|\^/| 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, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] + array_const_1[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_tmp3[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; > #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_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1; > array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[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_tmp3[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; > #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_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2; > array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[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_tmp3[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; > #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_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3; > array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre add FULL CONST $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[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_tmp3[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; > #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_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4; > array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre add FULL CONST $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[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_tmp3[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; > #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_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sin LINEAR $eq_no = 1 > array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[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_tmp3[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; > #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_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_tmp2[1] + array_const_1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp3[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; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_tmp1_g[1]*array_x[2]; array_tmp1_g[2] := -array_tmp1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp3[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; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2]; array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2]; array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := array_tmp2[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp3[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; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := 1/3*array_tmp1_g[3]*array_x[2]; array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2]; array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := array_tmp2[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp3[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; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := 1/4*array_tmp1_g[4]*array_x[2]; array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2]; array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := array_tmp2[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp3[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; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1); array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := array_tmp2[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_tmp3[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; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp3[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(2.0 - cos(x) + x); > end; exact_soln_y := proc(x) return 2.0 - cos(x) + 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, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > 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/add_sin_cpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin(x) + 1,0;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -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 := 1000000;"); > omniout_str(ALWAYS,"glob_display_interval := 0.1;"); > omniout_str(ALWAYS,"glob_max_minutes := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(2.0 - cos(x) + 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_tmp3:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0[1] := 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 := 1000000; > glob_display_interval := 0.1; > glob_max_minutes := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = sin(x) + 1,0;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-25T23:54:14-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"add_sin_c") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin(x) + 1,0;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"add_sin_c diffeq.mxt") > ; > logitem_str(html_log_file,"add_sin_c maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, 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/add_sin_cpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) + 1,0;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -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 := 1000000;"); omniout_str(ALWAYS, "glob_display_interval := 0.1;"); omniout_str(ALWAYS, "glob_max_minutes := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(2.0 - cos(x) + 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_tmp3 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0[term] := 0.; term := term + 1 end do; array_const_0[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 := 1000000; glob_display_interval := 0.1; glob_max_minutes := 10; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = sin(x) + 1,0;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-25T23:54:14-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "add_sin_c"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) + 1,0;") ; logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "add_sin_c diffeq.mxt"); logitem_str(html_log_file, "add_sin_c 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/add_sin_cpostode.ode################# diff ( y , x , 1 ) = sin(x) + 1,0; ! #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 := 1000000; glob_display_interval := 0.1; glob_max_minutes := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(2.0 - cos(x) + 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 = 7.0336765106047936865442669997952e-184 estimated_step_error = 7.0336765106047936865442669997952e-184 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 = 4.7202201082058432521732285308967e-176 estimated_step_error = 4.7202201082058432521732285308967e-176 best_h = 4.00e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.1676856963086583986489359336787e-168 estimated_step_error = 3.1676856963086583986489359336787e-168 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.1257973535651632877221290785610e-160 estimated_step_error = 2.1257973535651632877221290785610e-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 = 1.4265977404543836333905291745086e-152 estimated_step_error = 1.4265977404543836333905291745086e-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 = 9.5737257852944312852911266276024e-145 estimated_step_error = 9.5737257852944312852911266276024e-145 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 = 6.4248057463193448693887472357508e-137 estimated_step_error = 6.4248057463193448693887472357508e-137 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 = 4.3115968758362803361960226316435e-129 estimated_step_error = 4.3115968758362803361960226316435e-129 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.8934404978658147772802222161222e-121 estimated_step_error = 2.8934404978658147772802222161222e-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 = 1.9417239291603407964146484450800e-113 estimated_step_error = 1.9417239291603407964146484450800e-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 = 1.3030271028561254178470410097110e-105 estimated_step_error = 1.3030271028561254178470410097110e-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 = 8.7439062579714225441007668007794e-98 estimated_step_error = 8.7439062579714225441007668007794e-98 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 = 5.8671837148857333684032552207181e-90 estimated_step_error = 5.8671837148857333684032552207181e-90 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 = 3.9363903937503392920293610734909e-82 estimated_step_error = 3.9363903937503392920293610734909e-82 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.6403112611569484542505579307515e-74 estimated_step_error = 2.6403112611569484542505579307515e-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 = 1.7700631820108302428345798962214e-66 estimated_step_error = 1.7700631820108302428345798962214e-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 = 1.1854262842396269376477255859020e-58 estimated_step_error = 1.1854262842396269376477255859020e-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 = 7.9224545954147765948816900198149e-51 estimated_step_error = 7.9224545954147765948816900198149e-51 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (analytic) = -3.2836621854632262644666391715136 y[1] (numeric) = -3.2836621854632262644666391715136 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.99 y[1] (analytic) = -3.264058919545427243963091597697 y[1] (numeric) = -3.264058919545427243963091597697 absolute 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=4000908, alloc=3145152, time=0.34 x[1] = -4.98 y[1] (analytic) = -3.2444282479640553524162533206808 y[1] (numeric) = -3.2444282479640553524162533206808 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.97 y[1] (analytic) = -3.2247711337782431941159535140125 y[1] (numeric) = -3.2247711337782431941159535140126 absolute error = 1e-31 relative error = 3.1009952598662980973860078455424e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -3.2050885426913617819484480229353 y[1] (numeric) = -3.2050885426913617819484480229354 absolute error = 1e-31 relative error = 3.1200386094803007620629225443973e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -3.1853814429544510050452574116347 y[1] (numeric) = -3.1853814429544510050452574116348 absolute error = 1e-31 relative error = 3.1393414506505599203670932643987e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -3.1656508052693953316674308040397 y[1] (numeric) = -3.1656508052693953316674308040398 absolute error = 1e-31 relative error = 3.1589081093070860360374715420938e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = -3.1458976026918544296742604464858 y[1] (numeric) = -3.1458976026918544296742604464858 absolute 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] = -4.92 y[1] (analytic) = -3.1261228105339584114335092408118 y[1] (numeric) = -3.1261228105339584114335092408118 absolute 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] = -4.91 y[1] (analytic) = -3.1063274062667774335675731995194 y[1] (numeric) = -3.1063274062667774335675731995194 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (analytic) = -3.0865123694225754044943291441219 y[1] (numeric) = -3.0865123694225754044943291441219 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.89 y[1] (analytic) = -3.0666786814968575743104585897138 y[1] (numeric) = -3.0666786814968575743104585897138 absolute 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] = -4.88 y[1] (analytic) = -3.0468273258502218021766327470316 y[1] (numeric) = -3.0468273258502218021766327470316 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.87 y[1] (analytic) = -3.026959287610023315996029785628 y[1] (numeric) = -3.026959287610023315996029785628 absolute 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] = -4.86 y[1] (analytic) = -3.0070755535718627978282707459854 y[1] (numeric) = -3.0070755535718627978282707459854 absolute 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] = -4.85 y[1] (analytic) = -2.9871771121009076461481397184653 y[1] (numeric) = -2.9871771121009076461481397184653 absolute 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] = -4.84 y[1] (analytic) = -2.9672649530330562827406304097327 y[1] (numeric) = -2.9672649530330562827406304097327 absolute 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] = -4.83 y[1] (analytic) = -2.9473400675759553877192667889538 y[1] (numeric) = -2.9473400675759553877192667889538 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.82 y[1] (analytic) = -2.9274034482098799608617106191698 y[1] (numeric) = -2.9274034482098799608617106191697 absolute error = 1e-31 relative error = 3.4159965228281205411373466740491e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.81 y[1] (analytic) = -2.9074560885884861211739226395384 y[1] (numeric) = -2.9074560885884861211739226395383 absolute error = 1e-31 relative error = 3.4394328565267540161811811877566e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.8 y[1] (analytic) = -2.8874989834394465693202152576495 y[1] (numeric) = -2.8874989834394465693202152576494 absolute error = 1e-31 relative error = 3.4632046824440757156956703983295e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.79 y[1] (analytic) = -2.8675331284649786492901502413476 y[1] (numeric) = -2.8675331284649786492901502413475 absolute error = 1e-31 relative error = 3.4873180367939140927010721404026e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.78 y[1] (analytic) = -2.8475595202422749564132217146596 y[1] (numeric) = -2.8475595202422749564132217146595 absolute error = 1e-31 relative error = 3.5117790967716748102939668714689e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.77 y[1] (analytic) = -2.8275791561238464485775487727873 y[1] (numeric) = -2.8275791561238464485775487727872 absolute error = 1e-31 relative error = 3.5365941845845200346282348980412e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.76 y[1] (analytic) = -2.8075930341377880262584087164105 y[1] (numeric) = -2.8075930341377880262584087164105 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 bytes used=8001820, alloc=4324584, time=0.72 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.75 y[1] (analytic) = -2.7876021528879765547154963123733 y[1] (numeric) = -2.7876021528879765547154963123733 absolute 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] = -4.74 y[1] (analytic) = -2.767607511454211308473521317219 y[1] (numeric) = -2.767607511454211308473521317219 absolute 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] = -4.73 y[1] (analytic) = -2.7476101092923068239584801849428 y[1] (numeric) = -2.7476101092923068239584801849428 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.72 y[1] (analytic) = -2.7276109461341481509210826531746 y[1] (numeric) = -2.7276109461341481509210826531746 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.71 y[1] (analytic) = -2.7076110218877184970389038522753 y[1] (numeric) = -2.7076110218877184970389038522753 absolute 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 = 0.002304 Order of pole (three term test) = -0.893 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.7 y[1] (analytic) = -2.6876113365371092628494917036729 y[1] (numeric) = -2.6876113365371092628494917036729 absolute 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 = 0.01195 Order of pole (three term test) = -0.8966 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.69 y[1] (analytic) = -2.667612890042522465927611603558 y[1] (numeric) = -2.667612890042522465927611603558 absolute 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 = 0.02158 Order of pole (three term test) = -0.905 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.68 y[1] (analytic) = -2.6476166822402755539808796320554 y[1] (numeric) = -2.6476166822402755539808796320554 absolute 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 = 0.03121 Order of pole (three term test) = -0.9182 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.67 y[1] (analytic) = -2.6276237127428186062991456798947 y[1] (numeric) = -2.6276237127428186062991456798947 absolute 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 = 0.04083 Order of pole (three term test) = -0.9363 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.66 y[1] (analytic) = -2.607634980838773921754162833204 y[1] (numeric) = -2.607634980838773921754162833204 absolute 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 = 0.05043 Order of pole (three term test) = -0.9592 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.65 y[1] (analytic) = -2.5876514853930079893074429838229 y[1] (numeric) = -2.5876514853930079893074429838229 absolute 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 = 0.06 Order of pole (three term test) = -0.9868 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.64 y[1] (analytic) = -2.5676742247467458337459747992399 y[1] (numeric) = -2.5676742247467458337459747992399 absolute 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 = 0.06956 Order of pole (three term test) = -1.019 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.63 y[1] (analytic) = -2.5477041966177377251279927125974 y[1] (numeric) = -2.5477041966177377251279927125974 absolute 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 = 0.07909 Order of pole (three term test) = -1.057 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.62 y[1] (analytic) = -2.5277423980004882351846582243842 y[1] (numeric) = -2.5277423980004882351846582243842 absolute 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 = 0.08858 Order of pole (three term test) = -1.099 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.61 y[1] (analytic) = -2.5077898250665576176888711718273 y[1] (numeric) = -2.5077898250665576176888711718273 absolute 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 = 0.09804 Order of pole (three term test) = -1.145 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.6 y[1] (analytic) = -2.4878474730649454825700921787708 y[1] (numeric) = -2.4878474730649454825700921787708 absolute 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 = 0.1075 Order of pole (three term test) = -1.197 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.59 y[1] (analytic) = -2.4679163362225667253247514756035 y[1] (numeric) = -2.4679163362225667253247514756035 absolute 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 = 0.1168 Order of pole (three term test) = -1.253 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.58 y[1] (analytic) = -2.4479974076448296640463665993177 y[1] (numeric) = -2.4479974076448296640463665993177 absolute 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 = 0.1262 Order of pole (three term test) = -1.314 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.57 y[1] (analytic) = -2.4280916792163263261788146856254 y[1] (numeric) = -2.4280916792163263261788146856254 absolute 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 = 0.1355 Order of pole (three term test) = -1.