|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre cos 1 $eq_no = 1 > array_tmp3[1] := cos(array_x[1]); > array_tmp3_g[1] := sin(array_x[1]); > #emit pre sub FULL FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp2[1] - array_tmp3[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1; > array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre cos ID_LINEAR iii = 2 $eq_no = 1 > array_tmp3[2] := -array_tmp3_g[1] * array_x[2] / 1; > array_tmp3_g[2] := array_tmp3[1] * array_x[2] / 1; > #emit pre sub FULL FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp2[2] - array_tmp3[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2; > array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre cos ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := -array_tmp3_g[2] * array_x[2] / 2; > array_tmp3_g[3] := array_tmp3[2] * array_x[2] / 2; > #emit pre sub FULL FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp2[3] - array_tmp3[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3; > array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre cos ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := -array_tmp3_g[3] * array_x[2] / 3; > array_tmp3_g[4] := array_tmp3[3] * array_x[2] / 3; > #emit pre sub FULL FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp2[4] - array_tmp3[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4; > array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre cos ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := -array_tmp3_g[4] * array_x[2] / 4; > array_tmp3_g[5] := array_tmp3[4] * array_x[2] / 4; > #emit pre sub FULL FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp2[5] - array_tmp3[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sin LINEAR $eq_no = 1 > array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit cos LINEAR $eq_no = 1 > array_tmp3[kkk] := -array_tmp3_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp3_g[kkk] := array_tmp3[kkk - 1] * array_x[2] / (kkk - 1); > #emit FULL - FULL sub $eq_no = 1 > array_tmp4[kkk] := array_tmp2[kkk] - array_tmp3[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := cos(array_x[1]); array_tmp3_g[1] := sin(array_x[1]); array_tmp4[1] := array_tmp2[1] - array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_tmp1_g[1]*array_x[2]; array_tmp1_g[2] := -array_tmp1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := -array_tmp3_g[1]*array_x[2]; array_tmp3_g[2] := array_tmp3[1]*array_x[2]; array_tmp4[2] := array_tmp2[2] - array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2]; array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2]; array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := -1/2*array_tmp3_g[2]*array_x[2]; array_tmp3_g[3] := 1/2*array_tmp3[2]*array_x[2]; array_tmp4[3] := array_tmp2[3] - array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := 1/3*array_tmp1_g[3]*array_x[2]; array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2]; array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := -1/3*array_tmp3_g[3]*array_x[2]; array_tmp3_g[4] := 1/3*array_tmp3[3]*array_x[2]; array_tmp4[4] := array_tmp2[4] - array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := 1/4*array_tmp1_g[4]*array_x[2]; array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2]; array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := -1/4*array_tmp3_g[4]*array_x[2]; array_tmp3_g[5] := 1/4*array_tmp3[4]*array_x[2]; array_tmp4[5] := array_tmp2[5] - array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1); array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := -array_tmp3_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp3_g[kkk] := array_tmp3[kkk - 1]*array_x[2]/(kkk - 1); array_tmp4[kkk] := array_tmp2[kkk] - array_tmp3[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp4[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(2.0 - cos(x) - sin(x)); > end; exact_soln_y := proc(x) return 2.0 - cos(x) - sin(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/subpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin ( x ) - cos ( x );"); > 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 := 0.0;"); > omniout_str(ALWAYS,"x_end := 10.0;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(2.0 - cos(x) - sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > 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_g:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3_g:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 10.0; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 100; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sin ( x ) - cos ( x );"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T05:15:28-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sub") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin ( x ) - cos ( x );") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"sub diffeq.mxt") > ; > logitem_str(html_log_file,"sub maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/subpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin ( x ) - cos ( x );"); 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 := 0.0;"); omniout_str(ALWAYS, "x_end := 10.0;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(2.0 - cos(x) - sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); 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_g := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3_g := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3_g[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.; x_end := 10.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 100; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sin ( x ) - cos ( x );"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T05:15:28-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sub"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sin ( x ) - cos ( x );"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "sub diffeq.mxt"); logitem_str(html_log_file, "sub 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/subpostode.ode################# diff ( y , x , 1 ) = sin ( x ) - cos ( x ); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 10.0; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 100; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(2.0 - cos(x) - sin(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 10 estimated_steps = 10000000 step_error = 1.0000000000000000000000000000000e-17 est_needed_step_err = 1.0000000000000000000000000000000e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.4795963091432459590803650205169e-183 estimated_step_error = 2.4795963091432459590803650205169e-183 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.6640289456673085494241237344671e-175 estimated_step_error = 1.6640289456673085494241237344671e-175 best_h = 4.00e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1167109634281658039768470129768e-167 estimated_step_error = 1.1167109634281658039768470129768e-167 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 = 7.4941209723208461003494033276293e-160 estimated_step_error = 7.4941209723208461003494033276293e-160 best_h = 1.60000e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.0292201963793928992805176661990e-152 estimated_step_error = 5.0292201963793928992805176661990e-152 best_h = 3.200000e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.3750535418631942033141002227260e-144 estimated_step_error = 3.3750535418631942033141002227260e-144 best_h = 6.4000000e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.2649614335316304211233775597983e-136 estimated_step_error = 2.2649614335316304211233775597983e-136 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.5199916895423777118956430947519e-128 estimated_step_error = 1.5199916895423777118956430947519e-128 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0200515736182804977695139837091e-120 estimated_step_error = 1.0200515736182804977695139837091e-120 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 = 6.8454826845994159350314380228140e-113 estimated_step_error = 6.8454826845994159350314380228140e-113 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.5939692205648102063552107208998e-105 estimated_step_error = 4.5939692205648102063552107208998e-105 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.0830190141819725294625088241667e-97 estimated_step_error = 3.0830190141819725294625088241667e-97 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.0690574936827564663477631480461e-89 estimated_step_error = 2.0690574936827564663477631480461e-89 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.3886262703084524939994435722306e-81 estimated_step_error = 1.3886262703084524939994435722306e-81 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 = 9.3203260310094456323386665946748e-74 estimated_step_error = 9.3203260310094456323386665946748e-74 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.2566604218990263383558127802095e-66 estimated_step_error = 6.2566604218990263383558127802095e-66 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.2013155974233946525901592832901e-58 estimated_step_error = 4.2013155974233946525901592832901e-58 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.8228608031194300273596148637954e-50 estimated_step_error = 2.8228608031194300273596148637954e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 0.9900501662491680575371996279787 y[1] (numeric) = 0.99005016624916805753719962797869 absolute error = 1e-32 relative error = 1.0100498278673364177533130571212e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -13.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 0.98020132664008914222081411446952 y[1] (numeric) = 0.98020132664008914222081411446955 absolute error = 3e-32 relative error = 3.0605957352489297705151550159651e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.22 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4814 Order of pole (three term test) = -13.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 0.97045446604851682295931495160714 y[1] (numeric) = 0.97045446604851682295931495160712 absolute error = 2e-32 relative error = 2.0608900983717170713279959577505e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.83 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4809 Order of pole (three term test) = -13.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 0.96081055915238790023288243015498 y[1] (numeric) = 0.96081055915238790023288243015495 absolute error = 3e-32 relative error = 3.1223636870170881978952783575183e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4802 Order of pole (three term test) = -13.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (analytic) = 0.95127057033435542464226418799801 y[1] (numeric) = 0.95127057033435542464226418799799 absolute error = 2e-32 relative error = 2.1024512503283203846060486802400e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.09 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4794 Order of pole (three term test) = -14.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=4001088, alloc=3145152, time=0.34 x[1] = 0.06 y[1] (analytic) = 0.94183545358535123525324717496022 y[1] (numeric) = 0.94183545358535123525324717496018 absolute error = 4e-32 relative error = 4.2470263619541171305610780571720e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4783 Order of pole (three term test) = -14.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07 y[1] (analytic) = 0.93250615240918766140254430325241 y[1] (numeric) = 0.93250615240918766140254430325238 absolute error = 3e-32 relative error = 3.2171369510531521454100273158447e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4771 Order of pole (three term test) = -14.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 0.923283599728207927715416878052 y[1] (numeric) = 0.923283599728207927715416878052 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4756 Order of pole (three term test) = -14.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 0.91416871778999469721590664556776 y[1] (numeric) = 0.91416871778999469721590664556773 absolute error = 3e-32 relative error = 3.2816699386219514996549684812426e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.474 Order of pole (three term test) = -15.13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.90516241807514608159762381378548 y[1] (numeric) = 0.90516241807514608159762381378552 absolute error = 4e-32 relative error = 4.4190964186362432691470777552431e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4721 Order of pole (three term test) = -15.37 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0.89626560120612834097721089849675 y[1] (numeric) = 0.89626560120612834097721089849671 absolute error = 4e-32 relative error = 4.4629627586031352002385497946687e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.02 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4701 Order of pole (three term test) = -15.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0.88747915685721438778455121787143 y[1] (numeric) = 0.88747915685721438778455121787141 absolute error = 2e-32 relative error = 2.2535740524684547050771561960182e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4679 Order of pole (three term test) = -15.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0.87880396366551710086428201813989 y[1] (numeric) = 0.87880396366551710086428201813989 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4655 Order of pole (three term test) = -16.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0.87024088914312634638306342128323 y[1] (numeric) = 0.87024088914312634638306342128324 absolute error = 1e-32 relative error = 1.1491071178977117640498829852702e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.06 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.463 Order of pole (three term test) = -16.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0.86179078959035849176729356265806 y[1] (numeric) = 0.86179078959035849176729356265803 absolute error = 3e-32 relative error = 3.4811233030536478583240801580004e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4602 Order of pole (three term test) = -16.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.85345451001012708764758431629571 y[1] (numeric) = 0.85345451001012708764758431629568 absolute error = 3e-32 relative error = 3.5151258383582764271087599440139e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4573 Order of pole (three term test) = -16.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0.84523288402344328067044563311665 y[1] (numeric) = 0.84523288402344328067044563311665 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4541 Order of pole (three term test) = -17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0.83712673378605440706548123568929 y[1] (numeric) = 0.83712673378605440706548123568927 absolute error = 2e-32 relative error = 2.3891245127898909754364940444395e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4508 Order of pole (three term test) = -17.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0.82913686990622910303927134282879 y[1] (numeric) = 0.82913686990622910303927134282879 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4473 Order of pole (three term test) = -17.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0.82126409136369715341639085613341 y[1] (numeric) = 0.82126409136369715341639085613345 absolute error = 4e-32 relative error = 4.8705404778602432437325711358276e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4437 Order of pole (three term test) = -17.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0.81350918542975218447514900567296 y[1] (numeric) = 0.81350918542975218447514900567302 absolute error = 6e-32 relative error = 7.3754545215496027962695261414537e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4398 Order of pole (three term test) = -17.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0.80587292758852519064218601349829 y[1] (numeric) = 0.8058729275885251906421860134983 absolute error = 1e-32 relative error = 1.2408904254823102225606346236022e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4358 Order of pole (three term test) = -18.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 0.79835608145943676762765213956833 y[1] (numeric) = 0.79835608145943676762765213956834 absolute error = 1e-32 relative error = 1.2525739118463876155113447148188e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4316 Order of pole (three term test) = -18.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 0.79095939872083580671303266854678 y[1] (numeric) = 0.79095939872083580671303266854681 absolute error = 3e-32 relative error = 3.7928621934977870014494221817615e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4272 Order of pole (three term test) = -18.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 0.78368361903483228625855584565641 y[1] (numeric) = 0.78368361903483228625855584565643 absolute error = 2e-32 relative error = 2.5520502807793233382279830300904e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4227 Order of pole (three term test) = -18.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 0.77652946997333167708839388918468 y[1] (numeric) = 0.77652946997333167708839388918472 absolute error = 4e-32 relative error = 5.1511245286510141750163842069443e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.418 Order of pole (three term test) = -18.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 0.76949766694527835825148076948726 y[1] (numeric) = 0.76949766694527835825148076948726 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4131 Order of pole (three term test) = -19.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0.76258891312511531875574038794565 y[1] (numeric) = 0.76258891312511531875574038794568 absolute error = 3e-32 relative error = 3.9339674998760444898813859473780e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4081 Order of pole (three term test) = -19.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 0.75580389938246729924593501656373 y[1] (numeric) = 0.75580389938246729924593501656377 absolute error = 4e-32 relative error = 5.2923780934025565856838393591250e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4029 Order of pole (three term test) = -19.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 bytes used=8002156, alloc=4259060, time=0.70 y[1] (analytic) = 0.74914330421305440525236902674697 y[1] (numeric) = 0.74914330421305440525236902674693 absolute error = 4e-32 relative error = 5.3394323589421155853784869265927e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3975 Order of pole (three term test) = -19.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 0.74260779367084310059155123983884 y[1] (numeric) = 0.74260779367084310059155123983884 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.392 Order of pole (three term test) = -19.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 0.73619802130144136576293518281675 y[1] (numeric) = 0.73619802130144136576293518281677 absolute error = 2e-32 relative error = 2.7166603850203587863562074247338e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3863 Order of pole (three term test) = -20.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0.72991462807674468177039372546358 y[1] (numeric) = 0.72991462807674468177039372546358 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3805 Order of pole (three term test) = -20.37 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 0.72375824233083937471558445294261 y[1] (numeric) = 0.72375824233083937471558445294264 absolute error = 3e-32 relative error = 4.1450305150772441168481057534884e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3745 Order of pole (three term test) = -20.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = 0.71772947969716973077533273577867 y[1] (numeric) = 0.71772947969716973077533273577871 absolute error = 4e-32 relative error = 5.5731304246938729435138009822318e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3683 Order of pole (three term test) = -20.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 0.71182894304697516479917419595457 y[1] (numeric) = 0.71182894304697516479917419595453 absolute error = 4e-32 relative error = 5.6193275632739074528677407730749e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3621 Order of pole (three term test) = -20.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 0.70605722242900359875889462638195 y[1] (numeric) = 0.70605722242900359875889462638197 absolute error = 2e-32 relative error = 2.8326316004806630948045569354413e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3556 Order of pole (three term test) = -21.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 0.7004148950105070786619837259262 y[1] (numeric) = 0.70041489501050707866198372592624 absolute error = 4e-32 relative error = 5.7109008224903542575680180083848e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3491 Order of pole (three term test) = -21.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 0.69490252501952553031814114927174 y[1] (numeric) = 0.69490252501952553031814114927174 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3424 Order of pole (three term test) = -21.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0.68952066368846442553516151115249 y[1] (numeric) = 0.6895206636884644255351615111525 absolute error = 1e-32 relative error = 1.4502828597633075487537104678756e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3355 Order of pole (three term test) = -21.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 0.68426984919897200093056030167186 y[1] (numeric) = 0.68426984919897200093056030167185 absolute error = 1e-32 relative error = 1.4614117532295654009979258213386e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3285 Order of pole (three term test) = -21.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 0.67915060662812154159112405224796 y[1] (numeric) = 0.679150606628121541591124052248 absolute error = 4e-32 relative error = 5.8897098242455906542627325549594e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3214 Order of pole (three term test) = -21.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 0.67416344789590411130717084971203 y[1] (numeric) = 0.674163447895904111307170849712 absolute error = 3e-32 relative error = 4.4499594413834528784744439222112e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3142 Order of pole (three term test) = -22.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 0.66930887171403698006474186022168 y[1] (numeric) = 0.66930887171403698006474186022173 absolute error = 5e-32 relative error = 7.4703925367005384770944732212126e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3068 Order of pole (three term test) = -22.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 0.6645873635360928679103151422817 y[1] (numeric) = 0.66458736353609286791031514228168 absolute error = 2e-32 relative error = 3.0093861390299856695858729593255e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2993 Order of pole (three term test) = -22.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 0.6599993955089549922220964525707 y[1] (numeric) = 0.65999939550895499222209645257072 absolute error = 2e-32 relative error = 3.0303058057465503164676245801618e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2917 Order of pole (three term test) = -22.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 0.65554542642560277284270592307019 y[1] (numeric) = 0.65554542642560277284270592307023 absolute error = 4e-32 relative error = 6.1017891953120905448488492127503e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.284 Order of pole (three term test) = -22.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 0.65122590167923291646340222625266 y[1] (numeric) = 0.65122590167923291646340222625265 absolute error = 1e-32 relative error = 1.5355654580406398723913717325519e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2762 Order of pole (three term test) = -22.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 0.64704125321872046811317350367534 y[1] (numeric) = 0.64704125321872046811317350367541 absolute error = 7e-32 relative error = 1.0818475584328435324547608672801e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2682 Order of pole (three term test) = -22.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0.64299189950542428361043048218063 y[1] (numeric) = 0.64299189950542428361043048218062 absolute error = 1e-32 relative error = 1.5552295460785412178629614765355e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2602 Order of pole (three term test) = -23.13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 0.63907824547134124239406128874993 y[1] (numeric) = 0.63907824547134124239406128874994 absolute error = 1e-32 relative error = 1.5647536230285339837864801067921e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.252 Order of pole (three term test) = -23.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 0.63530068247861338527769348546375 y[1] (numeric) = 0.63530068247861338527769348546376 absolute error = 1e-32 relative error = 1.5740578084986769519187464949979e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2438 Order of pole (three term test) = -23.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 0.63165958828039202637964395896972 y[1] (numeric) = 0.63165958828039202637964395896974 absolute error = 2e-32 relative error = 3.1662623937123000994917948173338e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2354 Order of pole (three term test) = -23.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 0.62815532698306275278475053812396 y[1] (numeric) = 0.62815532698306275278475053812398 absolute error = 2e-32 relative error = 3.1839258764320356383512118140085e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.227 Order of pole (three term test) = -23.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=12005388, alloc=4324584, time=1.07 x[1] = 0.55 y[1] (analytic) = 0.62478824900983508940664009462491 y[1] (numeric) = 0.62478824900983508940664009462496 absolute error = 5e-32 relative error = 8.0027113312774431174702752295854e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2184 Order of pole (three term test) = -23.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 0.62155869106570047005360505502167 y[1] (numeric) = 0.62155869106570047005360505502167 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2098 Order of pole (three term test) = -23.83 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = 0.61846697610376201887178014300517 y[1] (numeric) = 0.61846697610376201887178014300518 absolute error = 1e-32 relative error = 1.6169012067545334327938829430969e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2011 Order of pole (three term test) = -23.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 0.61551341329293950915941661237354 y[1] (numeric) = 0.61551341329293950915941661237354 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1923 Order of pole (three term test) = -24.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 0.61269829798705272902946009863353 y[1] (numeric) = 0.61269829798705272902946009863357 absolute error = 4e-32 relative error = 6.5284986316128566115492793616634e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1834 Order of pole (three term test) = -24.13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0.61002191169528634555810205538594 y[1] (numeric) = 0.61002191169528634555810205538599 absolute error = 5e-32 relative error = 8.1964268891665045480591897340711e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1745 Order of pole (three term test) = -24.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 0.60748452205403922090827738918248 y[1] (numeric) = 0.60748452205403922090827738918248 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1655 Order of pole (three term test) = -24.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 0.60508638280016099547303711805709 y[1] (numeric) = 0.60508638280016099547303711805711 absolute error = 2e-32 relative error = 3.3053131864323089498883604796181e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1564 Order of pole (three term test) = -24.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 0.60282773374557861435817894342828 y[1] (numeric) = 0.60282773374557861435817894342835 absolute error = 7e-32 relative error = 1.1611940871576300247886965335418e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1473 Order of pole (three term test) = -24.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 0.60070880075331533453034298153177 y[1] (numeric) = 0.60070880075331533453034298153177 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1381 Order of pole (three term test) = -24.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 0.59872979571490461070987375071416 y[1] (numeric) = 0.59872979571490461070987375071417 absolute error = 1e-32 relative error = 1.6702024972817070743475564510395e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1288 Order of pole (three term test) = -24.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 0.5968909165292011186010374293735 y[1] (numeric) = 0.59689091652920111860103742937347 absolute error = 3e-32 relative error = 5.0260439837891784931113816937517e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1195 Order of pole (three term test) = -24.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 0.59519234708259103433961394103531 y[1] (numeric) = 0.5951923470825910343396139410353 absolute error = 1e-32 relative error = 1.6801291295185897230109117606492e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1101 Order of pole (three term test) = -24.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 0.59363425723060354911342772853545 y[1] (numeric) = 0.59363425723060354911342772853544 absolute error = 1e-32 relative error = 1.6845389022277050809193004185158e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1007 Order of pole (three term test) = -24.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 0.59221680278092545778903147749348 y[1] (numeric) = 0.59221680278092545778903147749352 absolute error = 4e-32 relative error = 6.7542831969927937004928804829878e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09131 Order of pole (three term test) = -24.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0.59094012547782052007152565840938 y[1] (numeric) = 0.59094012547782052007152565840942 absolute error = 4e-32 relative error = 6.7688752676350967017501318995912e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08184 Order of pole (three term test) = -24.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 0.58980435298795515224841408300756 y[1] (numeric) = 0.58980435298795515224841408300762 absolute error = 6e-32 relative error = 1.0172864899358466770946712772456e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07233 Order of pole (three term test) = -24.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 0.58880959888763186693650920509983 y[1] (numeric) = 0.58880959888763186693650920509989 absolute error = 6e-32 relative error = 1.0190051268415270921649971805674e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0628 Order of pole (three term test) = -24.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 0.58795596265143173747727371068817 y[1] (numeric) = 0.58795596265143173747727371068814 absolute error = 3e-32 relative error = 5.1024229543846682678613121150027e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05324 Order of pole (three term test) = -24.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 0.58724352964226702272469428169303 y[1] (numeric) = 0.587243529642267022724694281693 absolute error = 3e-32 relative error = 5.1086131197180144003705125477496e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04366 Order of pole (three term test) = -24.