|\^/| 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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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 cos 1 $eq_no = 1 > array_tmp1[1] := cos(array_x[1]); > array_tmp1_g[1] := sin(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 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_tmp2[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 cos 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 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_tmp2[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 cos 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 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_tmp2[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 cos 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 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_tmp2[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 cos 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 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_tmp2[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 cos 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 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_tmp2[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_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] := cos(array_x[1]); array_tmp1_g[1] := sin(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[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]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[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]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[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]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[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]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[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]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[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(1.0 + sin(x)); > end; exact_soln_y := proc(x) return 1.0 + 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_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/cospostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = 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 := -5.0;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10000;"); > omniout_str(ALWAYS,"glob_display_interval := 0.1;"); > omniout_str(ALWAYS,"glob_max_minutes := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(1.0 + sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > 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_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_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_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -5.0; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 10000; > glob_display_interval := 0.1; > glob_max_minutes := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = cos ( 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,"2013-05-26T00:11:06-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"cos") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = 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,"cos diffeq.mxt") > ; > logitem_str(html_log_file,"cos 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_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/cospostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = 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 := -5.0;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10000;"); omniout_str(ALWAYS, "glob_display_interval := 0.1;"); omniout_str(ALWAYS, "glob_max_minutes := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(1.0 + sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; 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_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_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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := -5.0; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 10000; glob_display_interval := 0.1; glob_max_minutes := 10; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = cos ( 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, "2013-05-26T00:11:06-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "cos"); logitem_str(html_log_file, "diff ( y , x , 1 ) = 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, "cos diffeq.mxt"); logitem_str(html_log_file, "cos 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/cospostode.ode################# diff ( y , x , 1 ) = cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -5.0; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 10000; glob_display_interval := 0.1; glob_max_minutes := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(1.0 + 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 = 2.3777450611955943732797533891922e-183 estimated_step_error = 2.3777450611955943732797533891922e-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 = 1.5956777081256160619008740747256e-175 estimated_step_error = 1.5956777081256160619008740747256e-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 = 1.0708411947565045661970327052961e-167 estimated_step_error = 1.0708411947565045661970327052961e-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 = 7.1862937679176132330702885343963e-160 estimated_step_error = 7.1862937679176132330702885343963e-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 = 4.8226403227000255913195452206655e-152 estimated_step_error = 4.8226403227000255913195452206655e-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 = 3.2364194190356168085042457522636e-144 estimated_step_error = 3.2364194190356168085042457522636e-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 = 2.1719246871187506202952151683868e-136 estimated_step_error = 2.1719246871187506202952151683868e-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 = 1.4575544954631940368195334011604e-128 estimated_step_error = 1.4575544954631940368195334011604e-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 = 9.7814894993393649740462499302859e-121 estimated_step_error = 9.7814894993393649740462499302859e-121 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.5642556903639522743698069394296e-113 estimated_step_error = 6.5642556903639522743698069394296e-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 = 4.4052097781323668889876791239504e-105 estimated_step_error = 4.4052097781323668889876791239504e-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 = 2.9563028190094691990154760627172e-97 estimated_step_error = 2.9563028190094691990154760627172e-97 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.9839634875269747292572023413844e-89 estimated_step_error = 1.9839634875269747292572023413844e-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 = 1.3314452100654924958989130368116e-81 estimated_step_error = 1.3314452100654924958989130368116e-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 = 8.9355779140126794287549090660785e-74 estimated_step_error = 8.9355779140126794287549090660785e-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 = 5.9971013875699900220019585193844e-66 estimated_step_error = 5.9971013875699900220019585193844e-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 = 4.0253046264506033253741859410581e-58 estimated_step_error = 4.0253046264506033253741859410581e-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 = 2.7022941542008095516033119435620e-50 estimated_step_error = 2.7022941542008095516033119435620e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (analytic) = 1.958924274663138468893154406156 y[1] (numeric) = 1.958924274663138468893154406156 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 = 0.262 Order of pole (three term test) = -23.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.99 y[1] (analytic) = 1.9617129034267934979411460144111 y[1] (numeric) = 1.9617129034267934979411460144111 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 = 0.2538 Order of pole (three term test) = -23.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.98 y[1] (analytic) = 1.9644053617015305957417100779289 y[1] (numeric) = 1.9644053617015305957417100779289 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 = 0.2456 Order of pole (three term test) = -23.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.97 y[1] (analytic) = 1.9670013802437659963349767140779 y[1] (numeric) = 1.9670013802437659963349767140779 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 = 0.2373 Order of pole (three term test) = -23.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.96 y[1] (analytic) = 1.9695006994538088177549330230967 y[1] (numeric) = 1.9695006994538088177549330230967 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 = 0.2288 Order of pole (three term test) = -23.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.95 y[1] (analytic) = 1.9719030694018208147852650633774 y[1] (numeric) = 1.9719030694018208147852650633773 absolute error = 1e-31 relative error = 5.0712431838921535406739777612629e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2203 Order of pole (three term test) = -23.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.94 y[1] (analytic) = 1.9742082498528091545097085268232 y[1] (numeric) = 1.9742082498528091545097085268231 absolute error = 1e-31 relative error = 5.0653217565804260984277830335457e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2117 Order of pole (three term test) = -23.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.93 y[1] (analytic) = 1.9764160102906497154001803227491 y[1] (numeric) = 1.9764160102906497154001803227491 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 = 0.203 Order of pole (three term test) = -23.91 NO COMPLEX POLE (six term test) for Equation 1 bytes used=4000064, alloc=3079628, time=0.15 TOP MAIN SOLVE Loop x[1] = -4.92 y[1] (analytic) = 1.9785261299411385076328016063411 y[1] (numeric) = 1.9785261299411385076328016063411 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 = 0.1942 Order of pole (three term test) = -24.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.91 y[1] (analytic) = 1.9805383977940689095089901022697 y[1] (numeric) = 1.9805383977940689095089901022697 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 = 0.1854 Order of pole (three term test) = -24.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (analytic) = 1.9824526126243325122763772499183 y[1] (numeric) = 1.9824526126243325122763772499183 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 = 0.1765 Order of pole (three term test) = -24.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.89 y[1] (analytic) = 1.9842685830120414632826520572489 y[1] (numeric) = 1.9842685830120414632826520572489 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 = 0.1675 Order of pole (three term test) = -24.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.88 y[1] (analytic) = 1.9859861273616702952447848423184 y[1] (numeric) = 1.9859861273616702952447848423184 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 = 0.1584 Order of pole (three term test) = -24.37 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.87 y[1] (analytic) = 1.9876050739202153274666554112925 y[1] (numeric) = 1.9876050739202153274666554112925 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 = 0.1493 Order of pole (three term test) = -24.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.86 y[1] (analytic) = 1.9891252607943698230800966940429 y[1] (numeric) = 1.9891252607943698230800966940429 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 = 0.1401 Order of pole (three term test) = -24.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.85 y[1] (analytic) = 1.9905465359667131848079423162912 y[1] (numeric) = 1.9905465359667131848079423162912 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 = 0.1309 Order of pole (three term test) = -24.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.84 y[1] (analytic) = 1.9918687573109125703429927550405 y[1] (numeric) = 1.9918687573109125703429927550405 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 = 0.1216 Order of pole (three term test) = -24.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.83 y[1] (analytic) = 1.9930917926059354071940301512694 y[1] (numeric) = 1.9930917926059354071940301512694 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 = 0.1122 Order of pole (three term test) = -24.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.82 y[1] (analytic) = 1.9942155195492713857592409012983 y[1] (numeric) = 1.9942155195492713857592409012983 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 = 0.1028 Order of pole (three term test) = -24.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.81 y[1] (analytic) = 1.995239825769162608438756975404 y[1] (numeric) = 1.995239825769162608438756975404 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 = 0.0934 Order of pole (three term test) = -24.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.8 y[1] (analytic) = 1.9961646088358406717815964665036 y[1] (numeric) = 1.9961646088358406717815964665036 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 = 0.08394 Order of pole (three term test) = -24.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.79 y[1] (analytic) = 1.9969897762717695579681528787627 y[1] (numeric) = 1.9969897762717695579681528787627 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 = 0.07444 Order of pole (three term test) = -24.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.78 y[1] (analytic) = 1.9977152455608933113476206216477 y[1] (numeric) = 1.9977152455608933113476206216476 absolute error = 1e-31 relative error = 5.0057184186890089135139710878527e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06491 Order of pole (three term test) = -24.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.77 y[1] (analytic) = 1.9983409441568875752704093382995 y[1] (numeric) = 1.9983409441568875752704093382994 absolute error = 1e-31 relative error = 5.0041510830470733077738269445069e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05535 Order of pole (three term test) = -24.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.76 y[1] (analytic) = 1.9988668094904141640687400845694 y[1] (numeric) = 1.9988668094904141640687400845694 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 = 0.04578 Order of pole (three term test) = -24.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.75 y[1] (analytic) = 1.9992927889753779447342707555971 y[1] (numeric) = 1.999292788975377944734270755597 absolute error = 1e-31 relative error = 5.0017686529669936323667425758078e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03618 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.74 y[1] (analytic) = 1.9996188400141854026097970480728 y[1] (numeric) = 1.9996188400141854026097970480727 absolute error = 1e-31 relative error = 5.0009530816028215992927725888839e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02657 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.73 y[1] (analytic) = 1.9998449300020043652428419115577 y[1] (numeric) = 1.9998449300020043652428419115576 absolute error = 1e-31 relative error = 5.0003877050557001920560172246251e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01696 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.72 y[1] (analytic) = 1.9999710363300244584322978879616 y[1] (numeric) = 1.9999710363300244584322978879616 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 = 0.007329 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.71 y[1] (analytic) = 1.9999971463877179684252347125936 y[1] (numeric) = 1.9999971463877179684252347125935 absolute error = 1e-31 relative error = 5.0000071340408839722804225645299e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.999923257564100884179536541575 y[1] (numeric) = 1.9999232575641008841795365415749 absolute error = 1e-31 relative error = 5.0001918634517821144371667574917e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.69 y[1] (analytic) = 1.9997493772479939935891934069429 y[1] (numeric) = 1.9997493772479939935891934069428 absolute error = 1e-31 relative error = 5.0006266354045598136158498211902e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9994755228272840075628419497597 y[1] (numeric) = 1.9994755228272840075628419497596 absolute error = 1e-31 relative error = 5.0013115368673640350322282749130e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9991017216871847858425318492734 y[1] (numeric) = 1.9991017216871847858425318492733 absolute error = 1e-31 relative error = 5.0022467048651658728604137742610e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9986280112074988384386870978325 y[1] (numeric) = 1.9986280112074988384386870978324 absolute error = 1e-31 relative error = 5.0034323265380240905854002022477e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=8000884, alloc=4259060, time=0.31 x[1] = -4.65 y[1] (analytic) = 1.998054438758879376528836550896 y[1] (numeric) = 1.9980544387588793765288365508959 absolute error = 1e-31 relative error = 5.0048686392206839398734544271524e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9973810616980932866119089318828 y[1] (numeric) = 1.9973810616980932866119089318827 absolute error = 1e-31 relative error = 5.0065559305435693804450745180895e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9966079473622855016167293539807 y[1] (numeric) = 1.9966079473622855016167293539806 absolute error = 1e-31 relative error = 5.0084945385552424848456563611094e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9957351730622453425228268344515 y[1] (numeric) = 1.9957351730622453425228268344514 absolute error = 1e-31 relative error = 5.0106848518664195558183084028340e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9947628260746755038537793574031 y[1] (numeric) = 1.9947628260746755038537793574031 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.6 y[1] (analytic) = 1.9936910036334644561381046599088 y[1] (numeric) = 1.9936910036334644561381046599088 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.59 y[1] (analytic) = 1.9925198129199631380901776786878 y[1] (numeric) = 1.9925198129199631380901776786878 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.58 y[1] (analytic) = 1.9912493710522669108338538360973 y[1] (numeric) = 1.9912493710522669108338538360973 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.57 y[1] (analytic) = 1.9898798050735038459644441280651 y[1] (numeric) = 1.9898798050735038459644441280651 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.56 y[1] (analytic) = 1.9884112519391305186104760890381 y[1] (numeric) = 1.9884112519391305186104760890381 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.55 y[1] (analytic) = 1.9868438585032365759053476540251 y[1] (numeric) = 1.9868438585032365759053476540251 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.54 y[1] (analytic) = 1.9851777815038594504006139307825 y[1] (numeric) = 1.9851777815038594504006139307825 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.53 y[1] (analytic) = 1.983413187547310686937327855437 y[1] (numeric) = 1.9834131875473106869373278554369 absolute error = 1e-31 relative error = 5.0418138100442918050511844437544e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9815502530915154503296862467421 y[1] (numeric) = 1.981550253091515450329686246742 absolute error = 1e-31 relative error = 5.0465538203729634882570750985228e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9795891644283668798963291970477 y[1] (numeric) = 1.9795891644283668798963291970476 absolute error = 1e-31 relative error = 5.0515532109853890432691344775858e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9775301176650970553891350144986 y[1] (numeric) = 1.9775301176650970553891350144986 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.49 y[1] (analytic) = 1.9753733187046664372073936936592 y[1] (numeric) = 1.9753733187046664372073936936592 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.48 y[1] (analytic) = 1.9731189832251737419369954185327 y[1] (numeric) = 1.9731189832251737419369954185327 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.47 y[1] (analytic) = 1.9707673366582883122099217992716 y[1] (numeric) = 1.9707673366582883122099217992716 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.46 y[1] (analytic) = 1.9683186141667071376290809282464 y[1] (numeric) = 1.9683186141667071376290809282465 absolute error = 1e-31 relative error = 5.0804782965655823470218337484315e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9657730606206387810376080186917 y[1] (numeric) = 1.9657730606206387810376080186918 absolute error = 1e-31 relative error = 5.0870571991879749439782163352457e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9631309305733165617204080330778 y[1] (numeric) = 1.9631309305733165617204080330779 absolute error = 1e-31 relative error = 5.0939037454213920509827120066674e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9603924882355434441992145343005 y[1] (numeric) = 1.9603924882355434441992145343005 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.42 y[1] (analytic) = 1.9575580074492711781110727318389 y[1] (numeric) = 1.9575580074492711781110727318389 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.41 y[1] (analytic) = 1.9546277716602163312342415645362 y[1] (numeric) = 1.9546277716602163312342415645362 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.4 y[1] (analytic) = 1.9516020738895159540353923333804 y[1] (numeric) = 1.9516020738895159540353923333804 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.39 y[1] (analytic) = 1.9484812167044257101480289636141 y[1] (numeric) = 1.9484812167044257101480289636141 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.38 y[1] (analytic) = 1.9452655121880634029446639109382 y[1] (numeric) = 1.9452655121880634029446639109381 absolute error = 1e-31 relative error = 5.1406864190749221582649183925291e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=12002272, alloc=4324584, time=0.47 x[1] = -4.37 y[1] (analytic) = 1.9419552819082009238248788504083 y[1] (numeric) = 1.9419552819082009238248788504082 absolute error = 1e-31 relative error = 5.1494491624821640336446295069048e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.938550856885107742998434718885 y[1] (numeric) = 1.9385508568851077429984347188849 absolute error = 1e-31 relative error = 5.1584924710554915520202661814938e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9350525775584491583875557983414 y[1] (numeric) = 1.9350525775584491583875557983414 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.34 y[1] (analytic) = 1.9314607937532426127959129109888 y[1] (numeric) = 1.9314607937532426127959129109888 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.33 y[1] (analytic) = 1.927775864644875483684219186773 y[1] (numeric) = 1.9277758646448754836842191867729 absolute error = 1e-31 relative error = 5.1873250326443662023907392704245e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.923998158723187843744309098984 y[1] (numeric) = 1.9239981587231878437443090989839 absolute error = 1e-31 relative error = 5.1975101715462369097550678849057e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.31 y[1] (analytic) = 1.920128053755623783965712426991 y[1] (numeric) = 1.9201280537556237839657124269909 absolute error = 1e-31 relative error = 5.2079859884556990640262748958880e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9161659367494549840317093602846 y[1] (numeric) = 1.9161659367494549840317093602845 absolute error = 1e-31 relative error = 5.2187547060583892328965824080814e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.912112203913080307656346885248 y[1] (numeric) = 1.9121122039130803076563468852479 absolute error = 1e-31 relative error = 5.2298186160494660098514434769719e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9079672606164052928706325232994 y[1] (numeric) = 1.9079672606164052928706325232993 absolute error = 1e-31 relative error = 5.2411800801913701903259667064038e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9037315213503054992758598196613 y[1] (numeric) = 1.9037315213503054992758598196612 absolute error = 1e-31 relative error = 5.2528415314083044616053514487507e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.8994054096851777658955598188531 y[1] (numeric) = 1.899405409685177765895559818853 absolute error = 1e-31 relative error = 5.2648054749183207926837872684510e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.8949893582285835244657528284383 y[1] (numeric) = 1.8949893582285835244657528284382 absolute error = 1e-31 relative error = 5.2770744894039387604538382053203e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.8904838085819884037968743245822 y[1] (numeric) = 1.8904838085819884037968743245821 absolute error = 1e-31 relative error = 5.2896512282222542712435410913893e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.8858892112966024512108885972993 y[1] (numeric) = 1.8858892112966024512108885972992 absolute error = 1e-31 relative error = 5.3025384206555355847961602391149e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.8812060258283253869946467312212 y[1] (numeric) = 1.8812060258283253869946467312212 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.21 y[1] (analytic) = 1.8764347204918013973064980899522 y[1] (numeric) = 1.8764347204918013973064980899522 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.2 y[1] (analytic) = 1.8715757724135880600185770979088 y[1] (numeric) = 1.8715757724135880600185770979088 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.19 y[1] (analytic) = 1.8666296674844440865631553259225 y[1] (numeric) = 1.8666296674844440865631553259225 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.18 y[1] (analytic) = 1.8615969003107406509691141628009 y[1] (numeric) = 1.8615969003107406509691141628009 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.17 y[1] (analytic) = 1.8564779741650011649151440014129 y[1] (numeric) = 1.8564779741650011649151440014129 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.16 y[1] (analytic) = 1.8512734009355744447809479026467 y[1] (numeric) = 1.8512734009355744447809479026467 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.15 y[1] (analytic) = 1.8459837010754463033378057292122 y[1] (numeric) = 1.8459837010754463033378057292122 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.14 y[1] (analytic) = 1.8406094035501946848766728281409 y[1] (numeric) = 1.8406094035501946848766728281409 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.13 y[1] (analytic) = 1.8351510457850935482169298759564 y[1] (numeric) = 1.8351510457850935482169298759564 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.12 y[1] (analytic) = 1.8296091736113707871634030609722 y[1] (numeric) = 1.8296091736113707871634030609723 absolute error = 1e-31 relative error = 5.4656481527481182925268286618788e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.823984341211625562574823983696 y[1] (numeric) = 1.8239843412116255625748239836961 absolute error = 1e-31 relative error = 5.4825032068845826645859201433046e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.8182771110644105042650370243584 y[1] (numeric) = 1.8182771110644105042650370243585 absolute error = 1e-31 relative error = 5.4997117541374367510275810623965e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.8124880538879843244705827123527 y[1] (numeric) = 1.8124880538879843244705827123528 bytes used=16004740, alloc=4324584, time=0.63 absolute error = 1e-31 relative error = 5.5172777434581765213206126297831e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.8066177485832404675764376733801 y[1] (numeric) = 1.8066177485832404675764376733802 absolute error = 1e-31 relative error = 5.5352052241499646315526144876384e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.66 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] = -4.07 y[1] (analytic) = 1.8006667821758175031873792802757 y[1] (numeric) = 1.8006667821758175031873792802758 absolute error = 1e-31 relative error = 5.5534983479378683770878427074515e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.06 y[1] (analytic) = 1.7946357497573970514574266927463 y[1] (numeric) = 1.7946357497573970514574266927464 absolute error = 1e-31 relative error = 5.5721613711037589540856967547948e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.28 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] = -4.05 y[1] (analytic) = 1.7885252544261951108359071094194 y[1] (numeric) = 1.7885252544261951108359071094194 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 = 15.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.04 y[1] (analytic) = 1.7823359072266527390477822306665 y[1] (numeric) = 1.7823359072266527390477822306665 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 = 15.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.03 y[1] (analytic) = 1.7760683270883321181898793012325 y[1] (numeric) = 1.7760683270883321181898793012325 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.25 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] = -4.02 y[1] (analytic) = 1.7697231407640241142855973335445 y[1] (numeric) = 1.7697231407640241142855973335445 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.59 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] = -4.01 y[1] (analytic) = 1.7633009827670735204905561792977 y[1] (numeric) = 1.7633009827670735204905561792977 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.93 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 y[1] (analytic) = 1.7568024953079282513726390945118 y[1] (numeric) = 1.7568024953079282513726390945118 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 = 17.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.99 y[1] (analytic) = 1.7502283282299188332941252986201 y[1] (numeric) = 1.7502283282299188332941252986201 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 = 17.63 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] = -3.98 y[1] (analytic) = 1.7435791389442746128933574013766 y[1] (numeric) = 1.7435791389442746128933574013766 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 = 17.98 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] = -3.97 y[1] (analytic) = 1.7368555923643831819909425517513 y[1] (numeric) = 1.7368555923643831819909425517513 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 = 18.35 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] = -3.96 y[1] (analytic) = 1.7300583608392995929232130587317 y[1] (numeric) = 1.7300583608392995929232130587316 absolute error = 1e-31 relative error = 5.7801518297618127299743492282330e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.72 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] = -3.95 y[1] (analytic) = 1.7231881240865120133260043354428 y[1] (numeric) = 1.7231881240865120133260043354427 absolute error = 1e-31 relative error = 5.8031969117133688831298061025066e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.94 y[1] (analytic) = 1.7162455691239705437472433545408 y[1] (numeric) = 1.7162455691239705437472433545407 absolute error = 1e-31 relative error = 5.8266719984042471862142872707526e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.93 y[1] (analytic) = 1.7092313902013859951499438928516 y[1] (numeric) = 1.7092313902013859951499438928515 absolute error = 1e-31 relative error = 5.8505829329648424803604839697301e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.92 y[1] (analytic) = 1.7021462887308054963706074378206 y[1] (numeric) = 1.7021462887308054963706074378206 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 = 18.74 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] = -3.91 y[1] (analytic) = 1.6949909732164718739144304480765 y[1] (numeric) = 1.6949909732164718739144304480764 absolute error = 1e-31 relative error = 5.8997364340080606426504169852618e-30 % Correct digits = 32 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] = -3.9 y[1] (analytic) = 1.6877661591839738180908881253787 y[1] (numeric) = 1.6877661591839738180908881253786 absolute error = 1e-31 relative error = 5.9249914128121564662970719604804e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 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] = -3.89 y[1] (analytic) = 1.6804725691086939204140398081587 y[1] (numeric) = 1.6804725691086939204140398081586 absolute error = 1e-31 relative error = 5.9507070712281256637356430381436e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 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] = -3.88 y[1] (analytic) = 1.6731109323435617374041895193685 y[1] (numeric) = 1.6731109323435617374041895193685 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 = 17.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.87 y[1] (analytic) = 1.6656819850461191054243159231035 y[1] (numeric) = 1.6656819850461191054243159231035 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.86 y[1] (analytic) = 1.6581864701049049999590093452957 y[1] (numeric) = 1.6581864701049049999590093452957 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.61 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] = -3.85 y[1] (analytic) = 1.650625137065167300788642218662 y[1] (numeric) = 1.650625137065167300788642218662 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.28 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] = -3.84 y[1] (analytic) = 1.6429987420539088918203488788627 y[1] (numeric) = 1.6429987420539088918203488788627 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 = 15.