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.56 y[1] (analytic) = -2.4082001415016448158813262073901 y[1] (numeric) = -2.4082001415016448158813262073901 absolute 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 = 0.1447 Order of pole (three term test) = -1.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.55 y[1] (analytic) = -2.3883237836463136806858075749921 y[1] (numeric) = -2.3883237836463136806858075749921 absolute 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 = 0.1538 Order of pole (three term test) = -1.525 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.54 y[1] (analytic) = -2.3684635932778881829272807804022 y[1] (numeric) = -2.3684635932778881829272807804022 absolute 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 = 0.163 Order of pole (three term test) = -1.604 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.53 y[1] (analytic) = -2.3486205564071883672378692086186 y[1] (numeric) = -2.3486205564071883672378692086186 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 bytes used=12002964, alloc=4390108, time=1.10 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.172 Order of pole (three term test) = -1.688 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.52 y[1] (analytic) = -2.3287956573296988002152788818011 y[1] (numeric) = -2.3287956573296988002152788818011 absolute 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 = 0.181 Order of pole (three term test) = -1.777 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.51 y[1] (analytic) = -2.3089898785271398422096416782592 y[1] (numeric) = -2.3089898785271398422096416782592 absolute 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 = 0.1899 Order of pole (three term test) = -1.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.5 y[1] (analytic) = -2.2892042005692202940195181752062 y[1] (numeric) = -2.2892042005692202940195181752061 absolute error = 1e-31 relative error = 4.3683302684458895192577708922684e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1987 Order of pole (three term test) = -1.967 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.49 y[1] (analytic) = -2.2694396020155812431505179934839 y[1] (numeric) = -2.2694396020155812431505179934838 absolute error = 1e-31 relative error = 4.4063741511863082456856716106495e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2074 Order of pole (three term test) = -2.069 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.48 y[1] (analytic) = -2.2496970593179409151701985931512 y[1] (numeric) = -2.249697059317940915170198593151 absolute error = 2e-31 relative error = 8.8900858527430194627094674203568e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2161 Order of pole (three term test) = -2.175 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.47 y[1] (analytic) = -2.2299775467224503155925613446698 y[1] (numeric) = -2.2299775467224503155925613446697 absolute error = 1e-31 relative error = 4.4843500844650567016295376919433e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2247 Order of pole (three term test) = -2.286 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.46 y[1] (analytic) = -2.2102820361722694266465863988873 y[1] (numeric) = -2.2102820361722694266465863988872 absolute error = 1e-31 relative error = 4.5243094936960342727724529062646e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2332 Order of pole (three term test) = -2.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.45 y[1] (analytic) = -2.1906114972103737012279432702555 y[1] (numeric) = -2.1906114972103737012279432702554 absolute error = 1e-31 relative error = 4.5649354131184209891306744651259e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2415 Order of pole (three term test) = -2.519 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.44 y[1] (analytic) = -2.1709668968826005733034876438366 y[1] (numeric) = -2.1709668968826005733034876438365 absolute error = 1e-31 relative error = 4.6062425062120927537359893445714e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2498 Order of pole (three term test) = -2.643 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.43 y[1] (analytic) = -2.1513491996409456800367096510664 y[1] (numeric) = -2.1513491996409456800367096510662 absolute error = 2e-31 relative error = 9.2964917101035691969558466848461e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.258 Order of pole (three term test) = -2.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.42 y[1] (analytic) = -2.1317593672471184659313348565068 y[1] (numeric) = -2.1317593672471184659313348565066 absolute error = 2e-31 relative error = 9.3819219501436129212950670300211e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2661 Order of pole (three term test) = -2.901 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.41 y[1] (analytic) = -2.1121983586763668133522935335094 y[1] (numeric) = -2.1121983586763668133522935335092 absolute error = 2e-31 relative error = 9.4688076609117469715139970379767e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2741 Order of pole (three term test) = -3.037 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.4 y[1] (analytic) = -2.0926671300215803168808602577823 y[1] (numeric) = -2.0926671300215803168808602577821 absolute error = 2e-31 relative error = 9.5571817003661509178567446659480e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.282 Order of pole (three term test) = -3.176 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.39 y[1] (analytic) = -2.0731666343976817910966146332443 y[1] (numeric) = -2.0731666343976817910966146332441 absolute error = 2e-31 relative error = 9.6470778895255617865808878131191e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2897 Order of pole (three term test) = -3.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.38 y[1] (analytic) = -2.0536978218463165725557714761559 y[1] (numeric) = -2.0536978218463165725557714761558 absolute error = 1e-31 relative error = 4.8692655236931567505052263047397e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2974 Order of pole (three term test) = -3.467 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.37 y[1] (analytic) = -2.0342616392408491469562573075772 y[1] (numeric) = -2.0342616392408491469562573075771 absolute error = 1e-31 relative error = 4.9157885136799930236814565789734e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3049 Order of pole (three term test) = -3.618 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.36 y[1] (analytic) = -2.0148590301916766017476474330366 y[1] (numeric) = -2.0148590301916766017476474330365 absolute error = 1e-31 relative error = 4.9631263776546614290365730695247e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3123 Order of pole (three term test) = -3.772 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.35 y[1] (analytic) = -1.9954909349518683727617974225641 y[1] (numeric) = -1.9954909349518683727617974225641 absolute 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 = 0.3196 Order of pole (three term test) = -3.931 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.34 y[1] (analytic) = -1.9761582903231417208108726455763 y[1] (numeric) = -1.9761582903231417208108726455763 absolute 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 = 0.3267 Order of pole (three term test) = -4.093 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.33 y[1] (analytic) = -1.9568620295621823406267625493371 y[1] (numeric) = -1.9568620295621823406267625493371 absolute 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 = 0.3338 Order of pole (three term test) = -4.258 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.32 y[1] (analytic) = -1.9376030822873194700029198405699 y[1] (numeric) = -1.9376030822873194700029198405699 absolute 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 = 0.3406 Order of pole (three term test) = -4.428 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.31 y[1] (analytic) = -1.9183823743855648315499399031558 y[1] (numeric) = -1.9183823743855648315499399031557 absolute error = 1e-31 relative error = 5.2127251237923209336830959385944e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3474 Order of pole (three term test) = -4.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=16003824, alloc=4390108, time=1.49 x[1] = -4.3 y[1] (analytic) = -1.899200827920024703093237603664 y[1] (numeric) = -1.8992008279200247030932376036639 absolute error = 1e-31 relative error = 5.2653725993537212890042216981287e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.354 Order of pole (three term test) = -4.776 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.29 y[1] (analytic) = -1.8800593610376943754286253662208 y[1] (numeric) = -1.8800593610376943754286253662207 absolute error = 1e-31 relative error = 5.3189809892388309188573064254161e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3605 Order of pole (three term test) = -4.955 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.28 y[1] (analytic) = -1.860958887877644217913179263164 y[1] (numeric) = -1.8609588878776442179131792631639 absolute error = 1e-31 relative error = 5.3735738414966466631462757457801e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3668 Order of pole (three term test) = -5.137 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.27 y[1] (analytic) = -1.8419003184796065332083226779057 y[1] (numeric) = -1.8419003184796065332083226779056 absolute error = 1e-31 relative error = 5.4291754551921044740031352525148e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.373 Order of pole (three term test) = -5.323 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.26 y[1] (analytic) = -1.822884558692972342413475864514 y[1] (numeric) = -1.8228845586929723424134758645139 absolute error = 1e-31 relative error = 5.4858109101379994045482876929423e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.379 Order of pole (three term test) = -5.511 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.25 y[1] (analytic) = -1.8039125100862072008359222794552 y[1] (numeric) = -1.803912510086207200835922279455 absolute error = 2e-31 relative error = 1.1087012196087170387737703297844e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3849 Order of pole (three term test) = -5.703 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.24 y[1] (analytic) = -1.7849850698566951027398281302941 y[1] (numeric) = -1.7849850698566951027398281302939 absolute error = 2e-31 relative error = 1.1204575510318229464154561063283e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3906 Order of pole (three term test) = -5.897 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.23 y[1] (analytic) = -1.7661031307410194906088104104552 y[1] (numeric) = -1.766103130741019490608810410455 absolute error = 2e-31 relative error = 1.1324366993001378882884881209487e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3962 Order of pole (three term test) = -6.094 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.22 y[1] (analytic) = -1.7472675809256903407463615868448 y[1] (numeric) = -1.7472675809256903407463615868446 absolute error = 2e-31 relative error = 1.1446443703490530985403967318545e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4016 Order of pole (three term test) = -6.294 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.21 y[1] (analytic) = -1.7284793039583262524311770505132 y[1] (numeric) = -1.728479303958326252431177050513 absolute error = 2e-31 relative error = 1.1570864605783096660516585994530e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4068 Order of pole (three term test) = -6.497 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.2 y[1] (analytic) = -1.7097391786593004223444551186229 y[1] (numeric) = -1.7097391786593004223444551186227 absolute error = 2e-31 relative error = 1.1697690647577655037859388244154e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4119 Order of pole (three term test) = -6.702 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.19 y[1] (analytic) = -1.6910480790338593395980987485076 y[1] (numeric) = -1.6910480790338593395980987485074 absolute error = 2e-31 relative error = 1.1826984843285195620845289907576e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4168 Order of pole (three term test) = -6.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.18 y[1] (analytic) = -1.6724068741847229894210819669533 y[1] (numeric) = -1.6724068741847229894210819669531 absolute error = 2e-31 relative error = 1.1958812361226238556293150752240e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4216 Order of pole (three term test) = -7.