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 0.58667237110284494695491929422001 y[1] (numeric) = 0.58667237110284494695491929422002 absolute error = 1e-32 relative error = 1.7045288806087270431398370803302e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03406 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 0.58624254414854348851255599456327 y[1] (numeric) = 0.58624254414854348851255599456327 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02445 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 0.58595409176169988960882570022349 y[1] (numeric) = 0.58595409176169988960882570022345 absolute error = 4e-32 relative error = 6.8264733641057145416245386763931e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01483 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 0.58580704278731245841583765111748 y[1] (numeric) = 0.58580704278731245841583765111752 absolute error = 4e-32 relative error = 6.8281869418430162065116565140752e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005198 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 0.5858014119301560932731902639458 y[1] (numeric) = 0.58580141193015609327319026394586 absolute error = 6e-32 relative error = 1.0242378863906473059220504534705e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 0.58593719975331181745207540777631 y[1] (numeric) = 0.5859371997533118174520754077763 absolute error = 1e-32 relative error = 1.7066675411989795390221195706800e-30 % Correct digits = 32 h = 0.01 bytes used=16006292, alloc=4390108, time=1.45 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 0.58621439267811047152218390680536 y[1] (numeric) = 0.58621439267811047152218390680536 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 0.58663296298549056895212865687538 y[1] (numeric) = 0.58663296298549056895212865687535 absolute error = 3e-32 relative error = 5.1139301561446696560489919411712e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 0.58719286881877017915895685599752 y[1] (numeric) = 0.58719286881877017915895685599747 absolute error = 5e-32 relative error = 8.5150897865266619858382906595177e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = 0.58789405418783256082075629249945 y[1] (numeric) = 0.5878940541878325608207562924995 absolute error = 5e-32 relative error = 8.5049337791099627428087974164440e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 0.58873644897472512689251244630303 y[1] (numeric) = 0.58873644897472512689251244630307 absolute error = 4e-32 relative error = 6.7942115813721647724661324859478e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 0.58971996894067118143338060624745 y[1] (numeric) = 0.5897199689406711814333806062475 absolute error = 5e-32 relative error = 8.4786004601160544190374552232370e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 0.59084451573449372707753337079435 y[1] (numeric) = 0.59084451573449372707753337079432 absolute error = 3e-32 relative error = 5.0774779491193623029526291425618e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 0.59210997690245050077485626352191 y[1] (numeric) = 0.59210997690245050077485626352192 absolute error = 1e-32 relative error = 1.6888754437670097793219826197199e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 0.59351622589947925430611322964662 y[1] (numeric) = 0.59351622589947925430611322964657 absolute error = 5e-32 relative error = 8.4243695147886721897766690559818e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 0.59506312210185215505390153287935 y[1] (numeric) = 0.59506312210185215505390153287932 absolute error = 3e-32 relative error = 5.0414819681709568230921274148259e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 0.59675051082123804159986425595375 y[1] (numeric) = 0.59675051082123804159986425595378 absolute error = 3e-32 relative error = 5.0272265303492582344623293570174e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 0.59857822332017112793431919084398 y[1] (numeric) = 0.59857822332017112793431919084401 absolute error = 3e-32 relative error = 5.0118762813650538000412511408889e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 0.60054607682892460942077369965635 y[1] (numeric) = 0.60054607682892460942077369965637 absolute error = 2e-32 relative error = 3.3303023317721760293087937431001e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 0.60265387456378748316879038614185 y[1] (numeric) = 0.60265387456378748316879038614184 absolute error = 1e-32 relative error = 1.6593272560038202999823925904308e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 0.60490140574674275514839692413694 y[1] (numeric) = 0.60490140574674275514839692413699 absolute error = 5e-32 relative error = 8.2658098534711890386271416023804e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 0.60728844562654506624172705321767 y[1] (numeric) = 0.60728844562654506624172705321772 absolute error = 5e-32 relative error = 8.2333198268599595760309615552341e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 0.60981475550119562948685220729376 y[1] (numeric) = 0.6098147555011956294868522072938 absolute error = 4e-32 relative error = 6.5593689951179894416547826541964e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 0.61248008274181223103880844492095 y[1] (numeric) = 0.61248008274181223103880844492092 absolute error = 3e-32 relative error = 4.8981184605551235164627442779102e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 0.61528416081789190786761417979929 y[1] (numeric) = 0.61528416081789190786761417979928 absolute error = 1e-32 relative error = 1.6252653061484772466159049081793e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 0.6182267093239637759465610709267 y[1] (numeric) = 0.61822670932396377594656107092673 absolute error = 3e-32 relative error = 4.8525887910610102937689759487294e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 0.62130743400762934367016985943879 y[1] (numeric) = 0.62130743400762934367016985943882 absolute error = 3e-32 relative error = 4.8285274500082056070538478123874e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = 0.62452602679898750649383620651082 y[1] (numeric) = 0.62452602679898750649383620651082 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = 0.62788216584144128032022331486818 y[1] (numeric) = 0.62788216584144128032022331486823 absolute error = 5e-32 relative error = 7.9632776212067904219996055558330e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = 0.63137551552388319298473488689163 y[1] (numeric) = 0.63137551552388319298473488689166 absolute error = 3e-32 relative error = 4.7515304699624803249327745426371e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 0.63500572651425611532774094218763 y[1] (numeric) = 0.63500572651425611532774094218763 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 bytes used=20007164, alloc=4455632, time=1.81 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 0.63877243579448617579841653804618 y[1] (numeric) = 0.63877243579448617579841653804617 absolute error = 1e-32 relative error = 1.5655027423909262975568119674194e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = 0.64267526669678426532784367404728 y[1] (numeric) = 0.64267526669678426532784367404726 absolute error = 2e-32 relative error = 3.1119915510045679172392879804066e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 0.64671382894131250235114022384924 y[1] (numeric) = 0.64671382894131250235114022384921 absolute error = 3e-32 relative error = 4.6388369410796096213879685965478e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = 0.65088771867521189136350229748885 y[1] (numeric) = 0.65088771867521189136350229748881 absolute error = 4e-32 relative error = 6.1454531791465097757807699461233e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0.6551965185129872722768273703436 y[1] (numeric) = 0.65519651851298727227682737034358 absolute error = 2e-32 relative error = 3.0525192724453649566797706618982e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 0.65963979757824552211563652872703 y[1] (numeric) = 0.65963979757824552211563652872706 absolute error = 3e-32 relative error = 4.5479366330139356450836254570644e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 0.66421711154678283526690795869975 y[1] (numeric) = 0.66421711154678283526690795869973 absolute error = 2e-32 relative error = 3.0110636495686454553257250528822e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 0.6689280026910167735917026419351 y[1] (numeric) = 0.66892800269101677359170264193507 absolute error = 3e-32 relative error = 4.4847875824174819856827273295008e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = 0.6737719999257586432305976810752 y[1] (numeric) = 0.67377199992575864323059768107522 absolute error = 2e-32 relative error = 2.9683631854995091963985274223468e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = 0.67874861885532162090339023143642 y[1] (numeric) = 0.67874861885532162090339023143641 absolute error = 1e-32 relative error = 1.4732994988431123178704677247712e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 0.68385736182195991892969870973167 y[1] (numeric) = 0.68385736182195991892969870973166 absolute error = 1e-32 relative error = 1.4622932439240842854255882469048e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 0.68909771795563414509432505598747 y[1] (numeric) = 0.68909771795563414509432505598747 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 0.69446916322509788086286250741244 y[1] (numeric) = 0.69446916322509788086286250741247 absolute error = 3e-32 relative error = 4.3198462348825872443734614153192e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 0.69997116049030036933229933004683 y[1] (numeric) = 0.69997116049030036933229933004686 absolute error = 3e-32 relative error = 4.2858908614158133711250334653787e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 0.70560315955610007269149220888207 y[1] (numeric) = 0.7056031595561000726914922088821 absolute error = 3e-32 relative error = 4.2516816419690087156199244020202e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 0.71136459722728372788052439779159 y[1] (numeric) = 0.71136459722728372788052439779161 absolute error = 2e-32 relative error = 2.8114977998560593241342067605974e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 0.71725489736488539858923175367643 y[1] (numeric) = 0.71725489736488539858923175367644 absolute error = 1e-32 relative error = 1.3942044922577574791066650405764e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 0.72327347094379989173662918911306 y[1] (numeric) = 0.7232734709437998917366291891131 absolute error = 4e-32 relative error = 5.5304116087382523824824379844546e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 0.72941971611168477713760062122081 y[1] (numeric) = 0.72941971611168477713760062122084 absolute error = 3e-32 relative error = 4.1128583910400583786772503587086e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 0.73569301824914512020397060052595 y[1] (numeric) = 0.73569301824914512020397060052592 absolute error = 3e-32 relative error = 4.0777877804788940830566689621729e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = 0.74209275003119490925684128939808 y[1] (numeric) = 0.7420927500311949092568412893981 absolute error = 2e-32 relative error = 2.6950809045310403527635978844535e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 0.74861827148998903135868124172911 y[1] (numeric) = 0.74861827148998903135868124172916 absolute error = 5e-32 relative error = 6.6789713668735414680698678448081e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 0.75526893007881952351985924724711 y[1] (numeric) = 0.75526893007881952351985924724713 absolute error = 2e-32 relative error = 2.6480633855695360137468171102714e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 0.76204406073736969970783261865343 y[1] (numeric) = 0.76204406073736969970783261865345 absolute error = 2e-32 relative error = 2.6245201597198439653872845010460e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=24008616, alloc=4455632, time=2.18 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0.76894298595821962830066726066755 y[1] (numeric) = 0.76894298595821962830066726066758 absolute error = 3e-32 relative error = 3.9014596072575456622490773130695e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 0.7759650158545963094925652154463 y[1] (numeric) = 0.77596501585459630949256521544631 absolute error = 1e-32 relative error = 1.2887178926470885352566601108070e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 0.78310944822936177769011742459983 y[1] (numeric) = 0.78310944822936177769011742459988 absolute error = 5e-32 relative error = 6.3848035690351805118355367188103e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 0.7903755686452322301465319762256 y[1] (numeric) = 0.79037556864523223014653197622563 absolute error = 3e-32 relative error = 3.7956638831109659601897840624702e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 0.79776265049622115997949015961035 y[1] (numeric) = 0.79776265049622115997949015961031 absolute error = 4e-32 relative error = 5.0140226513637055630228655702393e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 0.80526995508029934931886428772418 y[1] (numeric) = 0.80526995508029934931886428772416 absolute error = 2e-32 relative error = 2.4836391664464439021464597887795e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 0.81289673167326445664553230818147 y[1] (numeric) = 0.81289673167326445664553230818152 absolute error = 5e-32 relative error = 6.1508427887365389982472489501841e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 0.82064221760381281142411310546277 y[1] (numeric) = 0.82064221760381281142411310546277 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 0.82850563832980590891271884119575 y[1] (numeric) = 0.82850563832980590891271884119576 absolute error = 1e-32 relative error = 1.2069923893528492536085183823267e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 0.83648620751572397856379855775309 y[1] (numeric) = 0.83648620751572397856379855775305 absolute error = 4e-32 relative error = 4.7819078952653375133633494538146e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0.8445831271112988807237773859903 y[1] (numeric) = 0.84458312711129888072377738599027 absolute error = 3e-32 relative error = 3.5520482279356037951654347981636e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 0.85279558743131846840734858869686 y[1] (numeric) = 0.85279558743131846840734858869686 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 0.8611227672365944337767444236884 y[1] (numeric) = 0.8611227672365944337767444236884 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 0.86956383381608554260881087994327 y[1] (numeric) = 0.86956383381608554260881087994326 absolute error = 1e-32 relative error = 1.1500018297811382557143845922614e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 0.87811794307016804449487537991282 y[1] (numeric) = 0.87811794307016804449487537991286 absolute error = 4e-32 relative error = 4.5551967495559656862566186023716e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.35 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] = 1.45 y[1] (analytic) = 0.88678423959504493180177923842899 y[1] (numeric) = 0.88678423959504493180177923842898 absolute error = 1e-32 relative error = 1.1276700186469886849886734351772e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 0.89556185676828560653851958962657 y[1] (numeric) = 0.89556185676828560653851958962661 absolute error = 4e-32 relative error = 4.4664698141950292372827266426438e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16 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] = 1.47 y[1] (analytic) = 0.90444991683548740123309693580203 y[1] (numeric) = 0.90444991683548740123309693580204 absolute error = 1e-32 relative error = 1.1056444158885277847506688142278e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = 0.91344753099805028773969832678951 y[1] (numeric) = 0.91344753099805028773969832678949 absolute error = 2e-32 relative error = 2.1895072591796943716816966943488e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 0.9225537995020559965784807983926 y[1] (numeric) = 0.9225537995020559965784807983926 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17 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] = 1.5 y[1] (analytic) = 0.93176781172824265897008677742421 y[1] (numeric) = 0.93176781172824265897008677742426 absolute error = 5e-32 relative error = 5.3661437292258481144428705847985e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.35 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] = 1.51 y[1] (analytic) = 0.94108864628306597417566662024709 y[1] (numeric) = 0.94108864628306597417566662024711 absolute error = 2e-32 relative error = 2.1251983093189168815624634705694e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = 0.95051537109083779610155833573045 y[1] (numeric) = 0.95051537109083779610155833573044 absolute error = 1e-32 relative error = 1.0520608402706547203275686256139e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.06 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] = 1.53 y[1] (analytic) = 0.96004704348693292538674592421492 y[1] (numeric) = 0.96004704348693292538674592421492 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=28012144, alloc=4455632, time=2.55 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = 0.96968271031205478637155965448357 y[1] (numeric) = 0.96968271031205478637155965448359 absolute error = 2e-32 relative error = 2.0625303294893002048539711290692e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 0.97942140800755056245847587766993 y[1] (numeric) = 0.97942140800755056245847587766999 absolute error = 6e-32 relative error = 6.1260658087981519365420446374042e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.18 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] = 1.56 y[1] (analytic) = 0.98926216271176625843090931282562 y[1] (numeric) = 0.98926216271176625843090931282563 absolute error = 1e-32 relative error = 1.0108543899615034028145123662168e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 0.99920399035743205430406154253127 y[1] (numeric) = 0.99920399035743205430406154253134 absolute error = 7e-32 relative error = 7.0055765064508823645860245888743e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 1.009245896770068212253594824731 y[1] (numeric) = 1.009245896770068212253594824731 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.65 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] = 1.59 y[1] (analytic) = 1.0193868777674016961134430024979 y[1] (numeric) = 1.0193868777674016961134430024979 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.28 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] = 1.6 y[1] (analytic) = 1.0296259192597835618636566374003 y[1] (numeric) = 1.0296259192597835618636566374003 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = 1.0399619973515970774529144617567 y[1] (numeric) = 1.0399619973515970774529144617568 absolute error = 1e-31 relative error = 9.6157359840709019008911403935397e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = 1.0503940784436464312282253834655 y[1] (numeric) = 1.0503940784436464312282253834656 absolute error = 1e-31 relative error = 9.5202364571750575609447045594885e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 1.0609211193365157901863017124867 y[1] (numeric) = 1.0609211193365157901863017124868 absolute error = 1e-31 relative error = 9.4257714525033213817523788632264e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.87 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] = 1.64 y[1] (analytic) = 1.0715420673348883722269107330887 y[1] (numeric) = 1.0715420673348883722269107330888 absolute error = 1e-31 relative error = 9.3323447626015659293682456143318e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = 1.0822558603528151005879115571391 y[1] (numeric) = 1.0822558603528151005879115571392 absolute error = 1e-31 relative error = 9.2399592058942539367208595232290e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = 1.0930614270199223136842573410376 y[1] (numeric) = 1.0930614270199223136842573410378 absolute error = 2e-31 relative error = 1.8297233353597680999839701671377e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (analytic) = 1.1039576867885479096684850959144 y[1] (numeric) = 1.1039576867885479096684850959145 absolute error = 1e-31 relative error = 9.0583181943235115288233869929807e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = 1.1149435500417952121875168649792 y[1] (numeric) = 1.1149435500417952121875168649794 absolute error = 2e-31 relative error = 1.7938127898269174379496633633752e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 1.1260179182024937520392411758875 y[1] (numeric) = 1.1260179182024937520392411758876 absolute error = 1e-31 relative error = 8.8808533490864775777335527750618e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 1.137179683843056068741509458687 y[1] (numeric) = 1.1371796838430560687415094586871 absolute error = 1e-31 relative error = 8.7936850632130317798306016079694e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = 1.14842773079621954642493755919 y[1] (numeric) = 1.1484277307962195464249375591901 absolute error = 1e-31 relative error = 8.7075570641845028105388523373559e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 1.1597609342666622099582076232457 y[1] (numeric) = 1.1597609342666622099582076232458 absolute error = 1e-31 relative error = 8.6224666692391916545532577064503e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = 1.1711781609434813198192706751205 y[1] (numeric) = 1.1711781609434813198192706751206 absolute error = 1e-31 relative error = 8.5384105796031656850544253172223e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = 1.1826782691135235179466946196796 y[1] (numeric) = 1.1826782691135235179466946196796 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 1.1942601087755551916510140069746 y[1] (numeric) = 1.1942601087755551916510140069747 absolute error = 1e-31 relative error = 8.3733852671783101913220302538852e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (analytic) = 1.2059225217552616386448320770481 y[1] (numeric) = 1.2059225217552616386448320770482 absolute error = 1e-31 relative error = 8.2924067007593959072226937593134e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = 1.217664341821063533371004392832 y[1] (numeric) = 1.217664341821063533371004392832 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=32014540, alloc=4455632, time=2.92 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 1.229484394800739113078784643007 y[1] (numeric) = 1.2294843948007391130787846430071 absolute error = 1e-31 relative error = 8.1334907887307399199060372558986e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = 1.241381498698840421526509831356 y[1] (numeric) = 1.2413814986988404215265098313561 absolute error = 1e-31 relative error = 8.0555413549191322681563612804121e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 1.2533544638148918687843011276872 y[1] (numeric) = 1.2533544638148918687843011276873 absolute error = 1e-31 relative error = 7.9785888898201599887810726844995e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (analytic) = 1.2654020928623592873792985817516 y[1] (numeric) = 1.2654020928623592873792985817517 absolute error = 1e-31 relative error = 7.9026264113249914869786358991413e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = 1.2775231810883775879769557263328 y[1] (numeric) = 1.2775231810883775879769557263329 absolute error = 1e-31 relative error = 7.8276466118450898566584531975853e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = 1.2897165163942250419325986538757 y[1] (numeric) = 1.2897165163942250419325986538758 absolute error = 1e-31 relative error = 7.7536418839993518414010930543888e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = 1.3019808794565321433853893115545 y[1] (numeric) = 1.3019808794565321433853893115546 absolute error = 1e-31 relative error = 7.6806043451069431840966328378021e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = 1.3143150438492129301094906668387 y[1] (numeric) = 1.3143150438492129301094906668388 absolute error = 1e-31 relative error = 7.6085258605221194749516208807010e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = 1.3267177761661065700919577223859 y[1] (numeric) = 1.326717776166106570091957722386 absolute error = 1e-31 relative error = 7.5373980658475692722340551246979e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = 1.3391878361443169497808975726373 y[1] (numeric) = 1.3391878361443169497808975726373 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = 1.3517239767882379301478563337071 y[1] (numeric) = 1.3517239767882379301478563337072 absolute error = 1e-31 relative error = 7.3979600656048785440579557244744e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 1.3643249444942518681421807434129 y[1] (numeric) = 1.364324944494251868142180743413 absolute error = 1e-31 relative error = 7.3296321674357040916565415608896e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 1.3769894791760889337891240834453 y[1] (numeric) = 1.3769894791760889337891240834454 absolute error = 1e-31 relative error = 7.2622196111356080243026050530038e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 1.3897163143908346871044523624493 y[1] (numeric) = 1.3897163143908346871044523624494 absolute error = 1e-31 relative error = 7.1957131800552970199784990833319e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (analytic) = 1.402504177465573314172865263472 y[1] (numeric) = 1.4025041774655733141728652634721 absolute error = 1e-31 relative error = 7.1301035395635859590667757022759e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (analytic) = 1.4153517896246538581721596919631 y[1] (numeric) = 1.4153517896246538581721596919632 absolute error = 1e-31 relative error = 7.0653812524248572813409339493135e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = 1.428257866117566718826088346975 y[1] (numeric) = 1.4282578661175667188260883469751 absolute error = 1e-31 relative error = 7.0015367933404067052880744792473e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = 1.4412211163474176327425314240392 y[1] (numeric) = 1.4412211163474176327425314240393 absolute error = 1e-31 relative error = 6.9385605626870524666046992747490e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 1.4542402439999862873460089259574 y[1] (numeric) = 1.4542402439999862873460089259575 absolute error = 1e-31 relative error = 6.8764428994856604272891859433392e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = 1.4673139471733566626506888167261 y[1] (numeric) = 1.4673139471733566626506888167262 absolute error = 1e-31 relative error = 6.8151740936314729677578773954084e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 1.4804409185081061379477386425052 y[1] (numeric) = 1.4804409185081061379477386425053 absolute error = 1e-31 relative error = 6.7547443974173327404641175952158e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = 1.4936198453180403446048424450727 y[1] (numeric) = 1.4936198453180403446048424450728 absolute error = 1e-31 relative error = 6.6951440363800697114402807262858e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 1.5068494097214606916015483635891 y[1] (numeric) = 1.5068494097214606916015483635891 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 1.5201282887729514371572826298917 y[1] (numeric) = 1.5201282887729514371572826298918 absolute error = 1e-31 relative error = 6.5783921487784472664306570506797e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=36015800, alloc=4521156, time=3.29 x[1] = 2.02 y[1] (analytic) = 1.5334551545956731278546893495365 y[1] (numeric) = 1.5334551545956731278546893495366 absolute error = 1e-31 relative error = 6.5212210282319634583074953665302e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = 1.5468286745141491760246278997285 y[1] (numeric) = 1.5468286745141491760246278997286 absolute error = 1e-31 relative error = 6.4648400723117884247922198352298e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = 1.5602475111875322968457445567072 y[1] (numeric) = 1.5602475111875322968457445567072 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = 1.5737103227433374786259633894871 y[1] (numeric) = 1.5737103227433374786259633894871 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = 1.587215762911628113080312041288 y[1] (numeric) = 1.587215762911628113080312041288 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = 1.6007624811596418671038760185679 y[1] (numeric) = 1.6007624811596418671038760185679 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 1.6143491228268428335648920447478 y[1] (numeric) = 1.6143491228268428335648920447477 absolute error = 1e-31 relative error = 6.1944469499195267202933663818424e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = 1.6279743292603864560154442531429 y[1] (numeric) = 1.6279743292603864560154442531429 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 1.6416367379509836809401792104502 y[1] (numeric) = 1.6416367379509836809401792104501 absolute error = 1e-31 relative error = 6.0914816102870268526829592852521e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = 1.655334982669150751241034648761 y[1] (numeric) = 1.655334982669150751241034648761 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = 1.6690676936018310160921745493298 y[1] (numeric) = 1.6690676936018310160921745493297 absolute error = 1e-31 relative error = 5.9913687373698440312485383932696e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 1.6828334974893750950979962132938 y[1] (numeric) = 1.6828334974893750950979962132938 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = 1.6966310177628656988519432749397 y[1] (numeric) = 1.6966310177628656988519432749397 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = 1.7104588746817733735285057452202 y[1] (numeric) = 1.7104588746817733735285057452202 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 1.7243156854719294040486606236371 y[1] (numeric) = 1.724315685471929404048660623637 absolute error = 1e-31 relative error = 5.7994020957149105937238567582193e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 1.7382000644638020786434135704731 y[1] (numeric) = 1.7382000644638020786434135704731 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 1.7521106232310624873042151215786 y[1] (numeric) = 1.7521106232310624873042151215785 absolute error = 1e-31 relative error = 5.7074021853477646856365372782358e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 1.766045970729425997655877517892 y[1] (numeric) = 1.7660459707294259976558775178919 absolute error = 1e-31 relative error = 5.6623667592694217792792924702701e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 1.7800047134357555242201057022388 y[1] (numeric) = 1.7800047134357555242201057022388 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = 1.7939854554874126808586351349626 y[1] (numeric) = 1.7939854554874126808586351349627 absolute error = 1e-31 relative error = 5.5741812005287821006656160831340e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = 1.807986798821842881396857687891 y[1] (numeric) = 1.807986798821842881396857687891 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = 1.8220073433163804300341937834971 y[1] (numeric) = 1.8220073433163804300341937834971 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 1.8360456869282596211486735957059 y[1] (numeric) = 1.836045686928259621148673595706 absolute error = 1e-31 relative error = 5.4464875635693988486352444323244e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 1.8501004258348178475024223818086 y[1] (numeric) = 1.8501004258348178475024223818087 absolute error = 1e-31 relative error = 5.4051119930355759150017557986075e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 1.8641701545738766966540649310045 y[1] (numeric) = 1.8641701545738766966540649310046 absolute error = 1e-31 relative error = 5.3643171871753630558442989244401e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=40016880, alloc=4521156, time=3.65 x[1] = 2.27 y[1] (analytic) = 1.8782534661842869975853917461896 y[1] (numeric) = 1.8782534661842869975853917461897 absolute error = 1e-31 relative error = 5.3240950596062089239908552635253e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = 1.8923489523466237631547447741598 y[1] (numeric) = 1.8923489523466237631547447741599 absolute error = 1e-31 relative error = 5.2844376231980962594104898859920e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 1.9064552035240169590001227402154 y[1] (numeric) = 1.9064552035240169590001227402154 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 1.9205708091031040159324743595225 y[1] (numeric) = 1.9205708091031040159324743595226 absolute error = 1e-31 relative error = 5.2067853747448889387786839429134e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = 1.9346943575350899906854001313727 y[1] (numeric) = 1.9346943575350899906854001313729 absolute error = 2e-31 relative error = 1.0337550177941869280789569541256e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 1.9488244364769012691227374882835 y[1] (numeric) = 1.9488244364769012691227374882837 absolute error = 2e-31 relative error = 1.0262597094767624527574428059977e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = 1.9629596329324186966513362353406 y[1] (numeric) = 1.9629596329324186966513362353407 absolute error = 1e-31 relative error = 5.0943482648500712675891137698272e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 1.9770985333937760126436768852674 y[1] (numeric) = 1.9770985333937760126436768852675 absolute error = 1e-31 relative error = 5.0579168569988077917246479543899e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 1.9912397239827094591446379302457 y[1] (numeric) = 1.9912397239827094591446379302459 absolute error = 2e-31 relative error = 1.0043994080229420980552526169725e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = 2.0053817905919444290193323217124 y[1] (numeric) = 2.0053817905919444290193323217126 absolute error = 2e-31 relative error = 9.9731632618926102682035409101823e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00367 Order of pole (three term test) = -0.8932 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = 2.0195233190266050149950201885332 y[1] (numeric) = 2.0195233190266050149950201885333 absolute error = 1e-31 relative error = 4.9516635464352669438509191471921e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01331 Order of pole (three term test) = -0.8975 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = 2.0336628951456323187600345003473 y[1] (numeric) = 2.0336628951456323187600345003475 absolute error = 2e-31 relative error = 9.8344716067447270291716874023276e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02295 Order of pole (three term test) = -0.9066 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 2.047799105003197378406657981605 y[1] (numeric) = 2.0477991050031973784066579816052 absolute error = 2e-31 relative error = 9.7665830359705975837380568920863e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03257 Order of pole (three term test) = -0.9205 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 2.0619305349900945730430507019935 y[1] (numeric) = 2.0619305349900945730430507019937 absolute error = 2e-31 relative error = 9.6996478109268987341997287752460e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04219 Order of pole (three term test) = -0.9392 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 2.0760557719751013653515945949133 y[1] (numeric) = 2.0760557719751013653515945949134 absolute error = 1e-31 relative error = 4.8168262794242178950943045893511e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05178 Order of pole (three term test) = -0.9628 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = 2.0901734034462902462371984623505 y[1] (numeric) = 2.0901734034462902462371984623507 absolute error = 2e-31 relative error = 9.5685841026509484508480110670117e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06136 Order of pole (three term test) = -0.9912 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 2.104282017652278750488858196988 y[1] (numeric) = 2.1042820176522787504888581969882 absolute error = 2e-31 relative error = 9.5044294596566248315496976832314e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07091 Order of pole (three term test) = -1.024 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = 2.1183802037434034185706140195549 y[1] (numeric) = 2.1183802037434034185706140195551 absolute error = 2e-31 relative error = 9.4411758402282414102828717475271e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08043 Order of pole (three term test) = -1.062 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = 2.1324665519128035872633702117027 y[1] (numeric) = 2.1324665519128035872633702117029 absolute error = 2e-31 relative error = 9.3788106463194826439158944393724e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08992 Order of pole (three term test) = -1.105 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = 2.1465396535374009008960825960703 y[1] (numeric) = 2.1465396535374009008960825960705 absolute error = 2e-31 relative error = 9.3173214699485745060732980065317e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09938 Order of pole (three term test) = -1.152 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = 2.1605981013187604453326731792058 y[1] (numeric) = 2.160598101318760445332673179206 absolute error = 2e-31 relative error = 9.2566960916019667609305844681363e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1088 Order of pole (three term test) = -1.205 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = 2.1746404894238194187186571529247 y[1] (numeric) = 2.174640489423819418718657152925 absolute error = 3e-31 relative error = 1.3795383717861627882021402701993e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1182 Order of pole (three term test) = -1.262 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = 2.1886654136254692662376810927798 y[1] (numeric) = 2.18866541362546926623768109278 absolute error = 2e-31 relative error = 9.1379887832514804129412796148077e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1275 Order of pole (three term test) = -1.323 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 2.2026714714429772207816480882812 y[1] (numeric) = 2.2026714714429772207816480882814 absolute error = 2e-31 relative error = 9.0798833413400207027204072317109e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1368 Order of pole (three term test) = -1.389 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=44018456, alloc=4521156, time=4.03 x[1] = 2.51 y[1] (analytic) = 2.2166572622822332074973803528544 y[1] (numeric) = 2.2166572622822332074973803528546 absolute error = 2e-31 relative error = 9.0225946700521193006708595042928e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.146 Order of pole (three term test) = -1.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 2.2306213875758080876362366781547 y[1] (numeric) = 2.230621387575808087636236678155 absolute error = 3e-31 relative error = 1.3449167199371006817406695786482e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1551 Order of pole (three term test) = -1.536 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = 2.2445624509228092359990145851528 y[1] (numeric) = 2.2445624509228092359990145851531 absolute error = 3e-31 relative error = 1.3365633906807123849825071044416e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1642 Order of pole (three term test) = -1.616 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 2.2584790582285194665349386078246 y[1] (numeric) = 2.2584790582285194665349386078248 absolute error = 2e-31 relative error = 8.8555171353624931191794807193730e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1733 Order of pole (three term test) = -1.