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.83 y[1] (analytic) = 1.6353080477042755909033702386223 y[1] (numeric) = 1.6353080477042755909033702386222 absolute error = 1e-31 relative error = 6.1150558232979302685714448612639e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.63 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] = -3.82 y[1] (analytic) = 1.6275538230792934707727719568899 y[1] (numeric) = 1.6275538230792934707727719568898 absolute error = 1e-31 relative error = 6.1441900465572534531909953642409e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.31 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 bytes used=20005520, alloc=4324584, time=0.79 x[1] = -3.81 y[1] (analytic) = 1.6197368435949631973258897105178 y[1] (numeric) = 1.6197368435949631973258897105177 absolute error = 1e-31 relative error = 6.1738423988709572043621127898811e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.8 y[1] (analytic) = 1.6118578909427190757335860861189 y[1] (numeric) = 1.6118578909427190757335860861188 absolute error = 1e-31 relative error = 6.2040208731747134212984858482352e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.79 y[1] (analytic) = 1.6039177530112605584170907202327 y[1] (numeric) = 1.6039177530112605584170907202326 absolute error = 1e-31 relative error = 6.2347336583971294302549049626843e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.78 y[1] (analytic) = 1.5959172238077640316744858109002 y[1] (numeric) = 1.5959172238077640316744858109001 absolute error = 1e-31 relative error = 6.2659891445626433634644199183822e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.77 y[1] (analytic) = 1.5878571033784827597125177264744 y[1] (numeric) = 1.5878571033784827597125177264743 absolute error = 1e-31 relative error = 6.2977959280611618217141008793348e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.76 y[1] (analytic) = 1.579738197728742926023165037754 y[1] (numeric) = 1.5797381977287429260231650377538 absolute error = 2e-31 relative error = 1.2660325634180938433649142428847e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.75 y[1] (analytic) = 1.5715613187423437724341555733503 y[1] (numeric) = 1.5715613187423437724341555733501 absolute error = 2e-31 relative error = 1.2726197674555378951830234547707e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.74 y[1] (analytic) = 1.5633272841003698957523611196795 y[1] (numeric) = 1.5633272841003698957523611196793 absolute error = 2e-31 relative error = 1.2793226474972687288153697350808e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.73 y[1] (analytic) = 1.5550369171994238207027492321657 y[1] (numeric) = 1.5550369171994238207027492321656 absolute error = 1e-31 relative error = 6.4307154958158219377964995256535e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.72 y[1] (analytic) = 1.5466910470692870258374589670562 y[1] (numeric) = 1.5466910470692870258374589670561 absolute error = 1e-31 relative error = 6.4654153258003766031183124324093e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.71 y[1] (analytic) = 1.5382905082900176562437940432504 y[1] (numeric) = 1.5382905082900176562437940432502 absolute error = 2e-31 relative error = 1.3001445365630086360305503787793e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.7 y[1] (analytic) = 1.5298361409084932132107776257012 y[1] (numeric) = 1.529836140908493213210777625701 absolute error = 2e-31 relative error = 1.3073295541392426332892267738334e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.69 y[1] (analytic) = 1.5213287903544065665157545481247 y[1] (numeric) = 1.5213287903544065665157545481245 absolute error = 2e-31 relative error = 1.3146402097169822685539611821911e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.68 y[1] (analytic) = 1.512769307355723689659809225044 y[1] (numeric) = 1.5127693073557236896598092250439 absolute error = 1e-31 relative error = 6.6103932380011769549181948782446e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.67 y[1] (analytic) = 1.5041585478536115722080240589139 y[1] (numeric) = 1.5041585478536115722080240589138 absolute error = 1e-31 relative error = 6.6482353301583103575680661201057e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.66 y[1] (analytic) = 1.4954973729168448163724511464104 y[1] (numeric) = 1.4954973729168448163724511464102 absolute error = 2e-31 relative error = 1.3373477187052252983949685349721e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.65 y[1] (analytic) = 1.4867866486556994771068113882953 y[1] (numeric) = 1.4867866486556994771068113882952 absolute error = 1e-31 relative error = 6.7259145816527546094462981301637e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.64 y[1] (analytic) = 1.4780272461353427562571566388729 y[1] (numeric) = 1.4780272461353427562571566388728 absolute error = 1e-31 relative error = 6.7657751412549409418440470343120e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.63 y[1] (analytic) = 1.4692200412887272117269048145319 y[1] (numeric) = 1.4692200412887272117269048145318 absolute error = 1e-31 relative error = 6.8063324205872485904358889197117e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.62 y[1] (analytic) = 1.4603659148289981921627435407948 y[1] (numeric) = 1.4603659148289981921627435407947 absolute error = 1e-31 relative error = 6.8475988781010078474062724623123e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.61 y[1] (analytic) = 1.4514657521614232563449401863925 y[1] (numeric) = 1.4514657521614232563449401863924 absolute error = 1e-31 relative error = 6.8895872914043516367782635919596e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.6 y[1] (analytic) = 1.4425204432948523842667273474927 y[1] (numeric) = 1.4425204432948523842667273474926 absolute error = 1e-31 relative error = 6.9323107665351759884966837015420e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.59 y[1] (analytic) = 1.433530882752717833807872932044 y[1] (numeric) = 1.4335308827527178338078729320439 absolute error = 1e-31 relative error = 6.9757827475593957390188679164873e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.58 y[1] (analytic) = 1.4244979694835825429426009483438 y[1] (numeric) = 1.4244979694835825429426009483436 absolute error = 2e-31 relative error = 1.4040034053014844719404699420603e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.57 y[1] (analytic) = 1.4154226067712460225670994560663 y[1] (numeric) = 1.4154226067712460225670994560661 absolute error = 2e-31 relative error = 1.4130055507324750818147839640320e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.56 y[1] (analytic) = 1.4063057021444167292824214226859 y[1] (numeric) = 1.4063057021444167292824214226857 absolute error = 2e-31 relative error = 1.4221658896428306266803128618371e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.55 y[1] (analytic) = 1.397148167285959950820227423437 y[1] (numeric) = 1.3971481672859599508202274234367 absolute error = 3e-31 relative error = 2.1472311027882398527650304938284e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.54 y[1] (analytic) = 1.3879509179417302792472011004845 y[1] (numeric) = 1.3879509179417302792472011004843 absolute error = 2e-31 relative error = 1.4409731454811899211550297775891e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO 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=24006808, alloc=4324584, time=0.95 TOP MAIN SOLVE Loop x[1] = -3.53 y[1] (analytic) = 1.3787148738289977886248442540066 y[1] (numeric) = 1.3787148738289977886248442540064 absolute error = 2e-31 relative error = 1.4506262592537028785338636874779e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.52 y[1] (analytic) = 1.369440958544477074430574321433 y[1] (numeric) = 1.3694409585444770744305743214327 absolute error = 3e-31 relative error = 2.1906749475264545969147536512242e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.51 y[1] (analytic) = 1.3601300994719683517595399234174 y[1] (numeric) = 1.3601300994719683517595399234171 absolute error = 3e-31 relative error = 2.2056713553833300808943419143317e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.5 y[1] (analytic) = 1.3507832276896198481203688000436 y[1] (numeric) = 1.3507832276896198481203688000434 absolute error = 2e-31 relative error = 1.4806224707281869118240261821323e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.49 y[1] (analytic) = 1.3414012778768207645082874807375 y[1] (numeric) = 1.3414012778768207645082874807373 absolute error = 2e-31 relative error = 1.4909781532082732584417893476356e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.48 y[1] (analytic) = 1.3319851882207341153819164354428 y[1] (numeric) = 1.3319851882207341153819164354425 absolute error = 3e-31 relative error = 2.2522772974731049059890151985644e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.47 y[1] (analytic) = 1.3225359003224787941818539871573 y[1] (numeric) = 1.322535900322478794181853987157 absolute error = 3e-31 relative error = 2.2683694251842229485094556082917e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.46 y[1] (analytic) = 1.3130543591029702461063157759749 y[1] (numeric) = 1.3130543591029702461063157759747 absolute error = 2e-31 relative error = 1.5231661858739232919904908511474e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.45 y[1] (analytic) = 1.3035415127084291639980863662199 y[1] (numeric) = 1.3035415127084291639980863662197 absolute error = 2e-31 relative error = 1.5342817858132545894240957970724e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.44 y[1] (analytic) = 1.2939983124155676563944518105603 y[1] (numeric) = 1.2939983124155676563944518105601 absolute error = 2e-31 relative error = 1.5455970698033645100857626675555e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.43 y[1] (analytic) = 1.2844257125364623690442969145914 y[1] (numeric) = 1.2844257125364623690442969145912 absolute error = 2e-31 relative error = 1.5571161340661995326373142205480e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.42 y[1] (analytic) = 1.2748246703231240725009433576662 y[1] (numeric) = 1.274824670323124072500943357666 absolute error = 2e-31 relative error = 1.5688431880542984785198200974896e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.41 y[1] (analytic) = 1.2651961458717732587524443075741 y[1] (numeric) = 1.2651961458717732587524443075739 absolute error = 2e-31 relative error = 1.5807825581241523921376495051245e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.4 y[1] (analytic) = 1.2555411020268313192499024293637 y[1] (numeric) = 1.2555411020268313192499024293635 absolute error = 2e-31 relative error = 1.5929386913509896017938883917418e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.39 y[1] (analytic) = 1.2458605042846369051360013715579 y[1] (numeric) = 1.2458605042846369051360013715577 absolute error = 2e-31 relative error = 1.6053161594912136139100283917243e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.38 y[1] (analytic) = 1.2361553206968970979574917775896 y[1] (numeric) = 1.2361553206968970979574917775894 absolute error = 2e-31 relative error = 1.6179196630990323142062128426569e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.37 y[1] (analytic) = 1.2264265217738830456641034843086 y[1] (numeric) = 1.2264265217738830456641034843083 absolute error = 3e-31 relative error = 2.4461310537062176349204124927867e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.36 y[1] (analytic) = 1.2166750803873797442496139819055 y[1] (numeric) = 1.2166750803873797442496139819053 absolute error = 2e-31 relative error = 1.6438242487577010149044294936431e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.35 y[1] (analytic) = 1.2069019716733996699760341160255 y[1] (numeric) = 1.2069019716733996699760341160253 absolute error = 2e-31 relative error = 1.6571354152541072934102333134436e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.34 y[1] (analytic) = 1.1971081729346699907366169105927 y[1] (numeric) = 1.1971081729346699907366169105925 absolute error = 2e-31 relative error = 1.6706927955366539593483144592423e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.33 y[1] (analytic) = 1.187294663542903107755292824136 y[1] (numeric) = 1.1872946635429031077552928241357 absolute error = 3e-31 relative error = 2.5267527026929945066036971064197e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.32 y[1] (analytic) = 1.1774624248408603004869205523084 y[1] (numeric) = 1.1774624248408603004869205523082 absolute error = 2e-31 relative error = 1.6985680033656357243486038114125e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.31 y[1] (analytic) = 1.167612440044218268272249994317 y[1] (numeric) = 1.1676124400442182682722499943168 absolute error = 2e-31 relative error = 1.7128971321376626092544621975425e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.3 y[1] (analytic) = 1.1577456941432483820116542776025 y[1] (numeric) = 1.1577456941432483820116542776023 absolute error = 2e-31 relative error = 1.7274950881851771531481017532625e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.29 y[1] (analytic) = 1.1478631738043184778505297837426 y[1] (numeric) = 1.1478631738043184778505297837425 absolute error = 1e-31 relative error = 8.7118397281249011118826148732561e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.28 y[1] (analytic) = 1.1379658672712270426149140705852 y[1] (numeric) = 1.1379658672712270426149140705851 absolute error = 1e-31 relative error = 8.7876097935866846031082477587381e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.27 y[1] (analytic) = 1.1280547642663796574965568907536 y[1] (numeric) = 1.1280547642663796574965568907535 absolute error = 1e-31 relative error = 8.8648178410942758624083430641294e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=28008288, alloc=4390108, time=1.11 x[1] = -3.26 y[1] (analytic) = 1.1181308558918175822607231103361 y[1] (numeric) = 1.118130855891817582260723110336 absolute error = 1e-31 relative error = 8.9434970399989830285402269016876e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.25 y[1] (analytic) = 1.1081951345301083770358308425608 y[1] (numeric) = 1.1081951345301083770358308425607 absolute error = 1e-31 relative error = 9.0236815596922399169309039439051e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.24 y[1] (analytic) = 1.0982485937451084725401549594376 y[1] (numeric) = 1.0982485937451084725401549594375 absolute error = 1e-31 relative error = 9.1054066055293224421158072617601e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.23 y[1] (analytic) = 1.0882922281826076124058757285297 y[1] (numeric) = 1.0882922281826076124058757285296 absolute error = 1e-31 relative error = 9.1887084562751025064803856867190e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.22 y[1] (analytic) = 1.078327033470865103073444147916 y[1] (numeric) = 1.0783270334708651030734441479159 absolute error = 1e-31 relative error = 9.2736245031458595014763091746466e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.21 y[1] (analytic) = 1.0683540061210478175483883606769 y[1] (numeric) = 1.0683540061210478175483883606767 absolute error = 2e-31 relative error = 1.8720386581050493164624032052564e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.2 y[1] (analytic) = 1.0583741434275799091372174146191 y[1] (numeric) = 1.0583741434275799091372174146189 absolute error = 2e-31 relative error = 1.8896909116873673771178760922463e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.19 y[1] (analytic) = 1.0483884433684142001080071484512 y[1] (numeric) = 1.048388443368414200108007148451 absolute error = 2e-31 relative error = 1.9076898573720541930297837234879e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.18 y[1] (analytic) = 1.0383979045052352180536952467261 y[1] (numeric) = 1.038397904505235218053695246726 absolute error = 1e-31 relative error = 9.6302197419829093075232787051802e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.17 y[1] (analytic) = 1.0284035258836038595712852748967 y[1] (numeric) = 1.0284035258836038595712852748966 absolute error = 1e-31 relative error = 9.7238095244840826215855691609518e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.16 y[1] (analytic) = 1.0184063069330536667073792711874 y[1] (numeric) = 1.0184063069330536667073792711872 absolute error = 2e-31 relative error = 1.9638527239909097882265143425024e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.15 y[1] (analytic) = 1.0084072473671487064591415165711 y[1] (numeric) = 1.0084072473671487064591415165709 absolute error = 2e-31 relative error = 1.9833256903119266638062868103450e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.14 y[1] (analytic) = 0.99840734708351304745945856367556 y[1] (numeric) = 0.99840734708351304745945856367539 absolute error = 1.7e-31 relative error = 1.7027118289603305034756063611381e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001536 Order of pole (three term test) = -0.8929 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.13 y[1] (analytic) = 0.98840760606384183081531851688169 y[1] (numeric) = 0.98840760606384183081531851688153 absolute error = 1.6e-31 relative error = 1.6187653658106866646129561982977e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01118 Order of pole (three term test) = -0.8961 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.12 y[1] (analytic) = 0.97840902427390393390900189579811 y[1] (numeric) = 0.97840902427390393390900189579794 absolute error = 1.7e-31 relative error = 1.7375146363368863469138015822298e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02082 Order of pole (three term test) = -0.9041 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.11 y[1] (analytic) = 0.96841260156354622681237312729664 y[1] (numeric) = 0.96841260156354622681237312729647 absolute error = 1.7e-31 relative error = 1.7554501018008983123224637425672e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03044 Order of pole (three term test) = -0.917 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.1 y[1] (analytic) = 0.95841933756670942080530172840333 y[1] (numeric) = 0.95841933756670942080530172840316 absolute error = 1.7e-31 relative error = 1.7737538605137690132571626221782e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04006 Order of pole (three term test) = -0.9347 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.09 y[1] (analytic) = 0.94843023160146550733004148942538 y[1] (numeric) = 0.94843023160146550733004148942522 absolute error = 1.6e-31 relative error = 1.6869981013767673028661671689421e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04966 Order of pole (three term test) = -0.9572 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.08 y[1] (analytic) = 0.9384462825700867835543703628643 y[1] (numeric) = 0.93844628257008678355437036286413 absolute error = 1.7e-31 relative error = 1.8115048581622331175874130900427e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05924 Order of pole (three term test) = -0.9845 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.07 y[1] (analytic) = 0.9284684888591564575576592096811 y[1] (numeric) = 0.92846848885915645755765920968093 absolute error = 1.7e-31 relative error = 1.8309722089640896924655676031862e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0688 Order of pole (three term test) = -1.017 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.06 y[1] (analytic) = 0.91849784823973082199610991116428 y[1] (numeric) = 0.91849784823973082199610991116411 absolute error = 1.7e-31 relative error = 1.8508481029737749182882748114373e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07833 Order of pole (three term test) = -1.053 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.05 y[1] (analytic) = 0.90853535776756297994659841130358 y[1] (numeric) = 0.90853535776756297994659841130342 absolute error = 1.6e-31 relative error = 1.7610762050378443336114495956612e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08783 Order of pole (three term test) = -1.095 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.04 y[1] (analytic) = 0.89858201368339810047339168739121 y[1] (numeric) = 0.89858201368339810047339168739105 absolute error = 1.6e-31 relative error = 1.7805831583935264591357357824551e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09729 Order of pole (three term test) = -1.142 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.03 y[1] (analytic) = 0.88863881131335017430909496708274 y[1] (numeric) = 0.88863881131335017430909496708258 absolute error = 1.6e-31 relative error = 1.8005065496017492295164055529252e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1067 Order of pole (three term test) = -1.193 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.02 y[1] (analytic) = 0.87870674496937023189124200366089 y[1] (numeric) = 0.87870674496937023189124200366073 absolute error = 1.6e-31 relative error = 1.8208577653011784393554488851644e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1161 Order of pole (three term test) = -1.249 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.01 y[1] (analytic) = 0.86878680784981597684978187531515 y[1] (numeric) = 0.86878680784981597684978187531499 absolute error = 1.6e-31 relative error = 1.8416485903600255800951303781468e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1254 Order of pole (three term test) = -1.309 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3 y[1] (analytic) = 0.85887999194013277789925519719189 y[1] (numeric) = 0.85887999194013277789925519719173 absolute error = 1.6e-31 relative error = 1.8628912246351712925858474042321e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1347 Order of pole (three term test) = -1.374 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.99 y[1] (analytic) = 0.84898728791365595095370496438948 y[1] (numeric) = 0.84898728791365595095370496438932 absolute error = 1.6e-31 relative error = 1.8845983005610371967032402358408e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1439 Order of pole (three term test) = -1.444 NO COMPLEX POLE (six term test) for Equation 1 bytes used=32012896, alloc=4390108, time=1.28 TOP MAIN SOLVE Loop x[1] = -2.98 y[1] (analytic) = 0.83910968503254425115344604545867 y[1] (numeric) = 0.83910968503254425115344604545851 absolute error = 1.6e-31 relative error = 1.9067829016154725688271962436417e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1531 Order of pole (three term test) = -1.519 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.97 y[1] (analytic) = 0.82924817104885448137193550133203 y[1] (numeric) = 0.82924817104885448137193550133187 absolute error = 1.6e-31 relative error = 1.9294585817129734756590526685540e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1622 Order of pole (three term test) = -1.598 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.96 y[1] (analytic) = 0.81940373210576710965945549119865 y[1] (numeric) = 0.81940373210576710965945549119849 absolute error = 1.6e-31 relative error = 1.9526393855788235242991458318901e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1713 Order of pole (three term test) = -1.681 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.95 y[1] (analytic) = 0.80957735263897277297955268594262 y[1] (numeric) = 0.80957735263897277297955268594246 absolute error = 1.6e-31 relative error = 1.9763398701612549961909183693828e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1803 Order of pole (three term test) = -1.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.94 y[1] (analytic) = 0.79977001527822952850568290557688 y[1] (numeric) = 0.79977001527822952850568290557672 absolute error = 1.6e-31 relative error = 2.0005751271424959907192153342259e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1892 Order of pole (three term test) = -1.862 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.93 y[1] (analytic) = 0.78998270074910069667089596574089 y[1] (numeric) = 0.78998270074910069667089596574073 absolute error = 1.6e-31 relative error = 2.0253608066136142079514067832388e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.198 Order of pole (three term test) = -1.959 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.92 y[1] (analytic) = 0.78021638777488312210437090693542 y[1] (numeric) = 0.78021638777488312210437090693526 absolute error = 1.6e-31 relative error = 2.0507131419824139094891928362249e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2067 Order of pole (three term test) = -2.061 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.91 y[1] (analytic) = 0.77047205297873565954698177617301 y[1] (numeric) = 0.77047205297873565954698177617285 absolute error = 1.6e-31 relative error = 2.0766489761883142188819664407505e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2154 Order of pole (three term test) = -2.167 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.9 y[1] (analytic) = 0.76075067078601767181574308126042 y[1] (numeric) = 0.76075067078601767181574308126027 absolute error = 1.5e-31 relative error = 1.9717366774717137315698648699419e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.224 Order of pole (three term test) = -2.277 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.89 y[1] (analytic) = 0.75105321332684730588595415941951 y[1] (numeric) = 0.75105321332684730588595415941936 absolute error = 1.5e-31 relative error = 1.9971953696271878862323051399578e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2325 Order of pole (three term test) = -2.391 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.88 y[1] (analytic) = 0.74138065033888929118223307988232 y[1] (numeric) = 0.74138065033888929118223307988217 absolute error = 1.5e-31 relative error = 2.0232521570590512587715015246525e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2409 Order of pole (three term test) = -2.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.87 y[1] (analytic) = 0.73173394907038198121760107901286 y[1] (numeric) = 0.73173394907038198121760107901271 absolute error = 1.5e-31 relative error = 2.0499253887367773198567892989582e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2492 Order of pole (three term test) = -2.633 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.86 y[1] (analytic) = 0.72211407418341333579564309024676 y[1] (numeric) = 0.72211407418341333579564309024661 absolute error = 1.5e-31 relative error = 2.0772341291038284889493917742525e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2574 Order of pole (three term test) = -2.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.85 y[1] (analytic) = 0.71252198765745551609692107330828 y[1] (numeric) = 0.71252198765745551609692107330812 absolute error = 1.6e-31 relative error = 2.2455447378687757258580691471514e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2655 Order of pole (three term test) = -2.891 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.84 y[1] (analytic) = 0.70295864869316773910974393190269 y[1] (numeric) = 0.70295864869316773910974393190253 absolute error = 1.6e-31 relative error = 2.2760940532910052926458070140581e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2735 Order of pole (three term test) = -3.026 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.83 y[1] (analytic) = 0.6934250136164770110396869221319 y[1] (numeric) = 0.69342501361647701103968692213174 absolute error = 1.6e-31 relative error = 2.3073871991657572873666429996971e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2814 Order of pole (three term test) = -3.165 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.82 y[1] (analytic) = 0.68392203578294633154458714397543 y[1] (numeric) = 0.68392203578294633154458714397527 absolute error = 1.6e-31 relative error = 2.3394479433146759410116757235377e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2891 Order of pole (three term test) = -3.308 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.81 y[1] (analytic) = 0.67445066548243993189489871879367 y[1] (numeric) = 0.67445066548243993189489871879351 absolute error = 1.6e-31 relative error = 2.3723010175332946831137580414313e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2968 Order of pole (three term test) = -3.455 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.8 y[1] (analytic) = 0.66501184984409508045614624728758 y[1] (numeric) = 0.66501184984409508045614624728742 absolute error = 1.6e-31 relative error = 2.4059721648194733624384762992604e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3043 Order of pole (three term test) = -3.606 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.79 y[1] (analytic) = 0.65560653274160995823373840443771 y[1] (numeric) = 0.65560653274160995823373840443755 absolute error = 1.6e-31 relative error = 2.4404881893246750870459537229113e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3117 Order of pole (three term test) = -3.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.78 y[1] (analytic) = 0.64623565469885707561366068277266 y[1] (numeric) = 0.6462356546988570756136606827725 absolute error = 1.6e-31 relative error = 2.4758770092089592967043725912697e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.319 Order of pole (three term test) = -3.918 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.77 y[1] (analytic) = 0.63690015279583166887871799082754 y[1] (numeric) = 0.63690015279583166887871799082738 absolute error = 1.6e-31 relative error = 2.5121677125941985593731297905834e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3262 Order of pole (three term test) = -4.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.76 y[1] (analytic) = 0.62760096057494448158229940755025 y[1] (numeric) = 0.62760096057494448158229940755009 absolute error = 1.6e-31 relative error = 2.5493906168248084474868903856425e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3332 Order of pole (three term test) = -4.245 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.75 y[1] (analytic) = 0.61833900794766830142343862762222 y[1] (numeric) = 0.61833900794766830142343862762206 absolute error = 1.6e-31 relative error = 2.5875773312613205165007324292832e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3401 Order of pole (three term test) = -4.414 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.74 y[1] (analytic) = 0.60911522110154758789168829835973 y[1] (numeric) = 0.60911522110154758789168829835957 absolute error = 1.6e-31 relative error = 2.6267608238495468074499070536993e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3469 Order of pole (three term test) = -4.586 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.73 y[1] (analytic) = 0.59993052240758048964155204210555 y[1] (numeric) = 0.59993052240758048964155204210539 absolute error = 1.6e-31 relative error = 2.6669754917270117209003837536437e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3535 Order of pole (three term test) = -4.762 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.72 y[1] (analytic) = 0.59078583032798251331755532599258 y[1] (numeric) = 0.59078583032798251331755532599242 absolute error = 1.6e-31 relative error = 2.7082572361489086239211678415204e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.36 Order of pole (three term test) = -4.941 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.71 y[1] (analytic) = 0.58168205932434106738620931889141 y[1] (numeric) = 0.58168205932434106738620931889125 bytes used=36013568, alloc=4390108, time=1.44 absolute error = 1.6e-31 relative error = 2.7506435420382345634221038920160e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3663 Order of pole (three term test) = -5.123 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.7 y[1] (analytic) = 0.57262011976617006544394691414212 y[1] (numeric) = 0.57262011976617006544394691414196 absolute error = 1.6e-31 relative error = 2.7941735624891444981973221017357e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3725 Order of pole (three term test) = -5.308 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.69 y[1] (analytic) = 0.56360091783987373346449588123901 y[1] (numeric) = 0.56360091783987373346449588123885 absolute error = 1.6e-31 relative error = 2.8388882085791431765401128937389e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3785 Order of pole (three term test) = -5.496 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.68 y[1] (analytic) = 0.55462535545812872452910116807055 y[1] (numeric) = 0.55462535545812872452910116807039 absolute error = 1.6e-31 relative error = 2.8848302448747161936593607014022e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3844 Order of pole (three term test) = -5.687 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.67 y[1] (analytic) = 0.5456943301696936027526086788087 y[1] (numeric) = 0.54569433016969360275260867880855 absolute error = 1.5e-31 relative error = 2.7487916166062191765157670328756e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3902 Order of pole (three term test) = -5.881 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.66 y[1] (analytic) = 0.53680873506965471538185940620365 y[1] (numeric) = 0.5368087350696547153818594062035 absolute error = 1.5e-31 relative error = 2.7942913406678533872437569976247e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3957 Order of pole (three term test) = -6.078 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.65 y[1] (analytic) = 0.52796945871011742840438922160261 y[1] (numeric) = 0.52796945871011742840438922160246 absolute error = 1.5e-31 relative error = 2.8410734281195944544876897736441e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4011 Order of pole (three term test) = -6.278 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.64 y[1] (analytic) = 0.51917738501135165646944973046714 y[1] (numeric) = 0.51917738501135165646944973046699 absolute error = 1.5e-31 relative error = 2.8891859378027472320615395406634e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4064 Order of pole (three term test) = -6.481 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.63 y[1] (analytic) = 0.51043339317340057249431294638837 y[1] (numeric) = 0.51043339317340057249431294638822 absolute error = 1.5e-31 relative error = 2.9386792088080164904406152835225e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4115 Order of pole (three term test) = -6.686 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.62 y[1] (analytic) = 0.50173835758816133601123999000237 y[1] (numeric) = 0.50173835758816133601123999000221 absolute error = 1.6e-31 relative error = 3.1889130575767493806178561924717e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4164 Order of pole (three term test) = -6.893 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.61 y[1] (analytic) = 0.4930931477519466321090133004445 y[1] (numeric) = 0.49309314775194663210901330044435 absolute error = 1.5e-31 relative error = 3.0420215872774279555011199252902e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4212 Order of pole (three term test) = -7.103 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.6 y[1] (analytic) = 0.48449862817853576474227306479063 y[1] (numeric) = 0.48449862817853576474227306479048 absolute error = 1.5e-31 relative error = 3.0959839982194049252252131685056e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4258 Order of pole (three term test) = -7.315 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.59 y[1] (analytic) = 0.47595565831272399922686975112409 y[1] (numeric) = 0.47595565831272399922686975112393 absolute error = 1.6e-31 relative error = 3.3616576923826146897203992312226e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4302 Order of pole (three term test) = -7.