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.17 y[1] (analytic) = -1.6538164282251753054107794572422 y[1] (numeric) = -1.653816428225175305410779457242 absolute error = 2e-31 relative error = 1.2093240615261865599905848161302e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4262 Order of pole (three term test) = -7.332 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.16 y[1] (analytic) = -1.6352776001926535612316097892908 y[1] (numeric) = -1.6352776001926535612316097892906 absolute error = 2e-31 relative error = 1.2230339361123629142237624707952e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4306 Order of pole (three term test) = -7.547 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.15 y[1] (analytic) = -1.6167912439628453427498138283373 y[1] (numeric) = -1.6167912439628453427498138283371 absolute error = 2e-31 relative error = 1.2370180797725553384839043260372e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4348 Order of pole (three term test) = -7.764 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.14 y[1] (analytic) = -1.5983582081643016908355692264027 y[1] (numeric) = -1.5983582081643016908355692264025 absolute error = 2e-31 relative error = 1.2512839673761114307392261657974e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4389 Order of pole (three term test) = -7.983 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.13 y[1] (analytic) = -1.5799793360935749534470053079295 y[1] (numeric) = -1.5799793360935749534470053079293 absolute error = 2e-31 relative error = 1.2658393399909308324580269845786e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4428 Order of pole (three term test) = -8.204 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.12 y[1] (analytic) = -1.5616554656308898331401917272407 y[1] (numeric) = -1.5616554656308898331401917272405 absolute error = 2e-31 relative error = 1.2806922166996830514740936757006e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4465 Order of pole (three term test) = -8.427 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.11 y[1] (analytic) = -1.5433874291563560628300760061255 y[1] (numeric) = -1.5433874291563560628300760061253 absolute error = 2e-31 relative error = 1.2958509070488132465921910612713e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.45 Order of pole (three term test) = -8.652 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.1 y[1] (analytic) = -1.5251760534667310884649713203402 y[1] (numeric) = -1.52517605346673108846497132034 absolute error = 2e-31 relative error = 1.3113240241701882470277558700875e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4534 Order of pole (three term test) = -8.878 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.09 y[1] (analytic) = -1.5070221596927410822769628863557 y[1] (numeric) = -1.5070221596927410822769628863555 absolute error = 2e-31 relative error = 1.3271204986181288854395237643258e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4565 Order of pole (three term test) = -9.106 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=20006524, alloc=4390108, time=1.89 x[1] = -4.08 y[1] (analytic) = -1.4889265632169685544380089817521 y[1] (numeric) = -1.4889265632169685544380089817519 absolute error = 2e-31 relative error = 1.3432495929677070833239964427856e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.92 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4595 Order of pole (three term test) = -9.336 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.07 y[1] (analytic) = -1.4708900735923147742921442269604 y[1] (numeric) = -1.4708900735923147742921442269602 absolute error = 2e-31 relative error = 1.3597209172235790946251143982340e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.22 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4623 Order of pole (three term test) = -9.567 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.06 y[1] (analytic) = -1.4529134944610451548537141522107 y[1] (numeric) = -1.4529134944610451548537141522105 absolute error = 2e-31 relative error = 1.3765444450923042037280428687759e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4649 Order of pole (three term test) = -9.799 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.05 y[1] (analytic) = -1.4349976234744256959657292715176 y[1] (numeric) = -1.4349976234744256959657292715175 absolute error = 1e-31 relative error = 6.9686526558754391147816327161413e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.82 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4674 Order of pole (three term test) = -10.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.04 y[1] (analytic) = -1.4171432522129585224070534208273 y[1] (numeric) = -1.4171432522129585224070534208272 absolute error = 1e-31 relative error = 7.0564496457110949218347543733441e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.13 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4696 Order of pole (three term test) = -10.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.03 y[1] (analytic) = -1.3993511661072244933281454781476 y[1] (numeric) = -1.3993511661072244933281454781474 absolute error = 2e-31 relative error = 1.4292338109551774431242919625047e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4717 Order of pole (three term test) = -10.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.02 y[1] (analytic) = -1.3816221443593407986884466192346 y[1] (numeric) = -1.3816221443593407986884466192345 absolute error = 1e-31 relative error = 7.2378689360375063558057629892016e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4736 Order of pole (three term test) = -10.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.01 y[1] (analytic) = -1.363956959865041396870317585315 y[1] (numeric) = -1.3639569598650413968703175853148 absolute error = 2e-31 relative error = 1.4663219286610720907428927363392e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4752 Order of pole (three term test) = -10.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4 y[1] (analytic) = -1.3463563791363880853608318169022 y[1] (numeric) = -1.3463563791363880853608318169021 absolute error = 1e-31 relative error = 7.4274539453026825799251556675101e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4767 Order of pole (three term test) = -11.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.99 y[1] (analytic) = -1.3288211622251199333299490479899 y[1] (numeric) = -1.3288211622251199333299490479897 absolute error = 2e-31 relative error = 1.5050934293151883650820579084305e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.478 Order of pole (three term test) = -11.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.98 y[1] (analytic) = -1.3113520626466487410979362833252 y[1] (numeric) = -1.311352062646648741097936283325 absolute error = 2e-31 relative error = 1.5251434431448416882091394929425e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.09 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4791 Order of pole (three term test) = -11.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.97 y[1] (analytic) = -1.2939498273047081268827525106807 y[1] (numeric) = -1.2939498273047081268827525106805 absolute error = 2e-31 relative error = 1.5456549842940906895988613746045e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4801 Order of pole (three term test) = -11.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.96 y[1] (analytic) = -1.2766151964166637758559301912485 y[1] (numeric) = -1.2766151964166637758559301912483 absolute error = 2e-31 relative error = 1.5666427954279471834201023552181e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.79 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4808 Order of pole (three term test) = -12.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.95 y[1] (analytic) = -1.2593489034394923204198066883598 y[1] (numeric) = -1.2593489034394923204198066883596 absolute error = 2e-31 relative error = 1.5881222388312450629464340598253e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -12.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.94 y[1] (analytic) = -1.2421516749964362537563938505644 y[1] (numeric) = -1.2421516749964362537563938505642 absolute error = 2e-31 relative error = 1.6101093290444888874566606488806e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -12.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.93 y[1] (analytic) = -1.225024230804342211095410160473 y[1] (numeric) = -1.2250242308043422110954101604728 absolute error = 2e-31 relative error = 1.6326207675800944785592861931395e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.89 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.92 y[1] (analytic) = -1.2079672836016898848127974157074 y[1] (numeric) = -1.2079672836016898848127974157072 absolute error = 2e-31 relative error = 1.6556739798753288865036814873082e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.27 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.91 y[1] (analytic) = -1.1909815390773187704082363861256 y[1] (numeric) = -1.1909815390773187704082363861254 absolute error = 2e-31 relative error = 1.6792871546518233495808830678029e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.33 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4815 Order of pole (three term test) = -13.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.9 y[1] (analytic) = -1.1740676957998598706276695153856 y[1] (numeric) = -1.1740676957998598706276695153854 absolute error = 2e-31 relative error = 1.7034792858664382881175823645110e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4811 Order of pole (three term test) = -13.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.89 y[1] (analytic) = -1.1572264451478794145016116973683 y[1] (numeric) = -1.1572264451478794145016116973681 absolute error = 2e-31 relative error = 1.7282702174546524575336963248517e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4805 Order of pole (three term test) = -13.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.88 y[1] (analytic) = -1.1404584712407415768691319229587 y[1] (numeric) = -1.1404584712407415768691319229585 absolute error = 2e-31 relative error = 1.7536806910856959605178648649884e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4797 Order of pole (three term test) = -14.11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.87 y[1] (analytic) = -1.1237644508701971120579391906727 y[1] (numeric) = -1.1237644508701971120579391906725 absolute error = 2e-31 relative error = 1.7797323971685365271592158677858e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.84 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4786 Order of pole (three term test) = -14.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=24007688, alloc=4390108, time=2.28 x[1] = -3.86 y[1] (analytic) = -1.1071450534327047428001953906352 y[1] (numeric) = -1.1071450534327047428001953906349 absolute error = 3e-31 relative error = 2.7096720440546574479472923547462e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4775 Order of pole (three term test) = -14.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.85 y[1] (analytic) = -1.0906009408624920721887649260472 y[1] (numeric) = -1.0906009408624920721887649260469 absolute error = 3e-31 relative error = 2.7507770143930708813866383182979e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.14 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4761 Order of pole (three term test) = -14.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.84 y[1] (analytic) = -1.0741327675653627125269230597523 y[1] (numeric) = -1.074132767565362712526923059752 absolute error = 3e-31 relative error = 2.7929508256226297072563663681242e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.79 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4745 Order of pole (three term test) = -15.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.83 y[1] (analytic) = -1.0577411803532562503034774729765 y[1] (numeric) = -1.0577411803532562503034774729762 absolute error = 3e-31 relative error = 2.8362325829066077514102882412896e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4727 Order of pole (three term test) = -15.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.82 y[1] (analytic) = -1.0414268183795675912422723433438 y[1] (numeric) = -1.0414268183795675912422723433435 absolute error = 3e-31 relative error = 2.8806632852684936097262928827812e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.12 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4708 Order of pole (three term test) = -15.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.81 y[1] (analytic) = -1.025190313075232153437669625635 y[1] (numeric) = -1.0251903130752321534376696256347 absolute error = 3e-31 relative error = 2.9262859409985950648407055822415e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.79 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4686 Order of pole (three term test) = -15.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.8 y[1] (analytic) = -1.0090322880855833000034318256493 y[1] (numeric) = -1.0090322880855833000034318256489 absolute error = 4e-31 relative error = 3.9641942554574935205277596342486e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4663 Order of pole (three term test) = -16.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.79 y[1] (analytic) = -0.9929533592079883254391227481598 y[1] (numeric) = -0.99295335920798832543912274815947 absolute error = 3.3e-31 relative error = 3.3234189394677979633557264114938e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4638 Order of pole (three term test) = -16.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.78 y[1] (analytic) = -0.9769541343302692320634197407623 y[1] (numeric) = -0.97695413433026923206341974076191 absolute error = 3.9e-31 relative error = 3.9919990744228382898602758850954e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.84 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.461 Order of pole (three term test) = -16.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.77 y[1] (analytic) = -0.9610352133699144543853782538038 y[1] (numeric) = -0.96103521336991445438537825380341 absolute error = 3.9e-31 relative error = 4.0581239331745914906777466716682e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4582 Order of pole (three term test) = -16.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.76 y[1] (analytic) = -0.9451971882140876101905548624369 y[1] (numeric) = -0.94519718821408761019055486243653 absolute error = 3.7e-31 relative error = 3.9145270914220581134137566920128e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4551 Order of pole (three term test) = -16.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.75 y[1] (analytic) = -0.9294406426604392774168875977093 y[1] (numeric) = -0.92944064266043927741688759770891 absolute error = 3.9e-31 relative error = 4.1960721545774077934519395763864e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4518 Order of pole (three term test) = -17.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.74 y[1] (analytic) = -0.9137661523587277155933226437975 y[1] (numeric) = -0.91376615235872771559332264379709 absolute error = 4.1e-31 relative error = 4.4869247885977896460179483515624e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4484 Order of pole (three term test) = -17.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.73 y[1] (analytic) = -0.8981742847532543697203943020784 y[1] (numeric) = -0.898174284753254369720394302078 absolute error = 4.0e-31 relative error = 4.4534786487445211105339467342111e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4448 Order of pole (three term test) = -17.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.72 y[1] (analytic) = -0.8826655990261199129943999105103 y[1] (numeric) = -0.88266559902611991299439991050996 absolute error = 3.4e-31 relative error = 3.8519684054203033694907195712939e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.441 Order of pole (three term test) = -17.83 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.71 y[1] (analytic) = -0.8672406460413065027236108273902 y[1] (numeric) = -0.86724064604130650272361082738988 absolute error = 3.2e-31 relative error = 3.6898639548400325144580997624763e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.437 Order of pole (three term test) = -18.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.7 y[1] (analytic) = -0.8518999682895918411643298936456 y[1] (numeric) = -0.85189996828959184116432989364522 absolute error = 3.8e-31 relative error = 4.4606176094001702483498308744161e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4329 Order of pole (three term test) = -18.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.69 y[1] (analytic) = -0.8366440998343005498248069716278 y[1] (numeric) = -0.83664409983430054982480697162746 absolute error = 3.4e-31 relative error = 4.0638546314656118151383169634887e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4286 Order of pole (three term test) = -18.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.68 y[1] (analytic) = -0.8214735662578982820543751314638 y[1] (numeric) = -0.82147356625789828205437513146346 absolute error = 3.4e-31 relative error = 4.1389037208929299141845453311225e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4241 Order of pole (three term test) = -18.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.67 y[1] (analytic) = -0.8063888846094339144620438135202 y[1] (numeric) = -0.80638888460943391446204381351981 absolute error = 3.9e-31 relative error = 4.8363761882567671006978562110174e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4194 Order of pole (three term test) = -18.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.66 y[1] (analytic) = -0.7913905633528350729016090798401 y[1] (numeric) = -0.79139056335283507290160907983969 absolute error = 4.1e-31 relative error = 5.1807542190417150671015742817088e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4146 Order of pole (three term test) = -19.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.65 y[1] (analytic) = -0.7764791023160621634275955254717 y[1] (numeric) = -0.77647910231606216342759552547134 absolute error = 3.6e-31 relative error = 4.6363127987115317708990744325662e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4096 Order of pole (three term test) = -19.