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = 2.2723698178438053423185401940661 y[1] (numeric) = 2.2723698178438053423185401940663 absolute error = 2e-31 relative error = 8.8013842830290263982069398022494e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1822 Order of pole (three term test) = -1.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = 2.2862333407042809291896047402451 y[1] (numeric) = 2.2862333407042809291896047402454 absolute error = 3e-31 relative error = 1.3122020165604973394764244959145e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1911 Order of pole (three term test) = -1.883 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 2.3000682404692130767967911728213 y[1] (numeric) = 2.3000682404692130767967911728215 absolute error = 2e-31 relative error = 8.6953941835743131434935924012761e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1999 Order of pole (three term test) = -1.981 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = 2.3138731336601543366325737300976 y[1] (numeric) = 2.3138731336601543366325737300978 absolute error = 2e-31 relative error = 8.6435162365031640966455585864638e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2087 Order of pole (three term test) = -2.084 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = 2.3276466397992896538832294965324 y[1] (numeric) = 2.3276466397992896538832294965326 absolute error = 2e-31 relative error = 8.5923695023247074378844613403058e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2173 Order of pole (three term test) = -2.191 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 2.3413873815474829985399752164358 y[1] (numeric) = 2.341387381547482998539975216436 absolute error = 2e-31 relative error = 8.5419440446379645287244004630221e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2259 Order of pole (three term test) = -2.302 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = 2.3550939848420101312231807491671 y[1] (numeric) = 2.3550939848420101312231807491673 absolute error = 2e-31 relative error = 8.4922300887884465117642609748298e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2343 Order of pole (three term test) = -2.417 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = 2.3687650790339637305578536667508 y[1] (numeric) = 2.3687650790339637305578536667509 absolute error = 1e-31 relative error = 4.2216090099057975892538696529306e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2427 Order of pole (three term test) = -2.537 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = 2.3823992970253171417021613365833 y[1] (numeric) = 2.3823992970253171417021613365835 absolute error = 2e-31 relative error = 8.3948983803731642757149654666691e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.251 Order of pole (three term test) = -2.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = 2.3959952754056330397683570467331 y[1] (numeric) = 2.3959952754056330397683570467333 absolute error = 2e-31 relative error = 8.3472618687088499347951062704016e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2592 Order of pole (three term test) = -2.788 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = 2.4095516545884033373836915876564 y[1] (numeric) = 2.4095516545884033373836915876566 absolute error = 2e-31 relative error = 8.3002993365653227739774874030733e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2673 Order of pole (three term test) = -2.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = 2.4230670789470067025141704100862 y[1] (numeric) = 2.4230670789470067025141704100864 absolute error = 2e-31 relative error = 8.2540017871446664857909723581547e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2752 Order of pole (three term test) = -3.056 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 2.4365401969502700909126715372384 y[1] (numeric) = 2.4365401969502700909126715372386 absolute error = 2e-31 relative error = 8.2083603730540879786306309562712e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2831 Order of pole (three term test) = -3.196 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 2.4499696612976207371511469866912 y[1] (numeric) = 2.4499696612976207371511469866914 absolute error = 2e-31 relative error = 8.1633663942626320041212357933867e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2908 Order of pole (three term test) = -3.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = 2.4633541290538150891504307655679 y[1] (numeric) = 2.4633541290538150891504307655681 absolute error = 2e-31 relative error = 8.1190112960665083015714572563229e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2985 Order of pole (three term test) = -3.488 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 2.4766922617832312134264741960854 y[1] (numeric) = 2.4766922617832312134264741960857 absolute error = 3e-31 relative error = 1.2112930000596781909790382187759e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.306 Order of pole (three term test) = -3.639 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = 2.4899827256837112419243939126075 y[1] (numeric) = 2.4899827256837112419243939126077 absolute error = 2e-31 relative error = 8.0321842371449807306820029098578e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3134 Order of pole (three term test) = -3.795 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = 2.5032241917199404763071841259797 y[1] (numeric) = 2.5032241917199404763071841259799 absolute error = 2e-31 relative error = 7.9896958754853670019736240257554e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3206 Order of pole (three term test) = -3.954 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 2.5164153357563498118998131669984 y[1] (numeric) = 2.5164153357563498118998131669986 absolute error = 2e-31 relative error = 7.9478135885659243478077850938922e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3277 Order of pole (three term test) = -4.116 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = 2.529554838689528191157061550139 y[1] (numeric) = 2.5295548386895281911570615501393 absolute error = 3e-31 relative error = 1.1859794277297394374369462716706e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3347 Order of pole (three term test) = -4.282 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = 2.5426413865801318455200981171489 y[1] (numeric) = 2.5426413865801318455200981171492 absolute error = 3e-31 relative error = 1.1798753909354941617287293406282e-29 % Correct digits = 31 h = 0.01 bytes used=48019912, alloc=4521156, time=4.40 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3416 Order of pole (three term test) = -4.452 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 2.5556736707842771348475326046904 y[1] (numeric) = 2.5556736707842771348475326046906 absolute error = 2e-31 relative error = 7.8257252593060766696115259692610e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3483 Order of pole (three term test) = -4.625 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = 2.5686503880844038452464951986566 y[1] (numeric) = 2.5686503880844038452464951986569 absolute error = 3e-31 relative error = 1.1679285020322595740715097308078e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3549 Order of pole (three term test) = -4.801 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 2.5815702408195958590830123518903 y[1] (numeric) = 2.5815702408195958590830123518905 absolute error = 2e-31 relative error = 7.7472228660531848320305950099490e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3614 Order of pole (three term test) = -4.981 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 2.5944319370153461652132780240618 y[1] (numeric) = 2.594431937015346165213278024062 absolute error = 2e-31 relative error = 7.7088166063081034400482461491237e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3677 Order of pole (three term test) = -5.163 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 2.6072341905127532330429343646538 y[1] (numeric) = 2.6072341905127532330429343646539 absolute error = 1e-31 relative error = 3.8354820738344736750951992272932e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3738 Order of pole (three term test) = -5.349 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = 2.6199757210971358308846191971525 y[1] (numeric) = 2.6199757210971358308846191971527 absolute error = 2e-31 relative error = 7.6336585255167325409098610229342e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3798 Order of pole (three term test) = -5.538 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = 2.6326552546260534272391232077354 y[1] (numeric) = 2.6326552546260534272391232077357 absolute error = 3e-31 relative error = 1.1395339343153476467172084573210e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3857 Order of pole (three term test) = -5.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = 2.6452715231567193730667120348564 y[1] (numeric) = 2.6452715231567193730667120348567 absolute error = 3e-31 relative error = 1.1340990797118503223050890339480e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3914 Order of pole (three term test) = -5.925 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = 2.6578232650727941238365634254889 y[1] (numeric) = 2.6578232650727941238365634254892 absolute error = 3e-31 relative error = 1.1287432236085246721628645437893e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3969 Order of pole (three term test) = -6.122 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 2.6703092252105458221377751804832 y[1] (numeric) = 2.6703092252105458221377751804835 absolute error = 3e-31 relative error = 1.1234653918268432209136676166267e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4023 Order of pole (three term test) = -6.323 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = 2.6827281549843656248988162566396 y[1] (numeric) = 2.6827281549843656248988162566398 absolute error = 2e-31 relative error = 7.4550975143870124220453596875746e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4075 Order of pole (three term test) = -6.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 2.6950788125116252237872948377508 y[1] (numeric) = 2.6950788125116252237872948377511 absolute error = 3e-31 relative error = 1.1131399891063703349565965641007e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4126 Order of pole (three term test) = -6.731 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = 2.7073599627368640731420509846478 y[1] (numeric) = 2.7073599627368640731420509846481 absolute error = 3e-31 relative error = 1.1080905536356188018554392796205e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4175 Order of pole (three term test) = -6.939 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = 2.7195703775552939068182696666288 y[1] (numeric) = 2.7195703775552939068182696666291 absolute error = 3e-31 relative error = 1.1031154129192982942572308016503e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4222 Order of pole (three term test) = -7.15 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 2.7317088359356081935968497506059 y[1] (numeric) = 2.7317088359356081935968497506063 absolute error = 4e-31 relative error = 1.4642849001255300511126432983314e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4268 Order of pole (three term test) = -7.363 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = 2.7437741240420842503148288827758 y[1] (numeric) = 2.7437741240420842503148288827761 absolute error = 3e-31 relative error = 1.0933844640171939075134872137335e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4312 Order of pole (three term test) = -7.578 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = 2.7557650353559658026073026420937 y[1] (numeric) = 2.755765035355965802607302642094 absolute error = 3e-31 relative error = 1.0886269190263117062260294953674e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4354 Order of pole (three term test) = -7.795 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = 2.7676803707961138551059155704172 y[1] (numeric) = 2.7676803707961138551059155704175 absolute error = 3e-31 relative error = 1.0839401947042967945354562563950e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4394 Order of pole (three term test) = -8.014 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = 2.7795189388389138061074462869052 y[1] (numeric) = 2.7795189388389138061074462869055 absolute error = 3e-31 relative error = 1.0793234606464626461228362038554e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4433 Order of pole (three term test) = -8.235 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 2.7912795556374268161009420906446 y[1] (numeric) = 2.7912795556374268161009420906449 absolute error = 3e-31 relative error = 1.0747759012317592887093743901530e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.447 Order of pole (three term test) = -8.459 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 2.8029610451397735151158428141748 y[1] (numeric) = 2.8029610451397735151158428141751 absolute error = 3e-31 relative error = 1.0702967153974131901900772770055e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4505 Order of pole (three term test) = -8.684 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = 2.8145622392067382106190118761381 y[1] (numeric) = 2.8145622392067382106190118761385 absolute error = 4e-31 relative error = 1.4211801552227773484820043681157e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4538 Order of pole (three term test) = -8.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 2.8260819777285818356378880098541 y[1] (numeric) = 2.8260819777285818356378880098544 absolute error = 3e-31 relative error = 1.0615403316825232336631170325852e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.457 Order of pole (three term test) = -9.138 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = 2.8375191087410519559122891516003 y[1] (numeric) = 2.8375191087410519559122891516007 absolute error = 4e-31 relative error = 1.4096821366516599666963978405083e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.96 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4599 Order of pole (three term test) = -9.368 NO COMPLEX POLE (six term test) for Equation 1 bytes used=52022856, alloc=4521156, time=4.78 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 2.8488724885405782351708279919232 y[1] (numeric) = 2.8488724885405782351708279919235 absolute error = 3e-31 relative error = 1.0530481838226608165550512193167e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.26 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4627 Order of pole (three term test) = -9.599 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = 2.8601409817986418390814074494976 y[1] (numeric) = 2.8601409817986418390814074494979 absolute error = 3e-31 relative error = 1.0488993441551981660069820225772e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4653 Order of pole (three term test) = -9.832 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = 2.8713234616753073410307085369239 y[1] (numeric) = 2.8713234616753073410307085369243 absolute error = 4e-31 relative error = 1.3930858203158180926572178613410e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.86 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4677 Order of pole (three term test) = -10.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = 2.8824188099319057766367022757911 y[1] (numeric) = 2.8824188099319057766367022757915 absolute error = 4e-31 relative error = 1.3877233891956512545900160900929e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.17 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4699 Order of pole (three term test) = -10.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = 2.8934259170428575787826366422344 y[1] (numeric) = 2.8934259170428575787826366422347 absolute error = 3e-31 relative error = 1.0368331818448848988534967289263e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.472 Order of pole (three term test) = -10.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = 2.9043436823066242109721806128685 y[1] (numeric) = 2.9043436823066242109721806128688 absolute error = 3e-31 relative error = 1.0329356054781387731733306817433e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4738 Order of pole (three term test) = -10.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = 2.9151710139557774039348491829575 y[1] (numeric) = 2.9151710139557774039348491829577 absolute error = 2e-31 relative error = 6.8606609712617690835999971602896e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.13 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4755 Order of pole (three term test) = -11.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = 2.9259068292661749886497728724079 y[1] (numeric) = 2.9259068292661749886497728724081 absolute error = 2e-31 relative error = 6.8354876511963478355951263558810e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4769 Order of pole (three term test) = -11.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = 2.9365500546652324082954889002241 y[1] (numeric) = 2.9365500546652324082954889002243 absolute error = 2e-31 relative error = 6.8107131251607444609693080491456e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.79 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4782 Order of pole (three term test) = -11.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = 2.9470996258392790820647850075112 y[1] (numeric) = 2.9470996258392790820647850075114 absolute error = 2e-31 relative error = 6.7863331882797726972513752618410e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.13 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4793 Order of pole (three term test) = -11.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = 2.9575544878399888852976777829448 y[1] (numeric) = 2.957554487839988885297677782945 absolute error = 2e-31 relative error = 6.7623437141158936293774635250370e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4802 Order of pole (three term test) = -11.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = 2.9679135951898741029732039640134 y[1] (numeric) = 2.9679135951898741029732039640137 absolute error = 3e-31 relative error = 1.0108110980259427496867424067419e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.84 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4809 Order of pole (three term test) = -12.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = 2.9781759119868323072525868697737 y[1] (numeric) = 2.9781759119868323072525868697739 absolute error = 2e-31 relative error = 6.7155200334211916439807628821886e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4814 Order of pole (three term test) = -12.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = 2.9883404120077357044731457560209 y[1] (numeric) = 2.9883404120077357044731457560211 absolute error = 2e-31 relative error = 6.6926779558433476825730718059629e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -12.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = 2.9984060788110525927445728700206 y[1] (numeric) = 2.9984060788110525927445728700208 absolute error = 2e-31 relative error = 6.6702105966682570209957684495449e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.94 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = 3.0083719058384906680873361733658 y[1] (numeric) = 3.008371905838490668087336173366 absolute error = 2e-31 relative error = 6.6481142046251154173848653294643e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -13.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (analytic) = 3.0182368965156520148672963654614 y[1] (numeric) = 3.0182368965156520148672963654615 absolute error = 1e-31 relative error = 3.3131925501090771855347893052905e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.28 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4815 Order of pole (three term test) = -13.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (analytic) = 3.028000064351689715111373625032 y[1] (numeric) = 3.0280000643516897151113736250322 absolute error = 2e-31 relative error = 6.6050196746881847200330490539139e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.89 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.481 Order of pole (three term test) = -13.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = 3.0376604330379561111263794005864 y[1] (numeric) = 3.0376604330379561111263794005866 absolute error = 2e-31 relative error = 6.5840143889941158601494212398467e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4804 Order of pole (three term test) = -13.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = 3.0472170365456328566769579781507 y[1] (numeric) = 3.0472170365456328566769579781508 absolute error = 1e-31 relative error = 3.2816828864071124837272018405310e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4795 Order of pole (three term test) = -14.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = 3.0566689192223329937988781369027 y[1] (numeric) = 3.0566689192223329937988781369028 absolute error = 1e-31 relative error = 3.2715352117834747355723458512057e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.79 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4785 Order of pole (three term test) = -14.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = 3.0660151358876653951204950258811 y[1] (numeric) = 3.0660151358876653951204950258812 absolute error = 1e-31 relative error = 3.2615625027254876327634271073866e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4773 Order of pole (three term test) = -14.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = 3.0752547519277520153277868853919 y[1] (numeric) = 3.075254751927752015327786885392 absolute error = 1e-31 relative error = 3.2517631242521963697005094532748e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.09 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4758 Order of pole (three term test) = -14.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=56023544, alloc=4521156, time=5.15 x[1] = 3.23 y[1] (analytic) = 3.0843868433886885001265842231147 y[1] (numeric) = 3.0843868433886885001265842231148 absolute error = 1e-31 relative error = 3.2421354738413463091877851927773e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4742 Order of pole (three term test) = -15.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (analytic) = 3.0934104970689388067189788031801 y[1] (numeric) = 3.0934104970689388067189788031802 absolute error = 1e-31 relative error = 3.2326779809776869188288270702613e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4724 Order of pole (three term test) = -15.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = 3.1023248106106545964088600677324 y[1] (numeric) = 3.1023248106106545964088600677325 absolute error = 1e-31 relative error = 3.2233891067104680847306259766689e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.07 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4705 Order of pole (three term test) = -15.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = 3.1111288925899102674734176775078 y[1] (numeric) = 3.1111288925899102674734176775078 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4683 Order of pole (three term test) = -15.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = 3.1198218626058446048725186312483 y[1] (numeric) = 3.1198218626058446048725186312484 absolute error = 1e-31 relative error = 3.2053112133932727388613636904586e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4659 Order of pole (three term test) = -16.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (analytic) = 3.128402851368700132705272486717 y[1] (numeric) = 3.128402851368700132705272486717 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.11 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4634 Order of pole (three term test) = -16.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = 3.1368710007867513655519049092821 y[1] (numeric) = 3.1368710007867513655519049092822 absolute error = 1e-31 relative error = 3.1878900973268977629933357599924e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4607 Order of pole (three term test) = -16.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = 3.1452254640521132659482453287053 y[1] (numeric) = 3.1452254640521132659482453287054 absolute error = 1e-31 relative error = 3.1794223066974094419862849859685e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4577 Order of pole (three term test) = -16.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = 3.1534654057254213272185880649025 y[1] (numeric) = 3.1534654057254213272185880649026 absolute error = 1e-31 relative error = 3.1711145401639837813638803171833e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4546 Order of pole (three term test) = -16.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = 3.1615900018193748137292101370396 y[1] (numeric) = 3.1615900018193748137292101370397 absolute error = 1e-31 relative error = 3.1629654680857986932744207984064e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4514 Order of pole (three term test) = -17.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (analytic) = 3.1695984398811348043081395389952 y[1] (numeric) = 3.1695984398811348043081395389953 absolute error = 1e-31 relative error = 3.1549737891639726377615412111293e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4479 Order of pole (three term test) = -17.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = 3.1774899190735687990954968116626 y[1] (numeric) = 3.1774899190735687990954968116627 absolute error = 1e-31 relative error = 3.1471382300767792993982191143252e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4443 Order of pole (three term test) = -17.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = 3.185263650255333765431428491297 y[1] (numeric) = 3.1852636502553337654314284912971 absolute error = 1e-31 relative error = 3.1394575451229572420454572127086e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4404 Order of pole (three term test) = -17.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = 3.1929188560597896145437792896838 y[1] (numeric) = 3.1929188560597896145437792896839 absolute error = 1e-31 relative error = 3.1319305158730106737413601429584e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4364 Order of pole (three term test) = -18.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = 3.2004547709727352177535952502794 y[1] (numeric) = 3.2004547709727352177535952502795 absolute error = 1e-31 relative error = 3.1245559508283987987081116103383e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4323 Order of pole (three term test) = -18.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = 3.2078706414089591886616171275802 y[1] (numeric) = 3.2078706414089591886616171275803 absolute error = 1e-31 relative error = 3.1173326850885126306805653606183e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4279 Order of pole (three term test) = -18.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (analytic) = 3.2151657257875977763013374462304 y[1] (numeric) = 3.2151657257875977763013374462305 absolute error = 1e-31 relative error = 3.1102595800253395868270867557882e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4234 Order of pole (three term test) = -18.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = 3.2223392946062923335321039691294 y[1] (numeric) = 3.2223392946062923335321039691295 absolute error = 1e-31 relative error = 3.1033355229657176703404104053729e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4187 Order of pole (three term test) = -18.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = 3.2293906305141389449872279485271 y[1] (numeric) = 3.2293906305141389449872279485271 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4139 Order of pole (three term test) = -19.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (analytic) = 3.2363190283834229196750935032676 y[1] (numeric) = 3.2363190283834229196750935032676 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4089 Order of pole (three term test) = -19.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = 3.243123795380130974843786555817 y[1] (numeric) = 3.2431237953801309748437865558169 absolute error = 1e-31 relative error = 3.0834468959356780660816319591105e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4037 Order of pole (three term test) = -19.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = 3.2498042510332340599496168235328 y[1] (numeric) = 3.2498042510332340599496168235328 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3984 Order of pole (three term test) = -19.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (analytic) = 3.2563597273027338925048715061677 y[1] (numeric) = 3.2563597273027338925048715061676 absolute error = 1e-31 relative error = 3.0709137925259478907815771584411e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3929 Order of pole (three term test) = -19.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = 3.2627895686464664012079211517569 y[1] (numeric) = 3.2627895686464664012079211517569 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3872 Order of pole (three term test) = -20.15 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (analytic) = 3.269093132085655396067034040684 y[1] (numeric) = 3.2690931320856553960670340406839 absolute error = 1e-31 relative error = 3.0589523136711861129144253470793e-30 % bytes used=60024792, alloc=4521156, time=5.52 Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3814 Order of pole (three term test) = -20.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = 3.275269787269209910205514582825 y[1] (numeric) = 3.275269787269209910205514582825 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3754 Order of pole (three term test) = -20.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = 3.2813189165367587836675661535043 y[1] (numeric) = 3.2813189165367587836675661535042 absolute error = 1e-31 relative error = 3.0475550394090977970294951458743e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3693 Order of pole (three term test) = -20.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (analytic) = 3.2872399149804161858190264267154 y[1] (numeric) = 3.2872399149804161858190264267153 absolute error = 1e-31 relative error = 3.0420657629607710730867434545865e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3631 Order of pole (three term test) = -20.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (analytic) = 3.293032190505271899842206229175 y[1] (numeric) = 3.2930321905052718998422062291749 absolute error = 1e-31 relative error = 3.0367149245709721655599251545516e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3567 Order of pole (three term test) = -21.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = 3.2986951638886003203467908337052 y[1] (numeric) = 3.2986951638886003203467908337051 absolute error = 1e-31 relative error = 3.0315017008760826249981292062951e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3501 Order of pole (three term test) = -21.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = 3.3042282688377822432463832686906 y[1] (numeric) = 3.3042282688377822432463832686905 absolute error = 1e-31 relative error = 3.0264252909855302499035923843293e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3434 Order of pole (three term test) = -21.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = 3.3096309520469336557699699866143 y[1] (numeric) = 3.3096309520469336557699699866141 absolute error = 2e-31 relative error = 6.0429698325217926998804877627289e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3366 Order of pole (three term test) = -21.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = 3.3149026732522358637764982461474 y[1] (numeric) = 3.3149026732522358637764982461472 absolute error = 2e-31 relative error = 6.0333596402026764179689130920707e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3297 Order of pole (three term test) = -21.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (analytic) = 3.3200429052859614234059420357896 y[1] (numeric) = 3.3200429052859614234059420357894 absolute error = 2e-31 relative error = 6.0240185354705116634548655515815e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3226 Order of pole (three term test) = -21.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = 3.325051134129190474518712892103 y[1] (numeric) = 3.3250511341291904745187128921028 absolute error = 2e-31 relative error = 6.0149450920362677313809488567285e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3154 Order of pole (three term test) = -22.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = 3.3299268589632122043340018028928 y[1] (numeric) = 3.3299268589632122043340018028926 absolute error = 2e-31 relative error = 6.0061379264729828033682016062014e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.308 Order of pole (three term test) = -22.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = 3.3346695922196063011635227713918 y[1] (numeric) = 3.3346695922196063011635227713917 absolute error = 1e-31 relative error = 2.9987978489178741689446565912956e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3005 Order of pole (three term test) = -22.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = 3.3392788596289993901370190727586 y[1] (numeric) = 3.3392788596289993901370190727585 absolute error = 1e-31 relative error = 2.9946585536468254555219639938405e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.293 Order of pole (three term test) = -22.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = 3.3437542002684915753165898799309 y[1] (numeric) = 3.3437542002684915753165898799308 absolute error = 1e-31 relative error = 2.9906504488867738991571579671191e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2852 Order of pole (three term test) = -22.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = 3.3480951666077483455851478128628 y[1] (numeric) = 3.3480951666077483455851478128627 absolute error = 1e-31 relative error = 2.9867729268077781081489315934235e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2774 Order of pole (three term test) = -22.83 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = 3.3523013245537532351568283589299 y[1] (numeric) = 3.3523013245537532351568283589298 absolute error = 1e-31 relative error = 2.9830254001200698849017066863953e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2695 Order of pole (three term test) = -22.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = 3.356372253494216763480593883007 y[1] (numeric) = 3.3563722534942167634805938830069 absolute error = 1e-31 relative error = 2.9794073019133396363940030027700e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2615 Order of pole (three term test) = -23.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = 3.3603075463396373136792158628236 y[1] (numeric) = 3.3603075463396373136792158628235 absolute error = 1e-31 relative error = 2.9759180855017093651792800527691e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2533 Order of pole (three term test) = -23.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = 3.3641068095640097434708420665702 y[1] (numeric) = 3.3641068095640097434708420665702 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2451 Order of pole (three term test) = -23.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = 3.3677696632441776577459802453937 y[1] (numeric) = 3.3677696632441776577459802453936 absolute error = 1e-31 relative error = 2.9693242115516251590318142936899e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2367 Order of pole (three term test) = -23.