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.58 y[1] (analytic) = 0.46746509244437879891494123552835 y[1] (numeric) = 0.4674650924443787989149412355282 absolute error = 1.5e-31 relative error = 3.2087957459165297426449108210741e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4345 Order of pole (three term test) = -7.747 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.57 y[1] (analytic) = 0.45902777962301155035442745125416 y[1] (numeric) = 0.45902777962301155035442745125401 absolute error = 1.5e-31 relative error = 3.2677760836869477476461733274741e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4386 Order of pole (three term test) = -7.966 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.56 y[1] (analytic) = 0.45064456357287331968931661686272 y[1] (numeric) = 0.45064456357287331968931661686257 absolute error = 1.5e-31 relative error = 3.3285656174512718240139291306148e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4425 Order of pole (three term test) = -8.186 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.55 y[1] (analytic) = 0.44231628260858313065422971823376 y[1] (numeric) = 0.44231628260858313065422971823361 absolute error = 1.5e-31 relative error = 3.3912384847188362516003977120663e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4462 Order of pole (three term test) = -8.409 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.54 y[1] (analytic) = 0.43404376955129720126523425201797 y[1] (numeric) = 0.43404376955129720126523425201782 absolute error = 1.5e-31 relative error = 3.4558726682119172872765108683277e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4497 Order of pole (three term test) = -8.634 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.53 y[1] (analytic) = 0.4258278516454275222133594125978 y[1] (numeric) = 0.42582785164542752221335941259765 absolute error = 1.5e-31 relative error = 3.5225502376227832224601171153527e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4531 Order of pole (three term test) = -8.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.52 y[1] (analytic) = 0.41766935047591810503357241770287 y[1] (numeric) = 0.41766935047591810503357241770272 absolute error = 1.5e-31 relative error = 3.5913576092926327777883372580596e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4563 Order of pole (three term test) = -9.088 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.51 y[1] (analytic) = 0.40956908188608717235546284497595 y[1] (numeric) = 0.40956908188608717235546284497579 absolute error = 1.6e-31 relative error = 3.9065448803701583452123343302274e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4593 Order of pole (three term test) = -9.317 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.5 y[1] (analytic) = 0.40152785589604350594814529781384 y[1] (numeric) = 0.40152785589604350594814529781368 absolute error = 1.6e-31 relative error = 3.9847795775699400403582499258986e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.19 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4621 Order of pole (three term test) = -9.548 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.49 y[1] (analytic) = 0.3935464766216851108565897602082 y[1] (numeric) = 0.39354647662168511085658976020805 absolute error = 1.5e-31 relative error = 3.8114939126794543686033574327260e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4647 Order of pole (three term test) = -9.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.48 y[1] (analytic) = 0.3856257421942882956954651193344 y[1] (numeric) = 0.38562574219428829569546511933425 absolute error = 1.5e-31 relative error = 3.8897818165994243201370295855222e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.79 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4672 Order of pole (three term test) = -10.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.47 y[1] (analytic) = 0.37776644468069521012545759514423 y[1] (numeric) = 0.37776644468069521012545759514407 absolute error = 1.6e-31 relative error = 4.2354211776336838735227274375645e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4695 Order of pole (three term test) = -10.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.46 y[1] (analytic) = 0.36996937000410782069180628138407 y[1] (numeric) = 0.36996937000410782069180628138391 absolute error = 1.6e-31 relative error = 4.3246823378439003758800780260452e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4715 Order of pole (three term test) = -10.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.45 y[1] (analytic) = 0.36223529786549624556146714436622 y[1] (numeric) = 0.36223529786549624556146714436606 absolute error = 1.6e-31 relative error = 4.4170184668036011421764216251944e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4734 Order of pole (three term test) = -10.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.44 y[1] (analytic) = 0.35456500166562930725993892701747 y[1] (numeric) = 0.35456500166562930725993892701731 absolute error = 1.6e-31 relative error = 4.5125717216412457217207054686752e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.06 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4751 Order of pole (three term test) = -10.96 NO COMPLEX POLE (six term test) for Equation 1 bytes used=40015204, alloc=4390108, time=1.61 TOP MAIN SOLVE Loop x[1] = -2.43 y[1] (analytic) = 0.3469592484277351002875029528101 y[1] (numeric) = 0.34695924842773510028750295280995 absolute error = 1.5e-31 relative error = 4.3232742945960726662359069702501e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4766 Order of pole (three term test) = -11.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.42 y[1] (analytic) = 0.33941879872079930749366589343977 y[1] (numeric) = 0.33941879872079930749366589343961 absolute error = 1.6e-31 relative error = 4.7139404359159712722374863274986e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4779 Order of pole (three term test) = -11.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.41 y[1] (analytic) = 0.33194440658350893531425019934528 y[1] (numeric) = 0.33194440658350893531425019934512 absolute error = 1.6e-31 relative error = 4.8200842317777687803250660944082e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.06 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4791 Order of pole (three term test) = -11.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.4 y[1] (analytic) = 0.32453681944884907343422847465872 y[1] (numeric) = 0.32453681944884907343422847465856 absolute error = 1.6e-31 relative error = 4.9301031627697311085545794518507e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.48 Order of pole (three term test) = -11.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.39 y[1] (analytic) = 0.31719677806936021913749968898695 y[1] (numeric) = 0.3171967780693602191374996889868 absolute error = 1.5e-31 relative error = 4.7289257133374812408654266513353e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4807 Order of pole (three term test) = -12.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.38 y[1] (analytic) = 0.3099250164430636405488868929798 y[1] (numeric) = 0.30992501644306364054888689297965 absolute error = 1.5e-31 relative error = 4.8398803594983923082207305164830e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.12 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -12.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.37 y[1] (analytic) = 0.30272226174006218617030357971077 y[1] (numeric) = 0.30272226174006218617030357971062 absolute error = 1.5e-31 relative error = 4.9550369747435405945141511210042e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -12.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.36 y[1] (analytic) = 0.2955892342298238805689692870673 y[1] (numeric) = 0.29558923422982388056896928706714 absolute error = 1.6e-31 relative error = 5.4129170305166879076820261880712e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.86 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.35 y[1] (analytic) = 0.28852664720915557779750881798679 y[1] (numeric) = 0.28852664720915557779750881798663 absolute error = 1.6e-31 relative error = 5.5454150092422677327787883324869e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.24 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.34 y[1] (analytic) = 0.28153520693087387512057131320599 y[1] (numeric) = 0.28153520693087387512057131320583 absolute error = 1.6e-31 relative error = 5.6831258066876604325319607696155e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4815 Order of pole (three term test) = -13.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.33 y[1] (analytic) = 0.27461561253318041989715580752458 y[1] (numeric) = 0.27461561253318041989715580752442 absolute error = 1.6e-31 relative error = 5.8263256966378052046402452693812e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4811 Order of pole (three term test) = -13.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.32 y[1] (analytic) = 0.26776855596974867202910132227533 y[1] (numeric) = 0.26776855596974867202910132227516 absolute error = 1.7e-31 relative error = 6.3487663584818323975315533241693e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4805 Order of pole (three term test) = -13.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.31 y[1] (analytic) = 0.26099472194052911324123580790174 y[1] (numeric) = 0.26099472194052911324123580790158 absolute error = 1.6e-31 relative error = 6.1303921707833611232010732491543e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.23 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4797 Order of pole (three term test) = -14.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.3 y[1] (analytic) = 0.2542947878232798226145937883565 y[1] (numeric) = 0.25429478782327982261459378835634 absolute error = 1.6e-31 relative error = 6.2919103206783282871033214241665e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.87 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4787 Order of pole (three term test) = -14.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.29 y[1] (analytic) = 0.24766942360582926525809172202635 y[1] (numeric) = 0.24766942360582926525809172202619 absolute error = 1.6e-31 relative error = 6.4602241839365335350386579513743e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4776 Order of pole (three term test) = -14.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.28 y[1] (analytic) = 0.24111929181907806778334642369908 y[1] (numeric) = 0.24111929181907806778334642369893 absolute error = 1.5e-31 relative error = 6.2209870835449906822462145539389e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.16 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4762 Order of pole (three term test) = -14.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.27 y[1] (analytic) = 0.23464504747074648034925739806528 y[1] (numeric) = 0.23464504747074648034925739806513 absolute error = 1.5e-31 relative error = 6.3926343904062456539158878321769e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.82 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4746 Order of pole (three term test) = -15.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.26 y[1] (analytic) = 0.22824733797987415047493836225968 y[1] (numeric) = 0.22824733797987415047493836225953 absolute error = 1.5e-31 relative error = 6.5718181568990014829080600996483e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4729 Order of pole (three term test) = -15.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.25 y[1] (analytic) = 0.22192680311207875858903332441224 y[1] (numeric) = 0.22192680311207875858903332441209 absolute error = 1.5e-31 relative error = 6.7589853004031302979176096892961e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4709 Order of pole (three term test) = -15.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.24 y[1] (analytic) = 0.2156840749155799893979113293955 y[1] (numeric) = 0.21568407491557998939791132939535 absolute error = 1.5e-31 relative error = 6.9546163785486192636639211942250e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.82 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4688 Order of pole (three term test) = -15.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.23 y[1] (analytic) = 0.20951977765799523662228987281146 y[1] (numeric) = 0.20951977765799523662228987281131 absolute error = 1.5e-31 relative error = 7.1592286740991597874459400900588e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4665 Order of pole (three term test) = -15.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.22 y[1] (analytic) = 0.20343452776391336147914325039084 y[1] (numeric) = 0.20343452776391336147914325039069 absolute error = 1.5e-31 relative error = 7.3733796149921826831761486715379e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.18 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.464 Order of pole (three term test) = -16.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.21 y[1] (analytic) = 0.19742893375325274748102595744403 y[1] (numeric) = 0.19742893375325274748102595744388 absolute error = 1.5e-31 relative error = 7.5976705718053684022689254998756e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.87 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4613 Order of pole (three term test) = -16.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.2 y[1] (analytic) = 0.19150359618040981569596308958388 y[1] (numeric) = 0.19150359618040981569596308958373 absolute error = 1.5e-31 relative error = 7.8327510810130939843138614453432e-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 = 0.4584 Order of pole (three term test) = -16.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.19 y[1] (analytic) = 0.185659107574204085565672354095 y[1] (numeric) = 0.18565910757420408556567235409485 absolute error = 1.5e-31 relative error = 8.0793235494815743634958364661261e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4553 Order of pole (three term test) = -16.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.18 y[1] (analytic) = 0.17989605237862578672599025391606 y[1] (numeric) = 0.17989605237862578672599025391591 absolute error = 1.5e-31 relative error = 8.3381485039091461710858496707916e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4521 Order of pole (three term test) = -17.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.17 y[1] (analytic) = 0.17421500689439194701894357605662 y[1] (numeric) = 0.17421500689439194701894357605647 absolute error = 1.5e-31 relative error = 8.6100504585652065266554418535816e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4487 Order of pole (three term test) = -17.36 NO COMPLEX POLE (six term test) for Equation 1 bytes used=44017712, alloc=4390108, time=1.77 TOP MAIN SOLVE Loop x[1] = -2.16 y[1] (analytic) = 0.16861653922131680103896187965368 y[1] (numeric) = 0.16861653922131680103896187965353 absolute error = 1.5e-31 relative error = 8.8959244859792932321952802647588e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4451 Order of pole (three term test) = -17.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.15 y[1] (analytic) = 0.16310120920150228212435186295621 y[1] (numeric) = 0.16310120920150228212435186295607 absolute error = 1.4e-31 relative error = 8.5836273492637292481281207723556e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4413 Order of pole (three term test) = -17.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.14 y[1] (analytic) = 0.15766956836335427869749336293109 y[1] (numeric) = 0.15766956836335427869749336293095 absolute error = 1.4e-31 relative error = 8.8793291852848721483350159379069e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4373 Order of pole (three term test) = -18.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.13 y[1] (analytic) = 0.1523221598664302532814700036841 y[1] (numeric) = 0.15232215986643025328147000368396 absolute error = 1.4e-31 relative error = 9.1910461434347156412231607493080e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4332 Order of pole (three term test) = -18.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.12 y[1] (analytic) = 0.14705951844712373938527266634585 y[1] (numeric) = 0.1470595184471237393852726663457 absolute error = 1.5e-31 relative error = 1.0199951800735260191086066849174e-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 = 0.4289 Order of pole (three term test) = -18.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.11 y[1] (analytic) = 0.14188217036519114776262449168932 y[1] (numeric) = 0.14188217036519114776262449168917 absolute error = 1.5e-31 relative error = 1.0572152907861102950823459771473e-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 = 0.4244 Order of pole (three term test) = -18.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.1 y[1] (analytic) = 0.13679063335112622931924068673098 y[1] (numeric) = 0.13679063335112622931924068673083 absolute error = 1.5e-31 relative error = 1.0965663095876367975867029179032e-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 = 0.4198 Order of pole (three term test) = -18.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.09 y[1] (analytic) = 0.13178541655438745717837794127249 y[1] (numeric) = 0.13178541655438745717837794127235 absolute error = 1.4e-31 relative error = 1.0623330233373918743434014589414e-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 = 0.415 Order of pole (three term test) = -19.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.08 y[1] (analytic) = 0.12686702049248350512332319497538 y[1] (numeric) = 0.12686702049248350512332319497524 absolute error = 1.4e-31 relative error = 1.1035176790353848105133969695524e-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 = 0.41 Order of pole (three term test) = -19.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.07 y[1] (analytic) = 0.12203593700092191382654887955616 y[1] (numeric) = 0.12203593700092191382654887955602 absolute error = 1.4e-31 relative error = 1.1472030570711509154866976815238e-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 = 0.4049 Order of pole (three term test) = -19.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.06 y[1] (analytic) = 0.1172926491840259499572024148001 y[1] (numeric) = 0.11729264918402594995720241479996 absolute error = 1.4e-31 relative error = 1.1935956854410153199106194611632e-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 = 0.3996 Order of pole (three term test) = -19.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.05 y[1] (analytic) = 0.11263763136662457644003339531966 y[1] (numeric) = 0.11263763136662457644003339531952 absolute error = 1.4e-31 relative error = 1.2429238639111076905228984557662e-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 = 0.3941 Order of pole (three term test) = -19.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.04 y[1] (analytic) = 0.1080713490466203648284743514158 y[1] (numeric) = 0.10807134904662036482847435141565 absolute error = 1.5e-31 relative error = 1.3879719400494597488850523711685e-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 = 0.3885 Order of pole (three term test) = -20.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.03 y[1] (analytic) = 0.10359425884844009296111116803243 y[1] (numeric) = 0.10359425884844009296111116803228 absolute error = 1.5e-31 relative error = 1.4479566885984693526339265555900e-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 = 0.3827 Order of pole (three term test) = -20.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.02 y[1] (analytic) = 0.09920680847737268280298647544629 y[1] (numeric) = 0.09920680847737268280298647544614 absolute error = 1.50e-31 relative error = 1.5119930003011068057640147675423e-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 = 0.3768 Order of pole (three term test) = -20.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.01 y[1] (analytic) = 0.09490943667479904463990028972628 y[1] (numeric) = 0.094909436674799044639900289726133 absolute error = 1.47e-31 relative error = 1.5488449320765210272602647768556e-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 = 0.3707 Order of pole (three term test) = -20.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = 0.09070257317431830460398013408826 y[1] (numeric) = 0.090702573174318304603980134088108 absolute error = 1.52e-31 relative error = 1.6758069223447076683619191950769e-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 = 0.3645 Order of pole (three term test) = -20.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (analytic) = 0.08658663865877480287120672894239 y[1] (numeric) = 0.08658663865877480287120672894224 absolute error = 1.50e-31 relative error = 1.7323689003695814954591467160733e-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 = 0.3581 Order of pole (three term test) = -21.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (analytic) = 0.082562044718190159795264782598 y[1] (numeric) = 0.082562044718190159795264782597857 absolute error = 1.43e-31 relative error = 1.7320307471563150850467584793062e-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 = 0.3516 Order of pole (three term test) = -21.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (analytic) = 0.07862919380860461673604900284683 y[1] (numeric) = 0.078629193808604616736049002846682 absolute error = 1.48e-31 relative error = 1.8822525429963640078306728224144e-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 = 0.3449 Order of pole (three term test) = -21.39 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (analytic) = 0.07478847921183176741444371050997 y[1] (numeric) = 0.074788479211831767414443710509826 absolute error = 1.44e-31 relative error = 1.9254302469787185770855050620065e-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 = 0.3381 Order of pole (three term test) = -21.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (analytic) = 0.07104028499613070428670296490852 y[1] (numeric) = 0.07104028499613070428670296490837 absolute error = 1.50e-31 relative error = 2.1114780157226274195684391178497e-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 = 0.3312 Order of pole (three term test) = -21.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (analytic) = 0.0673849859777995126910206611343 y[1] (numeric) = 0.067384985977799512691020661134156 absolute error = 1.44e-31 relative error = 2.1369745487138911974892239568577e-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 = 0.3241 Order of pole (three term test) = -21.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (analytic) = 0.06382294768369395338487062725122 y[1] (numeric) = 0.063822947683693953384870627251072 absolute error = 1.48e-31 relative error = 2.3189151452779473934487628147521e-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 = 0.317 Order of pole (three term test) = -22.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.92 y[1] (analytic) = 0.06035452631467508157362866031297 y[1] (numeric) = 0.060354526314675081573628660312823 absolute error = 1.47e-31 relative error = 2.4356085446446001834648399781034e-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 = 0.3096 Order of pole (three term test) = -22.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (analytic) = 0.05698006870998945763811342305179 y[1] (numeric) = 0.056980068709989457638113423051639 absolute error = 1.51e-31 relative error = 2.6500494544599845881857702480037e-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 = 0.3022 Order of pole (three term test) = -22.37 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = 0.05369991231258551151029038836504 y[1] (numeric) = 0.053699912312585511510290388364896 absolute error = 1.44e-31 relative error = 2.6815686245776436251227267076692e-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 = 0.2946 Order of pole (three term test) = -22.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (analytic) = 0.05051438513536952903179832786168 y[1] (numeric) = 0.050514385135369529031798327861532 bytes used=48018500, alloc=4390108, time=1.92 absolute error = 1.48e-31 relative error = 2.9298584869119249199394481066984e-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 = 0.287 Order of pole (three term test) = -22.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (analytic) = 0.04742380572840463466854257418487 y[1] (numeric) = 0.047423805728404634668542574184729 absolute error = 1.41e-31 relative error = 2.9731903172745078794418520886886e-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 = 0.2792 Order of pole (three term test) = -22.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (analytic) = 0.04442848314705605065574950782737 y[1] (numeric) = 0.04442848314705605065574950782722 absolute error = 1.50e-31 relative error = 3.3762124964633054001757758650020e-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 = 0.2713 Order of pole (three term test) = -22.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.86 y[1] (analytic) = 0.0415287169210858180210222340968 y[1] (numeric) = 0.041528716921085818021022234096656 absolute error = 1.44e-31 relative error = 3.4674801119821100316063805471796e-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 = 0.2633 Order of pole (three term test) = -23.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (analytic) = 0.03872479702470006998754083136387 y[1] (numeric) = 0.038724797024700069987540831363725 absolute error = 1.45e-31 relative error = 3.7443708202657273756691574834066e-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 = 0.2551 Order of pole (three term test) = -23.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (analytic) = 0.03601700384755185300510632827288 y[1] (numeric) = 0.036017003847551853005106328272732 absolute error = 1.48e-31 relative error = 4.1091702304399163050081973338986e-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 = 0.2469 Order of pole (three term test) = -23.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (analytic) = 0.03340560816670239510276107025719 y[1] (numeric) = 0.033405608166702395102761070257042 absolute error = 1.48e-31 relative error = 4.4303938207453891823573732713770e-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 = 0.2386 Order of pole (three term test) = -23.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (analytic) = 0.03089087111954362541278468150195 y[1] (numeric) = 0.030890871119543625412784681501798 absolute error = 1.52e-31 relative error = 4.9205475433755140037624600887592e-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 = 0.2302 Order of pole (three term test) = -23.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (analytic) = 0.02847304417768465259154873090962 y[1] (numeric) = 0.028473044177684652591548730909477 absolute error = 1.43e-31 relative error = 5.0222940373925397211938396249093e-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 = 0.2217 Order of pole (three term test) = -23.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = 0.02615236912180481346762682115664 y[1] (numeric) = 0.026152369121804813467626821156495 absolute error = 1.45e-31 relative error = 5.5444307674253772034793828192594e-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 = 0.2131 Order of pole (three term test) = -23.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (analytic) = 0.02392907801747580659133956689138 y[1] (numeric) = 0.023929078017475806591339566891237 absolute error = 1.43e-31 relative error = 5.9759928859592795064546349222605e-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 = 0.2044 Order of pole (three term test) = -23.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (analytic) = 0.0218033931919553284522313526944 y[1] (numeric) = 0.021803393191955328452231352694257 absolute error = 1.43e-31 relative error = 6.5586121729328754544701879836149e-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 = 0.1956 Order of pole (three term test) = -24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (analytic) = 0.01977552721195453298151855110158 y[1] (numeric) = 0.019775527211954532981518551101428 absolute error = 1.52e-31 relative error = 7.6862678992504562353019399184256e-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 = 0.1868 Order of pole (three term test) = -24.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (analytic) = 0.01784568286238153757503190054404 y[1] (numeric) = 0.017845682862381537575031900543896 absolute error = 1.44e-31 relative error = 8.0691784736100005010096445660927e-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 = 0.1779 Order of pole (three term test) = -24.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (analytic) = 0.01601405312606310126833706303201 y[1] (numeric) = 0.016014053126063101268337063031867 absolute error = 1.43e-31 relative error = 8.9296569003674308981914643995902e-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 = 0.1689 Order of pole (three term test) = -24.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (analytic) = 0.01428082116444650287931730433445 y[1] (numeric) = 0.014280821164446502879317304334303 absolute error = 1.47e-31 relative error = 1.0293525722874454667207106236044e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1599 Order of pole (three term test) = -24.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (analytic) = 0.01264616029928354891432232377794 y[1] (numeric) = 0.012646160299283548914322323777788 absolute error = 1.52e-31 relative error = 1.2019458586857494930995926112849e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1507 Order of pole (three term test) = -24.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (analytic) = 0.01111023399529854282182934291452 y[1] (numeric) = 0.011110233995298542821829342914377 absolute error = 1.43e-31 relative error = 1.2871016043452597917185174179557e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1416 Order of pole (three term test) = -24.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (analytic) = 0.00967319584384194878224777613887 y[1] (numeric) = 0.0096731958438419487822477761387189 absolute error = 1.511e-31 relative error = 1.5620483906173753314453185203331e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1323 Order of pole (three term test) = -24.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = 0.00833518954753138465386660135212 y[1] (numeric) = 0.0083351895475313846538666013519769 absolute error = 1.431e-31 relative error = 1.7168175862585107305627452056248e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.123 Order of pole (three term test) = -24.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (analytic) = 0.00709634890588147996285070605441 y[1] (numeric) = 0.0070963489058814799628507060542598 absolute error = 1.502e-31 relative error = 2.1165813856124476899349756061856e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1137 Order of pole (three term test) = -24.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (analytic) = 0.00595679780192403593951213080643 y[1] (numeric) = 0.0059567978019240359395121308062817 absolute error = 1.483e-31 relative error = 2.4895926457684923055129263311554e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1043 Order of pole (three term test) = -24.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (analytic) = 0.00491665018981982557370275346576 y[1] (numeric) = 0.0049166501898198255737027534656171 absolute error = 1.429e-31 relative error = 2.9064504181298421876639421083895e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09491 Order of pole (three term test) = -24.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (analytic) = 0.00397601008346327249899940938704 y[1] (numeric) = 0.0039760100834632724989994093868921 absolute error = 1.479e-31 relative error = 3.7198094797378597509256238010311e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08545 Order of pole (three term test) = -24.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (analytic) = 0.00313497154608114822829695979781 y[1] (numeric) = 0.0031349715460811482282969597976612 absolute error = 1.488e-31 relative error = 4.7464545630727181156733307404651e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07595 Order of pole (three term test) = -24.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (analytic) = 0.00239361868082632786241802563206 y[1] (numeric) = 0.0023936186808263278624180256319144 absolute error = 1.456e-31 relative error = 6.0828402270714145820978052930377e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06643 Order of pole (three term test) = -24.