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=28008600, alloc=4390108, time=2.68 x[1] = -3.64 y[1] (analytic) = -0.7616549926411259927765627558659 y[1] (numeric) = -0.76165499264112599277656275586552 absolute error = 3.8e-31 relative error = 4.9891355491848933065641794361814e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4044 Order of pole (three term test) = -19.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.63 y[1] (analytic) = -0.746918716734973976570076455602 y[1] (numeric) = -0.7469187167349739765700764556016 absolute error = 4.0e-31 relative error = 5.3553350724497953080297099496005e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3991 Order of pole (three term test) = -19.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.62 y[1] (analytic) = -0.732270748221249846577595727932 y[1] (numeric) = -0.73227074822124984657759572793161 absolute error = 3.9e-31 relative error = 5.3258989376176005287655240358660e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3937 Order of pole (three term test) = -19.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.61 y[1] (analytic) = -0.7177115518929316810283503064616 y[1] (numeric) = -0.71771155189293168102835030646119 absolute error = 4.1e-31 relative error = 5.7126013775122274002987826925075e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.388 Order of pole (three term test) = -20.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.6 y[1] (analytic) = -0.7032415836658529941297082747341 y[1] (numeric) = -0.70324158366585299412970827473367 absolute error = 4.3e-31 relative error = 6.1145417163544125780662332690377e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3822 Order of pole (three term test) = -20.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.59 y[1] (analytic) = -0.6888612905331115326443501606522 y[1] (numeric) = -0.68886129053311153264435016065178 absolute error = 4.2e-31 relative error = 6.0970184530903299093960255305800e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3763 Order of pole (three term test) = -20.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.58 y[1] (analytic) = -0.674571110520370338608599145451 y[1] (numeric) = -0.6745711105203703386085991454506 absolute error = 4.0e-31 relative error = 5.9296936047474125167505974031374e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3702 Order of pole (three term test) = -20.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.57 y[1] (analytic) = -0.6603714726420555480483865639633 y[1] (numeric) = -0.66037147264205554804838656396288 absolute error = 4.2e-31 relative error = 6.3600566862714056168029125587558e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.364 Order of pole (three term test) = -20.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.56 y[1] (analytic) = -0.6462627968584553058764793868963 y[1] (numeric) = -0.64626279685845530587647938689596 absolute error = 3.4e-31 relative error = 5.2610176796927228015115661876972e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3576 Order of pole (three term test) = -21.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.55 y[1] (analytic) = -0.6322454940337240870437291772895 y[1] (numeric) = -0.63224549403372408704372917728915 absolute error = 3.5e-31 relative error = 5.5358243483397754003096051554737e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3511 Order of pole (three term test) = -21.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.54 y[1] (analytic) = -0.6183199658947966234772311138702 y[1] (numeric) = -0.61831996589479662347723111386986 absolute error = 3.4e-31 relative error = 5.4987711662839774664807092479731e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3444 Order of pole (three term test) = -21.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.53 y[1] (analytic) = -0.604486604991215545378460985316 y[1] (numeric) = -0.60448660499121554537846098531561 absolute error = 3.9e-31 relative error = 6.4517558665450910308242702505546e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3376 Order of pole (three term test) = -21.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.52 y[1] (analytic) = -0.5907457946558767540837834877278 y[1] (numeric) = -0.59074579465587675408378348772739 absolute error = 4.1e-31 relative error = 6.9403794950217900742183870150496e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3307 Order of pole (three term test) = -21.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.51 y[1] (analytic) = -0.5770979089666964519173336942424 y[1] (numeric) = -0.57709790896669645191733369424205 absolute error = 3.5e-31 relative error = 6.0648287675600992629373321779868e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3236 Order of pole (three term test) = -21.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.5 y[1] (analytic) = -0.5635433127092036623013423733282 y[1] (numeric) = -0.56354331270920366230134237332787 absolute error = 3.3e-31 relative error = 5.8558054466753059993616337145579e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3164 Order of pole (three term test) = -22.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.49 y[1] (analytic) = -0.5500823613400619808407213272332 y[1] (numeric) = -0.55008236134006198084072132723286 absolute error = 3.4e-31 relative error = 6.1808926061857733645393101897065e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3091 Order of pole (three term test) = -22.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.48 y[1] (analytic) = -0.5367154009515242051764018526177 y[1] (numeric) = -0.53671540095152420517640185261735 absolute error = 3.5e-31 relative error = 6.5211469501247231427383223167559e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3016 Order of pole (three term test) = -22.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.47 y[1] (analytic) = -0.5234427682368233981148199464733 y[1] (numeric) = -0.52344276823682339811481994647295 absolute error = 3.5e-31 relative error = 6.6864998666224391891726042748430e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.294 Order of pole (three term test) = -22.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.46 y[1] (analytic) = -0.510264790456503844898394624218 y[1] (numeric) = -0.5102647904565038448983946242176 absolute error = 4.0e-31 relative error = 7.8390672349182385616746105647472e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2863 Order of pole (three term test) = -22.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.45 y[1] (analytic) = -0.4971817854056952714932148600522 y[1] (numeric) = -0.49718178540569527149321486005188 absolute error = 3.2e-31 relative error = 6.4362776230606127340460011026353e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2785 Order of pole (three term test) = -22.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.44 y[1] (analytic) = -0.4841940613823335964448349870275 y[1] (numeric) = -0.48419406138233359644483498702714 absolute error = 3.6e-31 relative error = 7.4350354271638539685386263818678e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2706 Order of pole (three term test) = -22.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.43 y[1] (analytic) = -0.4713019171563313942005103587744 y[1] (numeric) = -0.47130191715633139420051035877407 absolute error = 3.3e-31 relative error = 7.0018811294276703759096489535482e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2626 Order of pole (three term test) = -23.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=32009240, alloc=4455632, time=3.07 x[1] = -3.42 y[1] (analytic) = -0.4585056419397011528258498543986 y[1] (numeric) = -0.45850564193970115282584985439822 absolute error = 3.8e-31 relative error = 8.2877933277421794152763488715127e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2545 Order of pole (three term test) = -23.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.41 y[1] (analytic) = -0.445805515357634313765216359047 y[1] (numeric) = -0.44580551535763431376521635904667 absolute error = 3.3e-31 relative error = 7.4023310307246253370459805227206e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2463 Order of pole (three term test) = -23.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.4 y[1] (analytic) = -0.4332018074205389857177984602343 y[1] (numeric) = -0.43320180742053898571779846023394 absolute error = 3.6e-31 relative error = 8.3102146351509350149973432536124e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2379 Order of pole (three term test) = -23.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.39 y[1] (analytic) = -0.4206947784970391288346639253275 y[1] (numeric) = -0.42069477849703912883466392532716 absolute error = 3.4e-31 relative error = 8.0818687889275273528482006068450e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2295 Order of pole (three term test) = -23.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.38 y[1] (analytic) = -0.4082846792879379092958746500094 y[1] (numeric) = -0.40828467928793790929587465000906 absolute error = 3.4e-31 relative error = 8.3275228596128400845270889162526e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.221 Order of pole (three term test) = -23.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.37 y[1] (analytic) = -0.3959717508011478279105082340292 y[1] (numeric) = -0.39597175080114782791050823402878 absolute error = 4.2e-31 relative error = 1.0606817257802788691030616693156e-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 = 0.2124 Order of pole (three term test) = -23.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.36 y[1] (analytic) = -0.3837562243275901297058346922217 y[1] (numeric) = -0.38375622432759012970583469222131 absolute error = 3.9e-31 relative error = 1.0162701613070904253040615243277e-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 = 0.2037 Order of pole (three term test) = -23.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.35 y[1] (analytic) = -0.3716383214180659045446056247285 y[1] (numeric) = -0.3716383214180659045446056247281 absolute error = 4.0e-31 relative error = 1.0763152693019224014956224405015e-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 = 0.1949 Order of pole (three term test) = -24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.34 y[1] (analytic) = -0.3596182538611011916411200989301 y[1] (numeric) = -0.35961825386110119164112009892972 absolute error = 3.8e-31 relative error = 1.0566760611288965484832109362850e-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 = 0.1861 Order of pole (three term test) = -24.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.33 y[1] (analytic) = -0.3476962236617683034471532851407 y[1] (numeric) = -0.34769622366176830344715328514037 absolute error = 3.3e-31 relative error = 9.4910435472838835346534461274298e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1772 Order of pole (three term test) = -24.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.32 y[1] (analytic) = -0.3358724230214854867577104152688 y[1] (numeric) = -0.33587242302148548675771041526844 absolute error = 3.6e-31 relative error = 1.0718355402967128733058015524439e-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 = 0.1682 Order of pole (three term test) = -24.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.31 y[1] (analytic) = -0.3241470343187969410536619294145 y[1] (numeric) = -0.3241470343187969410536619294141 absolute error = 4.0e-31 relative error = 1.2340078965726462804425251562755e-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 = 0.1591 Order of pole (three term test) = -24.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.3 y[1] (analytic) = -0.3125202300911351160634089488972 y[1] (numeric) = -0.31252023009113511606340894889678 absolute error = 4.2e-31 relative error = 1.3439130000560998331556431545406e-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 = 0.15 Order of pole (three term test) = -24.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.29 y[1] (analytic) = -0.3009921730175671122986248744605 y[1] (numeric) = -0.30099217301756711229862487446015 absolute error = 3.5e-31 relative error = 1.1628209348140511084151334703506e-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 = 0.1408 Order of pole (three term test) = -24.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.28 y[1] (analytic) = -0.2895630159025269099096415838683 y[1] (numeric) = -0.28956301590252690990964158386792 absolute error = 3.8e-31 relative error = 1.3123222895561914880645395560874e-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 = 0.1316 Order of pole (three term test) = -24.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.27 y[1] (analytic) = -0.2782329016605350526240382595053 y[1] (numeric) = -0.27823290166053505262403825950489 absolute error = 4.1e-31 relative error = 1.4735856095848457973230433442372e-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 = 0.1223 Order of pole (three term test) = -24.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.26 y[1] (analytic) = -0.2670019633019073147873054328283 y[1] (numeric) = -0.26700196330190731478730543282798 absolute error = 3.2e-31 relative error = 1.1984930599111969019156213751973e-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 = 0.113 Order of pole (three term test) = -24.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.25 y[1] (analytic) = -0.2558703239194537806269707748284 y[1] (numeric) = -0.25587032391945378062697077482804 absolute error = 3.6e-31 relative error = 1.4069626929980575852942192548055e-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 = 0.1036 Order of pole (three term test) = -24.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.24 y[1] (analytic) = -0.2448380966761696658211761562575 y[1] (numeric) = -0.24483809667616966582117615625717 absolute error = 3.3e-31 relative error = 1.3478294615092849089437903986850e-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 = 0.09415 Order of pole (three term test) = -24.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.23 y[1] (analytic) = -0.233905384793919112279291505415 y[1] (numeric) = -0.2339053847939191122792915054147 absolute error = 3.0e-31 relative error = 1.2825698744144481251817570537859e-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 = 0.08469 Order of pole (three term test) = -24.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.22 y[1] (analytic) = -0.2230722815431130877456572625241 y[1] (numeric) = -0.22307228154311308774565726252378 absolute error = 3.2e-31 relative error = 1.4345126063461799135736442905572e-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 = 0.07519 Order of pole (three term test) = -24.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.21 y[1] (analytic) = -0.2123388702333824224278933347958 y[1] (numeric) = -0.2123388702333824224278933347954 absolute error = 4.0e-31 relative error = 1.8837813329248599147087406677980e-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 = 0.06567 Order of pole (three term test) = -24.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.2 y[1] (analytic) = -0.2017052242052469153383392777164 y[1] (numeric) = -0.20170522420524691533833927771606 absolute error = 3.4e-31 relative error = 1.6856281305536738393861677988063e-28 % Correct digits = 30 h = 0.01 bytes used=36010700, alloc=4455632, time=3.48 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05612 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.19 y[1] (analytic) = -0.1911714068227813434310491703005 y[1] (numeric) = -0.19117140682278134343104917030016 absolute error = 3.4e-31 relative error = 1.7785086465110596430927196614969e-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 = 0.04654 Order of pole (three term test) = -24.