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (analytic) = 3.3712957410978254076054340935802 y[1] (numeric) = 3.3712957410978254076054340935801 absolute error = 1e-31 relative error = 2.9662185604469128833623370925104e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2283 Order of pole (three term test) = -23.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = 3.3746846905201060166909475764969 y[1] (numeric) = 3.3746846905201060166909475764967 absolute error = 2e-31 relative error = 5.9264796074674467730376243498012e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2198 Order of pole (three term test) = -23.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = 3.3779361726189013720464477320556 y[1] (numeric) = 3.3779361726189013720464477320555 absolute error = 1e-31 relative error = 2.9603874937184017692411674373936e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2112 Order of pole (three term test) = -23.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = 3.3810498622487111535201832158602 y[1] (numeric) = 3.38104986224871115352018321586 absolute error = 2e-31 relative error = 5.9153224042363422978109856078553e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2025 Order of pole (three term test) = -23.92 NO COMPLEX POLE (six term test) for Equation 1 bytes used=64026680, alloc=4521156, time=5.89 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = 3.3840254480431671128430590565459 y[1] (numeric) = 3.3840254480431671128430590565458 absolute error = 1e-31 relative error = 2.9550605199445410816773164015988e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1937 Order of pole (three term test) = -24.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = 3.3868626324461694509823549300873 y[1] (numeric) = 3.3868626324461694509823549300873 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1848 Order of pole (three term test) = -24.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (analytic) = 3.389561131741642180159038475882 y[1] (numeric) = 3.389561131741642180159038475882 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1759 Order of pole (three term test) = -24.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = 3.392120676081904495017267975641 y[1] (numeric) = 3.392120676081904495017267975641 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1669 Order of pole (three term test) = -24.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = 3.394541009514655315832610175317 y[1] (numeric) = 3.394541009514655315832610175317 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1578 Order of pole (three term test) = -24.37 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = 3.3968218900085683053271394726706 y[1] (numeric) = 3.3968218900085683053271394726706 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1487 Order of pole (three term test) = -24.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = 3.3989630894774947996110660701379 y[1] (numeric) = 3.3989630894774947996110660701379 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1395 Order of pole (three term test) = -24.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = 3.4009643938032722329779679720729 y[1] (numeric) = 3.4009643938032722329779679720728 absolute error = 1e-31 relative error = 2.9403424564574982744553132399115e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1303 Order of pole (three term test) = -24.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = 3.4028256028571357757301542604696 y[1] (numeric) = 3.4028256028571357757301542604696 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.121 Order of pole (three term test) = -24.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = 3.4045465305197310438882200848828 y[1] (numeric) = 3.4045465305197310438882200848828 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1116 Order of pole (three term test) = -24.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = 3.4061270046997258795304996135461 y[1] (numeric) = 3.4061270046997258795304996135461 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1022 Order of pole (three term test) = -24.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = 3.4075668673510193405998927656458 y[1] (numeric) = 3.4075668673510193405998927656458 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09282 Order of pole (three term test) = -24.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = 3.4088659744885461792934258191104 y[1] (numeric) = 3.4088659744885461792934258191105 absolute error = 1e-31 relative error = 2.9335268898333157659419927388195e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08335 Order of pole (three term test) = -24.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = 3.4100241962026752285998772926148 y[1] (numeric) = 3.4100241962026752285998772926149 absolute error = 1e-31 relative error = 2.9325305114068606181304935995132e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07385 Order of pole (three term test) = -24.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = 3.4110414166722002571588139546605 y[1] (numeric) = 3.4110414166722002571588139546606 absolute error = 1e-31 relative error = 2.9316559896115140250416599048393e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06432 Order of pole (three term test) = -24.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = 3.4119175341759219933663767324308 y[1] (numeric) = 3.4119175341759219933663767324309 absolute error = 1e-31 relative error = 2.9309031944159496991155780151698e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05476 Order of pole (three term test) = -24.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = 3.4126524611028201605350575964098 y[1] (numeric) = 3.4126524611028201605350575964099 absolute error = 1e-31 relative error = 2.9302720139185919175604866409125e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04518 Order of pole (three term test) = -24.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = 3.4132461239608145059124281107904 y[1] (numeric) = 3.4132461239608145059124281107904 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03559 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = 3.4136984633841139474632186099931 y[1] (numeric) = 3.4136984633841139474632186099931 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02598 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = 3.4140094341391531035061940619509 y[1] (numeric) = 3.4140094341391531035061940619509 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01636 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = 3.4141790051291156115578100221132 y[1] (numeric) = 3.4141790051291156115578100221133 absolute error = 1e-31 relative error = 2.9289618338631384389264839160841e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.006732 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = 3.4142071593970437840545337323786 y[1] (numeric) = 3.4142071593970437840545337323786 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = 3.4140938941275342899908495039764 y[1] (numeric) = 3.4140938941275342899908495039765 absolute error = 1e-31 relative error = 2.9290348508576922049752538104495e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = 3.413839220647019692906197647083 y[1] (numeric) = 3.4138392206470196929061976470832 absolute error = 2e-31 relative error = 5.8585067155592145268077330273460e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = 3.4134431644226358170672828674832 y[1] (numeric) = 3.4134431644226358170672828674833 absolute error = 1e-31 relative error = 2.9295932342530865616506462337819e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=68028600, alloc=4586680, time=6.27 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = 3.4129057650596750551081900410706 y[1] (numeric) = 3.4129057650596750551081900410708 absolute error = 2e-31 relative error = 5.8601090615375656786740321684543e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = 3.4122270762976258717954211180514 y[1] (numeric) = 3.4122270762976258717954211180516 absolute error = 2e-31 relative error = 5.8612746317283876531490991452792e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = 3.4114071660047988999641762506302 y[1] (numeric) = 3.4114071660047988999641762506304 absolute error = 2e-31 relative error = 5.8626833522843885499039682051353e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4 y[1] (analytic) = 3.4104461161715401660118072776096 y[1] (numeric) = 3.4104461161715401660118072776098 absolute error = 2e-31 relative error = 5.8643354325889108773547837463886e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = 3.4093440229020321236202385939827 y[1] (numeric) = 3.4093440229020321236202385939829 absolute error = 2e-31 relative error = 5.8662311182595204488135511963386e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = 3.4081009964046833155971507143099 y[1] (numeric) = 3.40810099640468331559715071431 absolute error = 1e-31 relative error = 2.9341853456072239432434639773374e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = 3.4067171609811076248617338230849 y[1] (numeric) = 3.4067171609811076248617338230851 absolute error = 2e-31 relative error = 5.8707544697488646301468372714598e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = 3.4051926550136942166407288098392 y[1] (numeric) = 3.4051926550136942166407288098393 absolute error = 1e-31 relative error = 2.9366914043105100940911097305748e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = 3.4035276309517694148701778379018 y[1] (numeric) = 3.4035276309517694148701778379019 absolute error = 1e-31 relative error = 2.9381280495741354053421238957428e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (analytic) = 3.4017222552963518966037125405356 y[1] (numeric) = 3.4017222552963518966037125405358 absolute error = 2e-31 relative error = 5.8793747693130332112520067313937e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (analytic) = 3.3997767085835027288952350533153 y[1] (numeric) = 3.3997767085835027288952350533154 absolute error = 1e-31 relative error = 2.9413696419393502084192726737801e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = 3.397691185366271913138428691628 y[1] (numeric) = 3.3976911853662719131384286916281 absolute error = 1e-31 relative error = 2.9431750722577801418355829074065e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = 3.395465894195243242193619825997 y[1] (numeric) = 3.3954658941952432421936198259971 absolute error = 1e-31 relative error = 2.9451039449683803412655198124380e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = 3.3931010575976794158000657040182 y[1] (numeric) = 3.3931010575976794158000657040183 absolute error = 1e-31 relative error = 2.9471565480221844144463282732420e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = 3.3905969120552694997447479775705 y[1] (numeric) = 3.3905969120552694997447479775706 absolute error = 1e-31 relative error = 2.9493331880427878564989067617105e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = 3.3879537079804809540232113337315 y[1] (numeric) = 3.3879537079804809540232113337316 absolute error = 1e-31 relative error = 2.9516341904095500361155658977343e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = 3.3851717096915185947699245680268 y[1] (numeric) = 3.385171709691518594769924568027 absolute error = 2e-31 relative error = 5.9081197986918498434952631152066e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = 3.3822511953858929940411036017382 y[1] (numeric) = 3.3822511953858929940411036017383 absolute error = 1e-31 relative error = 2.9566106780129512684665294105784e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = 3.3791924571126009605879919008749 y[1] (numeric) = 3.3791924571126009605879919008751 absolute error = 2e-31 relative error = 5.9185738172158694845448854822513e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = 3.3759958007429208835493381133559 y[1] (numeric) = 3.3759958007429208835493381133561 absolute error = 2e-31 relative error = 5.9241779849367124381870617667461e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = 3.3726615459398258595043645441707 y[1] (numeric) = 3.3726615459398258595043645441709 absolute error = 2e-31 relative error = 5.9300347003620845212446293822306e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (analytic) = 3.3691900261260176615480321958476 y[1] (numeric) = 3.3691900261260176615480321958478 absolute error = 2e-31 relative error = 5.9361448433932710770244842765483e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = 3.3655815884505847469650565774149 y[1] (numeric) = 3.3655815884505847469650565774152 absolute error = 3e-31 relative error = 8.9137639993482142569432947992424e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 3.3618365937542876376741219792859 y[1] (numeric) = 3.3618365937542876376741219792862 absolute error = 3e-31 relative error = 8.9236936904473060945425416040697e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=72029828, alloc=4586680, time=6.64 x[1] = 4.21 y[1] (analytic) = 3.357955416533475144875321039439 y[1] (numeric) = 3.3579554165334751448753210394393 absolute error = 3e-31 relative error = 8.9340078347347327842090787312247e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = 3.3539384449026350462482851443764 y[1] (numeric) = 3.3539384449026350462482851443767 absolute error = 3e-31 relative error = 8.9447079881845896785956627785738e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = 3.3497860805555829606020781868441 y[1] (numeric) = 3.3497860805555829606020781868444 absolute error = 3e-31 relative error = 8.9557957668223137619944076694676e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = 3.3454987387252933010570461942881 y[1] (numeric) = 3.3454987387252933010570461942884 absolute error = 3e-31 relative error = 8.9672728471661725299385330215454e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = 3.3410768481423763236298305489831 y[1] (numeric) = 3.3410768481423763236298305489834 absolute error = 3e-31 relative error = 8.9791409666855956495524768934940e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = 3.3365208509922054234820839543391 y[1] (numeric) = 3.3365208509922054234820839543394 absolute error = 3e-31 relative error = 8.9914019242765056439031709194689e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = 3.3318312028706989660675371417556 y[1] (numeric) = 3.3318312028706989660675371417559 absolute error = 3e-31 relative error = 9.0040575807538092603603297617585e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = 3.3270083727387610749574532601354 y[1] (numeric) = 3.3270083727387610749574532601357 absolute error = 3e-31 relative error = 9.0171098593612166081104341245106e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (analytic) = 3.3220528428753859322277215190272 y[1] (numeric) = 3.3220528428753859322277215190275 absolute error = 3e-31 relative error = 9.0305607462985605821866592643711e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = 3.3169651088294302809384717566206 y[1] (numeric) = 3.3169651088294302809384717566209 absolute error = 3e-31 relative error = 9.0444122912667945291908134139965e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = 3.3117456793700589524157725238352 y[1] (numeric) = 3.3117456793700589524157725238355 absolute error = 3e-31 relative error = 9.0586666080308515516140765871109e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = 3.3063950764358683737413892584141 y[1] (numeric) = 3.3063950764358683737413892584143 absolute error = 2e-31 relative error = 6.0488839166670361942832429351389e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = 3.3009138350826931430574566374359 y[1] (numeric) = 3.3009138350826931430574566374361 absolute error = 2e-31 relative error = 6.0589282238865129848526600282380e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (analytic) = 3.2953025034301008919850402654125 y[1] (numeric) = 3.2953025034301008919850402654128 absolute error = 3e-31 relative error = 9.1038683000340069609812818538790e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = 3.2895616426065807856257583757773 y[1] (numeric) = 3.2895616426065807856257583757776 absolute error = 3e-31 relative error = 9.1197561436266684051040497085102e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = 3.2836918266934311412507872858484 y[1] (numeric) = 3.2836918266934311412507872858487 absolute error = 3e-31 relative error = 9.1360583097741562120999012830842e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = 3.2776936426673517768686215428311 y[1] (numeric) = 3.2776936426673517768686215428314 absolute error = 3e-31 relative error = 9.1527773094700587027109213760315e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = 3.2715676903417468303888924347823 y[1] (numeric) = 3.2715676903417468303888924347826 absolute error = 3e-31 relative error = 9.1699157222286329545561361441924e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = 3.2653145823067439190514143303698 y[1] (numeric) = 3.2653145823067439190514143303702 absolute error = 4e-31 relative error = 1.2249968262397082795662128511521e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 3.2589349438679356371545320755981 y[1] (numeric) = 3.2589349438679356371545320755984 absolute error = 3e-31 relative error = 9.2054614518919692191752536545101e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = 3.2524294129838495178819480310268 y[1] (numeric) = 3.2524294129838495178819480310271 absolute error = 3e-31 relative error = 9.2238742769446753913515154017759e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = 3.2457986402021527121797378753321 y[1] (numeric) = 3.2457986402021527121797378753324 absolute error = 3e-31 relative error = 9.2427175328816945905235667520383e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = 3.2390432885945977641625048832341 y[1] (numeric) = 3.2390432885945977641625048832344 absolute error = 3e-31 relative error = 9.2619941529144636071905645299208e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = 3.2321640336907159884169203892412 y[1] (numeric) = 3.2321640336907159884169203892415 absolute error = 3e-31 relative error = 9.2817071433543102223740502299143e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = 3.2251615634102650798096647484362 bytes used=76031912, alloc=4586680, time=7.02 y[1] (numeric) = 3.2251615634102650798096647484364 absolute error = 2e-31 relative error = 6.2012397229651120861193442715779e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = 3.2180365779944377109824945293591 y[1] (numeric) = 3.2180365779944377109824945293594 absolute error = 3e-31 relative error = 9.3224546312325521947536725101087e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = 3.2107897899358379966173604546018 y[1] (numeric) = 3.210789789935837996617360454602 absolute error = 2e-31 relative error = 6.2289970096110418138588622077742e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (analytic) = 3.2034219239072328267667968253815 y[1] (numeric) = 3.2034219239072328267667968253818 absolute error = 3e-31 relative error = 9.3649855412766923536963524630373e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = 3.1959337166890851940568757001753 y[1] (numeric) = 3.1959337166890851940568757001755 absolute error = 2e-31 relative error = 6.2579520643874761410455141325753e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 3.1883259170958767613696168392924 y[1] (numeric) = 3.1883259170958767613696168392927 absolute error = 3e-31 relative error = 9.4093266435339346252753617661886e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (analytic) = 3.1805992859012270376866875187885 y[1] (numeric) = 3.1805992859012270376866875187887 absolute error = 2e-31 relative error = 6.2881231498273990843433049373302e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (analytic) = 3.172754595761816650114407364941 y[1] (numeric) = 3.1727545957618166501144073649413 absolute error = 3e-31 relative error = 9.4555059632012409462690346604121e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = 3.1647926311401223196994586468184 y[1] (numeric) = 3.1647926311401223196994586468187 absolute error = 3e-31 relative error = 9.4792940633182798025588980842936e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = 3.1567141882259712674733331503803 y[1] (numeric) = 3.1567141882259712674733331503807 absolute error = 4e-31 relative error = 1.2671403749250873527012967051634e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = 3.148520074856922895219540079033 y[1] (numeric) = 3.1485200748569228952195400790334 absolute error = 4e-31 relative error = 1.2704381439212423034764714359529e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = 3.140211110437485702729149881648 y[1] (numeric) = 3.1402111104374857027291498816484 absolute error = 4e-31 relative error = 1.2737997094223167814304022448481e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (analytic) = 3.1317881258571775197856294424397 y[1] (numeric) = 3.1317881258571775197856294424401 absolute error = 4e-31 relative error = 1.2772256101792297712540437694363e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = 3.1232519634074372467874872367796 y[1] (numeric) = 3.12325196340743724678748723678 absolute error = 4e-31 relative error = 1.2807163965202600074332182411802e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = 3.1146034766973964127654262030843 y[1] (numeric) = 3.1146034766973964127654262030847 absolute error = 4e-31 relative error = 1.2842726305055831365393970462893e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 3.105843530568518973568012481138 y[1] (numeric) = 3.1058435305685189735680124811384 absolute error = 4e-31 relative error = 1.2878948860852006029097510244003e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (analytic) = 3.0969730010081178861649081855758 y[1] (numeric) = 3.0969730010081178861649081855762 absolute error = 4e-31 relative error = 1.2915837492603039551493524743056e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (analytic) = 3.0879927750617571073381686100673 y[1] (numeric) = 3.0879927750617571073381686100677 absolute error = 4e-31 relative error = 1.2953398182481186536471242611169e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (analytic) = 3.0789037507445477764887366413833 y[1] (numeric) = 3.0789037507445477764887366413837 absolute error = 4e-31 relative error = 1.2991637036502718063701465626012e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = 3.0697068369513474528659341326429 y[1] (numeric) = 3.0697068369513474528659341326433 absolute error = 4e-31 relative error = 1.3030560286247285687792841465881e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = 3.0604029533658713872213935670731 y[1] (numeric) = 3.0604029533658713872213935670735 absolute error = 4e-31 relative error = 1.3070174290613422108101028768033e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (analytic) = 3.0509930303687249166845242646285 y[1] (numeric) = 3.0509930303687249166845242646289 absolute error = 4e-31 relative error = 1.3110485537610630763207892303698e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (analytic) = 3.0414780089443661795433861693787 y[1] (numeric) = 3.0414780089443661795433861693791 absolute error = 4e-31 relative error = 1.3151500646188518348641163166914e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = 3.0318588405870084535819623177043 y[1] (numeric) = 3.0318588405870084535819623177047 absolute error = 4e-31 relative error = 1.3193226368103425485304863028086e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.69 bytes used=80034044, alloc=4586680, time=7.40 y[1] (analytic) = 3.0221364872054715276615818033849 y[1] (numeric) = 3.0221364872054715276615818033854 absolute error = 5e-31 relative error = 1.6544586987278764301949247148249e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = 3.0123119210269916213300448379021 y[1] (numeric) = 3.0123119210269916213300448379026 absolute error = 5e-31 relative error = 1.6598546668086561117355791290462e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = 3.0023861244999994713863308603183 y[1] (numeric) = 3.0023861244999994713863308603188 absolute error = 5e-31 relative error = 1.6653420954750355196436012112354e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = 2.992360090195876307511215234787 y[1] (numeric) = 2.9923600901958763075112152347875 absolute error = 5e-31 relative error = 1.6709218975289521350929378623153e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = 2.9822348207096975412843617266149 y[1] (numeric) = 2.9822348207096975412843617266153 absolute error = 4e-31 relative error = 1.3412760028897052843630400993789e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = 2.9720113285599740941362757308538 y[1] (numeric) = 2.9720113285599740941362757308542 absolute error = 4e-31 relative error = 1.3458898899749875139285083356928e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = 2.9616906360874013900187744432238 y[1] (numeric) = 2.9616906360874013900187744432242 absolute error = 4e-31 relative error = 1.3505799529704686667277189658948e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = 2.9512737753526261378103313681589 y[1] (numeric) = 2.9512737753526261378103313681594 absolute error = 5e-31 relative error = 1.6941837256025447981692774043547e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = 2.9407617880330411266928605655122 y[1] (numeric) = 2.9407617880330411266928605655127 absolute error = 5e-31 relative error = 1.7002397203155654455861079721793e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = 2.9301557253186183549343989069881 y[1] (numeric) = 2.9301557253186183549343989069886 absolute error = 5e-31 relative error = 1.7063939492350057835321125320103e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = 2.9194566478067909086780026374151 y[1] (numeric) = 2.9194566478067909086780026374156 absolute error = 5e-31 relative error = 1.7126474557367357964199595206041e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = 2.9086656253963941024613812088541 y[1] (numeric) = 2.9086656253963941024613812088546 absolute error = 5e-31 relative error = 1.7190013029835968241876796398533e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = 2.8977837371806764872648343358656 y[1] (numeric) = 2.8977837371806764872648343358661 absolute error = 5e-31 relative error = 1.7254565742247626421961160283437e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = 2.8868120713393914248975302821285 y[1] (numeric) = 2.886812071339391424897530282129 absolute error = 5e-31 relative error = 1.7320143731005512945876833462933e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = 2.8757517250299800194747633623156 y[1] (numeric) = 2.875751725029980019474763362316 absolute error = 4e-31 relative error = 1.3909406591621881308095459498095e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = 2.8646038042778562876023623453078 y[1] (numeric) = 2.8646038042778562876023623453083 absolute error = 5e-31 relative error = 1.7454420721403950022856616725271e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = 2.8533694238658055386598025978259 y[1] (numeric) = 2.8533694238658055386598025978264 absolute error = 5e-31 relative error = 1.7523142843613617104101296458298e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = 2.8420497072225070252518259480575 y[1] (numeric) = 2.842049707222507025251825948058 absolute error = 5e-31 relative error = 1.7592936489792874701544369108849e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = 2.8306457863101920114706256256645 y[1] (numeric) = 2.830645786310192011470625625665 absolute error = 5e-31 relative error = 1.7663813763563854851896897117625e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = 2.8191588015114484930681520952868 y[1] (numeric) = 2.8191588015114484930681520952873 absolute error = 5e-31 relative error = 1.7735786991918749478634077611029e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = 2.8075899015151838889721934675351 y[1] (numeric) = 2.8075899015151838889721934675356 absolute error = 5e-31 relative error = 1.7808868728661649987240358107017e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = 2.7959402432017571077820481057964 y[1] (numeric) = 2.795940243201757107782048105797 absolute error = 6e-31 relative error = 2.1459686109489699775618117906271e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = 2.7842109915272914759414169027503 y[1] (numeric) = 2.7842109915272914759414169027509 absolute error = 6e-31 relative error = 2.1550090917171018650580842744490e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = 2.7724033194071800961992923655293 y[1] (numeric) = 2.77240331940718009619929236553 absolute error = 7e-31 relative error = 2.5248851604667686582974312896447e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=84037276, alloc=4586680, time=7.77 x[1] = 4.93 y[1] (analytic) = 2.7605184075987952857259198762633 y[1] (numeric) = 2.760518407598795285725919876264 absolute error = 7e-31 relative error = 2.5357555960254828698727168926178e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = 2.7485574445834138228422777227835 y[1] (numeric) = 2.7485574445834138228422777227841 absolute error = 6e-31 relative error = 2.1829632892789666004438818354967e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = 2.7365216264473698097400076517426 y[1] (numeric) = 2.7365216264473698097400076517433 absolute error = 7e-31 relative error = 2.5579918434949841962839132667498e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = 2.7244121567624470358064850001614 y[1] (numeric) = 2.7244121567624470358064850001621 absolute error = 7e-31 relative error = 2.5693616080169177816766859304329e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = 2.7122302464655228022190232000654 y[1] (numeric) = 2.712230246465522802219023200066 absolute error = 6e-31 relative error = 2.2122015665222287059766308760571e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = 2.6999771137374752433254567572481 y[1] (numeric) = 2.6999771137374752433254567572488 absolute error = 7e-31 relative error = 2.5926145686139417805362371536206e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = 2.6876539838813662539780544167141 y[1] (numeric) = 2.6876539838813662539780544167148 absolute error = 7e-31 relative error = 2.6045019343937176330353581243562e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5 y[1] (analytic) = 2.6752620891999122044265152346424 y[1] (numeric) = 2.6752620891999122044265152346431 absolute error = 7e-31 relative error = 2.6165660659040260895116775986339e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.01 y[1] (analytic) = 2.662802668872254695596450860034 y[1] (numeric) = 2.6628026688722546955964508600347 absolute error = 7e-31 relative error = 2.6288091422728771585509033497490e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.02 y[1] (analytic) = 2.6502769688300436775751354828495 y[1] (numeric) = 2.6502769688300436775751354828502 absolute error = 7e-31 relative error = 2.6412333813888620454470849647545e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.03 y[1] (analytic) = 2.6376862416328453228894111499265 y[1] (numeric) = 2.6376862416328453228894111499272 absolute error = 7e-31 relative error = 2.6538410404971775829304910875063e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.04 y[1] (analytic) = 2.6250317463428871136845942319657 y[1] (numeric) = 2.6250317463428871136845942319663 absolute error = 6e-31 relative error = 2.2856866429745141467721660154636e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.05 y[1] (analytic) = 2.6123147483991526681912864048498 y[1] (numeric) = 2.6123147483991526681912864048505 absolute error = 7e-31 relative error = 2.6796158480863210992018976103066e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.06 y[1] (analytic) = 2.5995365194908388968925228359918 y[1] (numeric) = 2.5995365194908388968925228359925 absolute error = 7e-31 relative error = 2.6927877133155500975789355178739e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.07 y[1] (analytic) = 2.5866983374301881425701888425363 y[1] (numeric) = 2.5866983374301881425701888425369 absolute error = 6e-31 relative error = 2.3195592285263657027273615742938e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.08 y[1] (analytic) = 2.573801486024708020910727516367 y[1] (numeric) = 2.5738014860247080209107275163676 absolute error = 6e-31 relative error = 2.3311821181932448008062760295164e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.09 y[1] (analytic) = 2.5608472549487917395795946339389 y[1] (numeric) = 2.5608472549487917395795946339396 absolute error = 7e-31 relative error = 2.7334703334892874197171793963835e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.1 y[1] (analytic) = 2.5478369396147517336255706946159 y[1] (numeric) = 2.5478369396147517336255706946166 absolute error = 7e-31 relative error = 2.7474285701574144276441494040077e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.11 y[1] (analytic) = 2.5347718410432795137439180440519 y[1] (numeric) = 2.5347718410432795137439180440526 absolute error = 7e-31 relative error = 2.7615897757168116407786781555340e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.12 y[1] (analytic) = 2.5216532657333446813056070002912 y[1] (numeric) = 2.5216532657333446813056070002919 absolute error = 7e-31 relative error = 2.7759565897194303592702721154474e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.13 y[1] (analytic) = 2.5084825255315461201426909338882 y[1] (numeric) = 2.5084825255315461201426909338889 absolute error = 7e-31 relative error = 2.7905316974519101754891594015295e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.14 y[1] (analytic) = 2.4952609375009284298617781206076 y[1] (numeric) = 2.4952609375009284298617781206083 absolute error = 7e-31 relative error = 2.8053178306116113193689914702730e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.15 y[1] (analytic) = 2.4819898237892767189329497450112 y[1] (numeric) = 2.481989823789276718932949745012 absolute error = 8e-31 relative error = 3.2232203062727817044183591242526e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.16 y[1] (analytic) = 2.468670511496902927965061189887 y[1] (numeric) = 2.4686705114969029279650611898877 absolute error = 7e-31 relative error = 2.8355343361538678362815656485016e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.17 y[1] (analytic) = 2.4553043325439369044249213847113 y[1] (numeric) = 2.4553043325439369044249213847121 absolute error = 8e-31 relative error = 3.2582518973162128356222003249578e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 bytes used=88038680, alloc=4586680, time=8.14 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.18 y[1] (analytic) = 2.441892623537135499582287892781 y[1] (numeric) = 2.4418926235371354995822878927818 absolute error = 8e-31 relative error = 3.2761473305127655348667830563469e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.19 y[1] (analytic) = 2.4284367256362230066599911882643 y[1] (numeric) = 2.428436725636223006659991188265 absolute error = 7e-31 relative error = 2.8825128223862118645094477937345e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.2 y[1] (analytic) = 2.4149379844197763060339905138132 y[1] (numeric) = 2.4149379844197763060339905138139 absolute error = 7e-31 relative error = 2.8986251593876233626772406939691e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.21 y[1] (analytic) = 2.4013977497506681288570793066914 y[1] (numeric) = 2.4013977497506681288570793066922 absolute error = 8e-31 relative error = 3.3313931441930527694357803283761e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.22 y[1] (analytic) = 2.3878173756410818946677475829961 y[1] (numeric) = 2.3878173756410818946677475829969 absolute error = 8e-31 relative error = 3.3503399722318201587005940548195e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.23 y[1] (analytic) = 2.3741982201171116213879531333671 y[1] (numeric) = 2.374198220117111621387953133368 absolute error = 9e-31 relative error = 3.7907534104528385678850163858081e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.24 y[1] (analytic) = 2.3605416450829604476059687208406 y[1] (numeric) = 2.3605416450829604476059687208414 