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (analytic) = 0.0017520256223675448883300150669 y[1] (numeric) = 0.00175202562236754488833001506675 absolute error = 1.500e-31 relative error = 8.5615186264971515310914559592536e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05688 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (analytic) = 0.0012102565294759860844811087532 y[1] (numeric) = 0.0012102565294759860844811087530563 absolute error = 1.437e-31 relative error = 1.1873515779519807668049941976282e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04731 Order of pole (three term test) = -24.98 NO COMPLEX POLE (six term test) for Equation 1 bytes used=52019580, alloc=4390108, time=2.09 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (analytic) = 0.0007683655786094678675868521557 y[1] (numeric) = 0.00076836557860946786758685215554899 absolute error = 1.5101e-31 relative error = 1.9653405124327265332096577371725e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03771 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = 0.00042639695849483565788617445377 y[1] (numeric) = 0.0004263969584948356578861744536184 absolute error = 1.5160e-31 relative error = 3.5553724523538344133991427552887e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02811 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (analytic) = 0.00018438486570912801841565625449 y[1] (numeric) = 0.00018438486570912801841565625434113 absolute error = 1.4887e-31 relative error = 8.0738730604303688142595787360795e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01849 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (analytic) = 4.235350125994744820576774828e-05 y[1] (numeric) = 4.2353501259947448205767748135080e-05 absolute error = 1.44920e-31 relative error = 3.4216769733048467989687601607867e-25 % Correct digits = 27 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008862 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (analytic) = 3.1706816537978947007617667e-07 y[1] (numeric) = 3.170681653797894700761765255680e-07 absolute error = 1.444320e-31 relative error = 4.5552349863631680539630099569782e-23 % Correct digits = 25 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 5.827977003370425482997658652e-05 y[1] (numeric) = 5.8279770033704254829976586367699e-05 absolute error = 1.52301e-31 relative error = 2.6132738669339558417670424465391e-25 % Correct digits = 27 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.00021623581064303610238865236553 y[1] (numeric) = 0.00021623581064303610238865236537956 absolute error = 1.5044e-31 relative error = 6.9572195073806539467798799689876e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = 0.00047416939452094399403646155997 y[1] (numeric) = 0.00047416939452094399403646155981819 absolute error = 1.5181e-31 relative error = 3.2015984530881521099341581118039e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = 0.00083205472852398407573493129102 y[1] (numeric) = 0.00083205472852398407573493129087576 absolute error = 1.4424e-31 relative error = 1.7335398148133024518855300139803e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = 0.00128985602441699282768760588315 y[1] (numeric) = 0.001289856024416992827687605883004 absolute error = 1.460e-31 relative error = 1.1319092769752432073831674781561e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = 0.00184752750245188075726213516329 y[1] (numeric) = 0.0018475275024518807572621351631404 absolute error = 1.496e-31 relative error = 8.0973084190337439100389474628533e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (analytic) = 0.00250501339594556905827662885851 y[1] (numeric) = 0.0025050133959455690582766288583653 absolute error = 1.447e-31 relative error = 5.7764162153464251471761220685957e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.49 y[1] (analytic) = 0.0032622479568566114467992829563 y[1] (numeric) = 0.0032622479568566114467992829561541 absolute error = 1.459e-31 relative error = 4.4723761629874437982152880983915e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.48 y[1] (analytic) = 0.00411915546235994351592486743731 y[1] (numeric) = 0.0041191554623599435159248674371665 absolute error = 1.435e-31 relative error = 3.4837238193915139491127588296031e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.47 y[1] (analytic) = 0.00507565022241910214007153726443 y[1] (numeric) = 0.0050756502224191021400715372642864 absolute error = 1.436e-31 relative error = 2.8291941664088685641073188708388e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.46 y[1] (analytic) = 0.00613163658835515771316769874997 y[1] (numeric) = 0.0061316365883551577131676987498222 absolute error = 1.478e-31 relative error = 2.4104494431501866248672770892381e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45 y[1] (analytic) = 0.00728700896241150233464586567699 y[1] (numeric) = 0.0072870089624115023346458656768398 absolute error = 1.502e-31 relative error = 2.0612023503027785106589609797144e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.44 y[1] (analytic) = 0.00854165180831353747239553604202 y[1] (numeric) = 0.0085416518083135374723955360418692 absolute error = 1.508e-31 relative error = 1.7654664856887198580218840232467e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.43 y[1] (analytic) = 0.00989543966282220514270850451817 y[1] (numeric) = 0.0098954396628222051427085045180232 absolute error = 1.468e-31 relative error = 1.4835116478102222896361962060405e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.42 y[1] (analytic) = 0.0113482371482802072637265266643 y[1] (numeric) = 0.011348237148280207263726526664154 absolute error = 1.46e-31 relative error = 1.2865434348287820240096818961229e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.41 y[1] (analytic) = 0.01289989898614965857091113805776 y[1] (numeric) = 0.012899898986149658570911138057615 absolute error = 1.45e-31 relative error = 1.1240398095805506029604305808478e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.4 y[1] (analytic) = 0.0145502700115398193405254211939 y[1] (numeric) = 0.014550270011539819340525421193756 absolute error = 1.44e-31 relative error = 9.8967235581053546137867040792142e-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] = -1.39 y[1] (analytic) = 0.01629918518872345515996177555709 y[1] (numeric) = 0.016299185188723455159961775556945 absolute error = 1.45e-31 relative error = 8.8961502259829428115837862911339e-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] = -1.38 y[1] (analytic) = 0.01814646962764027212186891479395 y[1] (numeric) = 0.018146469627640272121868914793806 absolute error = 1.44e-31 relative error = 7.9354278245208982978591121637654e-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] = -1.37 y[1] (analytic) = 0.02009193860138577711231149510807 y[1] (numeric) = 0.020091938601385777112311495107922 absolute error = 1.48e-31 relative error = 7.3661383770002250569805018629405e-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] = -1.36 y[1] (analytic) = 0.02213539756468381432150756057337 y[1] (numeric) = 0.022135397564683814321507560573224 absolute error = 1.46e-31 relative error = 6.5957703977694736353111933863721e-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] = -1.35 y[1] (analytic) = 0.02427664217334093073888646073478 y[1] (numeric) = 0.024276642173340930738886460734638 absolute error = 1.42e-31 relative error = 5.8492438528395577291983312203057e-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] = -1.34 y[1] (analytic) = 0.02651545830468062521212965191045 y[1] (numeric) = 0.026515458304680625212129651910302 absolute error = 1.48e-31 relative error = 5.5816497040850464828580209942117e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=56020752, alloc=4390108, time=2.25 TOP MAIN SOLVE Loop x[1] = -1.33 y[1] (analytic) = 0.0288516220789554376623169622362 y[1] (numeric) = 0.028851622078955437662316962236058 absolute error = 1.42e-31 relative error = 4.9217336762349916942451976776188e-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] = -1.32 y[1] (analytic) = 0.03128489988173473726410015402723 y[1] (numeric) = 0.031284899881734737264100154027079 absolute error = 1.51e-31 relative error = 4.8266096605972932511905509893627e-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] = -1.31 y[1] (analytic) = 0.0338150483872659708307421940625 y[1] (numeric) = 0.033815048387265970830742194062354 absolute error = 1.46e-31 relative error = 4.3176043496356639764435446922450e-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] = -1.3 y[1] (analytic) = 0.03644181458280703529865136996045 y[1] (numeric) = 0.036441814582807035298651369960298 absolute error = 1.52e-31 relative error = 4.1710326925298724792600539495778e-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] = -1.29 y[1] (analytic) = 0.03916493579392734109443870871463 y[1] (numeric) = 0.03916493579392734109443870871448 absolute error = 1.50e-31 relative error = 3.8299564893773685027495879603746e-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] = -1.28 y[1] (analytic) = 0.04198413971077503629924614083971 y[1] (numeric) = 0.041984139710775036299246140839568 absolute error = 1.42e-31 relative error = 3.3822295985632963512432238484758e-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] = -1.27 y[1] (analytic) = 0.04489914441530776490981825781711 y[1] (numeric) = 0.044899144415307764909818257816966 absolute error = 1.44e-31 relative error = 3.2071880628287678264230307668763e-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] = -1.26 y[1] (analytic) = 0.04790965840948423614318377857458 y[1] (numeric) = 0.047909658409484236143183778574429 absolute error = 1.51e-31 relative error = 3.1517653227539588011569628871181e-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] = -1.25 y[1] (analytic) = 0.05101538064441378565150915296395 y[1] (numeric) = 0.051015380644413785651509152963804 absolute error = 1.46e-31 relative error = 2.8618820080486273179860913123779e-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] = -1.24 y[1] (analytic) = 0.05421600055046101371529403691821 y[1] (numeric) = 0.054216000550461013715294036918064 absolute error = 1.46e-31 relative error = 2.6929319484588673045785367812077e-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] = -1.23 y[1] (analytic) = 0.05751119806830248997617643461076 y[1] (numeric) = 0.057511198068302489976176434610609 absolute error = 1.51e-31 relative error = 2.6255756282570682490265365565107e-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] = -1.22 y[1] (analytic) = 0.06090064368093241906475472811163 y[1] (numeric) = 0.060900643680932419064754728111481 absolute error = 1.49e-31 relative error = 2.4466079665862529367599974593720e-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] = -1.21 y[1] (analytic) = 0.06438399844661406658353511145639 y[1] (numeric) = 0.064383998446614066583535111456248 absolute error = 1.42e-31 relative error = 2.2055169518206232739456278665594e-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] = -1.2 y[1] (analytic) = 0.06796091403277365032986556450517 y[1] (numeric) = 0.067960914032773650329865564505027 absolute error = 1.43e-31 relative error = 2.1041506288605727558101536819905e-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] = -1.19 y[1] (analytic) = 0.07163103275083330739797888839733 y[1] (numeric) = 0.071631032750833307397978888397178 absolute error = 1.52e-31 relative error = 2.1219853206462632487160792080685e-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] = -1.18 y[1] (analytic) = 0.07539398759197965389246197412524 y[1] (numeric) = 0.07539398759197965389246197412509 absolute error = 1.50e-31 relative error = 1.9895485673443391142221269929429e-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] = -1.17 y[1] (analytic) = 0.07924940226386436042698699103797 y[1] (numeric) = 0.079249402263864360426986991037825 absolute error = 1.45e-31 relative error = 1.8296667969458765231992844102091e-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] = -1.16 y[1] (analytic) = 0.08319689122823307338133833312567 y[1] (numeric) = 0.08319689122823307338133833312552 absolute error = 1.50e-31 relative error = 1.8029519827670811378527513107853e-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] = -1.15 y[1] (analytic) = 0.08723605973947891905596695024632 y[1] (numeric) = 0.087236059739478919055966950246179 absolute error = 1.41e-31 relative error = 1.6163040882529688778461939136828e-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] = -1.14 y[1] (analytic) = 0.0913665038841167354057844218978 y[1] (numeric) = 0.09136650388411673540578442189765 absolute error = 1.50e-31 relative error = 1.6417395174740420723356584496726e-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] = -1.13 y[1] (analytic) = 0.0955878106211740839629184775886 y[1] (numeric) = 0.095587810621174083962918477588459 absolute error = 1.41e-31 relative error = 1.4750834764779773982682016090729e-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] = -1.12 y[1] (analytic) = 0.09989955782349500288089675266085 y[1] (numeric) = 0.099899557823495002880896752660706 absolute error = 1.44e-31 relative error = 1.4414478215651639178693554284434e-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] = -1.11 y[1] (analytic) = 0.10430131431995237075937404066063 y[1] (numeric) = 0.10430131431995237075937404066048 absolute error = 1.5e-31 relative error = 1.4381410337732021933868153174032e-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] = -1.1 y[1] (analytic) = 0.1087926399385646600481974221283 y[1] (numeric) = 0.10879263993856466004819742212815 absolute error = 1.5e-31 relative error = 1.3787697410845548720831524088974e-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] = -1.09 y[1] (analytic) = 0.11337308555051276839139937136395 y[1] (numeric) = 0.1133730855505127683913993713638 absolute error = 1.5e-31 relative error = 1.3230653401698969100149433119607e-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] = -1.08 y[1] (analytic) = 0.11804219311505252626466501237524 y[1] (numeric) = 0.11804219311505252626466501237509 absolute error = 1.5e-31 relative error = 1.2707320665738484334593839176130e-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] = -1.07 y[1] (analytic) = 0.12279949572531838969293674222318 y[1] (numeric) = 0.12279949572531838969293674222302 absolute error = 1.6e-31 relative error = 1.3029369465644453346200205639303e-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] = -1.06 y[1] (analytic) = 0.12764451765501373771705407800258 bytes used=60021920, alloc=4455632, time=2.42 y[1] (numeric) = 0.12764451765501373771705407800242 absolute error = 1.6e-31 relative error = 1.2534811752153256239298080857658e-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] = -1.05 y[1] (analytic) = 0.13257677440598310561859051499973 y[1] (numeric) = 0.13257677440598310561859051499957 absolute error = 1.6e-31 relative error = 1.2068478865690316691630471445231e-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] = -1.04 y[1] (analytic) = 0.13759577275666159671920830788383 y[1] (numeric) = 0.13759577275666159671920830788367 absolute error = 1.6e-31 relative error = 1.1628264211500183556900609768471e-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] = -1.03 y[1] (analytic) = 0.14270101081139662785372561470558 y[1] (numeric) = 0.14270101081139662785372561470542 absolute error = 1.6e-31 relative error = 1.1212254145239860572209127765663e-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] = -1.02 y[1] (analytic) = 0.14789197805063707638345001454462 y[1] (numeric) = 0.14789197805063707638345001454446 absolute error = 1.6e-31 relative error = 1.0818707147538268098624849633859e-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] = -1.01 y[1] (analytic) = 0.15316815538198480987690121521799 y[1] (numeric) = 0.15316815538198480987690121521783 absolute error = 1.6e-31 relative error = 1.0446035574495057978005667805704e-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] = -1 y[1] (analytic) = 0.1585290151921034933474976783697 y[1] (numeric) = 0.15852901519210349334749767836954 absolute error = 1.6e-31 relative error = 1.0092789626309984044021634783719e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = 0.16397402139947948321074058845289 y[1] (numeric) = 0.16397402139947948321074058845273 absolute error = 1.6e-31 relative error = 9.7576432311922248015650545411471e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.16950262950802953191546671228085 y[1] (numeric) = 0.1695026295080295319154667122807 absolute error = 1.5e-31 relative error = 8.8494202382208076469033714257426e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.17511428666154994252337996214366 y[1] (numeric) = 0.1751142866615499425233799621435 absolute error = 1.6e-31 relative error = 9.1368901447337703213371033612676e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.18080843169900172836677785356957 y[1] (numeric) = 0.18080843169900172836677785356942 absolute error = 1.5e-31 relative error = 8.2960732854378368828470107658811e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.18658449521062624931457789789744 y[1] (numeric) = 0.18658449521062624931457789789729 absolute error = 1.5e-31 relative error = 8.0392531989687688219269569151098e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.19244189959488571312978020136585 y[1] (numeric) = 0.1924418995948857131297802013657 absolute error = 1.5e-31 relative error = 7.7945603486438647566239528720038e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.61 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] = -0.93 y[1] (analytic) = 0.19838005911622284791568078408935 y[1] (numeric) = 0.1983800591162228479156807840892 absolute error = 1.5e-31 relative error = 7.5612438401442894374455857105777e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.92 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] = -0.92 y[1] (analytic) = 0.20439837996363396973172389751838 y[1] (numeric) = 0.20439837996363396973172389751823 absolute error = 1.5e-31 relative error = 7.3386100235573105532625041208828e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.91 y[1] (analytic) = 0.21049626031004958812104248212845 y[1] (numeric) = 0.2104962603100495881210424821283 absolute error = 1.5e-31 relative error = 7.1260173353701451048350115901447e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.55 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] = -0.9 y[1] (analytic) = 0.21667309037251661153861768428645 y[1] (numeric) = 0.2166730903725166115386176842863 absolute error = 1.5e-31 relative error = 6.9228716746556542930208821075149e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.87 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] = -0.89 y[1] (analytic) = 0.22292825247317613450966628702682 y[1] (numeric) = 0.22292825247317613450966628702667 absolute error = 1.5e-31 relative error = 6.7286222511455234154315812754510e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.88 y[1] (analytic) = 0.22926112110103070879035486924401 y[1] (numeric) = 0.22926112110103070879035486924386 absolute error = 1.5e-31 relative error = 6.5427578509440357175757902592561e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.87 y[1] (analytic) = 0.23567106297449492185519717627715 y[1] (numeric) = 0.235671062974494921855197176277 absolute error = 1.5e-31 relative error = 6.3648034725516335874622918340302e-29 % Correct digits = 31 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] = -0.86 y[1] (analytic) = 0.24215743710472302770541127047135 y[1] (numeric) = 0.24215743710472302770541127047121 absolute error = 1.4e-31 relative error = 5.7813628056963544040318961672977e-29 % Correct digits = 31 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] = -0.85 y[1] (analytic) = 0.24871959485970729728792847576453 y[1] (numeric) = 0.24871959485970729728792847576439 absolute error = 1.4e-31 relative error = 5.6288287249329253488217665993461e-29 % Correct digits = 31 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] = -0.84 y[1] (analytic) = 0.25535688002914067874342732937035 y[1] (numeric) = 0.25535688002914067874342732937021 absolute error = 1.4e-31 relative error = 5.4825231254401117169748415269425e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.93 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] = -0.83 y[1] (analytic) = 0.26206862889003728127141977386192 y[1] (numeric) = 0.26206862889003728127141977386177 absolute error = 1.5e-31 relative error = 5.7236915625997825378302251014268e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.82 y[1] (analytic) = 0.26885417027310412061868663531228 y[1] (numeric) = 0.26885417027310412061868663531213 absolute error = 1.5e-31 relative error = 5.5792327806419686096586315589310e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.66 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] = -0.81 y[1] (analytic) = 0.27571282562985748907182314748546 y[1] (numeric) = 0.27571282562985748907182314748531 absolute error = 1.5e-31 relative error = 5.4404433184176181576751165311260e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.04 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] = -0.8 y[1] (analytic) = 0.28264390910047723837282538941861 y[1] (numeric) = 0.28264390910047723837282538941847 absolute error = 1.4e-31 relative error = 4.9532289744206489573491959500534e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.79 y[1] (analytic) = 0.2896467275823921901859711250308 y[1] (numeric) = 0.28964672758239219018597112503066 absolute error = 1.4e-31 relative error = 4.8334742521879846550475285728800e-29 % Correct digits = 31 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] = -0.78 y[1] (analytic) = 0.29672058079958981563210267488208 y[1] (numeric) = 0.29672058079958981563210267488193 absolute error = 1.5e-31 relative error = 5.0552610673579322849096761088239e-29 % Correct digits = 31 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 bytes used=64022896, alloc=4455632, time=2.57 TOP MAIN SOLVE Loop x[1] = -0.77 y[1] (analytic) = 0.30386476137264325298011626554779 y[1] (numeric) = 0.30386476137264325298011626554765 absolute error = 1.4e-31 relative error = 4.6073127850554410824888682423686e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.76 y[1] (analytic) = 0.31107855488944866085224436123027 y[1] (numeric) = 0.31107855488944866085224436123013 absolute error = 1.4e-31 relative error = 4.5004709517746509093635915999796e-29 % Correct digits = 31 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] = -0.75 y[1] (analytic) = 0.31836123997666583326675804722011 y[1] (numeric) = 0.31836123997666583326675804721996 absolute error = 1.5e-31 relative error = 4.7116288405898341549099213834300e-29 % Correct digits = 31 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] = -0.74 y[1] (analytic) = 0.32571208837185493251611884239183 y[1] (numeric) = 0.32571208837185493251611884239168 absolute error = 1.5e-31 relative error = 4.6052942262538890674499263323624e-29 % Correct digits = 31 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] = -0.73 y[1] (analytic) = 0.33313036499630212626740586923847 y[1] (numeric) = 0.33313036499630212626740586923832 absolute error = 1.5e-31 relative error = 4.5027417420103705359084732112501e-29 % Correct digits = 31 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] = -0.72 y[1] (analytic) = 0.34061532802852684638199616735183 y[1] (numeric) = 0.34061532802852684638199616735168 absolute error = 1.5e-31 relative error = 4.4037947695482853405565408106191e-29 % Correct digits = 31 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] = -0.71 y[1] (analytic) = 0.34816622897846331878987202714716 y[1] (numeric) = 0.34816622897846331878987202714701 absolute error = 1.5e-31 relative error = 4.3082868904347015267843961651665e-29 % Correct digits = 31 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] = -0.7 y[1] (analytic) = 0.35578231276230894632738564860128 y[1] (numeric) = 0.35578231276230894632738564860113 absolute error = 1.5e-31 relative error = 4.2160611873983742018702687886282e-29 % Correct digits = 31 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] = -0.69 y[1] (analytic) = 0.36346281777803205976257079299128 y[1] (numeric) = 0.36346281777803205976257079299113 absolute error = 1.5e-31 relative error = 4.1269696008246294445379235978419e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.68 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] = -0.68 y[1] (analytic) = 0.37120697598153148629582181257975 y[1] (numeric) = 0.37120697598153148629582181257961 absolute error = 1.4e-31 relative error = 3.7714808464958741661647937426150e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.67 y[1] (analytic) = 0.37901401296344031964255608587341 y[1] (numeric) = 0.37901401296344031964255608587326 absolute error = 1.5e-31 relative error = 3.9576373133852704151813473320903e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.66 y[1] (analytic) = 0.3868831480265662113848545206037 y[1] (numeric) = 0.38688314802656621138485452060355 absolute error = 1.5e-31 relative error = 3.8771396677556994237903519760114e-29 % Correct digits = 31 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 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.65 y[1] (analytic) = 0.39481359426396043962747832139406 y[1] (numeric) = 0.39481359426396043962747832139391 absolute error = 1.5e-31 relative error = 3.7992612761888470417701412779370e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.64 y[1] (analytic) = 0.40280455863760794811645376079207 y[1] (numeric) = 0.40280455863760794811645376079192 absolute error = 1.5e-31 relative error = 3.7238903280374943744536905447973e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.15 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] = -0.63 y[1] (analytic) = 0.41085524205773048688188790920538 y[1] (numeric) = 0.41085524205773048688188790920523 absolute error = 1.5e-31 relative error = 3.6509209240884665589470578012941e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.62 y[1] (analytic) = 0.41896483946269492415703677241779 y[1] (numeric) = 0.41896483946269492415703677241763 absolute error = 1.6e-31 relative error = 3.8189362192109815585064266691057e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.61 y[1] (analytic) = 0.42713253989951873880902396783728 y[1] (numeric) = 0.42713253989951873880902396783712 absolute error = 1.6e-31 relative error = 3.7459098770053757757468772266227e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6 y[1] (analytic) = 0.43535752660496464279905455434134 y[1] (numeric) = 0.43535752660496464279905455434118 absolute error = 1.6e-31 relative error = 3.6751403208237407352789461822315e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.59 y[1] (analytic) = 0.44363897708721622427745662112423 y[1] (numeric) = 0.44363897708721622427745662112407 absolute error = 1.6e-31 relative error = 3.6065361310339770617832571011665e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.58 y[1] (analytic) = 0.45197606320812644381730394042354 y[1] (numeric) = 0.45197606320812644381730394042338 absolute error = 1.6e-31 relative error = 3.5400104789691710021735279796372e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.57 y[1] (analytic) = 0.46036795126603075900553650692117 y[1] (numeric) = 0.46036795126603075900553650692102 absolute error = 1.5e-31 relative error = 3.2582632997691052158462286558419e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.56 y[1] (analytic) = 0.46881380207911659614813055888797 y[1] (numeric) = 0.46881380207911659614813055888781 absolute error = 1.6e-31 relative error = 3.4128688039990457386906329830255e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.55 y[1] (analytic) = 0.47731277106934083221162189224271 y[1] (numeric) = 0.47731277106934083221162189224255 absolute error = 1.6e-31 relative error = 3.3520997068975609216778934749271e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.54 y[1] (analytic) = 0.48586400834688689532271931704176 y[1] (numeric) = 0.4858640083468868953227193170416 absolute error = 1.6e-31 relative error = 3.2931025400376351481194378935279e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.53 y[1] (analytic) = 0.49446665879515303818633897753392 y[1] (numeric) = 0.49446665879515303818633897753376 absolute error = 1.6e-31 relative error = 3.2358096780451395036420189845115e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.52 y[1] (analytic) = 0.50311986215626328566554105745225 y[1] (numeric) = 0.50311986215626328566554105745209 absolute error = 1.6e-31 relative error = 3.1801566989280543754287748480271e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.51 y[1] (analytic) = 0.51182275311709250549986976232543 y[1] (numeric) = 0.51182275311709250549986976232527 absolute error = 1.6e-31 relative error = 3.1260822037623622456716194712282e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5 y[1] (analytic) = 0.52057446139579699972671206478443 y[1] (numeric) = 0.52057446139579699972671206478427 absolute error = 1.6e-31 relative error = 3.0735276481100884783914309912681e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.49 y[1] (analytic) = 0.52937411182884196381864166281204 y[1] (numeric) = 0.52937411182884196381864166281188 absolute error = 1.6e-31 relative error = 3.0224371843051411115230020151642e-29 % bytes used=68023568, alloc=4455632, time=2.73 Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.48 y[1] (analytic) = 0.53822082445851711086335705741136 y[1] (numeric) = 0.5382208244585171108633570574112 absolute error = 1.6e-31 relative error = 2.9727575138135863235734969270828e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.47 y[1] (analytic) = 0.54711371462093170929672519960359 y[1] (numeric) = 0.54711371462093170929672519960343 absolute error = 1.6e-31 relative error = 2.9244377489395629915047054353119e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.46 y[1] (analytic) = 0.5560518930344802347584863560711 y[1] (numeric) = 0.55605189303448023475848635607094 absolute error = 1.6e-31 relative error = 2.8774292832068203440395188300703e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.45 y[1] (analytic) = 0.5650344658887697895791557537681 y[1] (numeric) = 0.56503446588876978957915575376794 absolute error = 1.6e-31 relative error = 2.8316856697994224531030272383593e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.44 y[1] (analytic) = 0.57406053493400039723027924922008 y[1] (numeric) = 0.57406053493400039723027924921992 absolute error = 1.6e-31 relative error = 2.7871625074940077849965132144271e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.43 y[1] (analytic) = 0.58312919757078923378308132737543 y[1] (numeric) = 0.58312919757078923378308132737527 absolute error = 1.6e-31 relative error = 2.7438173335605738954899607736725e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.42 y[1] (analytic) = 0.59223954694042981402721284191366 y[1] (numeric) = 0.59223954694042981402721284191349 absolute error = 1.7e-31 relative error = 2.8704601183463248918724422987667e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.41 y[1] (analytic) = 0.60139067201557710640620235994886 y[1] (numeric) = 0.60139067201557710640620235994869 absolute error = 1.7e-31 relative error = 2.8267814568895856177479107884933e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4 y[1] (analytic) = 0.61058165769134950833368824320429 y[1] (numeric) = 0.61058165769134950833368824320413 absolute error = 1.6e-31 relative error = 2.6204521210966409927179760733331e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.39 y[1] (analytic) = 0.61981158487683857176881790215284 y[1] (numeric) = 0.61981158487683857176881790215267 absolute error = 1.7e-31 relative error = 2.7427689986430365724465855821898e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.38 y[1] (analytic) = 0.6290795305870173281545145336508 y[1] (numeric) = 0.62907953058701732815451453365063 absolute error = 1.7e-31 relative error = 2.7023610169189057163238917048124e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.37 y[1] (analytic) = 0.63838456803503802196270753087285 y[1] (numeric) = 0.63838456803503802196270753087268 absolute error = 1.7e-31 relative error = 2.6629716398575203985767477246961e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.36 y[1] (analytic) = 0.64772576672491002315008656407927 y[1] (numeric) = 0.6477257667249100231500865640791 absolute error = 1.7e-31 relative error = 2.6245675057759315824854873606464e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.35 y[1] (analytic) = 0.65710219254454865081036509308237 y[1] (numeric) = 0.6571021925445486508103650930822 absolute error = 1.7e-31 relative error = 2.5871166148707492637356086730564e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.34 y[1] (analytic) = 0.66651290785918560321822851296921 y[1] (numeric) = 0.66651290785918560321822851296904 absolute error = 1.7e-31 relative error = 2.5505882631145675391918202521756e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.33 y[1] (analytic) = 0.67595697160513165329980430382978 y[1] (numeric) = 0.67595697160513165329980430382961 absolute error = 1.7e-31 relative error = 2.5149529798667056653847141902583e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.32 y[1] (analytic) = 0.68543343938388223333824245658285 y[1] (numeric) = 0.68543343938388223333824245658268 absolute error = 1.7e-31 relative error = 2.4801824689616609363125066288226e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.31 y[1] (analytic) = 0.69494136355655649843435667604104 y[1] (numeric) = 0.69494136355655649843435667604087 absolute error = 1.7e-31 relative error = 2.4462495530554912651743047235381e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3 y[1] (analytic) = 0.70447979333866042489467925431497 y[1] (numeric) = 0.7044797933386604248946792543148 absolute error = 1.7e-31 relative error = 2.4131281210258489347587106971978e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.29 y[1] (analytic) = 0.71404777489516446731605979449563 y[1] (numeric) = 0.71404777489516446731605979449546 absolute error = 1.7e-31 relative error = 2.3807930782356848749610286964941e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.28 y[1] (analytic) = 0.72364435143588626668033044154215 y[1] (numeric) = 0.72364435143588626668033044154198 absolute error = 1.7e-31 relative error = 2.3492202994838373775246154233185e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.27 y[1] (analytic) = 0.73326856331116887126771347897946 y[1] (numeric) = 0.73326856331116887126771347897929 absolute error = 1.7e-31 relative error = 2.3183865844779033072304251577359e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.26 y[1] (analytic) = 0.74291944810784490264661153563478 y[1] (numeric) = 0.74291944810784490264661153563461 absolute error = 1.7e-31 relative error = 2.2882696156760480795331358736711e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.25 y[1] (analytic) = 0.75259604074547707040315129515061 y[1] (numeric) = 0.75259604074547707040315129515044 absolute error = 1.7e-31 relative error = 2.2588479183548197667085682195498e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.24 y[1] (analytic) = 0.76229737357286541163920791551018 y[1] (numeric) = 0.76229737357286541163920791551001 absolute error = 1.7e-31 relative error = 2.2301008227696625870008356771109e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.23 y[1] (analytic) = 0.77202247646481160459538278763993 y[1] (numeric) = 0.77202247646481160459538278763975 absolute error = 1.8e-31 relative error = 2.3315383358298417272339656621895e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.22 y[1] (analytic) = 0.78177037691913068004820899454299 y[1] (numeric) = 0.78177037691913068004820899454281 absolute error = 1.8e-31 relative error = 2.3024663675459256872754459594368e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.21 y[1] (analytic) = 0.79154010015390042939128757377236 y[1] (numeric) = 0.79154010015390042939128757377218 absolute error = 1.8e-31 relative error = 2.2740477704793769408106092393844e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2 y[1] (analytic) = 0.80133066920493878454058737288161 y[1] (numeric) = 0.80133066920493878454058737288143 absolute error = 1.8e-31 relative error = 2.2462637075727017332122316645349e-29 % Correct digits = 31 h = 0.01 bytes used=72024548, alloc=4455632, time=2.89 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.19 y[1] (analytic) = 0.81114110502349942200714884701869 y[1] (numeric) = 0.81114110502349942200714884701851 absolute error = 1.8e-31 relative error = 2.2190960226924420580169768980973e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.18 y[1] (analytic) = 0.82097042657417582165819726030079 y[1] (numeric) = 0.82097042657417582165819726030061 absolute error = 1.8e-31 relative error = 2.1925272113774094548192896558279e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.17 y[1] (analytic) = 0.83081765093300398984237562332915 y[1] (numeric) = 0.83081765093300398984237562332897 absolute error = 1.8e-31 relative error = 2.1665403930436590618116952981388e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.16 y[1] (analytic) = 0.84068179338575403668853684031401 y[1] (numeric) = 0.84068179338575403668853684031383 absolute error = 1.8e-31 relative error = 2.1411192845638975232901285440012e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.15 y[1] (analytic) = 0.85056186752640077850227456131236 y[1] (numeric) = 0.85056186752640077850227456131218 absolute error = 1.8e-31 relative error = 2.1162481751442135991032714325003e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.14 y[1] (analytic) = 0.86045688535576351828201164829463 y[1] (numeric) = 0.86045688535576351828201164829445 absolute error = 1.8e-31 relative error = 2.0919119024258537505420297867259e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.13 y[1] (analytic) = 0.87036585738030514045879418929169 y[1] (numeric) = 0.87036585738030514045879418929151 absolute error = 1.8e-31 relative error = 2.0680958297442641123580530376522e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.12 y[1] (analytic) = 0.88028779271108064003264938572903 y[1] (numeric) = 0.88028779271108064003264938572885 absolute error = 1.8e-31 relative error = 2.0447858244818103613980206358942e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.11 y[1] (analytic) = 