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.18 y[1] (analytic) = -0.1807374714672791069273158461397 y[1] (numeric) = -0.18073747146727910692731584613933 absolute error = 3.7e-31 relative error = 2.0471681771147560345568609312494e-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 = 0.03695 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.17 y[1] (analytic) = -0.1704034615319141444599116498647 y[1] (numeric) = -0.17040346153191414445991164986436 absolute error = 3.4e-31 relative error = 1.9952646322053900078317640090875e-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 = 0.02734 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.16 y[1] (analytic) = -0.160169410417401651840082905726 y[1] (numeric) = -0.16016941041740165184008290572569 absolute error = 3.1e-31 relative error = 1.9354507155401251354954816322116e-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 = 0.01772 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.15 y[1] (analytic) = -0.1500353415286580383718053432053 y[1] (numeric) = -0.15003534152865803837180534320492 absolute error = 3.8e-31 relative error = 2.5327365947803487185791433406960e-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 = 0.008096 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.14 y[1] (analytic) = -0.140001268272460454714885693655 y[1] (numeric) = -0.1400012682724604547148856936546 absolute error = 4.0e-31 relative error = 2.8571169742658945775969400267878e-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] = -3.13 y[1] (analytic) = -0.1300671940561061263421727608608 y[1] (numeric) = -0.13006719405610612634217276086044 absolute error = 3.6e-31 relative error = 2.7678001560078973853863214071357e-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] = -3.12 y[1] (analytic) = -0.1202331122870716266564150260244 y[1] (numeric) = -0.12023311228707162665641502602406 absolute error = 3.4e-31 relative error = 2.8278399646530598112026489851833e-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] = -3.11 y[1] (analytic) = -0.1104990063736721238391691632832 y[1] (numeric) = -0.11049900637367212383916916328282 absolute error = 3.8e-31 relative error = 3.4389449504637366293976358712447e-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] = -3.1 y[1] (analytic) = -0.1008648497267205355076239454585 y[1] (numeric) = -0.10086484972672053550762394545819 absolute error = 3.1e-31 relative error = 3.0734195395115587433890377273483e-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] = -3.09 y[1] (analytic) = -0.0913306057621864252652564819142 y[1] (numeric) = -0.091330605762186425265256481913898 absolute error = 3.02e-31 relative error = 3.3066680931293783344480956800091e-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] = -3.08 y[1] (analytic) = -0.0818962279048543752588814626402 y[1] (numeric) = -0.081896227904854375258881462639862 absolute error = 3.38e-31 relative error = 4.1271742135997102207000184645840e-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] = -3.07 y[1] (analytic) = -0.0725616595929814689078863372732 y[1] (numeric) = -0.072561659592981468907886337272886 absolute error = 3.14e-31 relative error = 4.3273541669431671842202219469888e-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] = -3.06 y[1] (analytic) = -0.0633268342839534180612607282068 y[1] (numeric) = -0.063326834283953418061260728206504 absolute error = 2.96e-31 relative error = 4.6741638571850156945144021175910e-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] = -3.05 y[1] (analytic) = -0.0541916754609387689744177984351 y[1] (numeric) = -0.054191675460938768974417798434739 absolute error = 3.61e-31 relative error = 6.6615397462698480879253267786309e-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] = -3.04 y[1] (analytic) = -0.0451560966405405216907550451568 y[1] (numeric) = -0.045156096640540521690755045156471 absolute error = 3.29e-31 relative error = 7.2858378929198306938416499381593e-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] = -3.03 y[1] (analytic) = -0.0362200013814443976723926912916 y[1] (numeric) = -0.03622000138144439767239269129123 absolute error = 3.70e-31 relative error = 1.0215350245390989322013138675687e-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] = -3.02 y[1] (analytic) = -0.027383283294062890860533466737 y[1] (numeric) = -0.027383283294062890860533466736621 absolute error = 3.79e-31 relative error = 1.3840560897318435170950168860277e-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] = -3.01 y[1] (analytic) = -0.0186458260511741377683744258176 y[1] (numeric) = -0.01864582605117413776837442581724 absolute error = 3.60e-31 relative error = 1.9307270110316759334954239049376e-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] = -3 y[1] (analytic) = -0.0100075033995545427284272052687 y[1] (numeric) = -0.010007503399554542728427205268396 absolute error = 3.04e-31 relative error = 3.0377206768026853495237171360945e-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] = -2.99 y[1] (analytic) = -0.0014681791726039950414158127892 y[1] (numeric) = -0.0014681791726039950414158127888177 absolute error = 3.823e-31 relative error = 2.6039056208783037528846930201071e-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] = -2.98 y[1] (analytic) = 0.0069722926960375844844419643954 y[1] (numeric) = 0.0069722926960375844844419643957443 absolute error = 3.443e-31 relative error = 4.9381174171828547977471910754792e-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 bytes used=40012072, alloc=4455632, time=3.87 x[1] = -2.97 y[1] (analytic) = 0.0153140681578837292470763748061 y[1] (numeric) = 0.015314068157883729247076374806486 absolute error = 3.86e-31 relative error = 2.5205581953824987801236176993088e-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] = -2.96 y[1] (analytic) = 0.0235573130340064054563873229762 y[1] (numeric) = 0.023557313034006405456387322976501 absolute error = 3.01e-31 relative error = 1.2777348569655983425728053471647e-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] = -2.95 y[1] (analytic) = 0.031702202998454043121389404702 y[1] (numeric) = 0.031702202998454043121389404702311 absolute error = 3.11e-31 relative error = 9.8100438009044956495130491180216e-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] = -2.94 y[1] (analytic) = 0.0397489235606842776017633813283 y[1] (numeric) = 0.039748923560684277601763381328664 absolute error = 3.64e-31 relative error = 9.1574806911257584021599098186344e-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] = -2.93 y[1] (analytic) = 0.0476976700470131584350196046763 y[1] (numeric) = 0.047697670047013158435019604676668 absolute error = 3.68e-31 relative error = 7.7152615554864878331435885399298e-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] = -2.92 y[1] (analytic) = 0.0555486475810826805029317351583 y[1] (numeric) = 0.055548647581082680502931735158608 absolute error = 3.08e-31 relative error = 5.5446894463167931701004600807345e-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] = -2.91 y[1] (analytic) = 0.0633020710633485907678471066028 y[1] (numeric) = 0.063302071063348590767847106603095 absolute error = 2.95e-31 relative error = 4.6601950780533421900535216388849e-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] = -2.9 y[1] (analytic) = 0.0709581651495905217811066693455 y[1] (numeric) = 0.070958165149590521781106669345875 absolute error = 3.75e-31 relative error = 5.2848040702496097752872353479247e-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] = -2.89 y[1] (analytic) = 0.0785171642284466009323155072093 y[1] (numeric) = 0.078517164228446600932315507209626 absolute error = 3.26e-31 relative error = 4.1519584055723053756074350313735e-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] = -2.88 y[1] (analytic) = 0.0859793123979747819598179047655 y[1] (numeric) = 0.085979312397974781959817904765868 absolute error = 3.68e-31 relative error = 4.2800993603743699448147950164647e-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] = -2.87 y[1] (analytic) = 0.0933448634412432425696937587379 y[1] (numeric) = 0.09334486344124324256969375873828 absolute error = 3.80e-31 relative error = 4.0709256620123976252819877800138e-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] = -2.86 y[1] (analytic) = 0.1006140808009522891031731663928 y[1] (numeric) = 0.10061408080095228910317316639311 absolute error = 3.1e-31 relative error = 3.0810796812156129283404447557260e-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] = -2.85 y[1] (analytic) = 0.1077872375530903060408541071749 y[1] (numeric) = 0.10778723755309030604085410717527 absolute error = 3.7e-31 relative error = 3.4326883998465729517305392408441e-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] = -2.84 y[1] (analytic) = 0.1148646163796263847268194935862 y[1] (numeric) = 0.11486461637962638472681949358658 absolute error = 3.8e-31 relative error = 3.3082424507831365458045391646058e-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] = -2.83 y[1] (analytic) = 0.1218465095402423620270251127245 y[1] (numeric) = 0.12184650954024236202702511272487 absolute error = 3.7e-31 relative error = 3.0366072971322970053146732735546e-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] = -2.82 y[1] (analytic) = 0.12873321884310709569453606376 y[1] (numeric) = 0.12873321884310709569453606376038 absolute error = 3.8e-31 relative error = 2.9518410509343584077485422821728e-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] = -2.81 y[1] (analytic) = 0.1355250556146958989897204783588 y[1] (numeric) = 0.13552505561469589898972047835918 absolute error = 3.8e-31 relative error = 2.8039095669538616904115489623987e-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] = -2.8 y[1] (analytic) = 0.1422223406686581525867881173662 y[1] (numeric) = 0.1422223406686581525867881173665 absolute error = 3.0e-31 relative error = 2.1093732432580590647507600593752e-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] = -2.79 y[1] (analytic) = 0.1488254042737362069795396196241 y[1] (numeric) = 0.14882540427373620697953961962444 absolute error = 3.4e-31 relative error = 2.2845561996568425325715501660771e-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] = -2.78 y[1] (analytic) = 0.1553345861207387834693516691176 y[1] (numeric) = 0.15533458612073878346935166911794 absolute error = 3.4e-31 relative error = 2.1888235485156158817274286619275e-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] = -2.77 y[1] (analytic) = 0.1617502352885721763677772078291 y[1] (numeric) = 0.16175023528857217636777720782942 absolute error = 3.2e-31 relative error = 1.9783587914360723984046585817963e-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] = -2.76 y[1] (analytic) = 0.1680727102093326532652331971401 y[1] (numeric) = 0.16807271020933265326523319714045 absolute error = 3.5e-31 relative error = 2.0824320591015577235809907059130e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=44013024, alloc=4455632, time=4.27 x[1] = -2.75 y[1] (analytic) = 0.1743023786324635440966594895267 y[1] (numeric) = 0.17430237863246354409665948952706 absolute error = 3.6e-31 relative error = 2.0653762893224829793308662616540e-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] = -2.74 y[1] (analytic) = 0.1804396175879806032653732517793 y[1] (numeric) = 0.18043961758798060326537325177962 absolute error = 3.2e-31 relative error = 1.7734464541522934180729136097296e-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] = -2.73 y[1] (analytic) = 0.1864848133487693222582611248928 y[1] (numeric) = 0.18648481334876932225826112489313 absolute error = 3.3e-31 relative error = 1.7695810938922109501870334177007e-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] = -2.72 y[1] (analytic) = 0.1924383613919579629896287999871 y[1] (numeric) = 0.19243836139195796298962879998741 absolute error = 3.1e-31 relative error = 1.6109054232102547981561879491881e-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] = -2.71 y[1] (analytic) = 0.1983006663593701745381845937161 y[1] (numeric) = 0.19830066635937017453818459371642 absolute error = 3.2e-31 relative error = 1.6137111683733847659767261203038e-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] = -2.7 y[1] (analytic) = 0.2040721420170611479825272819433 y[1] (numeric) = 0.20407214201706114798252728194367 absolute error = 3.7e-31 relative error = 1.8130843158840695668392731887056e-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] = -2.69 y[1] (analytic) = 0.2097532112139413556859348843289 y[1] (numeric) = 0.20975321121394135568593488432921 absolute error = 3.1e-31 relative error = 1.4779273137506830676880881280962e-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] = -2.68 y[1] (analytic) = 0.2153443058394920126220458186207 y[1] (numeric) = 0.215344305839492012622045818621 absolute error = 3.0e-31 relative error = 1.3931178668991904759081845338709e-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] = -2.67 y[1] (analytic) = 0.2208458667805764881600628584297 y[1] (numeric) = 0.22084586678057648816006285843008 absolute error = 3.8e-31 relative error = 1.7206570606890850935805962073502e-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] = -2.66 y[1] (analytic) = 0.2262583438773519871323110038826 y[1] (numeric) = 0.22625834387735198713231100388293 absolute error = 3.3e-31 relative error = 1.4585097475074038475236868869776e-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] = -2.65 y[1] (analytic) = 0.2315821958782859089793023660538 y[1] (numeric) = 0.23158219587828590897930236605415 absolute error = 3.5e-31 relative error = 1.5113424357714945875672349179214e-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] = -2.64 y[1] (analytic) = 0.236817890394281383298907316266 y[1] (numeric) = 0.23681789039428138329890731626633 absolute error = 3.3e-31 relative error = 1.3934758030762727966604693364521e-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] = -2.63 y[1] (analytic) = 0.2419659038519165692078483901949 y[1] (numeric) = 0.24196590385191656920784839019527 absolute error = 3.7e-31 relative error = 1.5291410653727496049425316824190e-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] = -2.62 y[1] (analytic) = 0.2470267214458023945466136767484 y[1] (numeric) = 0.24702672144580239454661367674869 absolute error = 2.9e-31 relative error = 1.1739620649243241193726939284446e-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] = -2.61 y[1] (analytic) = 0.2520008370900634991141674487226 y[1] (numeric) = 0.25200083709006349911416744872299 absolute error = 3.9e-31 relative error = 1.5476139067768908889692547443955e-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] = -2.6 y[1] (analytic) = 0.2568887533689472337977021516452 y[1] (numeric) = 0.25688875336894723379770215164554 absolute error = 3.4e-31 relative error = 1.3235301099837844090960037121369e-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] = -2.59 y[1] (analytic) = 0.2616909814865656546563597454083 y[1] (numeric) = 0.26169098148656565465635974540865 absolute error = 3.5e-31 relative error = 1.3374553376344298547692821706085e-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] = -2.58 y[1] (analytic) = 0.2664080412157755377176324945692 y[1] (numeric) = 0.26640804121577553771763249456957 absolute error = 3.7e-31 relative error = 1.3888469668988737427407177249369e-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] = -2.57 y[1] (analytic) = 0.2710404608462015264423637215671 y[1] (numeric) = 0.27104046084620152644236372156746 absolute error = 3.6e-31 relative error = 1.3282149789594603601281248931964e-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] = -2.56 y[1] (analytic) = 0.2755887771314076095002881233824 y[1] (numeric) = 0.27558877713140760950028812338278 absolute error = 3.8e-31 relative error = 1.3788660189845340204984598605538e-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] = -2.55 y[1] (analytic) = 0.2800535352352222116643104758323 y[1] (numeric) = 0.28005353523522221166431047583262 absolute error = 3.2e-31 relative error = 1.1426386734637218705155407963524e-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] = -2.54 y[1] (analytic) = 0.2844352886772222652697043558066 y[1] (numeric) = 0.2844352886772222652697043558069 absolute error = 3.0e-31 relative error = 1.0547214496315209336894760004730e-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] = -2.53 y[1] (analytic) = 0.288734599277381713785655172555 y[1] (numeric) = 0.28873459927738171378565517255533 absolute error = 3.3e-31 relative error = 1.1429181013494521255176690469315e-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=48014068, alloc=4455632, time=4.67 TOP MAIN SOLVE Loop x[1] = -2.52 y[1] (analytic) = 0.2929520370998899826026642604518 y[1] (numeric) = 0.29295203709988998260266426045219 absolute error = 3.9e-31 relative error = 1.3312759448981707166787043112068e-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] = -2.51 y[1] (analytic) = 0.2970881803961460351419175078784 y[1] (numeric) = 0.29708818039614603514191750787875 absolute error = 3.5e-31 relative error = 1.1781013957987147218687067614597e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.5 y[1] (analytic) = 0.3011436155469337148335027904674 y[1] (numeric) = 0.30114361554693371483350279046769 absolute error = 2.9e-31 relative error = 9.6299567723959612053784650804234e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.49 y[1] (analytic) = 0.3051189370037841553810913325716 y[1] (numeric) = 0.30511893700378415538109133257191 absolute error = 3.1e-31 relative error = 1.0159972469888203253363893171853e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.48 y[1] (analytic) = 