absolute error = 8e-31 relative error = 3.3890526848632838554744209637335e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.25 y[1] (analytic) = 2.3468490161847513471789094752536 y[1] (numeric) = 2.3468490161847513471789094752544 absolute error = 8e-31 relative error = 3.4088260236721657086047678764700e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.26 y[1] (analytic) = 2.3331217026739636549699895386006 y[1] (numeric) = 2.3331217026739636549699895386014 absolute error = 8e-31 relative error = 3.4288824242778647253229878437617e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.27 y[1] (analytic) = 2.3193610772705090599541317197985 y[1] (numeric) = 2.3193610772705090599541317197993 absolute error = 8e-31 relative error = 3.4492257710104502107734551404002e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.28 y[1] (analytic) = 2.3055685160254607579785166391619 y[1] (numeric) = 2.3055685160254607579785166391628 absolute error = 9e-31 relative error = 3.9035925141426643144491414164335e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.29 y[1] (analytic) = 2.2917453981834494911484033162804 y[1] (numeric) = 2.2917453981834494911484033162813 absolute error = 9e-31 relative error = 3.9271378082110884498060721879100e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.3 y[1] (analytic) = 2.2778931060447402341196130342938 y[1] (numeric) = 2.2778931060447402341196130342946 absolute error = 8e-31 relative error = 3.5120173017648491551679111099898e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.31 y[1] (analytic) = 2.2640130248270033195141115205415 y[1] (numeric) = 2.2640130248270033195141115205424 absolute error = 9e-31 relative error = 3.9752421480383063148403131947883e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.32 y[1] (analytic) = 2.2501065425267938252309575405181 y[1] (numeric) = 2.250106542526793825230957540519 absolute error = 9e-31 relative error = 3.9998106000319892736038349020887e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.33 y[1] (analytic) = 2.2361750497807530755984533511439 y[1] (numeric) = 2.2361750497807530755984533511448 absolute error = 9e-31 relative error = 4.0247296386221685081477224882558e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.34 y[1] (analytic) = 2.2222199397265461361017167681517 y[1] (numeric) = 2.2222199397265461361017167681526 absolute error = 9e-31 relative error = 4.0500041598526423475058123123467e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.35 y[1] (analytic) = 2.2082426078635492078203170556062 y[1] (numeric) = 2.208242607863549207820317055607 absolute error = 8e-31 relative error = 3.6227903453687605925075396204308e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.36 y[1] (analytic) = 2.1942444519133008527204374229757 y[1] (numeric) = 2.1942444519133008527204374229766 absolute error = 9e-31 relative error = 4.1016396291453896123579974594020e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.37 y[1] (analytic) = 2.1802268716797310045627446555546 y[1] (numeric) = 2.1802268716797310045627446555555 absolute error = 9e-31 relative error = 4.1280107666345990534989779452325e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.38 y[1] (analytic) = 2.166191268909181742408399655278 y[1] (numeric) = 2.1661912689091817424083996552789 absolute error = 9e-31 relative error = 4.1547577673194508019887694466635e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.39 y[1] (analytic) = 2.1521390471502338245292093242972 y[1] (numeric) = 2.1521390471502338245292093242982 absolute error = 1.0e-30 relative error = 4.6465399218705465626495527751790e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.4 y[1] (analytic) = 2.1380716116133529999517179437535 y[1] (numeric) = 2.1380716116133529999517179437544 absolute error = 9e-31 relative error = 4.2094006351867470225764770568734e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.41 y[1] (analytic) = 2.1239903690303701328871226214372 y[1] (numeric) = 2.1239903690303701328871226214381 absolute error = 9e-31 relative error = 4.2373073490482067306990810012955e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=92040572, alloc=4586680, time=8.52 x[1] = 5.42 y[1] (analytic) = 2.1098967275138091919174703108124 y[1] (numeric) = 2.1098967275138091919174703108132 absolute error = 8e-31 relative error = 3.7916547742252661091621749714624e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.43 y[1] (analytic) = 2.0957920964160771710219914967793 y[1] (numeric) = 2.0957920964160771710219914967802 absolute error = 9e-31 relative error = 4.2943190860345872128038528684259e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.44 y[1] (analytic) = 2.08167788618853002333412657347 y[1] (numeric) = 2.0816778861885300233341265734708 absolute error = 8e-31 relative error = 3.8430537467291272303283021417660e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.45 y[1] (analytic) = 2.0675555082404287009184245477154 y[1] (numeric) = 2.0675555082404287009184245477162 absolute error = 8e-31 relative error = 3.8693036139127967531442841154888e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.46 y[1] (analytic) = 2.0534263747977994048458001365863 y[1] (numeric) = 2.0534263747977994048458001365872 absolute error = 9e-31 relative error = 4.3829182825638093234516994899285e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.47 y[1] (analytic) = 2.0392918987622121594245256670798 y[1] (numeric) = 2.0392918987622121594245256670807 absolute error = 9e-31 relative error = 4.4132965984235630349837551015297e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.48 y[1] (analytic) = 2.0251534935694918326118505495682 y[1] (numeric) = 2.0251534935694918326118505495691 absolute error = 9e-31 relative error = 4.4441075842289831941806360578409e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.49 y[1] (analytic) = 2.011012573048375731386466739209 y[1] (numeric) = 2.0110125730483757313864667392098 absolute error = 8e-31 relative error = 3.9780954665406543543678322995612e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.5 y[1] (analytic) = 1.9968705512791319062044979941963 y[1] (numeric) = 1.9968705512791319062044979941971 absolute error = 8e-31 relative error = 4.0062687062390969074189390826848e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.002134 Order of pole (three term test) = -0.893 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.51 y[1] (analytic) = 1.9827288424521523025907496450351 y[1] (numeric) = 1.982728842452152302590749645036 absolute error = 9e-31 relative error = 4.5391986071424641624615108216988e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01178 Order of pole (three term test) = -0.8965 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.52 y[1] (analytic) = 1.9685888607265349004322211023162 y[1] (numeric) = 1.9685888607265349004322211023171 absolute error = 9e-31 relative error = 4.5718027667180976184568645721083e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02141 Order of pole (three term test) = -0.9048 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.53 y[1] (analytic) = 1.954452020088668982642103927312 y[1] (numeric) = 1.9544520200886689826421039273129 absolute error = 9e-31 relative error = 4.6048712925639846340615316670258e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03104 Order of pole (three term test) = -0.9179 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.54 y[1] (analytic) = 1.9403197342108376745495538489584 y[1] (numeric) = 1.9403197342108376745495538489593 absolute error = 9e-31 relative error = 4.6384107945283868635209615826851e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04066 Order of pole (three term test) = -0.9359 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.55 y[1] (analytic) = 1.9261934163098518936434669256154 y[1] (numeric) = 1.9261934163098518936434669256164 absolute error = 1.0e-30 relative error = 5.1915866367966949013672811434957e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05026 Order of pole (three term test) = -0.9587 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.56 y[1] (analytic) = 1.912074479005729846157480824793 y[1] (numeric) = 1.912074479005729846157480824794 absolute error = 1.0e-30 relative error = 5.2299217994897119029395657100998e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05984 Order of pole (three term test) = -0.9863 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.57 y[1] (analytic) = 1.8979643341804362024287760270908 y[1] (numeric) = 1.8979643341804362024287760270917 absolute error = 9e-31 relative error = 4.7419226156777640959695588519678e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06939 Order of pole (three term test) = -1.019 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.58 y[1] (analytic) = 1.8838643928366950769954241127546 y[1] (numeric) = 1.8838643928366950769954241127555 absolute error = 9e-31 relative error = 4.7774139339445412059676852204283e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07892 Order of pole (three term test) = -1.056 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.59 y[1] (analytic) = 1.8697760649568909320166179382882 y[1] (numeric) = 1.8697760649568909320166179382891 absolute error = 9e-31 relative error = 4.8134106370687238668793901674680e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08842 Order of pole (three term test) = -1.098 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.6 y[1] (analytic) = 1.8557007593620715138078594915594 y[1] (numeric) = 1.8557007593620715138078594915603 absolute error = 9e-31 relative error = 4.8499198777576089615715211708184e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09788 Order of pole (three term test) = -1.145 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.61 y[1] (analytic) = 1.8416398835710669220799547453862 y[1] (numeric) = 1.8416398835710669220799547453871 absolute error = 9e-31 relative error = 4.8869488982549500608917469575606e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1073 Order of pole (three term test) = -1.196 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.62 y[1] (analytic) = 1.8275948436597388998574912258192 y[1] (numeric) = 1.8275948436597388998574912258201 absolute error = 9e-31 relative error = 4.9245050297786994080017322440952e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1167 Order of pole (three term test) = -1.252 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.63 y[1] (analytic) = 1.8135670441203744190305145799346 y[1] (numeric) = 1.8135670441203744190305145799356 absolute error = 1.0e-30 relative error = 5.5139952131465044584701061188010e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.126 Order of pole (three term test) = -1.313 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.64 y[1] (analytic) = 1.7995578877212376220636773540144 y[1] (numeric) = 1.7995578877212376220636773540153 absolute error = 9e-31 relative error = 5.0012283913781796159608904208097e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1353 Order of pole (three term test) = -1.379 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.65 y[1] (analytic) = 1.7855687753662941645516494087916 y[1] (numeric) = 1.7855687753662941645516494087925 absolute error = 9e-31 relative error = 5.0404107218741697393503786418654e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1445 Order of pole (three term test) = -1.449 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.66 y[1] (analytic) = 1.7716011059551219860696384391713 y[1] (numeric) = 1.7716011059551219860696384391723 absolute error = 1.0e-30 relative error = 5.6446115134979594859963023071491e-29 % Correct digits = 31 h = 0.01 bytes used=96041248, alloc=4586680, time=8.90 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1537 Order of pole (three term test) = -1.523 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.67 y[1] (analytic) = 1.7576562762430225181251949112187 y[1] (numeric) = 1.7576562762430225181251949112197 absolute error = 1.0e-30 relative error = 5.6893945279078837455362185827617e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1628 Order of pole (three term test) = -1.603 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.68 y[1] (analytic) = 1.7437356807013463179739326311258 y[1] (numeric) = 1.7437356807013463179739326311268 absolute error = 1.0e-30 relative error = 5.7348141181454228395290863222950e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1718 Order of pole (three term test) = -1.687 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.69 y[1] (analytic) = 1.7298407113780470956193884569321 y[1] (numeric) = 1.7298407113780470956193884569331 absolute error = 1.0e-30 relative error = 5.7808790914821725740609625610224e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1808 Order of pole (three term test) = -1.775 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.7 y[1] (analytic) = 1.7159727577584780784781165768751 y[1] (numeric) = 1.715972757758478078478116576876 absolute error = 9e-31 relative error = 5.2448385088329843256901588394742e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1897 Order of pole (three term test) = -1.868 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.71 y[1] (analytic) = 1.702133206626444633957548202174 y[1] (numeric) = 1.7021332066264446339575482021749 absolute error = 9e-31 relative error = 5.2874827686592260702482456612175e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1985 Order of pole (three term test) = -1.965 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.72 y[1] (analytic) = 1.6883234419255270445685697930567 y[1] (numeric) = 1.6883234419255270445685697930576 absolute error = 9e-31 relative error = 5.3307321195135045548656326173832e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2073 Order of pole (three term test) = -2.067 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.73 y[1] (analytic) = 1.674544844620687303179744591348 y[1] (numeric) = 1.674544844620687303179744591349 absolute error = 1.0e-30 relative error = 5.9717719905346392431343687109038e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2159 Order of pole (three term test) = -2.173 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.74 y[1] (analytic) = 1.6607987925601737676183247512693 y[1] (numeric) = 1.6607987925601737676183247512702 absolute error = 9e-31 relative error = 5.4190790843038944432973950224410e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2245 Order of pole (three term test) = -2.284 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.75 y[1] (analytic) = 1.6470866603377374840375148963345 y[1] (numeric) = 1.6470866603377374840375148963354 absolute error = 9e-31 relative error = 5.4641933643944011305482561135338e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.233 Order of pole (three term test) = -2.398 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.76 y[1] (analytic) = 1.6334098191551739573028310281927 y[1] (numeric) = 1.6334098191551739573028310281936 absolute error = 9e-31 relative error = 5.5099460615799076845756964448462e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2414 Order of pole (three term test) = -2.517 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.77 y[1] (analytic) = 1.619769636685204114105968008674 y[1] (numeric) = 1.6197696366852041141059680086749 absolute error = 9e-31 relative error = 5.5563456655590555165611662104365e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2497 Order of pole (three term test) = -2.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.78 y[1] (analytic) = 1.6061674769347081705955987451057 y[1] (numeric) = 1.6061674769347081705955987451066 absolute error = 9e-31 relative error = 5.6034007220567424576416246538883e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2579 Order of pole (three term test) = -2.768 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.79 y[1] (analytic) = 1.592604700108326081024370601911 y[1] (numeric) = 1.5926047001083260810243706019119 absolute error = 9e-31 relative error = 5.6511198286604556269123783011356e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.266 Order of pole (three term test) = -2.899 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.8 y[1] (analytic) = 1.5790826624724382072535684249411 y[1] (numeric) = 1.579082662472438207253568424942 absolute error = 9e-31 relative error = 5.6995116303210559493498240346765e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.274 Order of pole (three term test) = -3.034 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.81 y[1] (analytic) = 1.5656027162195398109351446479906 y[1] (numeric) = 1.5656027162195398109351446479915 absolute error = 9e-31 relative error = 5.7485848145002558724993743930118e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2818 Order of pole (three term test) = -3.174 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.82 y[1] (analytic) = 1.5521662093330229308088773987068 y[1] (numeric) = 1.5521662093330229308088773987076 absolute error = 8e-31 relative error = 5.1540872052856104750127631862737e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2896 Order of pole (three term test) = -3.317 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.83 y[1] (analytic) = 1.5387744854523791668142454947682 y[1] (numeric) = 1.5387744854523791668142454947691 absolute error = 9e-31 relative error = 5.8488102610787181639800843278164e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2972 Order of pole (three term test) = -3.464 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.84 y[1] (analytic) = 1.5254288837388368506262785040301 y[1] (numeric) = 1.525428883738836850626278504031 absolute error = 9e-31 relative error = 5.8999800619619428775836301097711e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3048 Order of pole (three term test) = -3.615 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.85 y[1] (analytic) = 1.5121307387414460387863596323048 y[1] (numeric) = 1.5121307387414460387863596323057 absolute error = 9e-31 relative error = 5.9518663098474837703997492386328e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3122 Order of pole (three term test) = -3.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.86 y[1] (analytic) = 1.4988813802636247198170728914176 y[1] (numeric) = 1.4988813802636247198170728914185 absolute error = 9e-31 relative error = 6.0044778182627575355647232231952e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3195 Order of pole (three term test) = -3.928 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.87 y[1] (analytic) = 1.4856821332301795805891719394539 y[1] (numeric) = 1.4856821332301795805891719394549 absolute error = 1.0e-30 relative error = 6.7309148951383942048494933316839e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3266 Order of pole (three term test) = -4.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.88 y[1] (analytic) = 1.4725343175548146297532182376728 y[1] (numeric) = 1.4725343175548146297532182376739 absolute error = 1.1e-30 relative error = 7.4701145289882376122479559863855e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3336 Order of pole (three term test) = -4.256 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.89 y[1] (analytic) = 1.4594392480081409272631362478279 y[1] (numeric) = 1.4594392480081409272631362478289 absolute error = 1.0e-30 relative error = 6.8519467416325224110770839145719e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3405 Order of pole (three term test) = -4.425 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.9 y[1] (analytic) = 1.4463982340862006189087417889509 y[1] (numeric) = 1.446398234086200618908741788952 absolute error = 1.1e-30 relative error = 7.6050977806603405078864193620040e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3473 Order of pole (three term test) = -4.597 NO COMPLEX POLE (six term test) for Equation 1 bytes used=100042976, alloc=4586680, time=9.28 TOP MAIN SOLVE Loop x[1] = 5.91 y[1] (analytic) = 1.4334125798795184233442273614185 y[1] (numeric) = 1.4334125798795184233442273614196 absolute error = 1.1e-30 relative error = 7.6739943226426650554716327912667e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3539 Order of pole (three term test) = -4.773 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.92 y[1] (analytic) = 1.4204835839426936663547781927022 y[1] (numeric) = 1.4204835839426936663547781927033 absolute error = 1.1e-30 relative error = 7.7438416919035448534208498653995e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3604 Order of pole (three term test) = -4.952 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.93 y[1] (analytic) = 1.4076125391645459030492194006656 y[1] (numeric) = 1.4076125391645459030492194006667 absolute error = 1.1e-30 relative error = 7.8146504765642267984369856136148e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3667 Order of pole (three term test) = -5.134 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.94 y[1] (analytic) = 1.394800732638827113308263388891 y[1] (numeric) = 1.3948007326388271133082633888921 absolute error = 1.1e-30 relative error = 7.8864311887684999647496335968893e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3729 Order of pole (three term test) = -5.319 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.95 y[1] (analytic) = 1.3820494455355133991610731713017 y[1] (numeric) = 1.3820494455355133991610731713029 absolute error = 1.2e-30 relative error = 8.6827573635401062587596493411723e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3789 Order of pole (three term test) = -5.508 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.96 y[1] (analytic) = 1.3693599529726890548131474084177 y[1] (numeric) = 1.3693599529726890548131474084189 absolute error = 1.2e-30 relative error = 8.7632181545470767616929620667295e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3848 Order of pole (three term test) = -5.699 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.97 y[1] (analytic) = 1.3567335238890358208117614476402 y[1] (numeric) = 1.3567335238890358208117614476414 absolute error = 1.2e-30 relative error = 8.8447729703047073617944893444809e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3905 Order of pole (three term test) = -5.894 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.98 y[1] (analytic) = 1.3441714209169400733172892227959 y[1] (numeric) = 1.3441714209169400733172892227972 absolute error = 1.3e-30 relative error = 9.6713855076102712134528715592819e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3961 Order of pole (three term test) = -6.091 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.99 y[1] (analytic) = 1.3316749002562306376557352242898 y[1] (numeric) = 1.331674900256230637655735224291 absolute error = 1.2e-30 relative error = 9.0112083645122787361332138099873e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4015 Order of pole (three term test) = -6.291 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6 y[1] (analytic) = 1.319245211548559852265903148689 y[1] (numeric) = 1.3192452115485598522659031486902 absolute error = 1.2e-30 relative error = 9.0961103326000544865760812357355e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4067 Order of pole (three term test) = -6.493 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.01 y[1] (analytic) = 1.3068835977524404448301244131061 y[1] (numeric) = 1.3068835977524404448301244131073 absolute error = 1.2e-30 relative error = 9.1821490610467733003534336139966e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4118 Order of pole (three term test) = -6.698 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.02 y[1] (analytic) = 1.2945912950189507167967978720894 y[1] (numeric) = 1.2945912950189507167967978720905 absolute error = 1.1e-30 relative error = 8.4968901322938200673204692068936e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4167 Order of pole (three term test) = -6.906 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.03 y[1] (analytic) = 1.2823695325681204656727098154137 y[1] (numeric) = 1.2823695325681204656727098154148 absolute error = 1.1e-30 relative error = 8.5778706688164953385306208868518e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4215 Order of pole (three term test) = -7.116 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.04 y[1] (analytic) = 1.2702195325660100063898936267222 y[1] (numeric) = 1.2702195325660100063898936267233 absolute error = 1.1e-30 relative error = 8.6599203665043299129641428534697e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4261 Order of pole (three term test) = -7.329 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.05 y[1] (analytic) = 1.2581425100024945837424586096369 y[1] (numeric) = 1.2581425100024945837424586096381 absolute error = 1.2e-30 relative error = 9.5378702369544821945243814247381e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4305 Order of pole (three term test) = -7.543 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.06 y[1] (analytic) = 1.2461396725697663973502983149748 y[1] (numeric) = 1.2461396725697663973502983149759 absolute error = 1.1e-30 relative error = 8.8272608938900095959846107052018e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4347 Order of pole (three term test) = -7.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.07 y[1] (analytic) = 1.2342122205415663888459340231986 y[1] (numeric) = 1.2342122205415663888459340231997 absolute error = 1.1e-30 relative error = 8.9125677228939224754779281207779e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4388 Order of pole (three term test) = -7.979 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.08 y[1] (analytic) = 1.222361346653157868005134855879 y[1] (numeric) = 1.2223613466531578680051348558801 absolute error = 1.1e-30 relative error = 8.9989756548815543509729501251310e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4427 Order of pole (three term test) = -8.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.09 y[1] (analytic) = 1.2105882359820539803586798093356 y[1] (numeric) = 1.2105882359820539803586798093366 absolute error = 1.0e-30 relative error = 8.2604470312631074870854211621672e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4464 Order of pole (three term test) = -8.423 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.1 y[1] (analytic) = 1.1988940658295109434391070885767 y[1] (numeric) = 1.1988940658295109434391070885777 absolute error = 1.0e-30 relative error = 8.3410205163381405197359125436321e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4499 Order of pole (three term test) = -8.648 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.11 y[1] (analytic) = 1.1872800056027989022400707593291 y[1] (numeric) = 1.1872800056027989022400707593301 absolute error = 1.0e-30 relative error = 8.4226129917203971902129240239991e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4533 Order of pole (three term test) = -8.874 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.12 y[1] (analytic) = 1.175747216698262176704651489065 y[1] (numeric) = 1.175747216698262176704651489066 absolute error = 1.0e-30 relative error = 8.5052295748418084144527383818166e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4565 Order of pole (three term test) = -9.102 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.13 y[1] (analytic) = 1.1642968523851805951204230770255 y[1] (numeric) = 1.1642968523851805951204230770265 absolute error = 1.0e-30 relative error = 8.5888748900368340585711331485744e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.92 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4595 Order of pole (three term test) = -9.332 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.14 y[1] (analytic) = 1.1529300576904435271911533670237 y[1] (numeric) = 1.1529300576904435271911533670247 absolute error = 1.0e-30 relative error = 8.6735530341121130558296325878345e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.21 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4623 Order of pole (three term test) = -9.563 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=104045800, alloc=4586680, time=9.65 x[1] = 6.15 y[1] (analytic) = 1.141647969284048149285727720845 y[1] (numeric) = 1.141647969284048149285727720846 absolute error = 1.0e-30 relative error = 8.7592675404759085294087446079592e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4649 Order of pole (three term test) = -9.795 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.16 y[1] (analytic) = 1.1304517153654333919423523656643 y[1] (numeric) = 1.1304517153654333919423523656653 absolute error = 1.0e-30 relative error = 8.8460213418026159709710651860020e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.81 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4673 Order of pole (three term test) = -10.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.17 y[1] (analytic) = 1.1193424155506609361385658004711 y[1] (numeric) = 1.119342415550660936138565800472 absolute error = 9e-31 relative error = 8.0404350580893930513221471471953e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.12 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4696 Order of pole (three term test) = -10.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.18 y[1] (analytic) = 1.1083211807604545401334157373048 y[1] (numeric) = 1.1083211807604545401334157373058 absolute error = 1.0e-30 relative error = 9.0226553219335579207975616675968e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4717 Order of pole (three term test) = -10.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.19 y[1] (analytic) = 1.0973891131091088928558171096453 y[1] (numeric) = 1.0973891131091088928558171096462 absolute error = 9e-31 relative error = 8.2012842049264680106267582319702e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4735 Order of pole (three term test) = -10.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.2 y[1] (analytic) = 1.0865473057942791028611766652291 y[1] (numeric) = 1.08654730579427910286117666523 absolute error = 9e-31 relative error = 8.2831184173991321386005626814191e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4752 Order of pole (three term test) = -10.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.21 y[1] (analytic) = 1.0757968429876618438155466944416 y[1] (numeric) = 1.0757968429876618438155466944426 absolute error = 1.0e-30 relative error = 9.2954353465366030388212028284193e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4767 Order of pole (three term test) = -11.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.22 y[1] (analytic) = 1.0651387997265790883016607371408 y[1] (numeric) = 1.0651387997265790883016607371418 absolute error = 1.0e-30 relative error = 9.3884477802958618646891316914353e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.478 Order of pole (three term test) = -11.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.23 y[1] (analytic) = 1.0545742418064752714831240770046 y[1] (numeric) = 1.0545742418064752714831240770056 absolute error = 1.0e-30 relative error = 9.4824997649004764831566068885266e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4791 Order of pole (three term test) = -11.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.24 y[1] (analytic) = 1.0441042256743386348208072060246 y[1] (numeric) = 1.0441042256743386348208072060256 absolute error = 1.0e-30 relative error = 9.5775879017647519331201612808035e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.48 Order of pole (three term test) = -11.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.25 y[1] (analytic) = 1.0337297983230574076182553689473 y[1] (numeric) = 1.0337297983230574076182553689482 absolute error = 9e-31 relative error = 8.7063370085684163824026779404038e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.78 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4808 Order of pole (three term test) = -12.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.26 y[1] (analytic) = 1.0234519971867213906899234247838 y[1] (numeric) = 1.0234519971867213906899234247847 absolute error = 9e-31 relative error = 8.7937685643677680998808182935304e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.14 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -12.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.27 y[1] (analytic) = 1.0132718500368794119066208124552 y[1] (numeric) = 1.0132718500368794119066208124561 absolute error = 9e-31 relative error = 8.8821178637030454529071744082077e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -12.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.28 y[1] (analytic) = 1.0031903748797630277861602438701 y[1] (numeric) = 1.0031903748797630277861602438709 absolute error = 8e-31 relative error = 7.9745581699374226243911228715130e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.88 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.29 y[1] (analytic) = 0.99320857985448674867340442971298 y[1] (numeric) = 0.99320857985448674867340442971383 absolute error = 8.5e-31 relative error = 8.5581218008057483036284921393537e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.26 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.3 y[1] (analytic) = 0.9833274631322349674023599703662 y[1] (numeric) = 0.98332746313223496740235997036708 absolute error = 8.8e-31 relative error = 8.9492059664122307145961134572851e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.34 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4815 Order of pole (three term test) = -13.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.31 y[1] (analytic) = 0.97354801281644567266344158982794 y[1] (numeric) = 0.97354801281644567266344158982877 absolute error = 8.3e-31 relative error = 8.5255168627876348127737076006084e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.96 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4811 Order of pole (three term test) = -13.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.32 y[1] (analytic) = 0.96387120684400092862139002461076 y[1] (numeric) = 0.96387120684400092862139002461163 absolute error = 8.7e-31 relative error = 9.0261021786161349231304151170952e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4805 Order of pole (three term test) = -13.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.33 y[1] (analytic) = 0.95429801288743400165354078331755 y[1] (numeric) = 0.95429801288743400165354078331847 absolute error = 9.2e-31 relative error = 9.6405943172441700598760351479191e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.21 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4797 Order of pole (three term test) = -14.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.34 y[1] (analytic) = 0.94482938825816291341427616061244 y[1] (numeric) = 0.9448293882581629134142761606133 absolute error = 8.6e-31 relative error = 9.1021724206255919820015408410728e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4787 Order of pole (three term test) = -14.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.35 y[1] (analytic) = 0.93546627981076009678971562340151 y[1] (numeric) = 0.93546627981076009678971562340237 absolute error = 8.6e-31 relative error = 9.1932763217715712011740832630431e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4775 Order of pole (three term test) = -14.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.36 y[1] (analytic) = 0.92620962384826772769727407939828 y[1] (numeric) = 0.92620962384826772769727407939916 absolute error = 8.8e-31 relative error = 9.5010889256767448704929431056188e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.14 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4761 Order of pole (three term test) = -14.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.37 y[1] (analytic) = 0.91706034602856820111800444509109 y[1] (numeric) = 0.91706034602856820111800444509199 absolute error = 9.0e-31 relative error = 9.8139670295150158156934967529377e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4745 Order of pole (three term test) = -15.