0.89022169916282519133505050991655 y[1] (numeric) = 0.89022169916282519133505050991636 absolute error = 1.9e-31 relative error = 2.1342998062019629850527875685954e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1 y[1] (analytic) = 0.90016658335317184769318580158938 y[1] (numeric) = 0.90016658335317184769318580158919 absolute error = 1.9e-31 relative error = 2.1107204323475235749159832101243e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.09 y[1] (analytic) = 0.91012145080198895030874601739286 y[1] (numeric) = 0.91012145080198895030874601739268 absolute error = 1.8e-31 relative error = 1.9777580216506927951776751398085e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.08 y[1] (analytic) = 0.9200853060308273126931236526855 y[1] (numeric) = 0.92008530603082731269312365268532 absolute error = 1.8e-31 relative error = 1.9563403395333554915168198043397e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.07 y[1] (analytic) = 0.93005715266246723602345269319211 y[1] (numeric) = 0.93005715266246723602345269319193 absolute error = 1.8e-31 relative error = 1.9353649341302889538878530045664e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.06 y[1] (analytic) = 0.94003599352055540080090886214302 y[1] (numeric) = 0.94003599352055540080090886214283 absolute error = 1.9e-31 relative error = 2.0211992020478452459420952680309e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.05 y[1] (analytic) = 0.95002083072932167120513499915451 y[1] (numeric) = 0.95002083072932167120513499915432 absolute error = 1.9e-31 relative error = 1.9999561467945799048246075694872e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.04 y[1] (analytic) = 0.96001066581336584054745318828408 y[1] (numeric) = 0.9600106658133658405474531882839 absolute error = 1.8e-31 relative error = 1.8749791685647117186467905904025e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.03 y[1] (analytic) = 0.97000449979750433923147365807374 y[1] (numeric) = 0.97000449979750433923147365807355 absolute error = 1.9e-31 relative error = 1.9587538000046795092340390925636e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.02 y[1] (analytic) = 0.98000133330666692063350970530702 y[1] (numeric) = 0.98000133330666692063350970530684 absolute error = 1.8e-31 relative error = 1.8367321949721623427010785678790e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.01 y[1] (analytic) = 0.9900001666658333353174575617309 y[1] (numeric) = 0.99000016666583333531745756173071 absolute error = 1.9e-31 relative error = 1.9191915960973063700044830402096e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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 y[1] (analytic) = 1 y[1] (numeric) = 0.99999999999999999999999999999981 absolute error = 1.9e-31 relative error = 1.9000000000000000000000000000000e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 1.0099998333341666646825424382691 y[1] (numeric) = 1.0099998333341666646825424382689 absolute error = 2e-31 relative error = 1.9801983465657500986123806865695e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009642 Order of pole (three term test) = -0.8953 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.02 y[1] (analytic) = 1.019998666693333079366490294693 y[1] (numeric) = 1.0199986666933330793664902946928 absolute error = 2e-31 relative error = 1.9607868767943286670247322610197e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01928 Order of pole (three term test) = -0.9025 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 1.0299955002024956607685263419263 y[1] (numeric) = 1.0299955002024956607685263419261 absolute error = 2e-31 relative error = 1.9417560558340330850208568304264e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02891 Order of pole (three term test) = -0.9146 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 1.0399893341866341594525468117159 y[1] (numeric) = 1.0399893341866341594525468117158 absolute error = 1e-31 relative error = 9.6154832278360869901409491156178e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03853 Order of pole (three term test) = -0.9315 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05 y[1] (analytic) = 1.0499791692706783287948650008455 y[1] (numeric) = 1.0499791692706783287948650008454 absolute error = 1e-31 relative error = 9.5239984684134814593878718895478e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04813 Order of pole (three term test) = -0.9532 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (analytic) = 1.059964006479444599199091137857 y[1] (numeric) = 1.0599640064794445991990911378569 absolute error = 1e-31 relative error = 9.4342826160804408979170185153014e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05772 Order of pole (three term test) = -0.9798 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.07 y[1] (analytic) = 1.0699428473375327639765473068079 y[1] (numeric) = 1.0699428473375327639765473068078 absolute error = 1e-31 relative error = 9.3462936126767897201305870160174e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06728 Order of pole (three term test) = -1.011 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 1.0799146939691726873068763473145 y[1] (numeric) = 1.0799146939691726873068763473144 absolute error = 1e-31 relative error = 9.2599906787502797218066607825604e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07681 Order of pole (three term test) = -1.047 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 1.0898785491980110496912539826071 y[1] (numeric) = 1.089878549198011049691253982607 absolute error = 1e-31 relative error = 9.1753342676195588013178870947670e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08632 Order of pole (three term test) = -1.088 NO COMPLEX POLE (six term test) for Equation 1 bytes used=76027804, alloc=4455632, time=3.04 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.0998334166468281523068141984106 y[1] (numeric) = 1.0998334166468281523068141984105 absolute error = 1e-31 relative error = 9.0922860213576684349079136797722e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09579 Order of pole (three term test) = -1.134 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 1.1097783008371748086649494900834 y[1] (numeric) = 1.1097783008371748086649494900833 absolute error = 1e-31 relative error = 9.0108087286049636460847024873501e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1052 Order of pole (three term test) = -1.184 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 1.119712207288919359967350614271 y[1] (numeric) = 1.1197122072889193599673506142708 absolute error = 2e-31 relative error = 1.7861732568250369765302667137980e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1146 Order of pole (three term test) = -1.239 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 1.1296341426196948595412058107083 y[1] (numeric) = 1.1296341426196948595412058107081 absolute error = 2e-31 relative error = 1.7704847300045926851243791841683e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1239 Order of pole (three term test) = -1.299 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 1.1395431146442364817179883517054 y[1] (numeric) = 1.1395431146442364817179883517052 absolute error = 2e-31 relative error = 1.7550893637090657749553200652311e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1332 Order of pole (three term test) = -1.364 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 1.1494381324735992214977254386876 y[1] (numeric) = 1.1494381324735992214977254386875 absolute error = 1e-31 relative error = 8.6999027763938257948745204743370e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1425 Order of pole (three term test) = -1.433 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 1.159318206614245963311463159686 y[1] (numeric) = 1.1593182066142459633114631596858 absolute error = 2e-31 relative error = 1.7251518940955305009267624609262e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1517 Order of pole (three term test) = -1.507 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 1.1691823490669960101576243766708 y[1] (numeric) = 1.1691823490669960101576243766707 absolute error = 1e-31 relative error = 8.5529857750418229057076547011110e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1608 Order of pole (three term test) = -1.585 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 1.1790295734258241783418027396992 y[1] (numeric) = 1.1790295734258241783418027396991 absolute error = 1e-31 relative error = 8.4815514601077358374588506352999e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1698 Order of pole (three term test) = -1.668 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 1.1888588949765005779928511529813 y[1] (numeric) = 1.1888588949765005779928511529812 absolute error = 1e-31 relative error = 8.4114271611667284337748517832377e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1788 Order of pole (three term test) = -1.755 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 1.1986693307950612154594126271184 y[1] (numeric) = 1.1986693307950612154594126271183 absolute error = 1e-31 relative error = 8.3425843500702022187891560514118e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1877 Order of pole (three term test) = -1.847 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 1.2084598998460995706087124262276 y[1] (numeric) = 1.2084598998460995706087124262276 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 = 0.1966 Order of pole (three term test) = -1.943 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 1.218229623080869319951791005457 y[1] (numeric) = 1.218229623080869319951791005457 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 = 0.2054 Order of pole (three term test) = -2.044 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 1.2279775235351883954046172123601 y[1] (numeric) = 1.2279775235351883954046172123601 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 = 0.214 Order of pole (three term test) = -2.149 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 1.2377026264271345883607920844898 y[1] (numeric) = 1.2377026264271345883607920844898 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 = 0.2226 Order of pole (three term test) = -2.259 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 1.2474039592545229295968487048494 y[1] (numeric) = 1.2474039592545229295968487048494 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 = 0.2311 Order of pole (three term test) = -2.373 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 1.2570805518921550973533884643652 y[1] (numeric) = 1.2570805518921550973533884643652 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 = 0.2395 Order of pole (three term test) = -2.491 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 1.2667314366888311287322865210205 y[1] (numeric) = 1.2667314366888311287322865210205 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 = 0.2479 Order of pole (three term test) = -2.613 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 1.2763556485641137333196695584578 y[1] (numeric) = 1.2763556485641137333196695584578 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 = 0.2561 Order of pole (three term test) = -2.739 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 1.2859522251048355326839402055044 y[1] (numeric) = 1.2859522251048355326839402055043 absolute error = 1e-31 relative error = 7.7763386576703993762228663985883e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2642 Order of pole (three term test) = -2.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 1.295520206661339575105320745685 y[1] (numeric) = 1.295520206661339575105320745685 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 = 0.2722 Order of pole (three term test) = -3.004 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 1.305058636443443501565643323959 y[1] (numeric) = 1.3050586364434435015656433239589 absolute error = 1e-31 relative error = 7.6624909569213548956184351464992e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2801 Order of pole (three term test) = -3.143 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 1.3145665606161177666617575434172 y[1] (numeric) = 1.3145665606161177666617575434171 absolute error = 1e-31 relative error = 7.6070701169464929556001576561235e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2879 Order of pole (three term test) = -3.285 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 1.3240430283948683467001956961702 y[1] (numeric) = 1.3240430283948683467001956961702 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 = 0.2956 Order of pole (three term test) = -3.431 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 1.3334870921408143967817714870308 y[1] (numeric) = 1.3334870921408143967817714870308 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 = 0.3031 Order of pole (three term test) = -3.581 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = 1.3428978074554513491896349069176 y[1] (numeric) = 1.3428978074554513491896349069176 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 = 0.3106 Order of pole (three term test) = -3.735 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 1.3522742332750899768499134359207 y[1] (numeric) = 1.3522742332750899768499134359207 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 = 0.3179 Order of pole (three term test) = -3.893 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 1.3616154319649619780372924691272 y[1] (numeric) = 1.3616154319649619780372924691271 absolute error = 1e-31 relative error = 7.3442175854080117807128590095045e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.325 Order of pole (three term test) = -4.054 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 1.3709204694129826718454854663492 y[1] (numeric) = 1.3709204694129826718454854663491 absolute error = 1e-31 relative error = 7.2943691651798890258868008186844e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3321 Order of pole (three term test) = -4.219 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=80029484, alloc=4521156, time=3.21 x[1] = 0.39 y[1] (analytic) = 1.3801884151231614282311820978472 y[1] (numeric) = 1.3801884151231614282311820978471 absolute error = 1e-31 relative error = 7.2453875792803605858750550935429e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.339 Order of pole (three term test) = -4.387 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 1.3894183423086504916663117567957 y[1] (numeric) = 1.3894183423086504916663117567956 absolute error = 1e-31 relative error = 7.1972563593654957565209332448654e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3458 Order of pole (three term test) = -4.559 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 1.3986093279844228935937976400511 y[1] (numeric) = 1.398609327984422893593797640051 absolute error = 1e-31 relative error = 7.1499594632414575740331010403020e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3524 Order of pole (three term test) = -4.734 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 1.4077604530595701859727871580863 y[1] (numeric) = 1.4077604530595701859727871580862 absolute error = 1e-31 relative error = 7.1034812622178727307631452987902e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3589 Order of pole (three term test) = -4.912 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 1.4168708024292107662169186726246 y[1] (numeric) = 1.4168708024292107662169186726244 absolute error = 2e-31 relative error = 1.4115613057810352777553867719432e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3653 Order of pole (three term test) = -5.093 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 1.4259394650659996027697207507799 y[1] (numeric) = 1.4259394650659996027697207507798 absolute error = 1e-31 relative error = 7.0129204254383618154964292748691e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3715 Order of pole (three term test) = -5.278 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 1.4349655341112302104208442462319 y[1] (numeric) = 1.4349655341112302104208442462318 absolute error = 1e-31 relative error = 6.9688084921103463695038126770442e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3776 Order of pole (three term test) = -5.466 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 1.4439481069655197652415136439289 y[1] (numeric) = 1.4439481069655197652415136439288 absolute error = 1e-31 relative error = 6.9254566363989086005517729136524e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3835 Order of pole (three term test) = -5.657 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 1.4528862853790682907032748003964 y[1] (numeric) = 1.4528862853790682907032748003963 absolute error = 1e-31 relative error = 6.8828511223718581594824423813170e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3892 Order of pole (three term test) = -5.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 1.4617791755414828891366429425886 y[1] (numeric) = 1.4617791755414828891366429425885 absolute error = 1e-31 relative error = 6.8409785604557727842596851575514e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3949 Order of pole (three term test) = -6.047 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 1.470625888171158036181358337188 y[1] (numeric) = 1.4706258881711580361813583371878 absolute error = 2e-31 relative error = 1.3599651795108553335897032276593e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4003 Order of pole (three term test) = -6.246 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 1.4794255386042030002732879352156 y[1] (numeric) = 1.4794255386042030002732879352154 absolute error = 2e-31 relative error = 1.3518760815004887495457772563323e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4056 Order of pole (three term test) = -6.448 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 1.4881772468829074945001302376746 y[1] (numeric) = 1.4881772468829074945001302376744 absolute error = 2e-31 relative error = 1.3439259363688979012428704319126e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4107 Order of pole (three term test) = -6.653 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 1.4968801378437367143344589425478 y[1] (numeric) = 1.4968801378437367143344589425476 absolute error = 2e-31 relative error = 1.3361123241844934559451623257491e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4157 Order of pole (three term test) = -6.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 1.5055333412048469618136610224661 y[1] (numeric) = 1.5055333412048469618136610224659 absolute error = 2e-31 relative error = 1.3284328850528422535436688681207e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4205 Order of pole (three term test) = -7.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 1.5141359916531131046772806829582 y[1] (numeric) = 1.5141359916531131046772806829581 absolute error = 1e-31 relative error = 6.6044265872592697963164134977544e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4251 Order of pole (three term test) = -7.281 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 1.5226872289306591677883781077573 y[1] (numeric) = 1.5226872289306591677883781077571 absolute error = 2e-31 relative error = 1.3134673766224100386001291625475e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4295 Order of pole (three term test) = -7.496 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 1.531186197920883403851869441112 y[1] (numeric) = 1.5311861979208834038518694411118 absolute error = 2e-31 relative error = 1.3061768730123704185584278128488e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4338 Order of pole (three term test) = -7.712 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = 1.5396320487339692409944634930788 y[1] (numeric) = 1.5396320487339692409944634930786 absolute error = 2e-31 relative error = 1.2990116707719800529642780620819e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4379 Order of pole (three term test) = -7.931 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 1.5480239367918735561826960595765 y[1] (numeric) = 1.5480239367918735561826960595762 absolute error = 3e-31 relative error = 1.9379545294481706612613473985737e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4418 Order of pole (three term test) = -8.151 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 1.5563610229127837757225433788758 y[1] (numeric) = 1.5563610229127837757225433788755 absolute error = 3e-31 relative error = 1.9275733302453152399987334892936e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4456 Order of pole (three term test) = -8.373 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 1.5646424733950353572009454456587 y[1] (numeric) = 1.5646424733950353572009454456584 absolute error = 3e-31 relative error = 1.9173709336232307994808196421009e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4492 Order of pole (three term test) = -8.598 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 1.5728674601004812611909760321627 y[1] (numeric) = 1.5728674601004812611909760321625 absolute error = 2e-31 relative error = 1.2715629579317711552779454373119e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4526 Order of pole (three term test) = -8.824 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 1.5810351605373050758429632275822 y[1] (numeric) = 1.581035160537305075842963227582 absolute error = 2e-31 relative error = 1.2649940051430053586700397545788e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4558 Order of pole (three term test) = -9.051 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 1.5891447579422695131181120907946 y[1] (numeric) = 1.5891447579422695131181120907944 absolute error = 2e-31 relative error = 1.2585385881332379195706824475417e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4588 Order of pole (three term test) = -9.281 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 1.5971954413623920518835462392079 y[1] (numeric) = 1.5971954413623920518835462392077 absolute error = 2e-31 relative error = 1.2521949087796166065122300387062e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4617 Order of pole (three term test) = -9.511 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 1.6051864057360395603725216786059 y[1] (numeric) = 1.6051864057360395603725216786057 absolute error = 2e-31 relative error = 1.2459612122636456400116671165425e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4643 Order of pole (three term test) = -9.743 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 1.6131168519734337886151454793963 y[1] (numeric) = 1.6131168519734337886151454793961 absolute error = 2e-31 relative error = 1.2398357859526829489548511754486e-29 % Correct digits = 31 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 = 0.4668 Order of pole (three term test) = -9.977 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 1.6209859870365596803574439141266 y[1] (numeric) = 1.6209859870365596803574439141264 absolute error = 2e-31 relative error = 1.2338169583170443819415541659175e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.05 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4691 Order of pole (three term test) = -10.21 NO COMPLEX POLE (six term test) for Equation 1 bytes used=84032096, alloc=4521156, time=3.37 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 1.6287930240184685137041781874202 y[1] (numeric) = 1.6287930240184685137041781874201 absolute error = 1e-31 relative error = 6.1395154894073344668541915317869e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4712 Order of pole (three term test) = -10.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 1.6365371822219679402374292070087 y[1] (numeric) = 1.6365371822219679402374292070086 absolute error = 1e-31 relative error = 6.1104630610486631158265560320066e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4731 Order of pole (three term test) = -10.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 1.6442176872376910536726143513987 y[1] (numeric) = 1.6442176872376910536726143513986 absolute error = 1e-31 relative error = 6.0819197346065175188260274521277e-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 Radius of convergence (three term test) for eq 1 = 0.4749 Order of pole (three term test) = -10.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 1.6518337710215366812101279728528 y[1] (numeric) = 1.6518337710215366812101279728527 absolute error = 1e-31 relative error = 6.0538779236943083185531773730902e-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 Radius of convergence (three term test) for eq 1 = 0.4764 Order of pole (three term test) = -11.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 1.6593846719714731536180038326482 y[1] (numeric) = 1.659384671971473153618003832648 absolute error = 2e-31 relative error = 1.2052660445656945536150895065502e-29 % Correct digits = 31 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 Radius of convergence (three term test) for eq 1 = 0.4777 Order of pole (three term test) = -11.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 1.6668696350036978737325941307615 y[1] (numeric) = 1.6668696350036978737325941307614 absolute error = 1e-31 relative error = 5.9992694029595274613422544528161e-30 % 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 Radius of convergence (three term test) for eq 1 = 0.4789 Order of pole (three term test) = -11.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 1.6742879116281450674838811576082 y[1] (numeric) = 1.674287911628145067483881157608 absolute error = 2e-31 relative error = 1.1945376814284703077492832633462e-29 % Correct digits = 31 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 Radius of convergence (three term test) for eq 1 = 0.4799 Order of pole (three term test) = -11.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 1.6816387600233341667332419527799 y[1] (numeric) = 1.6816387600233341667332419527797 absolute error = 2e-31 relative error = 1.1893160692681990159058726194793e-29 % Correct digits = 31 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 Radius of convergence (three term test) for eq 1 = 0.4806 Order of pole (three term test) = -12.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 1.6889214451105513391477556387697 y[1] (numeric) = 1.6889214451105513391477556387695 absolute error = 2e-31 relative error = 1.1841876990726981171496781810990e-29 % Correct digits = 31 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 Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -12.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 1.6961352386273567470198837344522 y[1] (numeric) = 1.696135238627356747019883734452 absolute error = 2e-31 relative error = 1.1791512577844641788356820844134e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -12.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 1.7032794192004101843678973251179 y[1] (numeric) = 1.7032794192004101843678973251177 absolute error = 2e-31 relative error = 1.1742054635632729773279155190613e-29 % Correct digits = 31 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 Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 1.7103532724176078098140288749692 y[1] (numeric) = 1.710353272417607809814028874969 absolute error = 2e-31 relative error = 1.1693490650460606702297887705380e-29 % Correct digits = 31 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 Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 1.7173560908995227616271746105814 y[1] (numeric) = 1.7173560908995227616271746105812 absolute error = 2e-31 relative error = 1.1645808406295243207824381777694e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -13.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 1.7242871743701425109281768525145 y[1] (numeric) = 1.7242871743701425109281768525144 absolute error = 1e-31 relative error = 5.7994979888734933269737662144258e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.04 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -13.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 1.7311458297268958793813133646877 y[1] (numeric) = 1.7311458297268958793813133646876 absolute error = 1e-31 relative error = 5.7765208616639718042472695734813e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4806 Order of pole (three term test) = -13.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 1.7379313711099627187285802261381 y[1] (numeric) = 1.737931371109962718728580226138 absolute error = 1e-31 relative error = 5.7539671394580506308555960959128e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.29 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4799 Order of pole (three term test) = -14.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = 1.7446431199708593212565726706296 y[1] (numeric) = 1.7446431199708593212565726706296 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 = 17.93 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4789 Order of pole (three term test) = -14.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 1.7512804051402927027120715242355 y[1] (numeric) = 1.7512804051402927027120715242354 absolute error = 1e-31 relative error = 5.7101078563138000370993153595601e-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 Radius of convergence (three term test) for eq 1 = 0.4778 Order of pole (three term test) = -14.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 1.7578425628952769722945887295286 y[1] (numeric) = 1.7578425628952769722945887295286 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 = 17.22 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4764 Order of pole (three term test) = -14.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 1.7643289370255050781448028237228 y[1] (numeric) = 1.7643289370255050781448028237228 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.87 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4749 Order of pole (three term test) = -15.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 1.770738878898969291209645130756 y[1] (numeric) = 1.7707388788989692912096451307559 absolute error = 1e-31 relative error = 5.6473600479241280545894125024680e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4732 Order of pole (three term test) = -15.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 1.7770717475268238654903337129732 y[1] (numeric) = 1.7770717475268238654903337129731 absolute error = 1e-31 relative error = 5.6272348113784054238570141075072e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4712 Order of pole (three term test) = -15.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 1.7833269096274833884613823157136 y[1] (numeric) = 1.7833269096274833884613823157135 absolute error = 1e-31 relative error = 5.6074968341552619311245879096031e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.87 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4691 Order of pole (three term test) = -15.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 1.7895037396899504118789575178716 y[1] (numeric) = 1.7895037396899504118789575178715 absolute error = 1e-31 relative error = 5.5881414373197124198260167760830e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4668 Order of pole (three term test) = -15.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 1.7956016200363660302682761024816 y[1] (numeric) = 1.7956016200363660302682761024816 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 = 15.23 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4644 Order of pole (three term test) = -16.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 1.8016199408837771520843192159106 y[1] (numeric) = 1.8016199408837771520843192159106 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 = 14.92 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4617 Order of pole (three term test) = -16.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 1.8075581004051142868702197986342 y[1] (numeric) = 1.8075581004051142868702197986341 absolute error = 1e-31 relative error = 5.5323256263567825837214471555805e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4589 Order of pole (three term test) = -16.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 1.8134155047893737506854221021026 y[1] (numeric) = 1.8134155047893737506854221021025 absolute error = 1e-31 relative error = 5.5144559940009386778827118227612e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4558 Order of pole (three term test) = -16.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=88033672, alloc=4521156, time=3.54 x[1] = 0.96 y[1] (analytic) = 1.8191915683009982716332221464304 y[1] (numeric) = 1.8191915683009982716332221464304 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 = 0.4526 Order of pole (three term test) = -17.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 1.8248857133384500574766200378563 y[1] (numeric) = 1.8248857133384500574766200378563 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 = 0.4492 Order of pole (three term test) = -17.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 1.8304973704919704680845332877192 y[1] (numeric) = 1.8304973704919704680845332877191 absolute error = 1e-31 relative error = 5.4629961021535732938417309594081e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4457 Order of pole (three term test) = -17.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 1.8360259786005205167892594115471 y[1] (numeric) = 1.8360259786005205167892594115471 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 = 0.4419 Order of pole (three term test) = -17.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 1.8414709848078965066525023216303 y[1] (numeric) = 1.8414709848078965066525023216303 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 = 0.438 Order of pole (three term test) = -18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 1.846831844618015190123098784782 y[1] (numeric) = 1.846831844618015190123098784782 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 = 0.4339 Order of pole (three term test) = -18.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = 1.8521080219493629236165499854554 y[1] (numeric) = 1.8521080219493629236165499854554 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 = 0.4296 Order of pole (three term test) = -18.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = 1.8572989891886033721462743852944 y[1] (numeric) = 1.8572989891886033721462743852944 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 = 0.4252 Order of pole (three term test) = -18.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = 1.8624042272433384032807916921162 y[1] (numeric) = 1.8624042272433384032807916921161 absolute error = 1e-31 relative error = 5.3694036201805817188446247790652e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4205 Order of pole (three term test) = -18.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 1.8674232255940168943814094850003 y[1] (numeric) = 1.8674232255940168943814094850002 absolute error = 1e-31 relative error = 5.3549724898698611141401121522493e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4158 Order of pole (three term test) = -19.