0.3090147472295311230231920335903 y[1] (numeric) = 0.30901474722953112302319203359067 absolute error = 3.7e-31 relative error = 1.1973538587307939195192145508189e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.47 y[1] (analytic) = 0.3128316566380652352072155840616 y[1] (numeric) = 0.31283165663806523520721558406189 absolute error = 2.9e-31 relative error = 9.2701615660182170949147689574112e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.46 y[1] (analytic) = 0.3165702835332930802042763146862 y[1] (numeric) = 0.31657028353329308020427631468654 absolute error = 3.4e-31 relative error = 1.0740111049123246659501145232004e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.45 y[1] (analytic) = 0.3202312540473073417019030673365 y[1] (numeric) = 0.32023125404730734170190306733683 absolute error = 3.3e-31 relative error = 1.0305052858808388962409579419229e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.44 y[1] (analytic) = 0.3238152020777741113106750925374 y[1] (numeric) = 0.32381520207777411131067509253774 absolute error = 3.4e-31 relative error = 1.0499815877030338283000835923658e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.43 y[1] (analytic) = 0.3273227692245436502013552441779 y[1] (numeric) = 0.32732276922454365020135524417824 absolute error = 3.4e-31 relative error = 1.0387300608677172731570251725334e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.42 y[1] (analytic) = 0.3307546047254909387435325689107 y[1] (numeric) = 0.33075460472549093874353256891108 absolute error = 3.8e-31 relative error = 1.1488880111446374856311504058834e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.41 y[1] (analytic) = 0.334111365391592430037344395568 y[1] (numeric) = 0.33411136539159243003734439556829 absolute error = 2.9e-31 relative error = 8.6797406505494934796887359540666e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.4 y[1] (analytic) = 0.3373937155412454996088222273348 y[1] (numeric) = 0.33739371554124549960882222733512 absolute error = 3.2e-31 relative error = 9.4844683009776107296881205291412e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.39 y[1] (analytic) = 0.3406023269338371592691582926181 y[1] (numeric) = 0.3406023269338371592691582926184 absolute error = 3.0e-31 relative error = 8.8079257326470273569745973239809e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.38 y[1] (analytic) = 0.3437378787025686782111476073675 y[1] (numeric) = 0.34373787870256867821114760736787 absolute error = 3.7e-31 relative error = 1.0764015923894018918991622761985e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.37 y[1] (analytic) = 0.3468010572865428288247166088224 y[1] (numeric) = 0.34680105728654282882471660882269 absolute error = 2.9e-31 relative error = 8.3621429031685100010798607403174e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.36 y[1] (analytic) = 0.3497925563621205484503630346451 y[1] (numeric) = 0.34979255636212054845036303464544 absolute error = 3.4e-31 relative error = 9.7200467481651363117952489928977e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.35 y[1] (analytic) = 0.3527130767735538813471291122589 y[1] (numeric) = 0.35271307677355388134712911225926 absolute error = 3.6e-31 relative error = 1.0206596344346042284204115687126e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.34 y[1] (analytic) = 0.3555633264629021375231055720614 y[1] (numeric) = 0.35556332646290213752310557206169 absolute error = 2.9e-31 relative error = 8.1560717435311001566220337256182e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.33 y[1] (analytic) = 0.358344020399238276754180427816 y[1] (numeric) = 0.35834402039923827675418042781634 absolute error = 3.4e-31 relative error = 9.4880891167431555055428823730488e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.32 y[1] (analytic) = 0.3610558805071525970936361660082 y[1] (numeric) = 0.36105588050715259709363616600857 absolute error = 3.7e-31 relative error = 1.0247721197070219658559035198614e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.31 y[1] (analytic) = 0.363699635594560877444164323471 y[1] (numeric) = 0.36369963559456087744416432347138 absolute error = 3.8e-31 relative error = 1.0448182038422776309739757406983e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=52015732, alloc=4455632, time=5.06 x[1] = -2.3 y[1] (analytic) = 0.366276021279824193317880571166 y[1] (numeric) = 0.36627602127982419331788057116636 absolute error = 3.6e-31 relative error = 9.8286532310279329976297525237353e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.29 y[1] (analytic) = 0.368785779918187693742031018189 y[1] (numeric) = 0.36878577991818769374203101818929 absolute error = 2.9e-31 relative error = 7.8636437680523984201762660690287e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.28 y[1] (analytic) = 0.3712296605275456953713983504607 y[1] (numeric) = 0.37122966052754569537139835046104 absolute error = 3.4e-31 relative error = 9.1587509337705946499817597702977e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.27 y[1] (analytic) = 0.3736084187135405172361343481243 y[1] (numeric) = 0.37360841871354051723613434812465 absolute error = 3.5e-31 relative error = 9.3680972501949435266137180771297e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.26 y[1] (analytic) = 0.3759228165940025461791265687448 y[1] (numeric) = 0.37592281659400254617912656874519 absolute error = 3.9e-31 relative error = 1.0374470045035889436382610497633e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.25 y[1] (analytic) = 0.3781736227227390889133890573964 y[1] (numeric) = 0.37817362272273908891338905739675 absolute error = 3.5e-31 relative error = 9.2550082546768525440120638337252e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.24 y[1] (analytic) = 0.3803616120126796317507622663104 y[1] (numeric) = 0.38036161201267963175076226631079 absolute error = 3.9e-31 relative error = 1.0253400650405253450129544292982e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.23 y[1] (analytic) = 0.3824875656583851934119039106856 y[1] (numeric) = 0.38248756565838519341190391068598 absolute error = 3.8e-31 relative error = 9.9349634894900887599623379294578e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.22 y[1] (analytic) = 0.3845522710579295199177144375002 y[1] (numeric) = 0.3845522710579295199177144375005 absolute error = 3.0e-31 relative error = 7.8012801530122171245542024986453e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.21 y[1] (analytic) = 0.3865565217341599333776091775186 y[1] (numeric) = 0.38655652173415993337760917751898 absolute error = 3.8e-31 relative error = 9.8303864670360175511945030608364e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.2 y[1] (analytic) = 0.3885011172553457085241426126549 y[1] (numeric) = 0.38850111725534570852414261265527 absolute error = 3.7e-31 relative error = 9.5237821351441393741785509429544e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.19 y[1] (analytic) = 0.390386863155221912090205163797 y[1] (numeric) = 0.39038686315522191209020516379729 absolute error = 2.9e-31 relative error = 7.4285286563214335876586721816211e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.3922145708524367005782248676625 y[1] (numeric) = 0.39221457085243670057822486766283 absolute error = 3.3e-31 relative error = 8.4137618672039659170993232722272e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.3939850575694101316244699944165 y[1] (numeric) = 0.39398505756941013162446999441685 absolute error = 3.5e-31 relative error = 8.8835856405122398617739299637314e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.3956991462506126030096987439834 y[1] (numeric) = 0.39569914625061260300969874398371 absolute error = 3.1e-31 relative error = 7.8342347446881829713240569013551e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.397357665480271091404153882264 y[1] (numeric) = 0.39735766548027109140415388226437 absolute error = 3.7e-31 relative error = 9.3115103128259795351828244531892e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.3989614493995114201544499120086 y[1] (numeric) = 0.39896144939951142015444991200894 absolute error = 3.4e-31 relative error = 8.5221266493728647941945963944038e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.4005113376229448418165262096097 y[1] (numeric) = 0.40051133762294484181652620961006 absolute error = 3.6e-31 relative error = 8.9885095921782966007131091849122e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.4020081751547072767069018829839 y[1] (numeric) = 0.40200817515470727670690188298423 absolute error = 3.3e-31 relative error = 8.2087882882730947420603047944721e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.4034528123039596034784101570717 y[1] (numeric) = 0.40345281230395960347841015707203 absolute error = 3.3e-31 relative error = 8.1793952089588962279723709363012e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.4048461045998574516209385237192 y[1] (numeric) = 0.40484610459985745162093852371951 absolute error = 3.1e-31 relative error = 7.6572306483323676416498231909184e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.09 y[1] (analytic) = 0.4061889127059989988370663118704 y[1] (numeric) = 0.40618891270599899883706631187079 absolute error = 3.9e-31 relative error = 9.6014437568433436712772666993349e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=56017008, alloc=4455632, time=5.46 x[1] = -2.08 y[1] (analytic) = 0.4074821023343593284415688497724 y[1] (numeric) = 0.40748210233435932844156884977269 absolute error = 2.9e-31 relative error = 7.1168769950548792136450696779964e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.4087265441587199532773271390117 y[1] (numeric) = 0.40872654415871995327732713901207 absolute error = 3.7e-31 relative error = 9.0525072395669669887974423446149e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.4099231137276021631231096264879 y[1] (numeric) = 0.40992311372760216312310962648824 absolute error = 3.4e-31 relative error = 8.2942383245540347308883940322999e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.4110726913767129021859299941674 y[1] (numeric) = 0.41107269137671290218592999416774 absolute error = 3.4e-31 relative error = 8.2710432274475545291889766072258e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.4121761621409119320172702052914 y[1] (numeric) = 0.4121761621409119320172702052917 absolute error = 3.0e-31 relative error = 7.2784412965987605436094663029080e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.4132344156657090830635167316961 y[1] (numeric) = 0.41323441566570908306351673169643 absolute error = 3.3e-31 relative error = 7.9857821006602083716198908826818e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.4142483461183004450517028740902 y[1] (numeric) = 0.41424834611830044505170287409053 absolute error = 3.3e-31 relative error = 7.9662357880786584018937560951157e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.4152188520981523925173823401654 y[1] (numeric) = 0.41521885209815239251738234016576 absolute error = 3.6e-31 relative error = 8.6701265653251368610421936898549e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.4161468365471423869975682295008 y[1] (numeric) = 0.41614683654714238699756822950109 absolute error = 2.9e-31 relative error = 6.9686940889949048702883411641176e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4170332066592655417336357161303 y[1] (numeric) = 0.41703320665926554173363571613062 absolute error = 3.2e-31 relative error = 7.6732498729160928390781923520866e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4178788737899159781524738599072 y[1] (numeric) = 0.41787887378991597815247385990752 absolute error = 3.2e-31 relative error = 7.6577214133317610899388478014630e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4186847533647520459146398138793 y[1] (numeric) = 0.41868475336475204591463981387963 absolute error = 3.3e-31 relative error = 7.8818251046392610517189277665438e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4194517647881545199315652154474 y[1] (numeric) = 0.41945176478815451993156521544777 absolute error = 3.7e-31 relative error = 8.8210381040325269625477114208200e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4201808313512869284558284591307 y[1] (numeric) = 0.42018083135128692845582845913101 absolute error = 3.1e-31 relative error = 7.3777758733793445579744994683050e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4208728801397672061350676858407 y[1] (numeric) = 0.42087288013976720613506768584105 absolute error = 3.5e-31 relative error = 8.3160502022313457145425007848162e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4215288419409599047872890647119 y[1] (numeric) = 0.4215288419409599047872890647122 absolute error = 3.0e-31 relative error = 7.1169507314998517914271782824968e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.422149651150898232599236603159 y[1] (numeric) = 0.42214965115089823259923660315937 absolute error = 3.7e-31 relative error = 8.7646643551943328255307439876870e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4227362456808452294663389393975 y[1] (numeric) = 0.42273624568084522946633893939785 absolute error = 3.5e-31 relative error = 8.2793941512230965415994701795924e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4232895668635034222788336950803 y[1] (numeric) = 0.42328956686350342227883369508063 absolute error = 3.3e-31 relative error = 7.7960815912671394918716458401362e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4238105593588823391103824155512 y[1] (numeric) = 0.42381055935888233911038241555155 absolute error = 3.5e-31 relative error = 8.2584067874443960108999937336705e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4243001710598332954793137595222 y[1] (numeric) = 0.42430017105983329547931375952256 absolute error = 3.6e-31 relative error = 8.4845593887171467839995313752048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4247593529972608991251480648099 y[1] (numeric) = 0.42475935299726089912514806481021 absolute error = 3.1e-31 relative error = 7.2982501223933982291736281088242e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4251890592450207520709354882891 y[1] (numeric) = 0.42518905924502075207093548828944 absolute error = 3.4e-31 relative error = 7.9964428201354672353367763870524e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO 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=60019604, alloc=4521156, time=5.86 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (analytic) = 0.4255902468245128601219498354748 y[1] (numeric) = 0.42559024682451286012194983547512 absolute error = 3.2e-31 relative error = 7.5189692994056849643539183009823e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4259638756089802903802829832816 y[1] (numeric) = 0.42596387560898029038028298328191 absolute error = 3.1e-31 relative error = 7.2776124397123522814905654177707e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4263109082275226468298375836185 y[1] (numeric) = 0.42631090822752264682983758361884 absolute error = 3.4e-31 relative error = 7.9753999590022591957727430174750e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4266323099688339625641710448309 y[1] (numeric) = 0.42663230996883396256417104483118 absolute error = 2.8e-31 relative error = 6.5630284780928654729423886791837e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (analytic) = 0.426929048684674634787749850842 y[1] (numeric) = 0.42692904868467463478774985084229 absolute error = 2.9e-31 relative error = 6.7926977771472980920429510197653e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4272020946930870553166743065306 y[1] (numeric) = 0.4272020946930870553166743065309 absolute error = 3.0e-31 relative error = 7.0224374769399877706643637054123e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4274524206813646149351702644646 y[1] (numeric) = 0.42745242068136461493517026446493 absolute error = 3.3e-31 relative error = 7.7201574732920166318663211038552e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4276810016087837846265532903126 y[1] (numeric) = 0.42768100160878378462655329031295 absolute error = 3.5e-31 relative error = 8.1836695734303022381719725845809e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4278888146091090003894858417304 y[1] (numeric) = 0.42788881460910900038948584173072 absolute error = 3.2e-31 relative error = 7.4785782912397673772524377603826e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4280768388928801010698001765041 y[1] (numeric) = 0.42807683889288010106980017650442 absolute error = 3.2e-31 relative error = 7.4752934736577810540499806465649e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4282460556494920903826769439426 