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.38 y[1] (analytic) = 0.90801936127181911423609693563169 y[1] (numeric) = 0.9080193612718191142360969356326 absolute error = 9.1e-31 relative error = 1.0021812736739519520949321782590e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4727 Order of pole (three term test) = -15.3 NO COMPLEX POLE (six term test) for Equation 1 bytes used=108048880, alloc=4586680, time=10.02 TOP MAIN SOLVE Loop x[1] = 6.39 y[1] (analytic) = 0.89908757366896201311008386978999 y[1] (numeric) = 0.89908757366896201311008386979087 absolute error = 8.8e-31 relative error = 9.7877006175152641011846995112710e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.13 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4708 Order of pole (three term test) = -15.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.4 y[1] (analytic) = 0.89026587639131405192484041252885 y[1] (numeric) = 0.89026587639131405192484041252977 absolute error = 9.2e-31 relative error = 1.0333991500710023747220766516926e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4686 Order of pole (three term test) = -15.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.41 y[1] (analytic) = 0.88155515160125160558311602230258 y[1] (numeric) = 0.88155515160125160558311602230348 absolute error = 9.0e-31 relative error = 1.0209230793617906718542495111111e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4663 Order of pole (three term test) = -16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.42 y[1] (analytic) = 0.87295627036399476720090737519323 y[1] (numeric) = 0.87295627036399476720090737519411 absolute error = 8.8e-31 relative error = 1.0080688230042361955291074829573e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.16 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4638 Order of pole (three term test) = -16.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.43 y[1] (analytic) = 0.86447009256050155198341055488262 y[1] (numeric) = 0.86447009256050155198341055488351 absolute error = 8.9e-31 relative error = 1.0295324357189507858211330931441e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4611 Order of pole (three term test) = -16.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.44 y[1] (analytic) = 0.85609746680148051798857699176355 y[1] (numeric) = 0.85609746680148051798857699176446 absolute error = 9.1e-31 relative error = 1.0629630798931202538152692421969e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4582 Order of pole (three term test) = -16.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.45 y[1] (analytic) = 0.84783923034253040244454088508621 y[1] (numeric) = 0.84783923034253040244454088508708 absolute error = 8.7e-31 relative error = 1.0261379384963309128350197118172e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4551 Order of pole (three term test) = -16.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.46 y[1] (analytic) = 0.8396962090004152595865696313847 y[1] (numeric) = 0.83969620900041525958656963138557 absolute error = 8.7e-31 relative error = 1.0360889934654566888879739945831e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4519 Order of pole (three term test) = -17.15 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.47 y[1] (analytic) = 0.83166921707048347242998307824102 y[1] (numeric) = 0.83166921707048347242998307824187 absolute error = 8.5e-31 relative error = 1.0220409539673547934126896319034e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4485 Order of pole (three term test) = -17.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.48 y[1] (analytic) = 0.823759057245238896509047050662 y[1] (numeric) = 0.8237590572452388965090470506629 absolute error = 9.0e-31 relative error = 1.0925524788883306149788431104655e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4448 Order of pole (three term test) = -17.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.49 y[1] (analytic) = 0.81596652053407227839961010669111 y[1] (numeric) = 0.81596652053407227839961010669195 absolute error = 8.4e-31 relative error = 1.0294540019242421315089293098189e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4411 Order of pole (three term test) = -17.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.5 y[1] (analytic) = 0.80829238618416097581674099698117 y[1] (numeric) = 0.80829238618416097581674099698207 absolute error = 9.0e-31 relative error = 1.1134584655050114531960790314553e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4371 Order of pole (three term test) = -18.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.51 y[1] (analytic) = 0.80073742160254488924944038438876 y[1] (numeric) = 0.8007374216025448892494403843896 absolute error = 8.4e-31 relative error = 1.0490330254815336173007754984154e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.433 Order of pole (three term test) = -18.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.52 y[1] (analytic) = 0.79330238227938639747432684523248 y[1] (numeric) = 0.79330238227938639747432684523331 absolute error = 8.3e-31 relative error = 1.0462593060859980900052862132130e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4286 Order of pole (three term test) = -18.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.53 y[1] (analytic) = 0.78598801171242197089079594304616 y[1] (numeric) = 0.78598801171242197089079594304705 absolute error = 8.9e-31 relative error = 1.1323327922788140853976066849666e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4242 Order of pole (three term test) = -18.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.54 y[1] (analytic) = 0.7787950413326130174533620798865 y[1] (numeric) = 0.77879504133261301745336207988734 absolute error = 8.4e-31 relative error = 1.0785893019589054595463621548703e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4195 Order of pole (three term test) = -18.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.55 y[1] (analytic) = 0.77172419043100339605463246914531 y[1] (numeric) = 0.77172419043100339605463246914614 absolute error = 8.3e-31 relative error = 1.0755137784866506633266269003723e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4147 Order of pole (three term test) = -19.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.56 y[1] (analytic) = 0.76477616608679091154662306346296 y[1] (numeric) = 0.76477616608679091154662306346386 absolute error = 9.0e-31 relative error = 1.1768149164547358039387833309523e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4097 Order of pole (three term test) = -19.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.57 y[1] (analytic) = 0.75795166309661998419097408513452 y[1] (numeric) = 0.75795166309661998419097408513535 absolute error = 8.3e-31 relative error = 1.0950566380566086902862949950767e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4045 Order of pole (three term test) = -19.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.58 y[1] (analytic) = 0.75125136390510256421219755840566 y[1] (numeric) = 0.75125136390510256421219755840647 absolute error = 8.1e-31 relative error = 1.0782010375189395512688820052810e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3992 Order of pole (three term test) = -19.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.59 y[1] (analytic) = 0.74467593853657423930460247403209 y[1] (numeric) = 0.74467593853657423930460247403294 absolute error = 8.5e-31 relative error = 1.1414361012797150325555781820767e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3938 Order of pole (three term test) = -19.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.6 y[1] (analytic) = 0.73822604452809235942527717273921 y[1] (numeric) = 0.73822604452809235942527717274008 absolute error = 8.7e-31 relative error = 1.1785008215961054884412680107463e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3881 Order of pole (three term test) = -20.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.61 y[1] (analytic) = 0.73190232686368287900481493945434 y[1] (numeric) = 0.73190232686368287900481493945526 absolute error = 9.2e-31 relative error = 1.2569983264602332559038642701257e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3823 Order of pole (three term test) = -20.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.62 y[1] (analytic) = 0.72570541790984249183676762024235 y[1] (numeric) = 0.72570541790984249183676762024324 absolute error = 8.9e-31 relative error = 1.2263929385608755801925578106783e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3764 Order of pole (three term test) = -20.5 NO COMPLEX POLE (six term test) for Equation 1 bytes used=112050004, alloc=4586680, time=10.40 TOP MAIN SOLVE Loop x[1] = 6.63 y[1] (analytic) = 0.7196359373523025083785902748168 y[1] (numeric) = 0.71963593735230250837859027481767 absolute error = 8.7e-31 relative error = 1.2089446271970792022128396127290e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3703 Order of pole (three term test) = -20.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.64 y[1] (analytic) = 0.71369449213406079902365017690234 y[1] (numeric) = 0.7136944921340607990236501769032 absolute error = 8.6e-31 relative error = 1.2049973896091902123402954060623e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3641 Order of pole (three term test) = -20.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.65 y[1] (analytic) = 0.70788167639468800009833308640711 y[1] (numeric) = 0.70788167639468800009833308640798 absolute error = 8.7e-31 relative error = 1.2290189575622253648458999916954e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3577 Order of pole (three term test) = -21.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.66 y[1] (analytic) = 0.70219807141091405191306908970309 y[1] (numeric) = 0.70219807141091405191306908970392 absolute error = 8.3e-31 relative error = 1.1820026767266617722368449562401e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3512 Order of pole (three term test) = -21.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.67 y[1] (analytic) = 0.69664424553850101016396185217604 y[1] (numeric) = 0.69664424553850101016396185217689 absolute error = 8.5e-31 relative error = 1.2201349619172639407524083446746e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3445 Order of pole (three term test) = -21.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.68 y[1] (analytic) = 0.69122075415540794335544195775286 y[1] (numeric) = 0.69122075415540794335544195775378 absolute error = 9.2e-31 relative error = 1.3309785542017382195692987442326e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3377 Order of pole (three term test) = -21.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.69 y[1] (analytic) = 0.68592813960625359970683964246542 y[1] (numeric) = 0.68592813960625359970683964246634 absolute error = 9.2e-31 relative error = 1.3412483711895997123765318277071e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3308 Order of pole (three term test) = -21.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.7 y[1] (analytic) = 0.68076693114808239722990530813655 y[1] (numeric) = 0.68076693114808239722990530813737 absolute error = 8.2e-31 relative error = 1.2045238428622074503034086930359e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3237 Order of pole (three term test) = -21.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.71 y[1] (analytic) = 0.67573764489743916033307520651799 y[1] (numeric) = 0.67573764489743916033307520651887 absolute error = 8.8e-31 relative error = 1.3022805620568364042030896505791e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3165 Order of pole (three term test) = -22.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.72 y[1] (analytic) = 0.6708407837787578954347176281642 y[1] (numeric) = 0.67084078377875789543471762816506 absolute error = 8.6e-31 relative error = 1.2819733397181565509526753108682e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3092 Order of pole (three term test) = -22.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.73 y[1] (analytic) = 0.66607683747406976666478906112911 y[1] (numeric) = 0.66607683747406976666478906112995 absolute error = 8.4e-31 relative error = 1.2611157643395774530773082675600e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3017 Order of pole (three term test) = -22.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.74 y[1] (analytic) = 0.66144628237403530081542027332393 y[1] (numeric) = 0.66144628237403530081542027332476 absolute error = 8.3e-31 relative error = 1.2548260109966885799289135911098e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2942 Order of pole (three term test) = -22.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.75 y[1] (analytic) = 0.65694958153030571827913090007311 y[1] (numeric) = 0.65694958153030571827913090007397 absolute error = 8.6e-31 relative error = 1.3090806725178306090967795360423e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2865 Order of pole (three term test) = -22.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.76 y[1] (analytic) = 0.65258718460921815380187995685478 y[1] (numeric) = 0.65258718460921815380187995685569 absolute error = 9.1e-31 relative error = 1.3944496941736997577106915906439e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2787 Order of pole (three term test) = -22.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.77 y[1] (analytic) = 0.64835952784682939749028978475927 y[1] (numeric) = 0.64835952784682939749028978476019 absolute error = 9.2e-31 relative error = 1.4189658059861871073537780250011e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2708 Order of pole (three term test) = -22.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.78 y[1] (analytic) = 0.64426703400529265266147094868322 y[1] (numeric) = 0.6442670340052926526614709486841 absolute error = 8.8e-31 relative error = 1.3658932609498855739950033747908e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2628 Order of pole (three term test) = -23.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.79 y[1] (analytic) = 0.64031011233058167282331052515318 y[1] (numeric) = 0.6403101123305816728233105251541 absolute error = 9.2e-31 relative error = 1.4368037959785008011970059927428e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2546 Order of pole (three term test) = -23.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.8 y[1] (analytic) = 0.63648915851156650533629598253336 y[1] (numeric) = 0.63648915851156650533629598253426 absolute error = 9.0e-31 relative error = 1.4140068027311809785848080152680e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2464 Order of pole (three term test) = -23.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.81 y[1] (analytic) = 0.63280455464044493414840503795799 y[1] (numeric) = 0.63280455464044493414840503795891 absolute error = 9.2e-31 relative error = 1.4538454144388032790417940054841e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2381 Order of pole (three term test) = -23.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.82 y[1] (analytic) = 0.62925666917453357842581431419592 y[1] (numeric) = 0.6292566691745335784258143141968 absolute error = 8.8e-31 relative error = 1.3984754442958777388283983452848e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2297 Order of pole (three term test) = -23.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.83 y[1] (analytic) = 0.62584585689942246793772308057454 y[1] (numeric) = 0.62584585689942246793772308057546 absolute error = 9.2e-31 relative error = 1.4700105303211267103510726273575e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2211 Order of pole (three term test) = -23.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.84 y[1] (analytic) = 0.62257245889349677970704917742639 y[1] (numeric) = 0.62257245889349677970704917742727 absolute error = 8.8e-31 relative error = 1.4134900884694310679010655760734e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2125 Order of pole (three term test) = -23.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.85 y[1] (analytic) = 0.61943680249382928372376693355664 y[1] (numeric) = 0.61943680249382928372376693355755 absolute error = 9.1e-31 relative error = 1.4690764196385720136053652297773e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2039 Order of pole (three term test) = -23.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.86 y[1] (analytic) = 0.61643920126344690844789287577948 y[1] (numeric) = 0.61643920126344690844789287578041 absolute error = 9.3e-31 relative error = 1.5086645983803145181091820385079e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1951 Order of pole (three term test) = -24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=116052648, alloc=4586680, time=10.77 x[1] = 6.87 y[1] (analytic) = 0.61357995495997469941829116079586 y[1] (numeric) = 0.61357995495997469941829116079669 absolute error = 8.3e-31 relative error = 1.3527169414361701274660325922438e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1863 Order of pole (three term test) = -24.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.88 y[1] (analytic) = 0.61085934950566030654530790147714 y[1] (numeric) = 0.61085934950566030654530790147798 absolute error = 8.4e-31 relative error = 1.3751119642840408792794155934695e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1773 Order of pole (three term test) = -24.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.89 y[1] (analytic) = 0.60827765695878199761352561346565 y[1] (numeric) = 0.60827765695878199761352561346651 absolute error = 8.6e-31 relative error = 1.4138280276473728296379523080803e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1683 Order of pole (three term test) = -24.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.9 y[1] (analytic) = 0.60583513548644305716946093065304 y[1] (numeric) = 0.60583513548644305716946093065396 absolute error = 9.2e-31 relative error = 1.5185649463220792320021344465732e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1593 Order of pole (three term test) = -24.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.91 y[1] (analytic) = 0.60353202933875529133164556107738 y[1] (numeric) = 0.60353202933875529133164556107828 absolute error = 9.0e-31 relative error = 1.4912216025818255149758594191928e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1502 Order of pole (three term test) = -24.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.92 y[1] (analytic) = 0.60136856882441422015109580086292 y[1] (numeric) = 0.60136856882441422015109580086376 absolute error = 8.4e-31 relative error = 1.3968139399803927314253727177016e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.141 Order of pole (three term test) = -24.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.93 y[1] (analytic) = 0.59934497028766839998258062073236 y[1] (numeric) = 0.59934497028766839998258062073324 absolute error = 8.8e-31 relative error = 1.4682696003565780043542538132054e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1318 Order of pole (three term test) = -24.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.94 y[1] (analytic) = 0.59746143608668517891525903089959 y[1] (numeric) = 0.59746143608668517891525903090046 absolute error = 8.7e-31 relative error = 1.4561609293118835360499979067543e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1225 Order of pole (three term test) = -24.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.95 y[1] (analytic) = 0.59571815457331504866911518355922 y[1] (numeric) = 0.59571815457331504866911518356006 absolute error = 8.4e-31 relative error = 1.4100627848108012936259910694910e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1131 Order of pole (three term test) = -24.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.96 y[1] (analytic) = 0.59411530007425661650513858558769 y[1] (numeric) = 0.59411530007425661650513858558855 absolute error = 8.6e-31 relative error = 1.4475304707562846554423827263180e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1037 Order of pole (three term test) = -24.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.97 y[1] (analytic) = 0.59265303287362408063636259901217 y[1] (numeric) = 0.59265303287362408063636259901307 absolute error = 9.0e-31 relative error = 1.5185951139676591407384067847765e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09432 Order of pole (three term test) = -24.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.98 y[1] (analytic) = 0.59133149919691895237769306999634 y[1] (numeric) = 0.59133149919691895237769306999721 absolute error = 8.7e-31 relative error = 1.4712559726338572997098484614449e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08486 Order of pole (three term test) = -24.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.99 y[1] (analytic) = 0.59015083119640762784895524979462 y[1] (numeric) = 0.59015083119640762784895524979549 absolute error = 8.7e-31 relative error = 1.4741993978662312402788692177593e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07536 Order of pole (three term test) = -24.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7 y[1] (analytic) = 0.58911114693790627146180338668716 y[1] (numeric) = 0.58911114693790627146180338668807 absolute error = 9.1e-31 relative error = 1.5447000192239040821725211560241e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06584 Order of pole (three term test) = -24.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.01 y[1] (analytic) = 0.58821255038897433269113173754996 y[1] (numeric) = 0.58821255038897433269113173755082 absolute error = 8.6e-31 relative error = 1.4620565294489169554456047045201e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05628 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.02 y[1] (analytic) = 0.58745513140851787676947115473058 y[1] (numeric) = 0.5874551314085178767694711547315 absolute error = 9.2e-31 relative error = 1.5660770513556541361161319648420e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04671 Order of pole (three term test) = -24.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.03 y[1] (analytic) = 0.58683896573780376896263794636405 y[1] (numeric) = 0.58683896573780376896263794636497 absolute error = 9.2e-31 relative error = 1.5677213915802766242843474636332e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03712 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.04 y[1] (analytic) = 0.58636411499288561100071929043072 y[1] (numeric) = 0.58636411499288561100071929043163 absolute error = 9.1e-31 relative error = 1.5519367177014935191114062591395e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02751 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.05 y[1] (analytic) = 0.58603062665844218706444040541493 y[1] (numeric) = 0.58603062665844218706444040541585 absolute error = 9.2e-31 relative error = 1.5698838220211417121249849848054e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01789 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.06 y[1] (analytic) = 0.58583853408302903547718022961729 y[1] (numeric) = 0.58583853408302903547718022961814 absolute error = 8.5e-31 relative error = 1.4509117283151131854967184262082e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008265 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.07 y[1] (analytic) = 0.58578785647574362094150939715216 y[1] (numeric) = 0.58578785647574362094150939715302 absolute error = 8.6e-31 relative error = 1.4681082758765092134315483250034e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.08 y[1] (analytic) = 0.58587859890430444080024784296141 y[1] (numeric) = 0.58587859890430444080024784296231 absolute error = 9.0e-31 relative error = 1.5361544212114208943054404669357e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.09 y[1] (analytic) = 0.58611075229454425740981519163572 y[1] (numeric) = 0.58611075229454425740981519163663 absolute error = 9.1e-31 relative error = 1.5526075855757178664720248786028e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.1 y[1] (analytic) = 0.58648429343131750730221429005751 y[1] (numeric) = 0.58648429343131750730221429005838 absolute error = 8.7e-31 relative error = 1.4834156852009280398002568597754e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.11 y[1] (analytic) = 0.58699918496082179639548785729313 y[1] (numeric) = 0.58699918496082179639548785729404 absolute error = 9.1e-31 relative error = 1.5502576891324581845616905550713e-28 % Correct digits = 30 h = 0.01 bytes used=120053792, alloc=4586680, time=11.15 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.12 y[1] (analytic) = 0.58765537539433324910506177896328 y[1] (numeric) = 0.58765537539433324910506177896419 absolute error = 9.1e-31 relative error = 1.5485266332999412476489500558707e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.13 y[1] (analytic) = 0.58845279911335533782417669231118 y[1] (numeric) = 0.58845279911335533782417669231208 absolute error = 9.0e-31 relative error = 1.5294344786124986007534253890261e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.14 y[1] (analytic) = 0.58939137637618067789475049574267 y[1] (numeric) = 0.58939137637618067789475049574356 absolute error = 8.9e-31 relative error = 1.5100322734141176774600889062053e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.15 y[1] (analytic) = 0.59047101332586513189464284083519 y[1] (numeric) = 0.59047101332586513189464284083607 absolute error = 8.8e-31 relative error = 1.4903356475423656023675443106288e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.16 y[1] (analytic) = 0.59169160199961342583753794512227 y[1] (numeric) = 0.59169160199961342583753794512314 absolute error = 8.7e-31 relative error = 1.4703605680051014200554663328915e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.17 y[1] (analytic) = 0.59305302033957533873164705813445 y[1] (numeric) = 0.5930530203395753387316470581354 absolute error = 9.5e-31 relative error = 1.6018803840777017305623594094291e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.18 y[1] (analytic) = 0.59455513220505138588727150509341 y[1] (numeric) = 0.59455513220505138588727150509433 absolute error = 9.2e-31 relative error = 1.5473754243579694216607880740422e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.19 y[1] (analytic) = 0.59619778738610677541506692080511 y[1] (numeric) = 0.596197787386106775415066920806 absolute error = 8.9e-31 relative error = 1.4927931951945041906737158255953e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.2 y[1] (analytic) = 0.59798082161859227653070377326272 y[1] (numeric) = 0.59798082161859227653070377326359 absolute error = 8.7e-31 relative error = 1.4548961581161019768478255677634e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.21 y[1] (analytic) = 0.59990405660057049759161105943477 y[1] (numeric) = 0.59990405660057049759161105943562 absolute error = 8.5e-31 relative error = 1.4168932359228051698114422102222e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.22 y[1] (analytic) = 0.60196730001014593125168801827152 y[1] (numeric) = 0.60196730001014593125168801827241 absolute error = 8.9e-31 relative error = 1.4784856253570574124018336677784e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.23 y[1] (analytic) = 0.60417034552469698374432671119311 y[1] (numeric) = 0.60417034552469698374432671119398 absolute error = 8.7e-31 relative error = 1.4399912316855620315431199453567e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.24 y[1] (analytic) = 0.60651297284150806510684380544745 y[1] (numeric) = 0.60651297284150806510684380544831 absolute error = 8.6e-31 relative error = 1.4179416410021823461441655567624e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.25 y[1] (analytic) = 0.60899494769979967715449246836974 y[1] (numeric) = 0.60899494769979967715449246837067 absolute error = 9.3e-31 relative error = 1.5271062650234625489527716795241e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.26 y[1] (analytic) = 0.61161602190415429621361531680418 y[1] (numeric) = 0.6116160219041542962136153168051 absolute error = 9.2e-31 relative error = 1.5042117391492602736010446515144e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.27 y[1] (analytic) = 0.61437593334933570804518661026465 y[1] (numeric) = 0.61437593334933570804518661026555 absolute error = 9.0e-31 relative error = 1.4649011316142452571809034936376e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.28 y[1] (analytic) = 0.61727440604649931304593404377702 y[1] (numeric) = 0.6172744060464993130459340437779 absolute error = 8.8e-31 relative error = 1.4256220432598165334029379234397e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.29 y[1] (analytic) = 0.62031115015079078071836187641728 y[1] (numeric) = 0.62031115015079078071836187641816 absolute error = 8.8e-31 relative error = 1.4186428855681245318976336205714e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.3 y[1] (analytic) = 0.62348586199033029356722719529539 y[1] (numeric) = 0.6234858619903302935672271952963 absolute error = 9.1e-31 relative error = 1.4595359020572519152021860394460e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.31 y[1] (analytic) = 0.62679822409657948202223312342711 y[1] (numeric) = 0.62679822409657948202223312342802 absolute error = 9.1e-31 relative error = 1.4518228753944007644577813470086e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.32 y[1] (analytic) = 0.63024790523608801371875239692257 y[1] (numeric) = 0.63024790523608801371875239692349 absolute error = 9.2e-31 relative error = 1.4597430508799107592083311257182e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.33 y[1] (analytic) = 0.63383456044361666250410864201688 y[1] (numeric) = 0.63383456044361666250410864201778 absolute error = 9.0e-31 relative error = 1.4199288839190085935400327617849e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.34 y[1] (analytic) = 0.63755783105663354489011718931125 y[1] (numeric) = 0.63755783105663354489011718931217 absolute error = 9.2e-31 relative error = 1.4430063520281306606454193404253e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.35 y[1] (analytic) = 0.64141734475118007435698693903173 y[1] (numeric) = 0.64141734475118007435698693903264 absolute error = 9.1e-31 relative error = 1.4187330720733924922167251491769e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=124054720, alloc=4586680, time=11.52 x[1] = 7.36 y[1] (analytic) = 0.64541271557910304694304108274388 y[1] (numeric) = 0.64541271557910304694304108274482 absolute error = 9.4e-31 relative error = 1.4564324149650128148267879940247e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.37 y[1] (analytic) = 0.64954354400664913494272434402149 y[1] (numeric) = 0.64954354400664913494272434402233 absolute error = 8.4e-31 relative error = 1.2932158401860757057552005213690e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.38 y[1] (analytic) = 0.65380941695441792929568890821861 y[1] (numeric) = 0.65380941695441792929568890821948 absolute error = 8.7e-31 relative error = 1.3306629997050874153073998688460e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.39 y[1] (analytic) = 0.65820990783866953539601422376479 y[1] (numeric) = 0.65820990783866953539601422376567 absolute error = 8.8e-31 relative error = 1.3369595162880658124633908525539e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.4 y[1] (analytic) = 0.66274457661398259159640263476514 y[1] (numeric) = 0.662744576613982591596402634766 absolute error = 8.6e-31 relative error = 1.2976341570289595509618265403246e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.41 y[1] (analytic) = 0.66741296981725844464104865560316 y[1] (numeric) = 0.66741296981725844464104865560403 absolute error = 8.7e-31 relative error = 1.3035407451524519567591344315492e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.42 y[1] (analytic) = 0.6722146206130670816463086245788 y[1] (numeric) = 0.67221462061306708164630862457965 absolute error = 8.5e-31 relative error = 1.2644771088507279253586042282783e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.43 y[1] (analytic) = 0.67714904884033028407376082030574 y[1] (numeric) = 0.67714904884033028407376082030662 absolute error = 8.8e-31 relative error = 1.2995661760244181663956937647689e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.44 y[1] (analytic) = 0.68221576106033733541916123349283 y[1] (numeric) = 0.68221576106033733541916123349375 absolute error = 9.2e-31 relative error = 1.3485469737170617330817410389161e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.45 y[1] (analytic) = 0.68741425060608848108653905489578 y[1] (numeric) = 0.68741425060608848108653905489669 absolute error = 9.1e-31 relative error = 1.3238014766171332261107537060162e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.46 y[1] (analytic) = 0.69274399763296120614256388272073 y[1] (numeric) = 0.69274399763296120614256388272164 absolute error = 9.1e-31 relative error = 1.3136165785764747175649167259307e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.47 y[1] (analytic) = 0.69820446917069426436563097014857 y[1] (numeric) = 0.69820446917069426436563097014946 absolute error = 8.9e-31 relative error = 1.2746982285248253310647056091002e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.48 y[1] (analytic) = 0.70379511917668426023007948426229 y[1] (numeric) = 0.70379511917668426023007948426323 absolute error = 9.4e-31 relative error = 1.3356159688911080393340916622573e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.49 y[1] (analytic) = 0.7095153885905894542117590248268 y[1] (numeric) = 0.70951538859058945421175902482774 absolute error = 9.4e-31 relative error = 1.3248479386292870352959213816056e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.5 y[1] (analytic) = 0.71536470539023533107991686567905 y[1] (numeric) = 0.71536470539023533107991686567996 absolute error = 9.1e-31 relative error = 1.2720784141895707013936580234745e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.51 y[1] (analytic) = 0.72134248464881634066516454828915 y[1] (numeric) = 0.72134248464881634066516454829006 absolute error = 9.1e-31 relative error = 1.2615366755266481581166694413858e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.52 y[1] (analytic) = 0.72744812859338809097711498924585 y[1] (numeric) = 0.7274481285933880909771149892468 absolute error = 9.5e-31 relative error = 1.3059350387455718360425012062349e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.53 y[1] (analytic) = 0.73368102666464414450112166974221 y[1] (numeric) = 0.73368102666464414450112166974312 absolute error = 9.1e-31 relative error = 1.2403210208895710166070087413375e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.54 y[1] (analytic) = 0.74004055557797144004430406400985 y[1] (numeric) = 0.74004055557797144004430406401072 absolute error = 8.7e-31 relative error = 1.1756112464951738691278953622945e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.55 y[1] (analytic) = 0.74652607938577823463955405276666 y[1] (numeric) = 0.7465260793857782346395540527676 absolute error = 9.4e-31 relative error = 1.2591656553692095415100819633983e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.56 y[1] (analytic) = 0.75313694954108833276527269949021 y[1] (numeric) = 0.75313694954108833276527269949106 absolute error = 8.5e-31 relative error = 1.1286127981344343560016860092201e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.57 y[1] (analytic) = 0.7598725049623952435109104302038 y[1] (numeric) = 0.75987250496239524351091043020471 absolute error = 9.1e-31 relative error = 1.1975693212442715014464105532258e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.58 y[1] (analytic) = 0.76673207209976978032663901358165 y[1] (numeric) = 0.76673207209976978032663901358257 absolute error = 9.2e-31 relative error = 1.1998976350115252209515587491195e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.59 