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 1.8723554823449862622829459219974 y[1] (numeric) = 1.8723554823449862622829459219973 absolute error = 1e-31 relative error = 5.3408661412285568070262524031186e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4108 Order of pole (three term test) = -19.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = 1.8772005042746816103070632577768 y[1] (numeric) = 1.8772005042746816103070632577767 absolute error = 1e-31 relative error = 5.3270814583889269437213141478418e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4057 Order of pole (three term test) = -19.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 1.8819578068849474737353349876248 y[1] (numeric) = 1.8819578068849474737353349876246 absolute error = 2e-31 relative error = 1.0627230816138424591468231301519e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4004 Order of pole (three term test) = -19.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = 1.886626914449487231608600628636 y[1] (numeric) = 1.8866269144494872316086006286359 absolute error = 1e-31 relative error = 5.3004650381116680305033592422926e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.395 Order of pole (three term test) = -19.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 1.8912073600614353399518025778717 y[1] (numeric) = 1.8912073600614353399518025778716 absolute error = 1e-31 relative error = 5.2876274760664810486298889444334e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3894 Order of pole (three term test) = -20.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 1.8956986856800476292406259593394 y[1] (numeric) = 1.8956986856800476292406259593393 absolute error = 1e-31 relative error = 5.2750999278203755255959132055767e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3836 Order of pole (three term test) = -20.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 1.9001004421765049971191032473392 y[1] (numeric) = 1.9001004421765049971191032473391 absolute error = 1e-31 relative error = 5.2628796762687535009278191791115e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3777 Order of pole (three term test) = -20.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 1.9044121893788259160370815224114 y[1] (numeric) = 1.9044121893788259160370815224113 absolute error = 1e-31 relative error = 5.2509640800302600469780576938800e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3717 Order of pole (three term test) = -20.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = 1.9086334961158832645942155781022 y[1] (numeric) = 1.9086334961158832645942155781021 absolute error = 1e-31 relative error = 5.2393505722027037878934821367571e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3655 Order of pole (three term test) = -20.83 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = 1.9127639402605210809440330497537 y[1] (numeric) = 1.9127639402605210809440330497536 absolute error = 1e-31 relative error = 5.2280366591593033891786913326237e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3591 Order of pole (three term test) = -21.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 1.9168031087717669266186616668743 y[1] (numeric) = 1.9168031087717669266186616668743 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 = 0.3526 Order of pole (three term test) = -21.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 1.920750597736135639573013008962 y[1] (numeric) = 1.920750597736135639573013008962 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 = 0.346 Order of pole (three term test) = -21.37 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 1.9246060124080203461075380258748 y[1] (numeric) = 1.9246060124080203461075380258747 absolute error = 1e-31 relative error = 5.1958686274123412040520623721069e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3392 Order of pole (three term test) = -21.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 1.9283689672491666926020211116027 y[1] (numeric) = 1.9283689672491666926020211116026 absolute error = 1e-31 relative error = 5.1857295827909311668193449338272e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3323 Order of pole (three term test) = -21.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 1.9320390859672263496701344354948 y[1] (numeric) = 1.9320390859672263496701344354948 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 = 0.3253 Order of pole (three term test) = -21.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 1.9356160015533859334164648885436 y[1] (numeric) = 1.9356160015533859334164648885436 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 = 0.3181 Order of pole (three term test) = -22.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 1.9390993563190675809352452718884 y[1] (numeric) = 1.9390993563190675809352452718884 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 = 0.3108 Order of pole (three term test) = -22.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 1.9424888019316975100238235653892 y[1] (numeric) = 1.9424888019316975100238235653893 absolute error = 1e-31 relative error = 5.1480348252486984463185370933518e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3034 Order of pole (three term test) = -22.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 1.9457839994495389862847059630818 y[1] (numeric) = 1.9457839994495389862847059630818 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 = 0.2959 Order of pole (three term test) = -22.49 bytes used=92035032, alloc=4521156, time=3.70 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 1.948984619355586214348490847036 y[1] (numeric) = 1.9489846193555862143484908470361 absolute error = 1e-31 relative error = 5.1308768169275793224616963221774e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2882 Order of pole (three term test) = -22.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = 1.9520903415905157638568162214254 y[1] (numeric) = 1.9520903415905157638568162214255 absolute error = 1e-31 relative error = 5.1227137325274828493281968055245e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2804 Order of pole (three term test) = -22.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 1.9551008555846922350901817421829 y[1] (numeric) = 1.955100855584692235090181742183 absolute error = 1e-31 relative error = 5.1148256477077757504971036809715e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2725 Order of pole (three term test) = -22.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 1.9580158602892249637007538591603 y[1] (numeric) = 1.9580158602892249637007538591604 absolute error = 1e-31 relative error = 5.1072109285789273967217335580500e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2645 Order of pole (three term test) = -23.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 1.9608350642060726589055612912854 y[1] (numeric) = 1.9608350642060726589055612912855 absolute error = 1e-31 relative error = 5.0998680014164907043302000758074e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2564 Order of pole (three term test) = -23.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 1.9635581854171929647013486300396 y[1] (numeric) = 1.9635581854171929647013486300397 absolute error = 1e-31 relative error = 5.0927953519621938824785291886094e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2482 Order of pole (three term test) = -23.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 1.9661849516127340291692578059375 y[1] (numeric) = 1.9661849516127340291692578059376 absolute error = 1e-31 relative error = 5.0859915247533800906999030424176e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2399 Order of pole (three term test) = -23.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 1.9687151001182652627358998459728 y[1] (numeric) = 1.9687151001182652627358998459729 absolute error = 1e-31 relative error = 5.0794551224802801103037495575985e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2315 Order of pole (three term test) = -23.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 1.9711483779210445623376830377638 y[1] (numeric) = 1.9711483779210445623376830377639 absolute error = 1e-31 relative error = 5.0731848053706262018646746885778e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.223 Order of pole (three term test) = -23.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 1.9734845416953193747878703480896 y[1] (numeric) = 1.9734845416953193747878703480897 absolute error = 1e-31 relative error = 5.0671792906011378093288912483107e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2145 Order of pole (three term test) = -23.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 1.9757233578266590692611135392652 y[1] (numeric) = 1.9757233578266590692611135392654 absolute error = 2e-31 relative error = 1.0122874703470863415713470931436e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2058 Order of pole (three term test) = -23.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 1.9778646024353161856784924394266 y[1] (numeric) = 1.9778646024353161856784924394268 absolute error = 2e-31 relative error = 1.0111915636375861210377309014810e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.197 Order of pole (three term test) = -23.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 1.9799080613986142228876885048919 y[1] (numeric) = 1.9799080613986142228876885048921 absolute error = 2e-31 relative error = 1.0101479149426730243932814239125e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1882 Order of pole (three term test) = -24.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 1.981853530372359727878131085206 y[1] (numeric) = 1.9818535303723597278781310852062 absolute error = 2e-31 relative error = 1.0091563121842969042260942984493e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1793 Order of pole (three term test) = -24.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 1.9837008148112765448400382244429 y[1] (numeric) = 1.9837008148112765448400382244431 absolute error = 2e-31 relative error = 1.0082165541633223111072689310665e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1703 Order of pole (three term test) = -24.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 1.9854497299884601806594745788061 y[1] (numeric) = 1.9854497299884601806594745788063 absolute error = 2e-31 relative error = 1.0073284504723392761674314487082e-29 % Correct digits = 31 h = 0.01 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) = -24.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 1.9871001010138503414290888619422 y[1] (numeric) = 1.9871001010138503414290888619424 absolute error = 2e-31 relative error = 1.0064918214133087322649379412998e-29 % Correct digits = 31 h = 0.01 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) = -24.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 1.9886517628517197927362734733357 y[1] (numeric) = 1.9886517628517197927362734733359 absolute error = 2e-31 relative error = 1.0057064979199811606020492374513e-29 % Correct digits = 31 h = 0.01 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) = -24.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 1.9901045603371777948572914954818 y[1] (numeric) = 1.990104560337177794857291495482 absolute error = 2e-31 relative error = 1.0049723214850307406707637042120e-29 % Correct digits = 31 h = 0.01 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) = -24.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 1.991458348191686462527604463958 y[1] (numeric) = 1.9914583481916864625276044639582 absolute error = 2e-31 relative error = 1.0042891440918509065468827275543e-29 % Correct digits = 31 h = 0.01 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) = -24.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 1.992712991037588497665354134323 y[1] (numeric) = 1.9927129910375884976653541343232 absolute error = 2e-31 relative error = 1.0036568281509607760961452352316e-29 % Correct digits = 31 h = 0.01 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) = -24.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 1.99386836341164484228683230125 y[1] (numeric) = 1.9938683634116448422868323012502 absolute error = 2e-31 relative error = 1.0030752464409754258069740119821e-29 % Correct digits = 31 h = 0.01 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) = -24.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = 1.9949243497775808978599284627356 y[1] (numeric) = 1.9949243497775808978599284627357 absolute error = 1e-31 relative error = 5.0127214102704821841242620645313e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09641 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = 1.9958808445376400564840751325627 y[1] (numeric) = 1.9958808445376400564840751325628 absolute error = 1e-31 relative error = 5.0103191417304127067601727394102e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08695 Order of pole (three term test) = -24.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 1.9967377520431433885532007170437 y[1] (numeric) = 1.9967377520431433885532007170438 absolute error = 1e-31 relative error = 5.0081689444533177841620622655524e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07747 Order of pole (three term test) = -24.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 1.9974949866040544309417233711415 y[1] (numeric) = 1.9974949866040544309417233711416 absolute error = 1e-31 relative error = 5.0062703871918205606571889060541e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06795 Order of pole (three term test) = -24.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = 1.9981524724975481192427378648367 y[1] (numeric) = 1.9981524724975481192427378648368 absolute error = 1e-31 relative error = 5.0046230893985347452258781746880e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0584 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=96036392, alloc=4521156, time=3.86 x[1] = 1.52 y[1] (analytic) = 1.9987101439755830071723123941168 y[1] (numeric) = 1.9987101439755830071723123941169 absolute error = 1e-31 relative error = 5.0032267210638441383542159379082e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04883 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (analytic) = 1.999167945271476015924265068709 y[1] (numeric) = 1.999167945271476015924265068709 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 = 0.03924 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = 1.99952583060547905600596353844 y[1] (numeric) = 1.9995258306054790560059635384401 absolute error = 1e-31 relative error = 5.0011857045987181874359925072167e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02964 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 1.9997837641893569638976113476345 y[1] (numeric) = 1.9997837641893569638976113476345 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 = 0.02002 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = 1.9999417202299662957451700234135 y[1] (numeric) = 1.9999417202299662957451700234135 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 = 0.0104 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 1.9999996829318346202105299238233 y[1] (numeric) = 1.9999996829318346202105299238233 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 = 0.0007668 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 1.9999576464987400525517942322517 y[1] (numeric) = 1.9999576464987400525517942322517 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] = 1.59 y[1] (analytic) = 1.9998156151342908719815843437455 y[1] (numeric) = 1.9998156151342908719815843437455 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] = 1.6 y[1] (analytic) = 1.9995736030415051643421138255462 y[1] (numeric) = 1.9995736030415051643421138255462 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] = 1.61 y[1] (analytic) = 1.9992316344213905321324131478443 y[1] (numeric) = 1.9992316344213905321324131478443 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] = 1.62 y[1] (analytic) = 1.9987897434705240139155188912468 y[1] (numeric) = 1.9987897434705240139155188912468 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] = 1.63 y[1] (analytic) = 1.9982479743776324551116699849331 y[1] (numeric) = 1.9982479743776324551116699849331 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = 1.9976063813191736721375819743679 y[1] (numeric) = 1.9976063813191736721375819743679 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] = 1.65 y[1] (analytic) = 1.9968650284539188517717030402022 y[1] (numeric) = 1.9968650284539188517717030402022 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] = 1.66 y[1] (analytic) = 1.996023989916536727501000590613 y[1] (numeric) = 1.996023989916536727501000590613 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] = 1.67 y[1] (analytic) = 1.9950833498101801744262972465342 y[1] (numeric) = 1.9950833498101801744262972465343 absolute error = 1e-31 relative error = 5.0123219167517177023992799637250e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9940432021980759640604878691936 y[1] (numeric) = 1.9940432021980759640604878691936 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] = 1.69 y[1] (analytic) = 1.9929036510941185200371492939456 y[1] (numeric) = 1.9929036510941185200371492939456 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] = 1.7 y[1] (analytic) = 1.9916648104524686153461333986479 y[1] (numeric) = 1.9916648104524686153461333986479 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] = 1.71 y[1] (analytic) = 1.9903268041561580512177522238611 y[1] (numeric) = 1.9903268041561580512177522238612 absolute error = 1e-31 relative error = 5.0243005214612057356568071563363e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9888897660047014571781706570855 y[1] (numeric) = 1.9888897660047014571781706570855 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] = 1.73 y[1] (analytic) = 1.9873538397007164510856776762221 y[1] (numeric) = 1.9873538397007164510856776762221 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] = 1.74 y[1] (analytic) = 1.9857191788355534971206826956656 y[1] (numeric) = 1.9857191788355534971206826956656 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) = 1.983985946873936898731662936968 y[1] (numeric) = 1.983985946873936898731662936968 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] = 1.76 y[1] (analytic) = 1.982154317137618462424968099456 y[1] (numeric) = 1.982154317137618462424968099456 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] = 1.77 y[1] (analytic) = 1.9802244727880454670184814488984 y[1] (numeric) = 1.9802244727880454670184814488985 absolute error = 1e-31 relative error = 5.0499325391734799011994076432569e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 1.9781966068080446715477686473056 y[1] (numeric) = 1.9781966068080446715477686473057 absolute error = 1e-31 relative error = 5.0551092674937315569886011239238e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9760709219825241934086604331086 y[1] (numeric) = 1.9760709219825241934086604331087 absolute error = 1e-31 relative error = 5.0605471133431501111877332917962e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9738476308781951865323731788434 y[1] (numeric) = 1.9738476308781951865323731788434 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=100037052, alloc=4521156, time=4.02 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (analytic) = 1.9715269558223153474084512690904 y[1] (numeric) = 1.9715269558223153474084512690904 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] = 1.82 y[1] (analytic) = 1.969109128880456374587215318498 y[1] (numeric) = 1.9691091288804563745872153184981 absolute error = 1e-31 relative error = 5.0784386976487858095515012631170e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9665943918332976048972389297428 y[1] (numeric) = 1.9665943918332976048972389297429 absolute error = 1e-31 relative error = 5.0849326335553134481580791756847e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9639829961524481469948936717271 y[1] (numeric) = 1.9639829961524481469948936717272 absolute error = 1e-31 relative error = 5.0916937771816537247673939979239e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9612752029752999300124591686361 y[1] (numeric) = 1.9612752029752999300124591686362 absolute error = 1e-31 relative error = 5.0987235166333456303367967199455e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9584712830789141819789777659032 y[1] (numeric) = 1.9584712830789141819789777659033 absolute error = 1e-31 relative error = 5.1060232980689879986702279614650e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9555715168529439493442504921726 y[1] (numeric) = 1.9555715168529439493442504921727 absolute error = 1e-31 relative error = 5.1135946263385799919092474160174e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9525761942715953653314574258151 y[1] (numeric) = 1.9525761942715953653314574258152 absolute error = 1e-31 relative error = 5.1214390656496147396653627917283e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9494856148646304709682016721383 y[1] (numeric) = 1.9494856148646304709682016721384 absolute error = 1e-31 relative error = 5.1295582402614373141324107594334e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.946300087687414488489709611635 y[1] (numeric) = 1.946300087687414488489709611635 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 1.9430199312900105423618865769482 y[1] (numeric) = 1.9430199312900105423618865769483 absolute error = 1e-31 relative error = 5.1466275970523864581213008447325e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.939645473685324918426371339687 y[1] (numeric) = 1.9396454736853249184263713396871 absolute error = 1e-31 relative error = 5.1555813346652507782178678239525e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9361770523163060466151293727488 y[1] (numeric) = 1.9361770523163060466151293727489 absolute error = 1e-31 relative error = 5.1648169200418439720928143642985e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9326150140222004873089793388657 y[1] (numeric) = 1.9326150140222004873089793388658 absolute error = 1e-31 relative error = 5.1743362891442005597916062389953e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9289597150038692957132970350915 y[1] (numeric) = 1.9289597150038692957132970350916 absolute error = 1e-31 relative error = 5.1841414427775859610102511549344e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.92521152078816823258555628949 y[1] (numeric) = 1.9252115207881682325855562894901 absolute error = 1e-31 relative error = 5.1942344474990828103291395378429e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.9213708061913953832639509971532 y[1] (numeric) = 1.9213708061913953832639509971532 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 1.917437955281809840204735217402 y[1] (numeric) = 1.917437955281809840204735217402 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = 1.9134133613412251971287932710576 y[1] (numeric) = 1.9134133613412251971287932710576 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 y[1] (analytic) = 1.9092974268256816953960198659117 y[1] (numeric) = 1.9092974268256816953960198659117 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) = 1.9050905633252009553600997102737 y[1] (numeric) = 1.9050905633252009553600997102737 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 1.9007931915226273171970135245537 y[1] (numeric) = 1.9007931915226273171970135245537 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] = 2.03 y[1] (analytic) = 1.8964057411515599070388888319676 y[1] (numeric) = 1.8964057411515599070388888319676 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] = 2.04 y[1] (analytic) = 1.8919286509533796351715256485842 y[1] (numeric) = 1.8919286509533796351715256485842 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) = 1.8873623686333754235599666046803 y[1] (numeric) = 1.8873623686333754235599666046803 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) = 1.8827073508159740500427975851999 y[1] (numeric) = 1.8827073508159740500427975851999 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) = 1.8779640629990780861734511204438 y[1] (numeric) = 1.8779640629990780861734511204438 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) = 1.8731329795075164948766768050246 y[1] (numeric) = 1.8731329795075164948766768050246 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=104038124, alloc=4521156, time=4.19 x[1] = 2.09 y[1] (analytic) = 1.8682145834456125428216220587275 y[1] (numeric) = 1.8682145834456125428216220587275 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) = 1.863209366648873770680759313269 y[1] (numeric) = 1.863209366648873770680759313269 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] = 2.11 y[1] (analytic) = 1.8581178296348088522373755083107 y[1] (numeric) = 1.8581178296348088522373755083107 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) = 1.8529404815528762606147273336542 y[1] (numeric) = 1.8529404815528762606147273336542 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 1.8476778401335697467185299963159 y[1] (numeric) = 1.8476778401335697467185299963159 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) = 1.8423304316366457213025066370689 y[1] (numeric) = 1.8423304316366457213025066370689 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) = 1.8368987907984977178756481370438 y[1] (numeric) = 1.8368987907984977178756481370438 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) = 1.8313834607786831989610381203463 y[1] (numeric) = 1.8313834607786831989610381203463 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 1.8257849931056080529810564239434 y[1] (numeric) = 1.8257849931056080529810564239434 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) = 1.8201039476213742132740097460839 y[1] (numeric) = 1.820103947621374213274009746084 absolute error = 1e-31 relative error = 5.4941916988140298536327700705833e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.814340892425795914434327645905 y[1] (numeric) = 1.8143408924257959144343276459051 absolute error = 1e-31 relative error = 5.5116433971952635456861645933305e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.8084964038195901843040369104161 y[1] (numeric) = 1.8084964038195901843040369104162 absolute error = 1e-31 relative error = 5.5294552861038301567256314290129e-30 % Correct digits = 32 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 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) = 1.802571066246747252518974042556 y[1] (numeric) = 1.802571066246747252518974042556 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 = 14.87 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] = 2.22 y[1] (analytic) = 1.7965654722360866385208567496092 y[1] (numeric) = 1.7965654722360866385208567496092 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 = 15.18 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] = 2.23 y[1] (analytic) = 1.7904802223420047633777101271885 y[1] (numeric) = 1.7904802223420047633777101271886 absolute error = 1e-31 relative error = 5.5850938062413689785812703547248e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 1.7843159250844200106020886706045 y[1] (numeric) = 1.7843159250844200106020886706046 absolute error = 1e-31 relative error = 5.6043886956436133623004795320691e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 1.7780731968879212414109666755878 y[1] (numeric) = 1.7780731968879212414109666755879 absolute error = 1e-31 relative error = 5.6240654307722171190821043758260e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 1.7717526620201258495250616377403 y[1] (numeric) = 1.7717526620201258495250616377405 absolute error = 2e-31 relative error = 1.1288257344677162523309845369758e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.48 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] = 2.27 y[1] (analytic) = 1.7653549525292535196507426019347 y[1] (numeric) = 1.7653549525292535196507426019349 absolute error = 2e-31 relative error = 1.1329166393050681408669489206921e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = 1.7588807081809219322166535763009 y[1] (numeric) = 1.7588807081809219322166535763011 absolute error = 2e-31 relative error = 1.1370867795056150350099992146104e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.16 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] = 2.29 y[1] (analytic) = 1.7523305763941707347419082779736 y[1] (numeric) = 1.7523305763941707347419082779738 absolute error = 2e-31 relative error = 1.1413371580352532145903746172057e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 1.7457052121767201773854062116435 y[1] (numeric) = 1.7457052121767201773854062116436 absolute error = 1e-31 relative error = 5.7283440126360154499912976992372e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.87 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] = 2.31 y[1] (analytic) = 1.7390052780594708867587641920983 y[1] (numeric) = 1.7390052780594708867587641920984 absolute error = 1e-31 relative error = 5.7504138291971404760439061093416e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 1.7322314440302513279708986777247 y[1] (numeric) = 1.7322314440302513279708986777248 absolute error = 1e-31 relative error = 5.7729006331473579286921492026410e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = 1.7253843874668195801028441924754 y[1] (numeric) = 1.7253843874668195801028441924755 absolute error = 1e-31 relative error = 5.7958099497363786177046107865010e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 1.718464793069126124879428686794 y[1] (numeric) = 1.7184647930691261248794286867941 absolute error = 1e-31 relative error = 5.8191474392328414070824568526825e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 1.7114733527908444222024911820132 y[1] (numeric) = 1.7114733527908444222024911820133 absolute error = 1e-31 relative error = 5.8429189000771308407099791936325e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.24 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] = 2.36 y[1] (analytic) = 1.7044107657701761194310307129327 y[1] (numeric) = 1.7044107657701761194310307129328 absolute error = 1e-31 relative error = 5.8671302721332415280843951046881e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.86 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=108039920, alloc=4521156, time=4.34 x[1] = 2.37 y[1] (analytic) = 1.6972777382599378138296964202892 y[1] (numeric) = 1.6972777382599378138296964202893 absolute error = 1e-31 relative error = 5.8917876400429766323243923406339e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.48 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] = 2.38 y[1] (analytic) = 1.6900749835569363594511131070202 y[1] (numeric) = 1.6900749835569363594511131070203 absolute error = 1e-31 relative error = 5.9168972366858972633842040931045e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 1.682803221930639780862500311013 y[1] (numeric) = 1.6828032219306397808625003110132 absolute error = 2e-31 relative error = 1.1884930893497149134414363654770e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 1.6754631805511509265657715253413 y[1] (numeric) = 1.6754631805511509265657715253414 absolute error = 1e-31 relative error = 5.9684988104068370815749986399565e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.4 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] = 2.41 y[1] (analytic) = 1.6680555934164910646857498006547 y[1] (numeric) = 1.6680555934164910646857498006548 absolute error = 1e-31 relative error = 5.9950040271248527805796052913975e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.06 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] = 2.42 y[1] (analytic) = 1.6605812012792006925063341065602 y[1] (numeric) = 1.6605812012792006925063341065603 absolute error = 1e-31 relative error = 6.0219879595750384454833072308559e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 1.6530407515722648997124970471899 y[1] (numeric) = 1.65304075157226489971249704719 absolute error = 1e-31 relative error = 6.0494576376829488891749456671227e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.38 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] = 2.44 y[1] (analytic) = 1.6454349983343706927400610729825 y[1] (numeric) = 1.6454349983343706927400610729826 absolute error = 1e-31 relative error = 6.0774202628014654497184761948944e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.06 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] = 2.45 y[1] (analytic) = 1.6377647021345037544385328556338 y[1] (numeric) = 1.6377647021345037544385328556338 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 = 15.73 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] = 2.46 y[1] (analytic) = 1.6300306299958921793081937186159 y[1] (numeric) = 1.6300306299958921793081937186159 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 = 15.41 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] = 2.47 y[1] (analytic) = 1.6222335553193047898745424048558 y[1] (numeric) = 1.6222335553193047898745424048557 absolute error = 1e-31 relative error = 6.1643404966011176812438993960883e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = 1.6143742578057117043045348806656 y[1] (numeric) = 1.6143742578057117043045348806655 absolute error = 1e-31 relative error = 6.1943505055588478063216065453407e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.79 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] = 2.49 y[1] (analytic) = 1.6064535233783148891434102397918 y[1] (numeric) = 1.6064535233783148891434102397917 absolute error = 1e-31 relative error = 6.2248921954308108540006066531960e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 1.5984721441039564940518547021862 y[1] (numeric) = 1.5984721441039564940518547021861 absolute error = 1e-31 relative error = 6.2559738916223809323680023061471e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = 1.590430918113912827644537155024 y[1] (numeric) = 1.590430918113912827644537155024 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 1.5823306495240818949664275822971 y[1] (numeric) = 1.5823306495240818949664275822971 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] = 2.53 y[1] (analytic) = 1.5741721483545724777866405874022 y[1] (numeric) = 1.5741721483545724777866405874022 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 1.565956230448702798734765747982 y[1] (numeric) = 1.565956230448702798734765747982 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = 1.5576837173914168693457702817662 y[1] (numeric) = 1.5576837173914168693457702817662 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = 1.5493554364271266803106833831373 y[1] (numeric) = 1.5493554364271266803106833831372 absolute error = 1e-31 relative error = 6.4542969062414659438401251231488e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 1.5409722203769884496455725487458 y[1] (numeric) = 1.5409722203769884496455725487458 