y[1] (numeric) = 0.42824605564949209038267694394296 absolute error = 3.6e-31 relative error = 8.4063821546239842929496143167037e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4283974479490770150673773153451 y[1] (numeric) = 0.42839744794907701506737731534542 absolute error = 3.2e-31 relative error = 7.4696990267327161365105434427603e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4285320006441977709049483513426 y[1] (numeric) = 0.4285320006441977709049483513429 absolute error = 3.0e-31 relative error = 7.0006440487296181123215708251813e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4286507002713636671363782803312 y[1] (numeric) = 0.42865070027136366713637828033152 absolute error = 3.2e-31 relative error = 7.4652858329035568124863407943778e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4287545349523775976426897830511 y[1] (numeric) = 0.42875453495237759764268978305144 absolute error = 3.4e-31 relative error = 7.9299452783109175619919095780811e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4288444942955246840876428573349 y[1] (numeric) = 0.42884449429552468408764285733521 absolute error = 3.1e-31 relative error = 7.2287275253293390347723544530450e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4289215692966122720763904698331 y[1] (numeric) = 0.42892156929661227207639046983342 absolute error = 3.2e-31 relative error = 7.4605714169321780155932677125957e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4289867522398711762480047341728 y[1] (numeric) = 0.42898675223987117624800473417316 absolute error = 3.6e-31 relative error = 8.3918675371752106296754255722134e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4290410365987280840947823424486 y[1] (numeric) = 0.42904103659872808409478234244895 absolute error = 3.5e-31 relative error = 8.1577278195732756248989349254301e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4290854169364590411852579316506 y[1] (numeric) = 0.42908541693645904118525793165096 absolute error = 3.6e-31 relative error = 8.3899378955894571879190511822869e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4291208888067339523596145973413 y[1] (numeric) = 0.42912088880673395235961459734162 absolute error = 3.2e-31 relative error = 7.4571061056904303343801461331698e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4291484486540620443644927074566 y[1] (numeric) = 0.42914844865406204436449270745695 absolute error = 3.5e-31 relative error = 8.1556860125605658334566284189117e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=64021056, alloc=4521156, time=6.25 x[1] = -1.63 y[1] (analytic) = 0.4291690937141482452979716974198 y[1] (numeric) = 0.42916909371414824529797169742015 absolute error = 3.5e-31 relative error = 8.1552936855495121233606338796993e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4291838219141704451437442747123 y[1] (numeric) = 0.42918382191417044514374427471268 absolute error = 3.8e-31 relative error = 8.8540150070240442724411024717689e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.429193631772987609585327609601 y[1] (numeric) = 0.42919363177298760958532760960137 absolute error = 3.7e-31 relative error = 8.6208175659908961626541352864459e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4291995223012887262057704629465 y[1] (numeric) = 0.42919952230128872620577046294685 absolute error = 3.5e-31 relative error = 8.1547155067499729237835839720199e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4292024929016925680950273462434 y[1] (numeric) = 0.42920249290169256809502734624375 absolute error = 3.5e-31 relative error = 8.1546590662549194253261790245120e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (analytic) = 0.4292035432688082648053890569827 y[1] (numeric) = 0.42920354326880826480538905698307 absolute error = 3.7e-31 relative error = 8.6206184874916246971151374125084e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (analytic) = 0.4292036732892666745145914663546 y[1] (numeric) = 0.42920367328926667451459146635499 absolute error = 3.9e-31 relative error = 9.0865951125528947864602364968801e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0007679 Order of pole (three term test) = -0.8929 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.56 y[1] (analytic) = 0.4292038829417325541760793362391 y[1] (numeric) = 0.42920388294173255417607933623944 absolute error = 3.4e-31 relative error = 7.9216431517269705436930620565218e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01041 Order of pole (three term test) = -0.8957 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (analytic) = 0.4292051721969075263560872253044 y[1] (numeric) = 0.42920517219690752635608722530479 absolute error = 3.9e-31 relative error = 9.0865633795549585824982206484444e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02005 Order of pole (three term test) = -0.9033 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = 0.4292085409175338423775231929236 y[1] (numeric) = 0.42920854091753384237752319292395 absolute error = 3.5e-31 relative error = 8.1545441582265109768441325275375e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02968 Order of pole (three term test) = -0.9158 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = 0.4292149887584089413110109929239 y[1] (numeric) = 0.42921498875840894131101099292423 absolute error = 3.3e-31 relative error = 7.6884547055216235982600045230208e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0393 Order of pole (three term test) = -0.9331 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = 0.4292255150664208032738707298473 y[1] (numeric) = 0.42922551506642080327387072984762 absolute error = 3.2e-31 relative error = 7.4552883919419696109371559049017e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0489 Order of pole (three term test) = -0.9552 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = 0.4292411187806140934184044850838 y[1] (numeric) = 0.42924111878061409341840448508415 absolute error = 3.5e-31 relative error = 8.1539252575400547421086995154216e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05848 Order of pole (three term test) = -0.9821 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (analytic) = 0.4292627983322970899118101485657 y[1] (numeric) = 0.42926279833229708991181014856607 absolute error = 3.7e-31 relative error = 8.6194285048102141643046853322066e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06804 Order of pole (three term test) = -1.014 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.49 y[1] (analytic) = 0.4292915515451993851316815154363 y[1] (numeric) = 0.42929155154519938513168151543662 absolute error = 3.2e-31 relative error = 7.4541415699467297444680801610919e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07757 Order of pole (three term test) = -1.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.48 y[1] (analytic) = 0.4293283755356903442237734593522 y[1] (numeric) = 0.4293283755356903442237734593525 absolute error = 3.0e-31 relative error = 6.9876583308913111168268699774182e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08707 Order of pole (three term test) = -1.092 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.47 y[1] (analytic) = 0.4293742666130682990930253985376 y[1] (numeric) = 0.42937426661306829909302539853793 absolute error = 3.3e-31 relative error = 7.6856026469182963511580039936218e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09654 Order of pole (three term test) = -1.138 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.46 y[1] (analytic) = 0.4294302201799304488253518908766 y[1] (numeric) = 0.42943022017993044882535189087696 absolute error = 3.6e-31 relative error = 8.3832013464064238868605890780194e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.106 Order of pole (three term test) = -1.188 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45 y[1] (analytic) = 0.429497230632633429467133372752 y[1] (numeric) = 0.42949723063263342946713337275232 absolute error = 3.2e-31 relative error = 7.4505719054032528777735440134915e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1154 Order of pole (three term test) = -1.244 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.44 y[1] (analytic) = 0.4295762912618545070224798438708 y[1] (numeric) = 0.42957629126185450702247984387117 absolute error = 3.7e-31 relative error = 8.6131382836130751937332826697780e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1247 Order of pole (three term test) = -1.304 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.43 y[1] (analytic) = 0.4296683941532633374661023754251 y[1] (numeric) = 0.42966839415326333746610237542542 absolute error = 3.2e-31 relative error = 7.4476038813749828036338463537613e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.134 Order of pole (three term test) = -1.369 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.42 y[1] (analytic) = 0.4297745300883142265130178970241 y[1] (numeric) = 0.42977453008831422651301789702443 absolute error = 3.3e-31 relative error = 7.6784447866696150836168868110903e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1432 Order of pole (three term test) = -1.438 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.41 y[1] (analytic) = 0.4298956884451688098364374506391 y[1] (numeric) = 0.42989568844516880983643745063942 absolute error = 3.2e-31 relative error = 7.4436661869618752322318001608565e-29 % Correct digits = 31 h = 0.01 bytes used=68022452, alloc=4521156, time=6.65 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1524 Order of pole (three term test) = -1.513 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.4 y[1] (analytic) = 0.4300328570997590613832519647964 y[1] (numeric) = 0.43003285709975906138325196479669 absolute error = 2.9e-31 relative error = 6.7436707500870282004838233408020e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1615 Order of pole (three term test) = -1.591 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.39 y[1] (analytic) = 0.430187022327000523403836782196 y[1] (numeric) = 0.43018702232700052340383678219628 absolute error = 2.8e-31 relative error = 6.5087969991610299544206635958851e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1706 Order of pole (three term test) = -1.675 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.38 y[1] (analytic) = 0.4303591687021656367908499264018 y[1] (numeric) = 0.43035916870216563679084992640213 absolute error = 3.3e-31 relative error = 7.6680136964475781306300120316315e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1795 Order of pole (three term test) = -1.762 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.37 y[1] (analytic) = 0.4305502790024270343118016103547 y[1] (numeric) = 0.43055027900242703431180161035503 absolute error = 3.3e-31 relative error = 7.6646100605160628136453900623193e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1885 Order of pole (three term test) = -1.855 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36 y[1] (analytic) = 0.4307613341085806423240247476081 y[1] (numeric) = 0.43076133410858064232402474760848 absolute error = 3.8e-31 relative error = 8.8215902847077404133191239445088e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1973 Order of pole (three term test) = -1.951 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.35 y[1] (analytic) = 0.4309933129069584185799778269894 y[1] (numeric) = 0.43099331290695841857997782698971 absolute error = 3.1e-31 relative error = 7.1926870027081347626180087962005e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.206 Order of pole (three term test) = -2.052 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.34 y[1] (analytic) = 0.4312471921915405347673605076999 y[1] (numeric) = 0.43124719219154053476736050770019 absolute error = 2.9e-31 relative error = 6.7246814646202981331562409466655e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2147 Order of pole (three term test) = -2.158 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.33 y[1] (analytic) = 0.4315239465662767924842150139894 y[1] (numeric) = 0.43152394656627679248421501398976 absolute error = 3.6e-31 relative error = 8.3425265935898278038264136474937e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2233 Order of pole (three term test) = -2.268 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.32 y[1] (analytic) = 0.4318245483476270404260172705726 y[1] (numeric) = 0.43182454834762704042601727057298 absolute error = 3.8e-31 relative error = 8.7998702587443619481766160043395e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2318 Order of pole (three term test) = -2.382 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.31 y[1] (analytic) = 0.4321499674673303386618230213838 y[1] (numeric) = 0.43214996746733033866182302138414 absolute error = 3.4e-31 relative error = 7.8676391437123806016624730863192e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2402 Order of pole (three term test) = -2.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.3 y[1] (analytic) = 0.4325011713754125930020158907071 y[1] (numeric) = 0.43250117137541259300201589070746 absolute error = 3.6e-31 relative error = 8.3236768782648842350062789671006e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2485 Order of pole (three term test) = -2.623 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.29 y[1] (analytic) = 0.4328791249434423586133939099388 y[1] (numeric) = 0.43287912494344235861339390993915 absolute error = 3.5e-31 relative error = 8.0853979744513922659287696379861e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2567 Order of pole (three term test) = -2.749 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.28 y[1] (analytic) = 0.4332847903680444872206131064074 y[1] (numeric) = 0.43328479036804448722061310640774 absolute error = 3.4e-31 relative error = 7.8470328882579580151839929970181e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2648 Order of pole (three term test) = -2.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.27 y[1] (analytic) = 0.433719127074681266448862983912 y[1] (numeric) = 0.43371912707468126644886298391237 absolute error = 3.7e-31 relative error = 8.5308665655478553081626579037974e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2728 Order of pole (three term test) = -3.015 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.26 y[1] (analytic) = 0.4341830916217106731136575108235 y[1] (numeric) = 0.43418309162171067311365751082384 absolute error = 3.4e-31 relative error = 7.8307978030667007869232084024517e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2807 Order of pole (three term test) = -3.154 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.25 y[1] (analytic) = 0.434677637604731334552461447562 y[1] (numeric) = 0.43467763760473133455246144756229 absolute error = 2.9e-31 relative error = 6.6716107503949367593049677270756e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2885 Order of pole (three term test) = -3.296 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.24 y[1] (analytic) = 0.4352037155612237634223065843026 y[1] (numeric) = 0.43520371556122376342230658430295 absolute error = 3.5e-31 relative error = 8.0422107506286342622255986750099e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2962 Order of pole (three term test) = -3.443 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.23 y[1] (analytic) = 0.4357622728754974017604527545023 y[1] (numeric) = 0.43576227287549740176045275450267 absolute error = 3.7e-31 relative error = 8.4908681414398973105197263168742e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3037 Order of pole (three term test) = -3.593 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.22 y[1] (analytic) = 0.4363542536839529795244770255648 y[1] (numeric) = 0.43635425368395297952447702556514 absolute error = 3.4e-31 relative error = 7.7918342064853250748850218424192e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3111 Order of pole (three term test) = -3.748 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.21 y[1] (analytic) = 0.4369805987806696612969892863352 y[1] (numeric) = 0.43698059878066966129698928633555 absolute error = 3.5e-31 relative error = 8.0095089113023260384169178321608e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3184 Order of pole (three term test) = -3.905 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.2 y[1] (analytic) = 0.4376422455233264223616266443769 y[1] (numeric) = 0.43764224552332642236162664437726 absolute error = 3.6e-31 relative error = 8.2258969211145756588411371663570e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3256 Order of pole (three term test) = -4.067 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.19 y[1] (analytic) = 0.4383401277394670619343204416495 y[1] (numeric) = 0.43834012773946706193432044164987 absolute error = 3.7e-31 relative error = 8.4409337996979854029088946511667e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3327 Order of pole (three term test) = -4.232 NO COMPLEX POLE (six term test) for Equation 1 bytes used=72023504, alloc=4521156, time=7.05 TOP MAIN SOLVE Loop x[1] = -1.18 y[1] (analytic) = 0.4390751756331182269704005332872 y[1] (numeric) = 0.43907517563311822697040053328757 absolute error = 3.7e-31 relative error = 8.4268029834864552204896896452725e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3396 Order of pole (three term test) = -4.