y[1] (analytic) = 0.77371496500221449265226985699767 y[1] (numeric) = 0.77371496500221449265226985699853 absolute error = 8.6e-31 relative error = 1.1115204421534467103760923761298e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=128056564, alloc=4586680, time=11.88 x[1] = 7.6 y[1] (analytic) = 0.78082048538625819403838423261938 y[1] (numeric) = 0.78082048538625819403838423262028 absolute error = 9.0e-31 relative error = 1.1526336934600093018516852001249e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.61 y[1] (analytic) = 0.78804792270578372736402523675188 y[1] (numeric) = 0.78804792270578372736402523675274 absolute error = 8.6e-31 relative error = 1.0913041900385535958136960905662e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.62 y[1] (analytic) = 0.79539655422308198443261932361648 y[1] (numeric) = 0.79539655422308198443261932361742 absolute error = 9.4e-31 relative error = 1.1818004428220864683453238639485e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.63 y[1] (analytic) = 0.80286564508112507460337930703817 y[1] (numeric) = 0.80286564508112507460337930703902 absolute error = 8.5e-31 relative error = 1.0587076495396838943680605367010e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.64 y[1] (analytic) = 0.81045444837705141520155312950598 y[1] (numeric) = 0.81045444837705141520155312950687 absolute error = 8.9e-31 relative error = 1.0981493183018982523144205570579e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.65 y[1] (analytic) = 0.81816220523685539525971474495037 y[1] (numeric) = 0.81816220523685539525971474495127 absolute error = 9.0e-31 relative error = 1.1000263691469991815859773525949e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.66 y[1] (analytic) = 0.82598814489127414368596416512567 y[1] (numeric) = 0.82598814489127414368596416512653 absolute error = 8.6e-31 relative error = 1.0411771710273188963197172624590e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.67 y[1] (analytic) = 0.83393148475286381324545861227259 y[1] (numeric) = 0.83393148475286381324545861227352 absolute error = 9.3e-31 relative error = 1.1151995301815546145970558913462e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.68 y[1] (analytic) = 0.84199143049425767279110664749629 y[1] (numeric) = 0.8419914304942576727911066474972 absolute error = 9.1e-31 relative error = 1.0807710946248236682775236120006e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.69 y[1] (analytic) = 0.85016717612759818199941706492118 y[1] (numeric) = 0.8501671761275981819994170649221 absolute error = 9.2e-31 relative error = 1.0821401082437472151000163524485e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.7 y[1] (analytic) = 0.85845790408513510547022214170434 y[1] (numeric) = 0.85845790408513510547022214170518 absolute error = 8.4e-31 relative error = 9.7849876622103464765267042908599e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.71 y[1] (analytic) = 0.86686278530098160644603014278012 y[1] (numeric) = 0.86686278530098160644603014278105 absolute error = 9.3e-31 relative error = 1.0728341506517627860638522168475e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.93 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] = 7.72 y[1] (analytic) = 0.87538097929402014460976499608769 y[1] (numeric) = 0.87538097929402014460976499608855 absolute error = 8.6e-31 relative error = 9.8242938828026096416809932405051e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.73 y[1] (analytic) = 0.88401163425194988744020138218134 y[1] (numeric) = 0.8840116342519498874402013821823 absolute error = 9.6e-31 relative error = 1.0859585584666557266480530707297e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.74 y[1] (analytic) = 0.89275388711646723045399897071758 y[1] (numeric) = 0.89275388711646723045399897071846 absolute error = 8.8e-31 relative error = 9.8571399430400533340233284481625e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.75 y[1] (analytic) = 0.90160686366957090835329513064641 y[1] (numeric) = 0.90160686366957090835329513064729 absolute error = 8.8e-31 relative error = 9.7603516062241337543733444436912e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.76 y[1] (analytic) = 0.91056967862098306663966204106089 y[1] (numeric) = 0.91056967862098306663966204106182 absolute error = 9.3e-31 relative error = 1.0213386430881855010962788704901e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.55 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] = 7.77 y[1] (analytic) = 0.9196414356966775516601174571664 y[1] (numeric) = 0.9196414356966775516601174571673 absolute error = 9.0e-31 relative error = 9.7864228933769375660326053289296e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.78 y[1] (analytic) = 0.92882122772850656632995785942085 y[1] (numeric) = 0.92882122772850656632995785942173 absolute error = 8.8e-31 relative error = 9.4743743330683549144292847257773e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.24 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] = 7.79 y[1] (analytic) = 0.93810813674491672894153033333811 y[1] (numeric) = 0.93810813674491672894153033333904 absolute error = 9.3e-31 relative error = 9.9135692738680356188435837422778e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.59 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] = 7.8 y[1] (analytic) = 0.94750123406274546352865876645141 y[1] (numeric) = 0.94750123406274546352865876645234 absolute error = 9.3e-31 relative error = 9.8152906462432480998045420402575e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.81 y[1] (analytic) = 0.95699958038008854222418465679748 y[1] (numeric) = 0.95699958038008854222418465679842 absolute error = 9.4e-31 relative error = 9.8223658533545346818290822927232e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.31 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] = 7.82 y[1] (analytic) = 0.96660222587022949293377613950805 y[1] (numeric) = 0.96660222587022949293377613950892 absolute error = 8.7e-31 relative error = 9.0006000060339323351437025735535e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.68 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] = 7.83 y[1] (analytic) = 0.97630821027662147946351209608496 y[1] (numeric) = 0.97630821027662147946351209608587 absolute error = 9.1e-31 relative error = 9.3208270751115152710424226187371e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=132057800, alloc=4586680, time=12.25 x[1] = 7.84 y[1] (analytic) = 0.98611656300891215599237989088459 y[1] (numeric) = 0.98611656300891215599237989088551 absolute error = 9.2e-31 relative error = 9.3295258847780389730457372882958e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.85 y[1] (analytic) = 0.99602630324000189348425993036111 y[1] (numeric) = 0.99602630324000189348425993036202 absolute error = 9.1e-31 relative error = 9.1363049052001486383461827169894e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.86 y[1] (analytic) = 1.0060364400041256722976374323518 y[1] (numeric) = 1.0060364400041256722976374323527 absolute error = 9e-31 relative error = 8.9459980196771915575896023024287e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.87 y[1] (analytic) = 1.016145972295948832885515072286 y[1] (numeric) = 1.0161459722959488328855150722869 absolute error = 9e-31 relative error = 8.8569952008615378415655617405107e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.88 y[1] (analytic) = 1.0263538891706667750930360320368 y[1] (numeric) = 1.0263538891706667750930360320377 absolute error = 9e-31 relative error = 8.7689052430758989612673656414938e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.04 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] = 7.89 y[1] (analytic) = 1.0366591698450985961663038271389 y[1] (numeric) = 1.0366591698450985961663038271398 absolute error = 9e-31 relative error = 8.6817348090836961483097002478905e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.68 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] = 7.9 y[1] (analytic) = 1.0470607837997645581928424479146 y[1] (numeric) = 1.0470607837997645581928424479155 absolute error = 9e-31 relative error = 8.5954895257743906133554804737785e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.91 y[1] (analytic) = 1.0575576908819371773120170411462 y[1] (numeric) = 1.0575576908819371773120170411471 absolute error = 9e-31 relative error = 8.5101740336213347702610697333535e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.92 y[1] (analytic) = 1.0681488414096556296723697116501 y[1] (numeric) = 1.068148841409655629672369711651 absolute error = 9e-31 relative error = 8.4257920348652298528018034646867e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.93 y[1] (analytic) = 1.0788331762766930727819530928743 y[1] (numeric) = 1.0788331762766930727819530928752 absolute error = 9e-31 relative error = 8.3423463403870428961178219359683e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.31 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] = 7.94 y[1] (analytic) = 1.0896096270584663856069991293797 y[1] (numeric) = 1.0896096270584663856069991293806 absolute error = 9e-31 relative error = 8.2598389152421439398036407160172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.95 y[1] (analytic) = 1.1004771161188777365331710268819 y[1] (numeric) = 1.1004771161188777365331710268828 absolute error = 9e-31 relative error = 8.1782709228346967861332279060057e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.96 y[1] (analytic) = 1.1114345567180772951216365878451 y[1] (numeric) = 1.111434556718077295121636587846 absolute error = 9e-31 relative error = 8.0976427677180001091272309900849e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.35 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] = 7.97 y[1] (analytic) = 1.1224808531211363114785892857504 y[1] (numeric) = 1.1224808531211363114785892857514 absolute error = 1.0e-30 relative error = 8.9088379300139529717194732199917e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.98 y[1] (analytic) = 1.1336149007076196960208407235378 y[1] (numeric) = 1.1336149007076196960208407235388 absolute error = 1.0e-30 relative error = 8.8213378227102057421763415899236e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.99 y[1] (analytic) = 1.144835586082047142470818095744 y[1] (numeric) = 1.144835586082047142470818095745 absolute error = 1.0e-30 relative error = 8.7348787210771837075882640753020e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8 y[1] (analytic) = 1.1561417871852317480607177835859 y[1] (numeric) = 1.1561417871852317480607177835869 absolute error = 1.0e-30 relative error = 8.6494581467781907511783926472596e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.01 y[1] (analytic) = 1.1675323734064849971765765418579 y[1] (numeric) = 1.1675323734064849971765765418589 absolute error = 1.0e-30 relative error = 8.5650729930710249595745919660623e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.02 y[1] (analytic) = 1.1790062056966768880373997118827 y[1] (numeric) = 1.1790062056966768880373997118836 absolute error = 9e-31 relative error = 7.6335476068863300075245081169665e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.03 y[1] (analytic) = 1.1905621366821398964908950058704 y[1] (numeric) = 1.1905621366821398964908950058714 absolute error = 1.0e-30 relative error = 8.3993936073492249161336628513780e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.04 y[1] (analytic) = 1.2021990107794053866243519427395 y[1] (numeric) = 1.2021990107794053866243519427404 absolute error = 9e-31 relative error = 7.4862813222289644138614532074901e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.05 y[1] (analytic) = 1.213915664310760994645219204251 y[1] (numeric) = 1.213915664310760994645219204252 absolute error = 1.0e-30 relative error = 8.2378045641892398053277161833465e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.06 y[1] (analytic) = 1.2257109256206174303892893526318 y[1] (numeric) = 1.2257109256206174303892893526327 absolute error = 9e-31 relative error = 7.3426774713972679777853027451650e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.07 y[1] (analytic) = 1.2375836151926730598733121025612 y[1] (numeric) = 1.2375836151926730598733121025622 absolute error = 1.0e-30 relative error = 8.0802621150112359670521208782739e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=136060088, alloc=4586680, time=12.63 x[1] = 8.08 y[1] (analytic) = 1.2495325457678645525314177128683 y[1] (numeric) = 1.2495325457678645525314177128693 absolute error = 1.0e-30 relative error = 8.0029928262931202760519432766732e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.09 y[1] (analytic) = 1.2615565224630917981689187339872 y[1] (numeric) = 1.2615565224630917981689187339882 absolute error = 1.0e-30 relative error = 7.9267157847797190759974590057409e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.1 y[1] (analytic) = 1.2736543428907052212407318320024 y[1] (numeric) = 1.2736543428907052212407318320032 absolute error = 8e-31 relative error = 6.2811390269694983486652596894840e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.11 y[1] (analytic) = 1.2858247972787435438225642770893 y[1] (numeric) = 1.2858247972787435438225642770903 absolute error = 1.0e-30 relative error = 7.7771093084870574250224739969178e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.12 y[1] (analytic) = 1.2980666685919099735987657795216 y[1] (numeric) = 1.2980666685919099735987657795225 absolute error = 9e-31 relative error = 6.9333881053758468664392095713166e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.13 y[1] (analytic) = 1.3103787326532747193488600420006 y[1] (numeric) = 1.3103787326532747193488600420014 absolute error = 8e-31 relative error = 6.1051051887888005810511942111464e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.14 y[1] (analytic) = 1.3227597582666916637826258000013 y[1] (numeric) = 1.3227597582666916637826258000022 absolute error = 9e-31 relative error = 6.8039566094703052581945653330902e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.15 y[1] (analytic) = 1.335208507339916952158457396012 y[1] (numeric) = 1.3352085073399169521584573960128 absolute error = 8e-31 relative error = 5.9915735677404297531340537254277e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.16 y[1] (analytic) = 1.3477237350084171849287415334612 y[1] (numeric) = 1.347723735008417184928741533462 absolute error = 8e-31 relative error = 5.9359346371903408975978646099696e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.17 y[1] (analytic) = 1.360304189759854833696158822621 y[1] (numeric) = 1.3603041897598548336961588226218 absolute error = 8e-31 relative error = 5.8810375357384606284709340851751e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.18 y[1] (analytic) = 1.3729486135592384320430519891663 y[1] (numeric) = 1.3729486135592384320430519891671 absolute error = 8e-31 relative error = 5.8268750345002078690291806914054e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.19 y[1] (analytic) = 1.3856557419747250263190692866238 y[1] (numeric) = 1.3856557419747250263190692866245 absolute error = 7e-31 relative error = 5.0517598188018644940328912047032e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.2 y[1] (analytic) = 1.398424304304062306246839374574 y[1] (numeric) = 1.3984243043040623062468393745748 absolute error = 8e-31 relative error = 5.7207243719789808187240782413057e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.21 y[1] (analytic) = 1.4112530237016577712379851860634 y[1] (numeric) = 1.4112530237016577712379851860643 absolute error = 9e-31 relative error = 6.3773114025955286791716811023440e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.22 y[1] (analytic) = 1.4241406173062622256087358017996 y[1] (numeric) = 1.4241406173062622256087358018005 absolute error = 9e-31 relative error = 6.3196006704895104004307908341889e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.23 y[1] (analytic) = 1.4370857963692548344520173279467 y[1] (numeric) = 1.4370857963692548344520173279475 absolute error = 8e-31 relative error = 5.5668214244491943169209846296718e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.24 y[1] (analytic) = 1.4500872663835169117673394253125 y[1] (numeric) = 1.4500872663835169117673394253134 absolute error = 9e-31 relative error = 6.2065230201253925489671935437201e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.25 y[1] (analytic) = 1.4631437272128815535770589667361 y[1] (numeric) = 1.4631437272128815535770589667369 absolute error = 8e-31 relative error = 5.4676788419406127376762267481989e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.26 y[1] (analytic) = 1.4762538732221461711735835309881 y[1] (numeric) = 1.4762538732221461711735835309889 absolute error = 8e-31 relative error = 5.4191221070524925713750634333240e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.27 y[1] (analytic) = 1.4894163934076349233525334293992 y[1] (numeric) = 1.4894163934076349233525334294001 absolute error = 9e-31 relative error = 6.0426352495079667376935492503849e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.28 y[1] (analytic) = 1.5026299715282979914974406131996 y[1] (numeric) = 1.5026299715282979914974406132004 absolute error = 8e-31 relative error = 5.3239986900190360873135667745035e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.29 y[1] (analytic) = 1.515893286237334587697725023419 y[1] (numeric) = 1.5158932862373345876977250234198 absolute error = 8e-31 relative error = 5.2774163409992743833550435072058e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.3 y[1] (analytic) = 1.5292050112143265337088220601935 y[1] (numeric) = 1.5292050112143265337088220601944 absolute error = 9e-31 relative error = 5.8854110037562519209618018940285e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.31 y[1] (analytic) = 1.542563815297869197506676107493 y[1] (numeric) = 1.5425638152978691975066761074938 absolute error = 8e-31 relative error = 5.1861711785681938564775937394080e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.32 y[1] (analytic) = 1.555968362618686524453470075961 y[1] (numeric) = 1.5559683626186865244534700759619 absolute error = 9e-31 relative error = 5.7841793035258426481334221625475e-29 % Correct digits = 31 bytes used=140061116, alloc=4586680, time=13.01 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.33 y[1] (analytic) = 1.5694173127332168516824032137891 y[1] (numeric) = 1.56941731273321685168240321379 absolute error = 9e-31 relative error = 5.7346124112305481833621461203385e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.34 y[1] (analytic) = 1.582909320757656147231399848758 y[1] (numeric) = 1.5829093207576561472313998487589 absolute error = 9e-31 relative error = 5.6857331509629176525763261538315e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.35 y[1] (analytic) = 1.5964430375024452697135380175099 y[1] (numeric) = 1.5964430375024452697135380175109 absolute error = 1.0e-30 relative error = 6.2639253422060685413417641207109e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.36 y[1] (analytic) = 1.6100171096071877999103032820059 y[1] (numeric) = 1.6100171096071877999103032820069 absolute error = 1.0e-30 relative error = 6.2111141181846206601942742081693e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.37 y[1] (analytic) = 1.6236301796759849526169395593417 y[1] (numeric) = 1.6236301796759849526169395593427 absolute error = 1.0e-30 relative error = 6.1590380156616828805674767211809e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.38 y[1] (analytic) = 1.6372808864131740353614911471161 y[1] (numeric) = 1.6372808864131740353614911471171 absolute error = 1.0e-30 relative error = 6.1076874975968308652758495761542e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.39 y[1] (analytic) = 1.6509678647594568802647790453627 y[1] (numeric) = 1.6509678647594568802647790453636 absolute error = 9e-31 relative error = 5.4513477773301688104757032417327e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.4 y[1] (analytic) = 1.6646897460284046363115655591631 y[1] (numeric) = 1.664689746028404636311565559164 absolute error = 9e-31 relative error = 5.4064128294609155415732227268356e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.41 y[1] (analytic) = 1.6784451580433252716674336798615 y[1] (numeric) = 1.6784451580433252716674336798625 absolute error = 1.0e-30 relative error = 5.9578949911343320643325199951202e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.42 y[1] (analytic) = 1.6922327252744800994052054286866 y[1] (numeric) = 1.6922327252744800994052054286876 absolute error = 1.0e-30 relative error = 5.9093526857412595465539891405841e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.43 y[1] (analytic) = 1.7060510689766356051026732445605 y[1] (numeric) = 1.7060510689766356051026732445614 absolute error = 9e-31 relative error = 5.2753403246003623204328327026828e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.44 y[1] (analytic) = 1.7198988073269368212435107838682 y[1] (numeric) = 1.7198988073269368212435107838691 absolute error = 9e-31 relative error = 5.2328660044760316078894606459215e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.45 y[1] (analytic) = 1.7337745555630884611988171367941 y[1] (numeric) = 1.7337745555630884611988171367951 absolute error = 1.0e-30 relative error = 5.7677625778469447231448388402820e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.46 y[1] (analytic) = 1.747676926121829994791046866951 y[1] (numeric) = 1.747676926121829994791046866952 absolute error = 1.0e-30 relative error = 5.7218813446203862198212200370002e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.47 y[1] (analytic) = 1.7616045287776908180481649929499 y[1] (numeric) = 1.7616045287776908180481649929509 absolute error = 1.0e-30 relative error = 5.6766429903189524891431661262211e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.48 y[1] (analytic) = 1.7755559707820116417466804191106 y[1] (numeric) = 1.7755559707820116417466804191117 absolute error = 1.1e-30 relative error = 6.1952426062667279130910037576817e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.49 y[1] (analytic) = 1.7895298570022181967205542829194 y[1] (numeric) = 1.7895298570022181967205542829205 absolute error = 1.1e-30 relative error = 6.1468658692439826905258256028958e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.5 y[1] (analytic) = 1.8035247900613333286815133626179 y[1] (numeric) = 1.803524790061333328681513362619 absolute error = 1.1e-30 relative error = 6.0991676192185402384886685890953e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.51 y[1] (analytic) = 1.8175393704777135314575462050684 y[1] (numeric) = 1.8175393704777135314575462050695 absolute error = 1.1e-30 relative error = 6.0521385003664660887757043124453e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.52 y[1] (analytic) = 1.8315721968049959451127048471569 y[1] (numeric) = 1.831572196804995945112704847158 absolute error = 1.1e-30 relative error = 6.0057692616149432403359366312604e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.53 y[1] (analytic) = 1.8456218657722418243650222602545 y[1] (numeric) = 1.8456218657722418243650222602556 absolute error = 1.1e-30 relative error = 5.9600507579581582001718744250558e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.54 y[1] (analytic) = 1.859686972424262463072489560388 y[1] (numeric) = 1.8596869724242624630724895603891 absolute error = 1.1e-30 relative error = 5.9149739515895789059111549375247e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.55 y[1] (analytic) = 1.8737661102621135423115822670094 y[1] (numeric) = 1.8737661102621135423115822670106 absolute error = 1.2e-30 relative error = 6.4042144503944351222597849505065e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.56 y[1] (analytic) = 1.8878578713837438527306059908769 y[1] (numeric) = 1.8878578713837438527306059908781 absolute error = 1.2e-30 relative error = 6.3564107139084340863002794241492e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=144063948, alloc=4586680, time=13.39 x[1] = 8.57 y[1] (analytic) = 1.901960846624784326422833094414 y[1] (numeric) = 1.9019608466247843264228330944152 absolute error = 1.2e-30 relative error = 6.3092781438141455329952551572316e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.58 y[1] (analytic) = 1.9160736256994632995335668130314 y[1] (numeric) = 1.9160736256994632995335668130326 absolute error = 1.2e-30 relative error = 6.2628073572169733830441500787742e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.59 y[1] (analytic) = 1.9301947973416339141923011250723 y[1] (numeric) = 1.9301947973416339141923011250735 absolute error = 1.2e-30 relative error = 6.2169890917367682045923206494122e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.6 y[1] (analytic) = 1.944322949445899557147305597597 y[1] (numeric) = 1.9443229494458995571473055975982 absolute error = 1.2e-30 relative error = 6.1718142057726598272283836323161e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.61 y[1] (analytic) = 1.9584566692088232226763758897024 y[1] (numeric) = 1.9584566692088232226763758897036 absolute error = 1.2e-30 relative error = 6.1272736786399040642784231391572e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.62 y[1] (analytic) = 1.9725945432702066789551329151711 y[1] (numeric) = 1.9725945432702066789551329151724 absolute error = 1.3e-30 relative error = 6.5903051614693914972563546953417e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.63 y[1] (analytic) = 1.9867351578544253100839660807336 y[1] (numeric) = 1.9867351578544253100839660807348 absolute error = 1.2e-30 relative error = 6.0400602227019530571945551659687e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.64 y[1] (analytic) = 2.0008770989118045004071965480436 y[1] (numeric) = 2.0008770989118045004071965480449 absolute error = 1.3e-30 relative error = 6.4971506781052020276959599592029e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0005981 Order of pole (three term test) = -0.8929 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.65 y[1] (analytic) = 2.0150189522600234236038418639322 y[1] (numeric) = 2.0150189522600234236038418639334 absolute error = 1.2e-30 relative error = 5.9552789746919898808398957749299e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01024 Order of pole (three term test) = -0.8956 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.66 y[1] (analytic) = 2.0291593037255320962889089805942 y[1] (numeric) = 2.0291593037255320962889089805954 absolute error = 1.2e-30 relative error = 5.9137791586732623377564987014418e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01988 Order of pole (three term test) = -0.9031 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.67 y[1] (analytic) = 2.0432967392849675545377026882523 y[1] (numeric) = 2.0432967392849675545377026882536 absolute error = 1.3e-30 relative error = 6.3622672860277883750811558201418e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02951 Order of pole (three term test) = -0.9155 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.68 y[1] (analytic) = 2.057429845206555011833343450402 y[1] (numeric) = 2.0574298452065550118333434504033 absolute error = 1.3e-30 relative error = 6.3185629538172025274108737284528e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03913 Order of pole (three term test) = -0.9327 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.69 y[1] (analytic) = 2.0715572081914798584395337953625 y[1] (numeric) = 2.0715572081914798584395337953637 absolute error = 1.2e-30 relative error = 5.7927437159586307950476559614531e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04873 Order of pole (three term test) = -0.9548 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.7 y[1] (analytic) = 2.0856774155152163651164455942737 y[1] (numeric) = 2.0856774155152163651164455942749 absolute error = 1.2e-30 relative error = 5.7535263654545969465699220758227e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05831 Order of pole (three term test) = -0.9816 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.71 y[1] (analytic) = 2.0997890551687989584271301639961 y[1] (numeric) = 2.0997890551687989584271301639973 absolute error = 1.2e-30 relative error = 5.7148597714903974594797160757763e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06787 Order of pole (three term test) = -1.013 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.72 y[1] (analytic) = 2.113890716000021940624646224237 y[1] (numeric) = 2.1138907160000219406246462242382 absolute error = 1.2e-30 relative error = 5.6767362234821771405430142175079e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0774 Order of pole (three term test) = -1.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.73 y[1] (analytic) = 2.1279809878545535342655830371279 y[1] (numeric) = 2.127980987854553534265583037129 absolute error = 1.1e-30 relative error = 5.1692191155759727356019563632546e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08691 Order of pole (three term test) = -1.091 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.74 y[1] (analytic) = 2.1420584617169501402631120221331 y[1] (numeric) = 2.1420584617169501402631120221342 absolute error = 1.1e-30 relative error = 5.1352473317572464261566530695822e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09637 Order of pole (three term test) = -1.137 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.75 y[1] (analytic) = 2.1561217298515567080712730311345 y[1] (numeric) = 2.1561217298515567080712730311356 absolute error = 1.1e-30 relative error = 5.1017527664160784536285399542936e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1058 Order of pole (three term test) = -1.188 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.76 y[1] (analytic) = 2.1701693859432791280808934388279 y[1] (numeric) = 2.170169385943279128080893438829 absolute error = 1.1e-30 relative error = 5.0687287689383628210925483734842e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1152 Order of pole (three term test) = -1.243 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.77 y[1] (analytic) = 2.1842000252382145691052103924856 y[1] (numeric) = 2.1842000252382145691052103924867 absolute error = 1.1e-30 relative error = 5.0361687908140698888395617004853e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1245 Order of pole (three term test) = -1.303 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.78 y[1] (analytic) = 2.1982122446841256980386392161264 y[1] (numeric) = 2.1982122446841256980386392161275 absolute error = 1.1e-30 relative error = 5.0040663846728121452288765829357e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1338 Order of pole (three term test) = -1.368 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.79 y[1] (analytic) = 2.212204643070744734383783551761 y[1] (numeric) = 2.2122046430707447343837835517621 absolute error = 1.1e-30 relative error = 4.9724152032928482589741858516958e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.143 Order of pole (three term test) = -1.437 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.8 y[1] (analytic) = 2.2261758211698933093581541924069 y[1] (numeric) = 2.2261758211698933093581541924081 absolute error = 1.2e-30 relative error = 5.3904098166396379333662751053290e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1522 Order of pole (three term test) = -1.511 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.81 y[1] (analytic) = 2.2401243818754041177114520950235 y[1] (numeric) = 2.2401243818754041177114520950247 bytes used=148065040, alloc=4586680, time=13.77 absolute error = 1.2e-30 relative error = 5.3568454042510577340905946206033e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1613 Order of pole (three term test) = -1.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.82 y[1] (analytic) = 2.2540489303428303702048348329082 y[1] (numeric) = 2.2540489303428303702048348329094 absolute error = 1.2e-30 relative error = 5.3237531086669248794331087827643e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1704 Order of pole (three term test) = -1.673 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.83 y[1] (analytic) = 2.2679480741289290759233427165629 y[1] (numeric) = 2.2679480741289290759233427165641 absolute error = 1.2e-30 relative error = 5.2911264313707651309347363906210e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1794 Order of pole (three term test) = -1.761 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.84 y[1] (analytic) = 2.2818204233309042062094890215573 y[1] (numeric) = 2.2818204233309042062094890215585 absolute error = 1.2e-30 relative error = 5.2589589773602391646699464713607e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1883 Order of pole (three term test) = -1.853 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.85 y[1] (analytic) = 2.2956645907253958160176565475257 y[1] (numeric) = 2.2956645907253958160176565475269 absolute error = 1.2e-30 relative error = 5.2272444539505567508896264205149e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1971 Order of pole (three term test) = -1.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.86 y[1] (analytic) = 2.3094791919072012238929889503568 y[1] (numeric) = 2.309479191907201223892988950358 absolute error = 1.2e-30 relative error = 5.1959766695668848769677030647382e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2059 Order of pole (three term test) = -2.051 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.87 y[1] (analytic) = 2.3232628454277143785723795564228 y[1] (numeric) = 2.3232628454277143785723795564239 absolute error = 1.1e-30 relative error = 4.7347204048170847428757873628941e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2146 Order of pole (three term test) = -2.156 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.88 y[1] (analytic) = 2.3370141729330695683862633142472 y[1] (numeric) = 2.3370141729330695683862633142483 absolute error = 1.1e-30 relative error = 4.7068606290027117492559834981758e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2232 Order of pole (three term test) = -2.266 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.89 y[1] (analytic) = 2.35073179930197565920539107852 y[1] (numeric) = 2.350731799301975659205391078521 absolute error = 1.0e-30 relative error = 4.2539944382295724520717888837353e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2317 Order of pole (three term test) = -2.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.9 y[1] (analytic) = 2.3644143527832270776236530311141 y[1] (numeric) = 2.3644143527832270776236530311151 absolute error = 1.0e-30 relative error = 4.2293771344386752846208812267677e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2401 Order of pole (three term test) = -2.498 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.91 y[1] (analytic) = 2.3780604651328777883932250607736 y[1] (numeric) = 2.3780604651328777883932250607746 absolute error = 1.0e-30 relative error = 4.2051075431512354795025767399070e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2484 Order of pole (three term test) = -2.621 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.92 y[1] (analytic) = 2.391668771751064548828605853659 y[1] (numeric) = 2.39166877175106454882860585366 absolute error = 1.0e-30 relative error = 4.1811809888199870579240725154873e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2566 Order of pole (three term test) = -2.747 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.93 y[1] (analytic) = 2.4052379118184657579681232896477 y[1] (numeric) = 2.4052379118184657579681232896487 absolute error = 1.0e-30 relative error = 4.1575928729809350647195880019040e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2647 Order of pole (three term test) = -2.878 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.94 y[1] (analytic) = 2.418766528432382254721709322332 y[1] (numeric) = 2.4187665284323822547217093223331 absolute error = 1.1e-30 relative error = 4.5477725405474206458659204783306e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2727 Order of pole (three term test) = -3.013 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.95 y[1] (analytic) = 2.4322532687424264570385288523496 y[1] (numeric) = 2.4322532687424264570385288523507 absolute error = 1.1e-30 relative error = 4.5225553363887330440804328624571e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2806 Order of pole (three term test) = -3.151 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.96 y[1] (analytic) = 2.4456967840858062732936197368834 y[1] (numeric) = 2.4456967840858062732936197368845 absolute error = 1.1e-30 relative error = 4.4976957370910414094863599559188e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2884 Order of pole (three term test) = -3.294 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.97 y[1] (analytic) = 2.4590957301221902576151414883655 y[1] (numeric) = 2.4590957301221902576151414883666 absolute error = 1.1e-30 relative error = 4.4731890122282550920596365806863e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.296 Order of pole (three term test) = -3.