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] = 2.58 y[1] (analytic) = 1.5325349075556212010850587644716 y[1] (numeric) = 1.5325349075556212010850587644716 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] = 2.59 y[1] (analytic) = 1.5240443416872760007731302488759 y[1] (numeric) = 1.5240443416872760007731302488759 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] = 2.6 y[1] (analytic) = 1.5155013718214642352577269352094 y[1] (numeric) = 1.5155013718214642352577269352094 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] = 2.61 y[1] (analytic) = 1.5069068522480533678909866995555 y[1] (numeric) = 1.5069068522480533678909866995555 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] = 2.62 y[1] (analytic) = 1.4982616424118386639887600099976 y[1] (numeric) = 1.4982616424118386639887600099976 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] = 2.63 y[1] (analytic) = 1.4895666068265994275056870536116 y[1] (numeric) = 1.4895666068265994275056870536116 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] = 2.64 y[1] (analytic) = 1.4808226149886483435305502695329 y[1] (numeric) = 1.4808226149886483435305502695328 absolute error = 1e-31 relative error = 6.7530032961285223035000128588586e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=112041232, alloc=4521156, time=4.51 x[1] = 2.65 y[1] (analytic) = 1.4720305412898825715956107783974 y[1] (numeric) = 1.4720305412898825715956107783973 absolute error = 1e-31 relative error = 6.7933373116276463929622807634632e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = 1.4631912649303452846181405937964 y[1] (numeric) = 1.4631912649303452846181405937963 absolute error = 1e-31 relative error = 6.8343765027028414840271986631591e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 1.4543056698303063972473913211913 y[1] (numeric) = 1.4543056698303063972473913211912 absolute error = 1e-31 relative error = 6.8761335443097295179643921677375e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 1.4453746445418712754708988319294 y[1] (numeric) = 1.4453746445418712754708988319294 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = 1.436399082160126266535504118761 y[1] (numeric) = 1.4363990821601262665355041187609 absolute error = 1e-31 relative error = 6.9618535156410134689666493987095e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 1.4273798802338299345560530858579 y[1] (numeric) = 1.4273798802338299345560530858578 absolute error = 1e-31 relative error = 7.0058434607904267797675710847523e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = 1.4183179406756589326137906811086 y[1] (numeric) = 1.4183179406756589326137906811085 absolute error = 1e-31 relative error = 7.0506053073235437914383616903355e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = 1.4092141696720174866824446740074 y[1] (numeric) = 1.4092141696720174866824446740073 absolute error = 1e-31 relative error = 7.0961534557429366788879393526631e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 1.4000694775924195103584479578944 y[1] (numeric) = 1.4000694775924195103584479578943 absolute error = 1e-31 relative error = 7.1425026829355283900967676110507e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = 1.3908847788984524121083117016403 y[1] (numeric) = 1.3908847788984524121083117016401 absolute error = 2e-31 relative error = 1.4379336306950977797316343373181e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = 1.3816609920523316985765613723778 y[1] (numeric) = 1.3816609920523316985765613723776 absolute error = 2e-31 relative error = 1.4475330862668287119521462972938e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 1.3723990394250555184177005924498 y[1] (numeric) = 1.3723990394250555184177005924496 absolute error = 2e-31 relative error = 1.4573020984027122311852859218502e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = 1.3630998472041683311212820091725 y[1] (numeric) = 1.3630998472041683311212820091723 absolute error = 2e-31 relative error = 1.4672439470242529137252962894959e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 1.3537643453011429243863393172273 y[1] (numeric) = 1.3537643453011429243863393172272 absolute error = 1e-31 relative error = 7.3868099974043225636108880988959e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 1.3443934672583900417662615955623 y[1] (numeric) = 1.3443934672583900417662615955621 absolute error = 2e-31 relative error = 1.4876597132523878476707375692431e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 1.3349881501559049195438537527124 y[1] (numeric) = 1.3349881501559049195438537527122 absolute error = 2e-31 relative error = 1.4981406387513121402988476048624e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = 1.3255493345175600681051012812063 y[1] (numeric) = 1.3255493345175600681051012812061 absolute error = 2e-31 relative error = 1.5088084222288938287329434848217e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = 1.3160779642170536684554128560246 y[1] (numeric) = 1.3160779642170536684554128560243 absolute error = 3e-31 relative error = 2.2795002131843506168479856380455e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = 1.3065749863835229889603130778681 y[1] (numeric) = 1.3065749863835229889603130778678 absolute error = 3e-31 relative error = 2.2960794682773765725803158632272e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = 1.2970413513068322608902560680973 y[1] (numeric) = 1.297041351306832260890256068097 absolute error = 3e-31 relative error = 2.3129563270880716746085794943971e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 1.2874780123425444839030789266917 y[1] (numeric) = 1.2874780123425444839030789266914 absolute error = 3e-31 relative error = 2.3301368809720879836539577894521e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = 1.2778859258165866642043569097532 y[1] (numeric) = 1.2778859258165866642043569097529 absolute error = 3e-31 relative error = 2.3476273894189411165786211289924e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 1.2682660509296180187823989209871 y[1] (numeric) = 1.2682660509296180187823989209868 absolute error = 3e-31 relative error = 2.3654342854963670011957727083442e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = 1.2586193496611107088177669201177 y[1] (numeric) = 1.2586193496611107088177669201173 absolute error = 4e-31 relative error = 3.1780855753385796650456475741914e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = 1.2489467866731526941140458405805 y[1] (numeric) = 1.2489467866731526941140458405801 absolute error = 4e-31 relative error = 3.2026984997934850976340977751985e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 1.2392493292139823281842569187396 y[1] (numeric) = 1.2392493292139823281842569187392 absolute error = 4e-31 relative error = 3.2277604721699359494621608101687e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = 1.229527947021264340453018223827 y[1] (numeric) = 1.2295279470212643404530182238266 absolute error = 4e-31 relative error = 3.2532810740013387622925457247450e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = 1.2197836122251168778956290930646 y[1] (numeric) = 1.2197836122251168778956290930642 absolute error = 4e-31 relative error = 3.2792701589942175252235791894286e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=116041944, alloc=4521156, time=4.67 x[1] = 2.93 y[1] (analytic) = 1.2100172992508993033291040342591 y[1] (numeric) = 1.2100172992508993033291040342587 absolute error = 4e-31 relative error = 3.3057378621581117357198114099627e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = 1.2002299847217704714943170944231 y[1] (numeric) = 1.2002299847217704714943170944227 absolute error = 4e-31 relative error = 3.3326946092979455514922821192404e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 1.1904226473610272270204473140574 y[1] (numeric) = 1.190422647361027227020447314057 absolute error = 4e-31 relative error = 3.3601511268853523048700450715492e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 1.1805962678942328903405445088014 y[1] (numeric) = 1.180596267894232890340544508801 absolute error = 4e-31 relative error = 3.3881184523262879701788275698032e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = 1.170751828951145518628064498668 y[1] (numeric) = 1.1707518289511455186280644986676 absolute error = 4e-31 relative error = 3.4166079446431653699229679897348e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 1.1608903149674557488465539545413 y[1] (numeric) = 1.160890314967455748846553954541 absolute error = 3e-31 relative error = 2.5842234716930183173243269372778e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = 1.1510127120863440490462950356105 y[1] (numeric) = 1.1510127120863440490462950356102 absolute error = 3e-31 relative error = 2.6064004059191944315529243141445e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 1.1411200080598672221007448028081 y[1] (numeric) = 1.1411200080598672221007448028078 absolute error = 3e-31 relative error = 2.6289960554636154528328783203420e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = 1.1312131921501840231502181246848 y[1] (numeric) = 1.1312131921501840231502181246845 absolute error = 3e-31 relative error = 2.6520199912959545544553436322264e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = 1.1212932550306297681087579963391 y[1] (numeric) = 1.1212932550306297681087579963388 absolute error = 3e-31 relative error = 2.6754820708504579425038196999236e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = 1.1113611886866498256909050329173 y[1] (numeric) = 1.1113611886866498256909050329169 absolute error = 4e-31 relative error = 3.5991899309773420495461350994889e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = 1.1014179863166018995266083126088 y[1] (numeric) = 1.1014179863166018995266083126084 absolute error = 4e-31 relative error = 3.6316821131430139406694916077635e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = 1.0914646422324370200534015886964 y[1] (numeric) = 1.091464642232437020053401588696 absolute error = 4e-31 relative error = 3.6648003473741156043474375626958e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = 1.0815021517602691780038900888357 y[1] (numeric) = 1.0815021517602691780038900888353 absolute error = 4e-31 relative error = 3.6985594466821354012012967012881e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = 1.0715315111408435424423407903189 y[1] (numeric) = 1.0715315111408435424423407903185 absolute error = 4e-31 relative error = 3.7329746800831456110202306009587e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = 1.0615537174299132164456296371357 y[1] (numeric) = 1.0615537174299132164456296371353 absolute error = 4e-31 relative error = 3.7680617893593230538051602323753e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = 1.0515697683985344926699585105746 y[1] (numeric) = 1.0515697683985344926699585105742 absolute error = 4e-31 relative error = 3.8038370065466162663557389723232e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = 1.0415806624332905791946982715967 y[1] (numeric) = 1.0415806624332905791946982715963 absolute error = 4e-31 relative error = 3.8403170721846857708863738592162e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = 1.0315873984364537731876268727034 y[1] (numeric) = 1.031587398436453773187626872703 absolute error = 4e-31 relative error = 3.8775192543672795921686194180398e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = 1.0215909757260960660909981042019 y[1] (numeric) = 1.0215909757260960660909981042015 absolute error = 4e-31 relative error = 3.9154613686333700268877518867403e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = 1.0115923939361581691846814831183 y[1] (numeric) = 1.0115923939361581691846814831179 absolute error = 4e-31 relative error = 3.9541617987416786850333532636119e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = 1.0015926529164869525405414363244 y[1] (numeric) = 1.001592652916486952540541436324 absolute error = 4e-31 relative error = 3.9936395183736646345327266444476e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = 0.99159275263285129354085848342893 y[1] (numeric) = 0.99159275263285129354085848342849 absolute error = 4.4e-31 relative error = 4.4373055251939210004885439927396e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008107 Order of pole (three term test) = -0.8946 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (analytic) = 0.98159369306694633329262072881263 y[1] (numeric) = 0.98159369306694633329262072881219 absolute error = 4.4e-31 relative error = 4.4825063884145317479488930755361e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01775 Order of pole (three term test) = -0.901 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (analytic) = 0.97159647411639614042871472510327 y[1] (numeric) = 0.97159647411639614042871472510283 absolute error = 4.4e-31 relative error = 4.5286290319255368759710430872690e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02738 Order of pole (three term test) = -0.9124 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = 0.96160209549476478194630475327388 y[1] (numeric) = 0.96160209549476478194630475327344 absolute error = 4.4e-31 relative error = 4.5756971834967832310669968290697e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.037 Order of pole (three term test) = -0.9285 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = 0.95161155663158579989199285154883 y[1] (numeric) = 0.95161155663158579989199285154839 absolute error = 4.4e-31 relative error = 4.6237353564459177357974584759506e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04661 Order of pole (three term test) = -0.9495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = 0.9416258565724200908627825853809 y[1] (numeric) = 0.94162585657242009086278258538046 absolute error = 4.4e-31 relative error = 4.6727688808549594592273188529471e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05619 Order of pole (three term test) = -0.9752 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=120042860, alloc=4521156, time=4.83 x[1] = 3.21 y[1] (analytic) = 0.93164599387895218245161163932314 y[1] (numeric) = 0.93164599387895218245161163932269 absolute error = 4.5e-31 relative error = 4.8301608438888220331470922256761e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06576 Order of pole (three term test) = -1.006 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = 0.92167296652913489692655585208396 y[1] (numeric) = 0.92167296652913489692655585208351 absolute error = 4.5e-31 relative error = 4.8824259400232186624363588292243e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0753 Order of pole (three term test) = -1.041 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (analytic) = 0.91170777181739238759412427147028 y[1] (numeric) = 0.91170777181739238759412427146983 absolute error = 4.5e-31 relative error = 4.9357920806463336885743435540541e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08481 Order of pole (three term test) = -1.081 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (analytic) = 0.90175140625489152745984504056236 y[1] (numeric) = 0.90175140625489152745984504056192 absolute error = 4.4e-31 relative error = 4.8793935551194293603994503288698e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09428 Order of pole (three term test) = -1.126 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = 0.89180486546989162296416915743917 y[1] (numeric) = 0.89180486546989162296416915743873 absolute error = 4.4e-31 relative error = 4.9338147506984521545413936187389e-29 % Correct digits = 31 h = 0.01 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) = -1.176 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = 0.88186914410818241773927688966392 y[1] (numeric) = 0.88186914410818241773927688966348 absolute error = 4.4e-31 relative error = 4.9894023726724635103575052408843e-29 % Correct digits = 31 h = 0.01 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) = -1.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = 0.87194523573362034250344310924638 y[1] (numeric) = 0.87194523573362034250344310924594 absolute error = 4.4e-31 relative error = 5.0461884756994095874845530100089e-29 % Correct digits = 31 h = 0.01 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) = -1.289 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (analytic) = 0.86203413272877295738508592941475 y[1] (numeric) = 0.86203413272877295738508592941431 absolute error = 4.4e-31 relative error = 5.1042062407340879198931845679909e-29 % Correct digits = 31 h = 0.01 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) = -1.353 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = 0.85213682619568152214947021625736 y[1] (numeric) = 0.85213682619568152214947021625692 absolute error = 4.4e-31 relative error = 5.1634900226569957120511496645365e-29 % Correct digits = 31 h = 0.01 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) = -1.421 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = 0.84225430585675161798834572239752 y[1] (numeric) = 0.84225430585675161798834572239708 absolute error = 4.4e-31 relative error = 5.2240754002726824273379813880667e-29 % Correct digits = 31 h = 0.01 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) = -1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = 0.83238755995578173172775000568302 y[1] (numeric) = 0.83238755995578173172775000568259 absolute error = 4.3e-31 relative error = 5.1658628827038519302295407078665e-29 % Correct digits = 31 h = 0.01 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) = -1.572 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = 0.82253757515913969951307944769159 y[1] (numeric) = 0.82253757515913969951307944769116 absolute error = 4.3e-31 relative error = 5.2277247020211343679749267165640e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1684 Order of pole (three term test) = -1.654 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (analytic) = 0.81270533645709689224470717586405 y[1] (numeric) = 0.81270533645709689224470717586362 absolute error = 4.3e-31 relative error = 5.2909705487420520704096066478282e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1774 Order of pole (three term test) = -1.741 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = 0.80289182706533000926338308940728 y[1] (numeric) = 0.80289182706533000926338308940685 absolute error = 4.3e-31 relative error = 5.3556405172500478764952038449259e-29 % Correct digits = 31 h = 0.01 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) = -1.832 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = 0.79309802832660033002396588397449 y[1] (numeric) = 0.79309802832660033002396588397406 absolute error = 4.3e-31 relative error = 5.4217761820348973426413875756893e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1952 Order of pole (three term test) = -1.928 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = 0.78332491961262025575038601809447 y[1] (numeric) = 0.78332491961262025575038601809404 absolute error = 4.3e-31 relative error = 5.4894206635561784153719234086793e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.204 Order of pole (three term test) = -2.028 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = 0.77357347822611695433589651569143 y[1] (numeric) = 0.773573478226116954335896515691 absolute error = 4.3e-31 relative error = 5.5586186975545483602973234604070e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2127 Order of pole (three term test) = -2.132 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = 0.76384467930310290204250822241037 y[1] (numeric) = 0.76384467930310290204250822240994 absolute error = 4.3e-31 relative error = 5.6294167080186042102323499937925e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2213 Order of pole (three term test) = -2.241 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (analytic) = 0.75413949571536309486399862844206 y[1] (numeric) = 0.75413949571536309486399862844163 absolute error = 4.3e-31 relative error = 5.7018628840292971538251515258835e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2298 Order of pole (three term test) = -2.354 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = 0.74445889797316868075009757063626 y[1] (numeric) = 0.74445889797316868075009757063583 absolute error = 4.3e-31 relative error = 5.7760072607191510723297311684589e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2382 Order of pole (three term test) = -2.472 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = 0.73480385412822674124755569242589 y[1] (numeric) = 0.73480385412822674124755569242546 absolute error = 4.3e-31 relative error = 5.8519018045999928866669396922807e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2465 Order of pole (three term test) = -2.593 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (analytic) = 0.7251753296768759274990566423338 y[1] (numeric) = 0.72517532967687592749905664233337 absolute error = 4.3e-31 relative error = 5.9296005035306381189283757785919e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2548 Order of pole (three term test) = -2.719 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = 0.71557428746353763095570308540863 y[1] (numeric) = 0.7155742874635376309557030854082 absolute error = 4.3e-31 relative error = 6.0091594616150991729638389297957e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2629 Order of pole (three term test) = -2.849 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = 0.70600168758443234360554818943968 y[1] (numeric) = 0.70600168758443234360554818943925 absolute error = 4.3e-31 relative error = 6.0906369993425167897985337895305e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2709 Order of pole (three term test) = -2.982 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (analytic) = 0.69645848729157083600191363378011 y[1] (numeric) = 0.69645848729157083600191363377967 absolute error = 4.4e-31 relative error = 6.3176773351000165754524667063483e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2789 Order of pole (three term test) = -3.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = 0.68694564089702975389368422402507 y[1] (numeric) = 0.68694564089702975389368422402464 absolute error = 4.3e-31 relative error = 6.2595928178319306243002720367419e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2867 Order of pole (three term test) = -3.262 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (analytic) = 0.67746409967752120581814601284274 y[1] (numeric) = 0.6774640996775212058181460128423 absolute error = 4.4e-31 relative error = 6.4948091007249508973879407364774e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2944 Order of pole (three term test) = -3.408 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = 0.66801481177926588461808356455725 y[1] (numeric) = 0.66801481177926588461808356455681 absolute error = 4.4e-31 relative error = 6.5866802987205395215721285304450e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3019 Order of pole (three term test) = -3.557 NO COMPLEX POLE (six term test) for Equation 1 bytes used=124045780, alloc=4521156, time=5.00 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = 0.6585987221231792354917125192625 y[1] (numeric) = 0.65859872212317923549171251926206 absolute error = 4.4e-31 relative error = 6.6808511043194187500047573359962e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3094 Order of pole (three term test) = -3.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (analytic) = 0.64921677231038015187963119995636 y[1] (numeric) = 0.64921677231038015187963119995593 absolute error = 4.3e-31 relative error = 6.6233655435264059947082791232531e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3167 Order of pole (three term test) = -3.867 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (analytic) = 0.63986990052803164824046007658263 y[1] (numeric) = 0.63986990052803164824046007658219 absolute error = 4.4e-31 relative error = 6.8763978370744495344013584060473e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3239 Order of pole (three term test) = -4.028 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = 0.63055904145552292556942567856704 y[1] (numeric) = 0.6305590414555229255694256785666 absolute error = 4.4e-31 relative error = 6.9779349921673562015181040686339e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.331 Order of pole (three term test) = -4.192 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = 0.62128512617100221137515574599336 y[1] (numeric) = 0.62128512617100221137515574599293 absolute error = 4.3e-31 relative error = 6.9211378461625526233408024711103e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3379 Order of pole (three term test) = -4.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = 0.61204908205826972075279889951549 y[1] (numeric) = 0.61204908205826972075279889951506 absolute error = 4.3e-31 relative error = 7.0255803432291095165365949225973e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3447 Order of pole (three term test) = -4.531 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = 0.60285183271404004917977257656305 y[1] (numeric) = 0.60285183271404004917977257656262 absolute error = 4.3e-31 relative error = 7.1327642492872455344072199426038e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3514 Order of pole (three term test) = -4.705 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (analytic) = 0.59369429785558327071757857731409 y[1] (numeric) = 0.59369429785558327071757857731365 absolute error = 4.4e-31 relative error = 7.4112215931545031993395191574636e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3579 Order of pole (three term test) = -4.883 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = 0.58457739322875397743290054393371 y[1] (numeric) = 0.58457739322875397743290054393328 absolute error = 4.3e-31 relative error = 7.3557411726959221458960176428654e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3643 Order of pole (three term test) = -5.064 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = 0.57550203051641745705739905165624 y[1] (numeric) = 0.5755020305164174570573990516558 absolute error = 4.4e-31 relative error = 7.6454986545429405816086674018052e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3705 Order of pole (three term test) = -5.249 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = 0.56646911724728216619212706795597 y[1] (numeric) = 0.56646911724728216619212706795554 absolute error = 4.3e-31 relative error = 7.5908816016229713618133726096388e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3766 Order of pole (three term test) = -5.436 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = 0.55747955670514761573327265250731 y[1] (numeric) = 0.55747955670514761573327265250687 absolute error = 4.4e-31 relative error = 7.8926661024220685791359430762306e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3826 Order of pole (three term test) = -5.626 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = 0.54853424783857674365505981360747 y[1] (numeric) = 0.54853424783857674365505981360704 absolute error = 4.3e-31 relative error = 7.8390729784759194961172454212873e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3883 Order of pole (three term test) = -5.819 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = 0.53963408517100180783725645920515 y[1] (numeric) = 0.53963408517100180783725645920472 absolute error = 4.3e-31 relative error = 7.9683624851780732299961663853924e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.394 Order of pole (three term test) = -6.015 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = 0.53077995871127278827309518546809 y[1] (numeric) = 0.53077995871127278827309518546766 absolute error = 4.3e-31 relative error = 8.1012855316548633724097039107679e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3994 Order of pole (three term test) = -6.214 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = 0.52197275386465724374284336112709 y[1] (numeric) = 0.52197275386465724374284336112666 absolute error = 4.3e-31 relative error = 8.2379778794257729248967092785617e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4048 Order of pole (three term test) = -6.416 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = 0.51321335134430052289318861170468 y[1] (numeric) = 0.51321335134430052289318861170425 absolute error = 4.3e-31 relative error = 8.3785817121410973102422518445146e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4099 Order of pole (three term test) = -6.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = 0.50450262708315518362754885358965 y[1] (numeric) = 0.50450262708315518362754885358922 absolute error = 4.3e-31 relative error = 8.5232460034172387242753993235820e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4149 Order of pole (three term test) = -6.827 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = 0.49584145214638842779197594108609 y[1] (numeric) = 0.49584145214638842779197594108566 absolute error = 4.3e-31 relative error = 8.6721269094914254488490465863527e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4197 Order of pole (three term test) = -7.036 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (analytic) = 0.48723069264427631034019077495596 y[1] (numeric) = 0.48723069264427631034019077495553 absolute error = 4.3e-31 relative error = 8.8253881886283376017507432420393e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4244 Order of pole (three term test) = -7.248 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = 0.47867120964559343348424545187534 y[1] (numeric) = 0.47867120964559343348424545187491 absolute error = 4.3e-31 relative error = 8.9832016493820584130726359155342e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4288 Order of pole (three term test) = -7.461 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = 0.47016385909150678678922237429879 y[1] (numeric) = 0.47016385909150678678922237429836 absolute error = 4.3e-31 relative error = 9.1457476300046746502332209215844e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4331 Order of pole (three term test) = -7.677 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = 0.46170949170998234375620595674963 y[1] (numeric) = 0.4617094917099823437562059567492 absolute error = 4.3e-31 relative error = 9.3132155114995923340004872130135e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4373 Order of pole (three term test) = -7.896 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = 0.45330895293071297416254103294378 y[1] (numeric) = 0.45330895293071297416254103294335 absolute error = 4.3e-31 relative error = 9.4858042670453128362100695368189e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4412 Order of pole (three term test) = -8.116 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = 0.44496308280057617929725076783427 y[1] (numeric) = 0.44496308280057617929725076783384 absolute error = 4.3e-31 relative error = 9.6637230507663858778977863050108e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.445 Order of pole (three term test) = -8.338 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (analytic) = 0.43667271589963010424763888032052 y[1] (numeric) = 0.43667271589963010424763888032009 absolute error = 4.3e-31 relative error = 9.8471918291051681308634541286438e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4486 Order of pole (three term test) = -8.562 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = 0.42843868125765622756584442664971 y[1] (numeric) = 0.42843868125765622756584442664928 absolute error = 4.3e-31 relative error = 1.0036442058353849243274485225434e-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 = 0.452 Order of pole (three term test) = -8.788 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = 0.42026180227125707397683496224605 y[1] (numeric) = 0.42026180227125707397683496224562 absolute error = 4.3e-31 bytes used=128047336, alloc=4521156, time=5.16 relative error = 1.0231717412244318775839571629412e-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 = 0.4553 Order of pole (three term test) = -9.015 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = 0.41214289662151724028748227352559 y[1] (numeric) = 0.41214289662151724028748227352516 absolute error = 4.3e-31 relative error = 1.0433274563867625140148984651194e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.81 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4584 Order of pole (three term test) = -9.244 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = 0.40408277619223596832551418909979 y[1] (numeric) = 0.40408277619223596832551418909936 absolute error = 4.3e-31 relative error = 1.0641384026609298579262141669442e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4612 Order of pole (three term test) = -9.474 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = 0.39608224698873944158290927976732 y[1] (numeric) = 0.39608224698873944158290927976688 absolute error = 4.4e-31 relative error = 1.1108803874577825587254071853189e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4639 Order of pole (three term test) = -9.706 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = 0.38814210905728092426641391388112 y[1] (numeric) = 0.38814210905728092426641391388068 absolute error = 4.4e-31 relative error = 1.1336054237162555160334667849512e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4664 Order of pole (three term test) = -9.939 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = 0.38026315640503680267411028948219 y[1] (numeric) = 0.38026315640503680267411028948176 absolute error = 4.3e-31 relative error = 1.1307958521808146555106616401153e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4688 Order of pole (three term test) = -10.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = 0.37244617692070652922722804311009 y[1] (numeric) = 0.37244617692070652922722804310965 absolute error = 4.4e-31 relative error = 1.1813787528652109687566786077511e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.31 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4709 Order of pole (three term test) = -10.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = 0.36469195229572440909662976137772 y[1] (numeric) = 0.36469195229572440909662976137728 absolute error = 4.4e-31 relative error = 1.2064976954665815656159574446606e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4728 Order of pole (three term test) = -10.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = 0.35700125794609110817965112113726 y[1] (numeric) = 0.35700125794609110817965112113682 absolute error = 4.4e-31 relative error = 1.2324886543297337555490322134309e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4746 Order of pole (three term test) = -10.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = 0.349374862934832699211357781338 y[1] (numeric) = 0.34937486293483269921135778133756 absolute error = 4.4e-31 relative error = 1.2593922650985660480976494675271e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.28 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4762 Order of pole (three term test) = -11.