909
TOP MAIN SOLVE Loop
bytes used=436117688, alloc=4586680, time=25.81
x[1] = 4.84
y[1] (analytic) = 0
y[1] (numeric) = 4.6801092672230524659342184915356
absolute error = 4.6801092672230524659342184915356
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.109
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.023
Order of pole (six term test) = -0.9096
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (analytic) = 0
y[1] (numeric) = 4.690093179135929594891443395609
absolute error = 4.690093179135929594891443395609
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.12
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.033
Order of pole (six term test) = -0.9101
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (analytic) = 0
y[1] (numeric) = 4.7000771810124731254624259712222
absolute error = 4.7000771810124731254624259712222
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.13
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 = 7.043
Order of pole (six term test) = -0.9106
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (analytic) = 0
y[1] (numeric) = 4.7100612722798498639750778666437
absolute error = 4.7100612722798498639750778666437
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.141
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 = 7.053
Order of pole (six term test) = -0.9111
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (analytic) = 0
y[1] (numeric) = 4.7200454523693703632969465447332
absolute error = 4.7200454523693703632969465447332
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.151
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 = 7.063
Order of pole (six term test) = -0.9115
TOP MAIN SOLVE Loop
bytes used=440118728, alloc=4586680, time=25.95
x[1] = 4.89
y[1] (analytic) = 0
y[1] (numeric) = 4.7300297207164550044167878655094
absolute error = 4.7300297207164550044167878655094
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.162
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 = 7.073
Order of pole (six term test) = -0.912
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (analytic) = 0
y[1] (numeric) = 4.7400140767606003905384173281138
absolute error = 4.7400140767606003905384173281138
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.173
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 = 7.083
Order of pole (six term test) = -0.9124
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (analytic) = 0
y[1] (numeric) = 4.7499985199453460504655000992056
absolute error = 4.7499985199453460504655000992056
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.183
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.093
Order of pole (six term test) = -0.9128
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (analytic) = 0
y[1] (numeric) = 4.7599830497182414480928478395239
absolute error = 4.7599830497182414480928478395239
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.194
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.103
Order of pole (six term test) = -0.9132
TOP MAIN SOLVE Loop
bytes used=444119468, alloc=4586680, time=26.08
x[1] = 4.93
y[1] (analytic) = 0
y[1] (numeric) = 4.7699676655308132948562312749177
absolute error = 4.7699676655308132948562312749177
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.204
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.113
Order of pole (six term test) = -0.9136
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (analytic) = 0
y[1] (numeric) = 4.7799523668385331620286979249781
absolute error = 4.7799523668385331620286979249781
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.215
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.123
Order of pole (six term test) = -0.914
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (analytic) = 0
y[1] (numeric) = 4.7899371531007853897869107857688
absolute error = 4.7899371531007853897869107857688
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.225
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 = 7.133
Order of pole (six term test) = -0.9143
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (analytic) = 0
y[1] (numeric) = 4.7999220237808352900061023507423
absolute error = 4.7999220237808352900061023507423
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.236
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 = 7.143
Order of pole (six term test) = -0.9147
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (analytic) = 0
y[1] (numeric) = 4.8099069783457976397768753385038
absolute error = 4.8099069783457976397768753385038
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.247
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 = 7.153
Order of pole (six term test) = -0.915
TOP MAIN SOLVE Loop
bytes used=448120724, alloc=4586680, time=26.22
x[1] = 4.98
y[1] (analytic) = 0
y[1] (numeric) = 4.8198920162666054626712829769806
absolute error = 4.8198920162666054626712829769806
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.257
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.163
Order of pole (six term test) = -0.9153
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (analytic) = 0
y[1] (numeric) = 4.829877137017979094819393678236
absolute error = 4.829877137017979094819393678236
relative error = -1 %
Correct digits = -1
h = 0.01
NO INFO (given) for Equation 1
Radius of convergence (ratio test) for eq 1 = 7.268
Order of pole (ratio test) Not computed
NO REAL POLE (three term test) for Equation 1
Radius of convergence (six term test) for eq 1 = 7.173
Order of pole (six term test) = -0.9156
Finished!
diff ( y , x , 1 ) = tanh(sqrt(2.0*x + 3.0));
Iterations = 490
Total Elapsed Time = 26 Seconds
Elapsed Time(since restart) = 25 Seconds
Time to Timeout = 2 Minutes 33 Seconds
Percent Done = 100.2 %
> quit
bytes used=449711448, alloc=4586680, time=26.27