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.98 y[1] (analytic) = 2.4724487669681405227490871923298 y[1] (numeric) = 2.4724487669681405227490871923309 absolute error = 1.1e-30 relative error = 4.4490305105447484430480485694542e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3036 Order of pole (three term test) = -3.591 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.99 y[1] (analytic) = 2.4857545593310999672821992271839 y[1] (numeric) = 2.485754559331099967282199227185 absolute error = 1.1e-30 relative error = 4.4252156588460716326657212761834e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.311 Order of pole (three term test) = -3.745 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9 y[1] (analytic) = 2.4990117766429204186120221448288 y[1] (numeric) = 2.4990117766429204186120221448298 absolute error = 1.0e-30 relative error = 4.0015817826331448888695659680150e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3183 Order of pole (three term test) = -3.903 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.01 y[1] (analytic) = 2.5122190931929183389610687884018 y[1] (numeric) = 2.5122190931929183389610687884029 absolute error = 1.1e-30 relative error = 4.3785989963238003122097159786335e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3255 Order of pole (three term test) = -4.064 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.02 y[1] (analytic) = 2.5253751882604447889753776159455 y[1] (numeric) = 2.5253751882604447889753776159466 absolute error = 1.1e-30 relative error = 4.3557884195326772190704751227642e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3325 Order of pole (three term test) = -4.229 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.03 y[1] (analytic) = 2.5384787462469563920215759756844 y[1] (numeric) = 2.5384787462469563920215759756855 absolute error = 1.1e-30 relative error = 4.3333039586260388129501009880259e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3394 Order of pole (three term test) = -4.397 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.04 y[1] (analytic) = 2.5515284568075740921960783966351 y[1] (numeric) = 2.5515284568075740921960783966363 absolute error = 1.2e-30 relative error = 4.7030633610938367977284308594682e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3462 Order of pole (three term test) = -4.569 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.05 y[1] (analytic) = 2.5645230149821165502802509076205 y[1] (numeric) = 2.5645230149821165502802509076216 absolute error = 1.1e-30 relative error = 4.2892966589643600531827073125584e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3528 Order of pole (three term test) = -4.745 NO COMPLEX POLE (six term test) for Equation 1 bytes used=152065916, alloc=4586680, time=14.14 TOP MAIN SOLVE Loop x[1] = 9.06 y[1] (analytic) = 2.5774611213255950744111400009037 y[1] (numeric) = 2.5774611213255950744111400009048 absolute error = 1.1e-30 relative error = 4.2677656353329088801392148531145e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3593 Order of pole (three term test) = -4.923 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.07 y[1] (analytic) = 2.590341482038157036083444580621 y[1] (numeric) = 2.5903414820381570360834445806221 absolute error = 1.1e-30 relative error = 4.2465443557445081496741088296701e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3657 Order of pole (three term test) = -5.105 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.08 y[1] (analytic) = 2.6031628090944647772494165178653 y[1] (numeric) = 2.6031628090944647772494165178664 absolute error = 1.1e-30 relative error = 4.2256289009547027940550979449673e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3719 Order of pole (three term test) = -5.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.09 y[1] (analytic) = 2.615923820372497070733795218897 y[1] (numeric) = 2.6159238203724970707337952188981 absolute error = 1.1e-30 relative error = 4.2050154191545394750732809789438e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3779 Order of pole (three term test) = -5.478 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.1 y[1] (analytic) = 2.62862323978176025392506890559 y[1] (numeric) = 2.6286232397817602539250689055911 absolute error = 1.1e-30 relative error = 4.1847001249647583168564093172072e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3839 Order of pole (three term test) = -5.669 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.11 y[1] (analytic) = 2.6412597973908962147365357372524 y[1] (numeric) = 2.6412597973908962147365357372536 absolute error = 1.2e-30 relative error = 4.5432865073908693207574435689172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3896 Order of pole (three term test) = -5.862 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.12 y[1] (analytic) = 2.6538322295546744691449083015452 y[1] (numeric) = 2.6538322295546744691449083015464 absolute error = 1.2e-30 relative error = 4.5217628553759995762698052094255e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3952 Order of pole (three term test) = -6.059 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.13 y[1] (analytic) = 2.6663392790403556312045339925759 y[1] (numeric) = 2.6663392790403556312045339925771 absolute error = 1.2e-30 relative error = 4.5005525344542536597807564212296e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4006 Order of pole (three term test) = -6.259 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.14 y[1] (analytic) = 2.6787796951534136392955323947999 y[1] (numeric) = 2.6787796951534136392955323948011 absolute error = 1.2e-30 relative error = 4.4796516942811754181240825019871e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4059 Order of pole (three term test) = -6.461 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.15 y[1] (analytic) = 2.6911522338626041664879930316364 y[1] (numeric) = 2.6911522338626041664879930316377 absolute error = 1.3e-30 relative error = 4.8306445976640764206192912569652e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.411 Order of pole (three term test) = -6.666 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.16 y[1] (analytic) = 2.7034556579243667082854203869158 y[1] (numeric) = 2.703455657924366708285420386917 absolute error = 1.2e-30 relative error = 4.4387633896733653348137000813654e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.416 Order of pole (three term test) = -6.873 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.17 y[1] (analytic) = 2.7156887370065479076423199155477 y[1] (numeric) = 2.715688737006547907642319915549 absolute error = 1.3e-30 relative error = 4.7869992694117268310856639611807e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4207 Order of pole (three term test) = -7.083 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.18 y[1] (analytic) = 2.7278502478114337450265257119842 y[1] (numeric) = 2.7278502478114337450265257119854 absolute error = 1.2e-30 relative error = 4.3990684641239572421175548526108e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4254 Order of pole (three term test) = -7.295 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.19 y[1] (analytic) = 2.7399389741980782904097900870034 y[1] (numeric) = 2.7399389741980782904097900870046 absolute error = 1.2e-30 relative error = 4.3796595884082214292964229332374e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4298 Order of pole (three term test) = -7.509 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.2 y[1] (analytic) = 2.7519537073039167844133762807175 y[1] (numeric) = 2.7519537073039167844133762807187 absolute error = 1.2e-30 relative error = 4.3605384669629397842228273791942e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4341 Order of pole (three term test) = -7.726 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.21 y[1] (analytic) = 2.7638932456656508874018836490052 y[1] (numeric) = 2.7638932456656508874018836490064 absolute error = 1.2e-30 relative error = 4.3417016987969600147713150229358e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4382 Order of pole (three term test) = -7.944 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.22 y[1] (analytic) = 2.775756395339394008101133312638 y[1] (numeric) = 2.7757563953393940081011333126391 absolute error = 1.1e-30 relative error = 3.9628837813251335370938009901642e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4421 Order of pole (three term test) = -8.165 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.23 y[1] (analytic) = 2.7875419700200646973073732539797 y[1] (numeric) = 2.7875419700200646973073732539809 absolute error = 1.2e-30 relative error = 4.3048679191415453838903825119810e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4458 Order of pole (three term test) = -8.387 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.24 y[1] (analytic) = 2.7992487911600161674479261038611 y[1] (numeric) = 2.7992487911600161674479261038623 absolute error = 1.2e-30 relative error = 4.2868644037271042221365202683843e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4494 Order of pole (three term test) = -8.612 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.25 y[1] (analytic) = 2.8108756880868900751401811572893 y[1] (numeric) = 2.8108756880868900751401811572906 absolute error = 1.3e-30 relative error = 4.6248932512728548235540414658901e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4528 Order of pole (three term test) = -8.838 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.26 y[1] (analytic) = 2.8224214981206827814688858768887 y[1] (numeric) = 2.8224214981206827814688858768899 absolute error = 1.2e-30 relative error = 4.2516682954655190357468515342914e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.456 Order of pole (three term test) = -9.066 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.27 y[1] (analytic) = 2.8338850666900123834532640466342 y[1] (numeric) = 2.8338850666900123834532640466354 absolute error = 1.2e-30 relative error = 4.2344695418491483658386370527842e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.87 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.459 Order of pole (three term test) = -9.295 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.28 y[1] (analytic) = 2.8452652474475748900977027339896 y[1] (numeric) = 2.8452652474475748900977027339909 absolute error = 1.3e-30 relative error = 4.5689940548291640480761053353039e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.16 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4618 Order of pole (three term test) = -9.526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.29 y[1] (analytic) = 2.8565609023847779975046161510853 y[1] (numeric) = 2.8565609023847779975046161510866 absolute error = 1.3e-30 relative error = 4.5509269517576360921265980110899e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4645 Order of pole (three term test) = -9.758 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=156067188, alloc=4586680, time=14.52 x[1] = 9.3 y[1] (analytic) = 2.8677709019455409997675029560489 y[1] (numeric) = 2.8677709019455409997675029560501 absolute error = 1.2e-30 relative error = 4.1844346742827367347699074506531e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.467 Order of pole (three term test) = -9.991 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.31 y[1] (analytic) = 2.8788941251392494557479406317273 y[1] (numeric) = 2.8788941251392494557479406317286 absolute error = 1.3e-30 relative error = 4.5156228172757836241481665335796e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.07 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4692 Order of pole (three term test) = -10.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.32 y[1] (analytic) = 2.8899294596528533163639678175814 y[1] (numeric) = 2.8899294596528533163639678175827 absolute error = 1.3e-30 relative error = 4.4983796945554503578438873057380e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4713 Order of pole (three term test) = -10.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.33 y[1] (analytic) = 2.900875801962097302670540551208 y[1] (numeric) = 2.9008758019620973026705405512093 absolute error = 1.3e-30 relative error = 4.4814052332771526721734361010486e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4732 Order of pole (three term test) = -10.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.34 y[1] (analytic) = 2.9117320574418724117869460466285 y[1] (numeric) = 2.9117320574418724117869460466297 absolute error = 1.2e-30 relative error = 4.1212583312156492294952593445818e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.02 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.475 Order of pole (three term test) = -10.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.35 y[1] (analytic) = 2.9224971404756775156125405497065 y[1] (numeric) = 2.9224971404756775156125405497077 absolute error = 1.2e-30 relative error = 4.1060775847489216757879503065765e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4765 Order of pole (three term test) = -11.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.36 y[1] (analytic) = 2.93316997456418010626215739178 y[1] (numeric) = 2.9331699745641801062621573917812 absolute error = 1.2e-30 relative error = 4.0911369283271757414503445346406e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4778 Order of pole (three term test) = -11.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.37 y[1] (analytic) = 2.9437494924328653322371086870076 y[1] (numeric) = 2.9437494924328653322371086870088 absolute error = 1.2e-30 relative error = 4.0764338238858040433017538949793e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.02 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.479 Order of pole (three term test) = -11.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.38 y[1] (analytic) = 2.9542346361387625605178708043778 y[1] (numeric) = 2.954234636138762560517870804379 absolute error = 1.2e-30 relative error = 4.0619657806477465006409689765620e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4799 Order of pole (three term test) = -11.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.39 y[1] (analytic) = 2.9646243571762387920111828511153 y[1] (numeric) = 2.9646243571762387920111828511164 absolute error = 1.1e-30 relative error = 3.7104194915531688559738572802604e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4807 Order of pole (three term test) = -12.13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.4 y[1] (analytic) = 2.9749176165818483510981743433053 y[1] (numeric) = 2.9749176165818483510981743433065 absolute error = 1.2e-30 relative error = 4.0337251469127687179911352755996e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -12.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.41 y[1] (analytic) = 2.9851133850382283644019417010112 y[1] (numeric) = 2.9851133850382283644019417010124 absolute error = 1.2e-30 relative error = 4.0199478050467164986538320138040e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -12.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.42 y[1] (analytic) = 2.9952106429770296393132760872758 y[1] (numeric) = 2.9952106429770296393132760872769 absolute error = 1.1e-30 relative error = 3.6725296852800877722787873627465e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.82 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.43 y[1] (analytic) = 3.0052083806808726492724654644099 y[1] (numeric) = 3.005208380680872649272465464411 absolute error = 1.1e-30 relative error = 3.6603119007367448306469313497659e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.44 y[1] (analytic) = 3.0151055983843184302936057252201 y[1] (numeric) = 3.0151055983843184302936057252212 absolute error = 1.1e-30 relative error = 3.6482967647615678348528588111941e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -13.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.45 y[1] (analytic) = 3.0249013063738442917259106013581 y[1] (numeric) = 3.0249013063738442917259106013592 absolute error = 1.1e-30 relative error = 3.6364822802058461135070901010046e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.02 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -13.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.46 y[1] (analytic) = 3.034594525086814343764257032392 y[1] (numeric) = 3.0345945250868143437642570323931 absolute error = 1.1e-30 relative error = 3.6248664884430678904532618778488e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4806 Order of pole (three term test) = -13.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.47 y[1] (analytic) = 3.0441842852094349447386901057381 y[1] (numeric) = 3.0441842852094349447386901057392 absolute error = 1.1e-30 relative error = 3.6134474688161718268157755154884e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.27 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4798 Order of pole (three term test) = -14.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.48 y[1] (analytic) = 3.0536696277736852727197878842677 y[1] (numeric) = 3.0536696277736852727197878842688 absolute error = 1.1e-30 relative error = 3.6022233380955761309892150634772e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4788 Order of pole (three term test) = -14.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.49 y[1] (analytic) = 3.0630496042532133284635007921944 y[1] (numeric) = 3.0630496042532133284635007921955 absolute error = 1.1e-30 relative error = 3.5911922499478602166438745127458e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4777 Order of pole (three term test) = -14.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.5 y[1] (analytic) = 3.072323276658187780175084144712 y[1] (numeric) = 3.0723232766581877801750841447131 absolute error = 1.1e-30 relative error = 3.5803523944149736036031193965873e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = -14.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.51 y[1] (analytic) = 3.0814897176290961649866903686239 y[1] (numeric) = 3.081489717629096164986690368625 absolute error = 1.1e-30 relative error = 3.5697019974038466548898470755042e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4748 Order of pole (three term test) = -15.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.52 y[1] (analytic) = 3.0905480105294800674066380620896 y[1] (numeric) = 3.0905480105294800674066380620907 absolute error = 1.1e-30 relative error = 3.5592393201862778131802628076058e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.473 Order of pole (three term test) = -15.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.53 y[1] (analytic) = 3.0994972495375980012997920243597 y[1] (numeric) = 3.0994972495375980012997920243608 absolute error = 1.1e-30 relative error = 3.5489626589089722298646702197376e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.18 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4711 Order of pole (three term test) = -15.49 NO COMPLEX POLE (six term test) for Equation 1 bytes used=160068520, alloc=4586680, time=14.89 TOP MAIN SOLVE Loop x[1] = 9.54 y[1] (analytic) = 3.1083365397370068291872416978607 y[1] (numeric) = 3.1083365397370068291872416978618 absolute error = 1.1e-30 relative error = 3.5388703441136070590649989955627e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.469 Order of pole (three term test) = -15.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.55 y[1] (analytic) = 3.1170649972060526607988323192548 y[1] (numeric) = 3.1170649972060526607988323192559 absolute error = 1.1e-30 relative error = 3.5289607402667992070790332066306e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4667 Order of pole (three term test) = -15.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.56 y[1] (analytic) = 3.1256817491062622818632690265674 y[1] (numeric) = 3.1256817491062622818632690265686 absolute error = 1.2e-30 relative error = 3.8391624494180203365550841324601e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.21 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4642 Order of pole (three term test) = -16.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.57 y[1] (analytic) = 3.1341859337696262740665741904323 y[1] (numeric) = 3.1341859337696262740665741904335 absolute error = 1.2e-30 relative error = 3.8287454074452630560378418715083e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4615 Order of pole (three term test) = -16.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.58 y[1] (analytic) = 3.1425767007847650979396378145668 y[1] (numeric) = 3.142576700784765097939637814568 absolute error = 1.2e-30 relative error = 3.8185225509383292940242847170347e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4587 Order of pole (three term test) = -16.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.59 y[1] (analytic) = 3.1508532110819695221383770801613 y[1] (numeric) = 3.1508532110819695221383770801624 absolute error = 1.1e-30 relative error = 3.4911178855655788705008791032596e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4556 Order of pole (three term test) = -16.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.6 y[1] (analytic) = 3.1590146370171068951444438064041 y[1] (numeric) = 3.1590146370171068951444438064053 absolute error = 1.2e-30 relative error = 3.7986528645308764499264740802632e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4524 Order of pole (three term test) = -17.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.61 y[1] (analytic) = 3.1670601624543848688292314164094 y[1] (numeric) = 3.1670601624543848688292314164106 absolute error = 1.2e-30 relative error = 3.7890028557905034310421946629083e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.449 Order of pole (three term test) = -17.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.62 y[1] (analytic) = 3.1749889828479642975777945475861 y[1] (numeric) = 3.1749889828479642975777945475873 absolute error = 1.2e-30 relative error = 3.7795406739446393604057646062250e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4454 Order of pole (three term test) = -17.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.63 y[1] (analytic) = 3.1828003053224131517507794370578 y[1] (numeric) = 3.182800305322413151750779437059 absolute error = 1.2e-30 relative error = 3.7702648136400807082677581007111e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4417 Order of pole (three term test) = -17.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.64 y[1] (analytic) = 3.1904933487519934001600635934959 y[1] (numeric) = 3.1904933487519934001600635934971 absolute error = 1.2e-30 relative error = 3.7611738023819951633868156128590e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4377 Order of pole (three term test) = -18.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.65 y[1] (analytic) = 3.1980673438387729329359293732203 y[1] (numeric) = 3.1980673438387729329359293732215 absolute error = 1.2e-30 relative error = 3.7522662001219467985941532355528e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4336 Order of pole (three term test) = -18.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.66 y[1] (analytic) = 3.2055215331895547136585777952904 y[1] (numeric) = 3.2055215331895547136585777952916 absolute error = 1.2e-30 relative error = 3.7435405988553046583807558789463e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4293 Order of pole (three term test) = -18.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.67 y[1] (analytic) = 3.2128551713916154679028768572878 y[1] (numeric) = 3.2128551713916154679028768572891 absolute error = 1.3e-30 relative error = 4.0462452574135741427941840918111e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4249 Order of pole (three term test) = -18.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.68 y[1] (analytic) = 3.2200675250872463343906052403635 y[1] (numeric) = 3.2200675250872463343906052403647 absolute error = 1.2e-30 relative error = 3.7266299251519159367318422192976e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4203 Order of pole (three term test) = -18.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.69 y[1] (analytic) = 3.2271578730470880247471931814128 y[1] (numeric) = 3.227157873047088024747193181414 absolute error = 1.2e-30 relative error = 3.7184421934305864378686171734960e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4155 Order of pole (three term test) = -19.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.7 y[1] (analytic) = 3.2341255062422531584080972677162 y[1] (numeric) = 3.2341255062422531584080972677174 absolute error = 1.2e-30 relative error = 3.7104311433921007320541183579344e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4105 Order of pole (three term test) = -19.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.71 y[1] (analytic) = 3.2409697279152285605014202619804 y[1] (numeric) = 3.2409697279152285605014202619815 absolute error = 1.1e-30 relative error = 3.3940458947377487372264539710937e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4054 Order of pole (three term test) = -19.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.72 y[1] (analytic) = 3.2476898536495504325360727470818 y[1] (numeric) = 3.247689853649550432536072747083 absolute error = 1.2e-30 relative error = 3.6949341041648886644618309534316e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4001 Order of pole (three term test) = -19.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.73 y[1] (analytic) = 3.2542852114382454284364702230493 y[1] (numeric) = 3.2542852114382454284364702230504 absolute error = 1.1e-30 relative error = 3.3801585556597549757883499472812e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3946 Order of pole (three term test) = -19.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.74 y[1] (analytic) = 3.2607551417510307918731962264869 y[1] (numeric) = 3.260755141751030791873196226488 absolute error = 1.1e-30 relative error = 3.3734517072916374167350506316909e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.389 Order of pole (three term test) = -20.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.75 y[1] (analytic) = 3.2670989976002668349318983339047 y[1] (numeric) = 3.2670989976002668349318983339059 absolute error = 1.2e-30 relative error = 3.6729832823597264109288794767778e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3833 Order of pole (three term test) = -20.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.76 y[1] (analytic) = 3.2733161446056551629275103750451 y[1] (numeric) = 3.2733161446056551629275103750462 absolute error = 1.1e-30 relative error = 3.3605064448564586683019496528940e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3774 Order of pole (three term test) = -20.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.77 y[1] (analytic) = 3.2794059610576761755952344416098 y[1] (numeric) = 3.279405961057676175595234441611 absolute error = 1.2e-30 relative error = 3.6591993008787945478106531804508e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3713 Order of pole (three term test) = -20.66 NO COMPLEX POLE (six term test) for Equation 1 bytes used=164069328, alloc=4586680, time=15.27 TOP MAIN SOLVE Loop x[1] = 9.78 y[1] (analytic) = 3.2853678379797595009610280013021 y[1] (numeric) = 3.2853678379797595009610280013033 absolute error = 1.2e-30 relative error = 3.6525590411145705072679499303701e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3651 Order of pole (three term test) = -20.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.79 y[1] (analytic) = 3.2912011791891811449000175906641 y[1] (numeric) = 3.2912011791891811449000175906653 absolute error = 1.2e-30 relative error = 3.6460852274476623302973148936348e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3587 Order of pole (three term test) = -21.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.8 y[1] (analytic) = 3.2969054013566812667186307008181 y[1] (numeric) = 3.2969054013566812667186307008192 absolute error = 1.1e-30 relative error = 3.3364621245952293136604436518961e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3522 Order of pole (three term test) = -21.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.81 y[1] (analytic) = 3.3024799340647966190325689569673 y[1] (numeric) = 3.3024799340647966190325689569684 absolute error = 1.1e-30 relative error = 3.3308302304991911155976095832448e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3456 Order of pole (three term test) = -21.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.82 y[1] (analytic) = 3.3079242198649018187452449988707 y[1] (numeric) = 3.3079242198649018187452449988719 absolute error = 1.2e-30 relative error = 3.6276526311990572966326958783378e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3388 Order of pole (three term test) = -21.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.83 y[1] (analytic) = 3.3132377143329537450471194526374 y[1] (numeric) = 3.3132377143329537450471194526386 absolute error = 1.2e-30 relative error = 3.6218349042957008018267327233493e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3319 Order of pole (three term test) = -21.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.84 y[1] (analytic) = 3.3184198861239334900425915702971 y[1] (numeric) = 3.3184198861239334900425915702983 absolute error = 1.2e-30 relative error = 3.6161789079731407827383303893232e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3248 Order of pole (three term test) = -21.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.85 y[1] (analytic) = 3.3234702170249804178547489890459 y[1] (numeric) = 3.3234702170249804178547489890471 absolute error = 1.2e-30 relative error = 3.6106837782171717323618101869000e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3177 Order of pole (three term test) = -22.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.86 y[1] (analytic) = 3.3283882020072130188463443701828 y[1] (numeric) = 3.328388202007213018846344370184 absolute error = 1.2e-30 relative error = 3.6053486768049764142405654902254e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3104 Order of pole (three term test) = -22.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.87 y[1] (analytic) = 3.3331733492762313769147607213119 y[1] (numeric) = 3.333173349276231376914760721313 absolute error = 1.1e-30 relative error = 3.3001583918185806613417606113852e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3029 Order of pole (three term test) = -22.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.88 y[1] (analytic) = 3.3378251803212961996563211544049 y[1] (numeric) = 3.337825180321296199656321154406 absolute error = 1.1e-30 relative error = 3.2955590558943381808864463874907e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2954 Order of pole (three term test) = -22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.89 y[1] (analytic) = 3.3423432299631794935379090372785 y[1] (numeric) = 3.3423432299631794935379090372796 absolute error = 1.1e-30 relative error = 3.2911042472801873568216377204012e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2877 Order of pole (three term test) = -22.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.9 y[1] (analytic) = 3.3467270464006820990482568061945 y[1] (numeric) = 3.3467270464006820990482568061956 absolute error = 1.1e-30 relative error = 3.2867932901281011028031553202566e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2799 Order of pole (three term test) = -22.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.91 y[1] (analytic) = 3.3509761912558134341141527941132 y[1] (numeric) = 3.3509761912558134341141527941143 absolute error = 1.1e-30 relative error = 3.2826255312418781342341742688477e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.272 Order of pole (three term test) = -22.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.92 y[1] (analytic) = 3.3550902396176289278448741145988 y[1] (numeric) = 3.3550902396176289278448741146 absolute error = 1.2e-30 relative error = 3.5766549162527471615954105949122e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.264 Order of pole (three term test) = -23.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.93 y[1] (analytic) = 3.3590687800847207608980022311041 y[1] (numeric) = 3.3590687800847207608980022311053 absolute error = 1.2e-30 relative error = 3.5724186629180430097151388632078e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2559 Order of pole (three term test) = -23.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.94 y[1] (analytic) = 3.3629114148063576634279934623528 y[1] (numeric) = 3.362911414806357663427993462354 absolute error = 1.2e-30 relative error = 3.5683366344905582484926210144125e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2477 Order of pole (three term test) = -23.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.95 y[1] (analytic) = 3.36661775952226965667199261745 y[1] (numeric) = 3.3666177595222696566719926174512 absolute error = 1.2e-30 relative error = 3.5644082153546371003765336453467e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2394 Order of pole (three term test) = -23.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.96 y[1] (analytic) = 3.3701874436010737597318850201653 y[1] (numeric) = 3.3701874436010737597318850201664 absolute error = 1.1e-30 relative error = 3.2639134125567826150360407531990e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.231 Order of pole (three term test) = -23.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.97 y[1] (analytic) = 3.3736201100773368190139300327654 y[1] (numeric) = 3.3736201100773368190139300327666 absolute error = 1.2e-30 relative error = 3.5570098613518497706968754211786e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2225 Order of pole (three term test) = -23.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.98 y[1] (analytic) = 3.3769154156872717540739177042946 y[1] (numeric) = 3.3769154156872717540739177042958 absolute error = 1.2e-30 relative error = 3.5535388136329002917547960179373e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2139 Order of pole (three term test) = -23.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.99 y[1] (analytic) = 3.3800730309030636502730108000159 y[1] (numeric) = 3.380073030903063650273010800017 absolute error = 1.1e-30 relative error = 3.2543675534315597192490388781434e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2052 Order of pole (three term test) = -23.89 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) - cos ( x ); Iterations = 1000 Total Elapsed Time = 15 Seconds Elapsed Time(since restart) = 15 Seconds Time to Timeout = 2 Minutes 44 Seconds Percent Done = 100.1 % > quit bytes used=167751752, alloc=4586680, time=15.60