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = 0.3418135298950950000409906547043 y[1] (numeric) = 0.34181352989509500004099065470386 absolute error = 4.4e-31 relative error = 1.2872515612095259218554632187004e-28 % Correct digits = 30 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 Radius of convergence (three term test) for eq 1 = 0.4775 Order of pole (three term test) = -11.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = 0.33431801495388089457568407689649 y[1] (numeric) = 0.33431801495388089457568407689605 absolute error = 4.4e-31 relative error = 1.3161121456787122727944504204334e-28 % Correct digits = 30 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 Radius of convergence (three term test) for eq 1 = 0.4787 Order of pole (three term test) = -11.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = 0.32688906765643826259581048063146 y[1] (numeric) = 0.32688906765643826259581048063102 absolute error = 4.4e-31 relative error = 1.3460223774214492439735880708809e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.29 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4797 Order of pole (three term test) = -11.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = 0.31952743089130607958596019184132 y[1] (numeric) = 0.31952743089130607958596019184087 absolute error = 4.5e-31 relative error = 1.4083297911066574006638833068111e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4805 Order of pole (three term test) = -12.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = 0.31223384081602618190911187462131 y[1] (numeric) = 0.31223384081602618190911187462087 absolute error = 4.4e-31 relative error = 1.4092002290656762813732500102040e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4811 Order of pole (three term test) = -12.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = 0.30500902678352812608556955192351 y[1] (numeric) = 0.30500902678352812608556955192307 absolute error = 4.4e-31 relative error = 1.4425802561977224737387203700223e-28 % Correct digits = 30 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 Radius of convergence (three term test) for eq 1 = 0.4815 Order of pole (three term test) = -12.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = 0.29785371126919450362939256217935 y[1] (numeric) = 0.29785371126919450362939256217891 absolute error = 4.4e-31 relative error = 1.4772352445269227872931577295702e-28 % Correct digits = 30 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 Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = 0.29076860979861400485005610714845 y[1] (numeric) = 0.29076860979861400485005610714801 absolute error = 4.4e-31 relative error = 1.5132307449031155029210505316551e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.11 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = 0.28375443087602945625275664545921 y[1] (numeric) = 0.28375443087602945625275664545877 absolute error = 4.4e-31 relative error = 1.5506365791067885028594810021876e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -13.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = 0.27681187591348798667399566455718 y[1] (numeric) = 0.27681187591348798667399566455673 absolute error = 4.5e-31 relative error = 1.6256527958382771710886321939845e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -13.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = 0.26994163916070040707678694126831 y[1] (numeric) = 0.26994163916070040707678694126787 absolute error = 4.4e-31 relative error = 1.6299819522769558228150096329330e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4807 Order of pole (three term test) = -13.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = 0.26314440763561681800905744824866 y[1] (numeric) = 0.26314440763561681800905744824822 absolute error = 4.4e-31 relative error = 1.6720856960383513317295894147611e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.48 Order of pole (three term test) = -14.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = 0.2564208610557253871066425986234 y[1] (numeric) = 0.25642086105572538710664259862296 absolute error = 4.4e-31 relative error = 1.7159290324057495088968714465184e-28 % Correct digits = 30 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 Radius of convergence (three term test) for eq 1 = 0.4791 Order of pole (three term test) = -14.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = 0.24977167177008116670587470137992 y[1] (numeric) = 0.24977167177008116670587470137947 absolute error = 4.5e-31 relative error = 1.8016454660808461240190550320117e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.478 Order of pole (three term test) = -14.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4 y[1] (analytic) = 0.24319750469207174862736090548817 y[1] (numeric) = 0.24319750469207174862736090548772 absolute error = 4.5e-31 relative error = 1.8503479325158965067943358182838e-28 % Correct digits = 30 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 Radius of convergence (three term test) for eq 1 = 0.4766 Order of pole (three term test) = -14.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = 0.2366990172329264795094438207023 y[1] (numeric) = 0.23669901723292647950944382070185 absolute error = 4.5e-31 relative error = 1.9011485778885687333802067937695e-28 % Correct digits = 30 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 Radius of convergence (three term test) for eq 1 = 0.4751 Order of pole (three term test) = -14.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = 0.23027685923597588571440266645551 y[1] (numeric) = 0.23027685923597588571440266645506 absolute error = 4.5e-31 relative error = 1.9541694354049841223702581550044e-28 % Correct digits = 30 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 Radius of convergence (three term test) for eq 1 = 0.4734 Order of pole (three term test) = -15.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = 0.2239316729116678818101206987675 y[1] (numeric) = 0.22393167291166788181012069876705 absolute error = 4.5e-31 relative error = 2.0095415451904700469827565529955e-28 % Correct digits = 30 h = 0.01 bytes used=132048692, alloc=4521156, time=5.33 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4716 Order of pole (three term test) = -15.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = 0.21766409277334726095221776933351 y[1] (numeric) = 0.21766409277334726095221776933305 absolute error = 4.6e-31 relative error = 2.1133481142385581192467725221500e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.92 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4695 Order of pole (three term test) = -15.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = 0.21147474557380488916409289058062 y[1] (numeric) = 0.21147474557380488916409289058016 absolute error = 4.6e-31 relative error = 2.1752006309399226042516461494023e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4672 Order of pole (three term test) = -15.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (analytic) = 0.20536425024260294854257330725366 y[1] (numeric) = 0.2053642502426029485425733072532 absolute error = 4.6e-31 relative error = 2.2399224765585451347063274626962e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.28 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4648 Order of pole (three term test) = -16.15 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (analytic) = 0.19933321782418249681262071972431 y[1] (numeric) = 0.19933321782418249681262071972385 absolute error = 4.6e-31 relative error = 2.3076936449484949105483608510652e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.97 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4621 Order of pole (three term test) = -16.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = 0.19338225141675953242356232661989 y[1] (numeric) = 0.19338225141675953242356232661943 absolute error = 4.6e-31 relative error = 2.3787084731403326614605861344101e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4593 Order of pole (three term test) = -16.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = 0.18751194611201567552941728764728 y[1] (numeric) = 0.18751194611201567552941728764682 absolute error = 4.6e-31 relative error = 2.4531770350525065599038713257999e-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 = 0.4563 Order of pole (three term test) = -16.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = 0.18172288893558949573496297564155 y[1] (numeric) = 0.18172288893558949573496297564108 absolute error = 4.7e-31 relative error = 2.5863555370099165897999748177517e-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 = 0.4531 Order of pole (three term test) = -17.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = 0.17601565878837443742517601630396 y[1] (numeric) = 0.17601565878837443742517601630349 absolute error = 4.7e-31 relative error = 2.6702169752129051743985794253083e-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 = 0.4498 Order of pole (three term test) = -17.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = 0.17039082638862921283659693902778 y[1] (numeric) = 0.17039082638862921283659693902732 absolute error = 4.6e-31 relative error = 2.6996758554995625020518334796071e-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 = 0.4462 Order of pole (three term test) = -17.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = 0.16484895421490645178307012404365 y[1] (numeric) = 0.16484895421490645178307012404318 absolute error = 4.7e-31 relative error = 2.8510948233695272813958883440131e-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 = 0.4425 Order of pole (three term test) = -17.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = 0.15939059644980531512332717185912 y[1] (numeric) = 0.15939059644980531512332717185866 absolute error = 4.6e-31 relative error = 2.8859920863955199724294567678862e-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 = 0.4386 Order of pole (three term test) = -17.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = 0.15401629892455369666219427078778 y[1] (numeric) = 0.15401629892455369666219427078732 absolute error = 4.6e-31 relative error = 2.9866968834599462687231441213041e-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 = 0.4345 Order of pole (three term test) = -18.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = 0.14872659906442555521905209735327 y[1] (numeric) = 0.14872659906442555521905209735281 absolute error = 4.6e-31 relative error = 3.0929235449049479264258568712996e-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 = 0.4303 Order of pole (three term test) = -18.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = 0.14352202583499883508485599858706 y[1] (numeric) = 0.1435220258349988350848559985866 absolute error = 4.6e-31 relative error = 3.2050829642611261824911018803224e-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 = 0.4259 Order of pole (three term test) = -18.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (analytic) = 0.13840309968925934903088583719909 y[1] (numeric) = 0.13840309968925934903088583719863 absolute error = 4.6e-31 relative error = 3.3236249840703379557772080683120e-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 = 0.4213 Order of pole (three term test) = -18.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = 0.13337033251555591343684467407746 y[1] (numeric) = 0.133370332515555913436844674077 absolute error = 4.6e-31 relative error = 3.4490429117461110552822142186291e-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 = 0.4165 Order of pole (three term test) = -19.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 0.12842422758641193998142290209118 y[1] (numeric) = 0.12842422758641193998142290209072 absolute error = 4.6e-31 relative error = 3.5818786582966435702993101059113e-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 = 0.4116 Order of pole (three term test) = -19.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = 0.1235652795081986026935019100478 y[1] (numeric) = 0.12356527950819860269350191004734 absolute error = 4.6e-31 relative error = 3.7227286000634088095300552585552e-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 = 0.4065 Order of pole (three term test) = -19.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = 0.11879397417167461300535326877877 y[1] (numeric) = 0.11879397417167461300535326877831 absolute error = 4.6e-31 relative error = 3.8722502821164390994932983731783e-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 = 0.4013 Order of pole (three term test) = -19.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = 0.11411078870339754878911140270074 y[1] (numeric) = 0.11411078870339754878911140270028 absolute error = 4.6e-31 relative error = 4.0311701043067446863892417621110e-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 = 0.3959 Order of pole (three term test) = -19.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = 0.10951619141801159620312567541779 y[1] (numeric) = 0.10951619141801159620312567541733 absolute error = 4.6e-31 relative error = 4.2002921581177816024090408223551e-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 = 0.3903 Order of pole (three term test) = -20.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = 0.10501064177141647553424717156172 y[1] (numeric) = 0.10501064177141647553424717156126 absolute error = 4.6e-31 relative error = 4.3805084155309902073921637137162e-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 = 0.3846 Order of pole (three term test) = -20.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = 0.10059459031482223410444018114688 y[1] (numeric) = 0.10059459031482223410444018114642 absolute error = 4.6e-31 relative error = 4.5728105115829546957464230251770e-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 = 0.3787 Order of pole (three term test) = -20.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = 0.09626847864969450072414018033867 y[1] (numeric) = 0.09626847864969450072414018033821 absolute error = 4.60e-31 relative error = 4.7783034120012009583388681962239e-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 = 0.3727 Order of pole (three term test) = -20.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = 0.09203273938359470712936747670058 y[1] (numeric) = 0.092032739383594707129367476700112 absolute error = 4.68e-31 relative error = 5.0851469067911209464237615091700e-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 = 0.3665 Order of pole (three term test) = -20.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (analytic) = 0.08788779608691969234365311475198 y[1] (numeric) = 0.087887796086919692343653114751512 absolute error = 4.68e-31 relative error = 5.3249713934930752472030142847274e-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 = 0.3601 Order of pole (three term test) = -20.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = 0.08383406325054501596829063971536 y[1] (numeric) = 0.0838340632505450159682906397149 absolute error = 4.60e-31 relative error = 5.4870297605073971070111229998958e-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 = 0.3537 Order of pole (three term test) = -21.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=136051292, alloc=4521156, time=5.49 x[1] = 4.31 y[1] (analytic) = 0.07987194624437621603428757300901 y[1] (numeric) = 0.079871946244376216034287573008542 absolute error = 4.68e-31 relative error = 5.8593789434917129160533222378748e-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 = 0.3471 Order of pole (three term test) = -21.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = 0.07600184127681215625569090101602 y[1] (numeric) = 0.076001841276812156255690901015554 absolute error = 4.66e-31 relative error = 6.1314303992023762985570122332177e-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 = 0.3403 Order of pole (three term test) = -21.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = 0.07222413535512451631578081322702 y[1] (numeric) = 0.072224135355124516315780813226558 absolute error = 4.62e-31 relative error = 6.3967536299099457707179922794738e-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 = 0.3334 Order of pole (three term test) = -21.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (analytic) = 0.06853920624675738720408708901116 y[1] (numeric) = 0.068539206246757387204087089010696 absolute error = 4.64e-31 relative error = 6.7698478784462432457340233873705e-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 = 0.3264 Order of pole (three term test) = -21.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = 0.06494742244155084161244420165858 y[1] (numeric) = 0.064947422441550841612444201658117 absolute error = 4.63e-31 relative error = 7.1288433411914829040270761300521e-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 = 0.3193 Order of pole (three term test) = -22.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = 0.06144914311489225700156528111504 y[1] (numeric) = 0.061449143114892257001565281114575 absolute error = 4.65e-31 relative error = 7.5672332668753979320973987624604e-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 = 0.312 Order of pole (three term test) = -22.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = 0.05804471809179907617512114959174 y[1] (numeric) = 0.058044718091799076175121149591272 absolute error = 4.68e-31 relative error = 8.0627491249048204334797698670447e-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 = 0.3046 Order of pole (three term test) = -22.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = 0.05473448781193659705533608906184 y[1] (numeric) = 0.054734487811936597055336089061371 absolute error = 4.69e-31 relative error = 8.5686377775461639295051718576714e-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 = 0.2971 Order of pole (three term test) = -22.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = 0.05151878329557428985197103638587 y[1] (numeric) = 0.051518783295574289851971036385403 absolute error = 4.67e-31 relative error = 9.0646550661090153484750643416998e-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 = 0.2894 Order of pole (three term test) = -22.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 0.04839792611048404596460766661961 y[1] (numeric) = 0.048397926110484045964607666619147 absolute error = 4.63e-31 relative error = 9.5665256181236267001530697398507e-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 = 0.2817 Order of pole (three term test) = -22.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = 0.04537222833978366876575843546385 y[1] (numeric) = 0.045372228339783668765758435463381 absolute error = 4.69e-31 relative error = 1.0336719556459768872344916426392e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2738 Order of pole (three term test) = -22.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = 0.04244199255072882188892726816111 y[1] (numeric) = 0.042441992550728821888927268160643 absolute error = 4.67e-31 relative error = 1.1003253427411965088163330684124e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2658 Order of pole (three term test) = -23.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = 0.03960751176445655580078546569952 y[1] (numeric) = 0.039607511764456555800785465699059 absolute error = 4.61e-31 relative error = 1.1639206288482314590582740267668e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2577 Order of pole (three term test) = -23.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = 0.03686906942668343827959196692216 y[1] (numeric) = 0.036869069426683438279591966921694 absolute error = 4.66e-31 relative error = 1.2639320906286272056032796330703e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2495 Order of pole (three term test) = -23.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = 0.03422693937936121896239198130831 y[1] (numeric) = 0.034226939379361218962391981307842 absolute error = 4.68e-31 relative error = 1.3673439941936588492996044826319e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2413 Order of pole (three term test) = -23.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = 0.03168138583329286237091907175356 y[1] (numeric) = 0.031681385833292862370919071753096 absolute error = 4.64e-31 relative error = 1.4645823968735565800287027272957e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2329 Order of pole (three term test) = -23.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = 0.02923266334171168779007820072841 y[1] (numeric) = 0.029232663341711687790078200727948 absolute error = 4.62e-31 relative error = 1.5804239066400033222513968885275e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2244 Order of pole (three term test) = -23.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (analytic) = 0.02688101677482625806300458146732 y[1] (numeric) = 0.026881016774826258063004581466851 absolute error = 4.69e-31 relative error = 1.7447256698980699928309806231084e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2158 Order of pole (three term test) = -23.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = 0.02462668129533356279260630634082 y[1] (numeric) = 0.024626681295333562792606306340353 absolute error = 4.67e-31 relative error = 1.8963172276424044708002199704352e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2072 Order of pole (three term test) = -23.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 0.02246988233490294461086498550137 y[1] (numeric) = 0.022469882334902944610864985500906 absolute error = 4.64e-31 relative error = 2.0649863363069728354422538264186e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1984 Order of pole (three term test) = -23.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (analytic) = 0.02041083557163312010367080295234 y[1] (numeric) = 0.020410835571633120103670802951872 absolute error = 4.68e-31 relative error = 2.2928997608036396182152772481993e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1896 Order of pole (three term test) = -24.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (analytic) = 0.01844974690848454967031375325789 y[1] (numeric) = 0.018449746908484549670313753257427 absolute error = 4.63e-31 relative error = 2.5095195196801240122514675462163e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1807 Order of pole (three term test) = -24.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = 0.01658681245268931306267214456304 y[1] (numeric) = 0.016586812452689313062672144562577 absolute error = 4.63e-31 relative error = 2.7913741794610525638619403477732e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1718 Order of pole (three term test) = -24.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = 0.01482221849614054959938606921746 y[1] (numeric) = 0.014822218496140549599386069216994 absolute error = 4.66e-31 relative error = 3.1439288263179926384322739473977e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1627 Order of pole (three term test) = -24.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = 0.01315614149676342409465234597491 y[1] (numeric) = 0.013156141496763424094652345974442 absolute error = 4.68e-31 relative error = 3.5572739934055427494281822051247e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1536 Order of pole (three term test) = -24.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = 0.01158874806086948138952391096191 y[1] (numeric) = 0.011588748060869481389523910961445 absolute error = 4.65e-31 relative error = 4.0125128060218779827316058265665e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1445 Order of pole (three term test) = -24.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (analytic) = 0.01012019492649615403555587193493 y[1] (numeric) = 0.010120194926496154035555871934461 absolute error = 4.69e-31 relative error = 4.6342980881928394490268596437045e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1353 Order of pole (three term test) = -24.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = 0.00875062894773308916614616390269 y[1] (numeric) = 0.0087506289477330891661461639022244 absolute error = 4.656e-31 relative error = 5.3207604022636212223616107008366e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.126 Order of pole (three term test) = -24.62 NO COMPLEX POLE (six term test) for Equation 1 bytes used=140053080, alloc=4521156, time=5.65 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = 0.00748018708003686190982232131219 y[1] (numeric) = 0.007480187080036861909822321311721 absolute error = 4.690e-31 relative error = 6.2698966614306763614622147857072e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1167 Order of pole (three term test) = -24.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 0.00630899636653554386189534009117 y[1] (numeric) = 0.0063089963665355438618953400907059 absolute error = 4.641e-31 relative error = 7.3561621062535341040151778794298e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1073 Order of pole (three term test) = -24.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (analytic) = 0.00523717392532449614622064259686 y[1] (numeric) = 0.0052371739253244961462206425963992 absolute error = 4.608e-31 relative error = 8.7986384750712428789255285556297e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09791 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (analytic) = 0.00426482693775465747717316554853 y[1] (numeric) = 0.0042648269377546574771731655480697 absolute error = 4.603e-31 relative error = 1.0792935017483695584811449733342e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08846 Order of pole (three term test) = -24.83 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (analytic) = 0.0033920526377144983832706460193 y[1] (numeric) = 0.0033920526377144983832706460188313 absolute error = 4.687e-31 relative error = 1.3817592179695692831583351906583e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07898 Order of pole (three term test) = -24.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = 0.00261893830190671338809106811717 y[1] (numeric) = 0.0026189383019067133880910681167044 absolute error = 4.656e-31 relative error = 1.7778196594437553010420629021515e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06947 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = 0.00194556124112062347116344910397 y[1] (numeric) = 0.00194556124112062347116344910351 absolute error = 4.600e-31 relative error = 2.3643563115753924163575413085437e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05992 Order of pole (three term test) = -24.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (analytic) = 0.00137198879250116156131290216748 y[1] (numeric) = 0.0013719887925011615613129021670122 absolute error = 4.678e-31 relative error = 3.4096488437576209164350805296635e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05036 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (analytic) = 0.00089827831281521415746815072662 y[1] (numeric) = 0.00089827831281521415746815072615302 absolute error = 4.6698e-31 relative error = 5.1986115365123256769199342919758e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04077 Order of pole (three term test) = -24.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = 0.00052447717271599243715805024033 y[1] (numeric) = 0.00052447717271599243715805023986265 absolute error = 4.6735e-31 relative error = 8.9107786632512384503224722418066e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03117 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = 0.00025062275200600641080659305708 y[1] (numeric) = 0.00025062275200600641080659305661878 absolute error = 4.6122e-31 relative error = 1.8402958083747577209959371504648e-25 % Correct digits = 27 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02155 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = 7.674243589911582046345842503e-05 y[1] (numeric) = 7.6742435899115820463458424563870e-05 absolute error = 4.66130e-31 relative error = 6.0739536677304044963069626578796e-25 % Correct digits = 27 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01193 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = 2.85361228203157476528740643e-06 y[1] (numeric) = 2.8536122820315747652874059615900e-06 absolute error = 4.684100e-31 relative error = 1.6414633583877219868690731180310e-23 % Correct digits = 25 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0023 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = 2.896366997554156770211203836e-05 y[1] (numeric) = 2.8963669975541567702112037895790e-05 absolute error = 4.64210e-31 relative error = 1.6027319755818344676772149394142e-24 % Correct digits = 26 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.00015506999799563475715808844232 y[1] (numeric) = 0.00015506999799563475715808844185403 absolute error = 4.6597e-31 relative error = 3.0049010512859948757127004258148e-25 % Correct digits = 27 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.00038115998581459739020295192723 y[1] (numeric) = 0.00038115998581459739020295192676497 absolute error = 4.6503e-31 relative error = 1.2200388742437365692909887326833e-25 % Correct digits = 27 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.00070721102462205526572924440292 y[1] (numeric) = 0.00070721102462205526572924440245605 absolute error = 4.6395e-31 relative error = 6.5602766903689348316990944381003e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = 0.00113319050958583593125991543056 y[1] (numeric) = 0.001133190509585835931259915430099 absolute error = 4.610e-31 relative error = 4.0681597321926792229926924031747e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = 0.00165905584311242472959066170051 y[1] (numeric) = 0.0016590558431124247295906617000496 absolute error = 4.604e-31 relative error = 2.7750723516110200283810515506890e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = 0.00228475443910668865237937835233 y[1] (numeric) = 0.0022847544391066886523793783518628 absolute error = 4.672e-31 relative error = 2.0448587034266559884885586017530e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = 0.00301022372823044203184712123726 y[1] (numeric) = 0.0030102237282304420318471212367973 absolute error = 4.627e-31 relative error = 1.5370950526391534353514589362971e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = 0.00383539116415932821840353349637 y[1] (numeric) = 0.0038353911641593282184035334959007 absolute error = 4.693e-31 relative error = 1.2236040078140633046010641575575e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = 0.00476017423083739156124302459597 y[1] (numeric) = 0.004760174230837391561243024595508 absolute error = 4.620e-31 relative error = 9.7055271003962124950860737923037e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = 0.00578448045072861424075909870166 y[1] (numeric) = 0.0057844804507286142407590987011953 absolute error = 4.647e-31 relative error = 8.0335650532186741331557698308175e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = 0.0069082073940645928059698487306 y[1] (numeric) = 0.0069082073940645928059698487301343 absolute error = 4.657e-31 relative error = 6.7412567897153904276934897766115e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = 0.00813124268908742965700724495948 y[1] (numeric) = 0.0081312426890874296570072449590192 absolute error = 4.608e-31 relative error = 5.6670304604045170776967352652323e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = 0.00945346403328681519205768370882 y[1] (numeric) = 0.0094534640332868151920576837083549 absolute error = 4.651e-31 relative error = 4.9198896654424813952961174238345e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = 0.01087473920563017691990330595709 y[1] (numeric) = 0.010874739205630176919903305956626 bytes used=144053868, alloc=4521156, time=5.82 absolute error = 4.64e-31 relative error = 4.2667689884440939713481024497452e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = 0.01239492607978467253334458870749 y[1] (numeric) = 0.012394926079784672533344588707027 absolute error = 4.63e-31 relative error = 3.7353994450610175885333733358617e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = 0.01401387263832970475521515768158 y[1] (numeric) = 0.014013872638329704755215157681113 absolute error = 4.67e-31 relative error = 3.3324121893522583229026778586469e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = 0.0157314169879585367173479427511 y[1] (numeric) = 0.015731416987958536717347942750637 absolute error = 4.63e-31 relative error = 2.9431550912063353203282039664558e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = 0.01754738737566748772362275008167 y[1] (numeric) = 0.017547387375667487723622750081207 absolute error = 4.63e-31 relative error = 2.6385694353680835232581507268867e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = 0.01946160220593109049100989773031 y[1] (numeric) = 0.019461602205931090491009897729846 absolute error = 4.64e-31 relative error = 2.3841819141621958196265477131650e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = 0.02147387005886149236719839365887 y[1] (numeric) = 0.02147387005886149236719839365841 absolute error = 4.60e-31 relative error = 2.1421383231765183192811636233364e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (analytic) = 0.02358398970935028459981967725086 y[1] (numeric) = 0.0235839897093502845998196772504 absolute error = 4.60e-31 relative error = 1.9504757493072724942264736690619e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = 0.02579175014719084549029147317684 y[1] (numeric) = 0.02579175014719084549029147317638 absolute error = 4.60e-31 relative error = 1.7835160366195689173659019837138e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = 0.02809693059817918521473493662265 y[1] (numeric) = 0.028096930598179185214734936622182 absolute error = 4.68e-31 relative error = 1.6656623696480519715528931964360e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = 0.03049930054619118224506697690327 y[1] (numeric) = 0.030499300546191182245066976902801 absolute error = 4.69e-31 relative error = 1.5377401828927179154957944824496e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = 0.03299861975623400366502328592209 y[1] (numeric) = 0.03299861975623400366502328592163 absolute error = 4.60e-31 relative error = 1.3939976986858613453781900731598e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = 0.03559463829846940425828992207108 y[1] (numeric) = 0.035594638298469404258289922070613 absolute error = 4.67e-31 relative error = 1.3119953518956852133191911380094e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = 0.03828709657320650205885398558889 y[1] (numeric) = 0.038287096573206502058853985588428 absolute error = 4.62e-31 relative error = 1.2066728515614575633282337601911e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cos ( x ) ; Iterations = 1000 Total Elapsed Time = 5 Seconds Elapsed Time(since restart) = 5 Seconds Time to Timeout = 2 Minutes 54 Seconds Percent Done = 100.1 % > quit bytes used=146021632, alloc=4521156, time=5.90