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.17 y[1] (analytic) = 0.4398483156917697846673380649495 y[1] (numeric) = 0.43984831569176978466733806494983 absolute error = 3.3e-31 relative error = 7.5025864196159019230395657201753e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3463 Order of pole (three term test) = -4.572 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.16 y[1] (analytic) = 0.440660470593726845548360376606 y[1] (numeric) = 0.44066047059372684554836037660633 absolute error = 3.3e-31 relative error = 7.4887588522603872990356509762005e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.353 Order of pole (three term test) = -4.748 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.15 y[1] (analytic) = 0.4415125591158427018474232811901 y[1] (numeric) = 0.44151255911584270184742328119042 absolute error = 3.2e-31 relative error = 7.2478119453911024120241744131482e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3595 Order of pole (three term test) = -4.926 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.14 y[1] (analytic) = 0.4424054960416419078248132591774 y[1] (numeric) = 0.44240549604164190782481325917776 absolute error = 3.6e-31 relative error = 8.1373310960430428480901805057818e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3658 Order of pole (three term test) = -5.108 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.13 y[1] (analytic) = 0.4433401920698426896287841643465 y[1] (numeric) = 0.4433401920698426896287841643468 absolute error = 3.0e-31 relative error = 6.7668126049969942888756868513850e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.372 Order of pole (three term test) = -5.293 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.12 y[1] (analytic) = 0.4443175537232878323860112060389 y[1] (numeric) = 0.44431755372328783238601120603921 absolute error = 3.1e-31 relative error = 6.9769919599679344846863720373033e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3781 Order of pole (three term test) = -5.481 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.11 y[1] (analytic) = 0.4453384832582931513562624880664 y[1] (numeric) = 0.44533848325829315135626248806676 absolute error = 3.6e-31 relative error = 8.0837388533342303068635590630344e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.384 Order of pole (three term test) = -5.672 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.1 y[1] (analytic) = 0.4464038785744226122286299482153 y[1] (numeric) = 0.44640387857442261222862994821562 absolute error = 3.2e-31 relative error = 7.1683964982990379800340868146060e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3897 Order of pole (three term test) = -5.866 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.09 y[1] (analytic) = 0.4475146331246991229721029261249 y[1] (numeric) = 0.44751463312469912297210292612519 absolute error = 2.9e-31 relative error = 6.4802350255034462206437330464735e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3953 Order of pole (three term test) = -6.063 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.08 y[1] (analytic) = 0.448671635826259976086475211474 y[1] (numeric) = 0.4486716358262599760864752114743 absolute error = 3.0e-31 relative error = 6.6864044001250305476703238175089e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4007 Order of pole (three term test) = -6.262 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.07 y[1] (analytic) = 0.4498757709714658756349069318241 y[1] (numeric) = 0.44987577097146587563490693182441 absolute error = 3.1e-31 relative error = 6.8907911917679663011676061746107e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.406 Order of pole (three term test) = -6.464 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.06 y[1] (analytic) = 0.4511279181394724380813624600436 y[1] (numeric) = 0.45112791813947243808136246004392 absolute error = 3.2e-31 relative error = 7.0933317831388917102789469942930e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4111 Order of pole (three term test) = -6.669 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.05 y[1] (analytic) = 0.4524289521082730097091504271879 y[1] (numeric) = 0.45242895210827300970915042718823 absolute error = 3.3e-31 relative error = 7.2939629186468612249446963047552e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.416 Order of pole (three term test) = -6.877 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.04 y[1] (analytic) = 0.4537797427672215962655265790078 y[1] (numeric) = 0.45377974276722159626552657900816 absolute error = 3.6e-31 relative error = 7.9333642750260799371660556257567e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4208 Order of pole (three term test) = -7.086 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.03 y[1] (analytic) = 0.4551811550300446524664977001626 y[1] (numeric) = 0.45518115503004465246649770016298 absolute error = 3.8e-31 relative error = 8.3483245253182274010427221601624e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4254 Order of pole (three term test) = -7.298 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.02 y[1] (analytic) = 0.4566340487483504301103861919662 y[1] (numeric) = 0.45663404874835043011038619196652 absolute error = 3.2e-31 relative error = 7.0077998098724999108135539457067e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4299 Order of pole (three term test) = -7.513 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.01 y[1] (analytic) = 0.4581392786256445337932686442208 y[1] (numeric) = 0.45813927862564453379326864422115 absolute error = 3.5e-31 relative error = 7.6395981818007910624492259417988e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4341 Order of pole (three term test) = -7.729 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = 0.459697694131860282599063392557 y[1] (numeric) = 0.45969769413186028259906339255735 absolute error = 3.5e-31 relative error = 7.6136992738450749377187536587966e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4382 Order of pole (three term test) = -7.948 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = 0.4613101394184124246568735913464 y[1] (numeric) = 0.46131013941841242465687359134671 absolute error = 3.1e-31 relative error = 6.7199910322982783140251561572566e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4422 Order of pole (three term test) = -8.169 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = 0.4629774532337826991233417326401 y[1] (numeric) = 0.46297745323378269912334173264038 absolute error = 2.8e-31 relative error = 6.0478107096634930265336609532042e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4459 Order of pole (three term test) = -8.391 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (analytic) = 0.4647004688396456869634722451501 y[1] (numeric) = 0.46470046883964568696347224515046 absolute error = 3.6e-31 relative error = 7.7469256895504724508743611599705e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4495 Order of pole (three term test) = -8.616 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=76024880, alloc=4521156, time=7.45 x[1] = -0.96 y[1] (analytic) = 0.4664800139275433378749491996481 y[1] (numeric) = 0.46648001392754333787494919964846 absolute error = 3.6e-31 relative error = 7.7173724329359479200890721235655e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4528 Order of pole (three term test) = -8.842 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = 0.4683169105361165058338190262395 y[1] (numeric) = 0.46831691053611650583381902623986 absolute error = 3.6e-31 relative error = 7.6871022997628199568195017378596e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.456 Order of pole (three term test) = -9.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.94 y[1] (analytic) = 0.470211974968901770039010184776 y[1] (numeric) = 0.4702119749689017700390101847763 absolute error = 3.0e-31 relative error = 6.3801012302981221506198455352494e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.88 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4591 Order of pole (three term test) = -9.299 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.93 y[1] (analytic) = 0.472166017712701761505092915567 y[1] (numeric) = 0.47216601771270176150509291556733 absolute error = 3.3e-31 relative error = 6.9890671420744783006400772423518e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.17 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4619 Order of pole (three term test) = -9.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.92 y[1] (analytic) = 0.4741798433565371582025952933256 y[1] (numeric) = 0.47417984335653715820259529332594 absolute error = 3.4e-31 relative error = 7.1702752608223594080021305632023e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4645 Order of pole (three term test) = -9.762 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.91 y[1] (analytic) = 0.4762542505111884534788217738253 y[1] (numeric) = 0.47625425051118845347882177382564 absolute error = 3.4e-31 relative error = 7.1390438958825106370103713637568e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.467 Order of pole (three term test) = -9.995 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9 y[1] (analytic) = 0.4783900317293355435152838485929 y[1] (numeric) = 0.47839003172933554351528384859319 absolute error = 2.9e-31 relative error = 6.0619992216743506991493093520420e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4693 Order of pole (three term test) = -10.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.89 y[1] (analytic) = 0.4805879734263031197964469426198 y[1] (numeric) = 0.48058797342630311979644694262007 absolute error = 2.7e-31 relative error = 5.6181181163370035471540972909462e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4714 Order of pole (three term test) = -10.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.88 y[1] (analytic) = 0.4828488558014197919845013942779 y[1] (numeric) = 0.48284885580141979198450139427823 absolute error = 3.3e-31 relative error = 6.8344368229323999598886890510208e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4733 Order of pole (three term test) = -10.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.87 y[1] (analytic) = 0.4851734527599988052223361945172 y[1] (numeric) = 0.48517345275999880522233619451749 absolute error = 2.9e-31 relative error = 5.9772437743714424691049593184637e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.475 Order of pole (three term test) = -10.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.86 y[1] (analytic) = 0.4875625318359481537279693357761 y[1] (numeric) = 0.48756253183594815372796933577646 absolute error = 3.6e-31 relative error = 7.3836682782903104894732791851682e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4765 Order of pole (three term test) = -11.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.85 y[1] (analytic) = 0.4900168541150178296045839705385 y[1] (numeric) = 0.49001685411501782960458397053885 absolute error = 3.5e-31 relative error = 7.1426114644996931710524926578921e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4778 Order of pole (three term test) = -11.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.84 y[1] (analytic) = 0.4925371741586918820773289631291 y[1] (numeric) = 0.49253717415869188207732896312946 absolute error = 3.6e-31 relative error = 7.3090929758737485251832172791600e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.479 Order of pole (three term test) = -11.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.83 y[1] (analytic) = 0.4951242399287328978875370821356 y[1] (numeric) = 0.49512423992873289788753708213586 absolute error = 2.6e-31 relative error = 5.2512072533032079454135908344746e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4799 Order of pole (three term test) = -11.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.82 y[1] (analytic) = 0.4977787927123864483334420215631 y[1] (numeric) = 0.49777879271238644833344202156338 absolute error = 2.8e-31 relative error = 5.6249885310357585472606688725170e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4807 Order of pole (three term test) = -12.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.81 y[1] (analytic) = 0.5005015670482529824503607593199 y[1] (numeric) = 0.50050156704825298245036075932021 absolute error = 3.1e-31 relative error = 6.1937868012731542840042504449617e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.09 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -12.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (analytic) = 0.5032932906528345790792500183577 y[1] (numeric) = 0.50329329065283457907925001835799 absolute error = 2.9e-31 relative error = 5.7620478036540800046568703991861e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -12.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.79 y[1] (analytic) = 0.506154684347763903087219138915 y[1] (numeric) = 0.50615468434776390308721913891536 absolute error = 3.6e-31 relative error = 7.1124502278172072556789913056680e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.83 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.78 y[1] (analytic) = 0.5090864619877226427837349762354 y[1] (numeric) = 0.50908646198772264278373497623575 absolute error = 3.5e-31 relative error = 6.8750600562707706970886045030318e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.21 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.77 y[1] (analytic) = 0.5120893303890566366287094346757 y[1] (numeric) = 0.51208933038905663662870943467597 absolute error = 2.7e-31 relative error = 5.2725175858452118920059105583679e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -13.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.76 y[1] (analytic) = 0.515163989259094827660311633333 y[1] (numeric) = 0.51516398925909482766031163333331 absolute error = 3.1e-31 relative error = 6.0175013483733555863849648058536e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.01 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -13.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.75 y[1] (analytic) = 0.5183111311261791136881612469999 y[1] (numeric) = 0.51831113112617911368816124700023 absolute error = 3.3e-31 relative error = 6.3668322014034438242185250618472e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4806 Order of pole (three term test) = -13.83 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.74 y[1] (analytic) = 0.5215314412704120902085754393012 y[1] (numeric) = 0.52153144127041209020857543930148 absolute error = 2.8e-31 relative error = 5.3688038312309737316048496928120e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.26 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4798 Order of pole (three term test) = -14.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=80027700, alloc=4521156, time=7.84 x[1] = -0.73 y[1] (analytic) = 0.5248255976551296112098678414497 y[1] (numeric) = 0.52482559765512961120986784144998 absolute error = 2.8e-31 relative error = 5.3351056284413931203047104553659e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4788 Order of pole (three term test) = -14.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.72 y[1] (analytic) = 0.528194270859105020554513037748 y[1] (numeric) = 0.52819427085910502055451303774837 absolute error = 3.7e-31 relative error = 7.0049983578617214870295273854701e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4777 Order of pole (three term test) = -14.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.71 y[1] (analytic) = 0.5316381240094918334585420558604 y[1] (numeric) = 0.53163812400949183345854205586076 absolute error = 3.6e-31 relative error = 6.7715234055256086705590199200973e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.19 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = -14.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7 y[1] (analytic) = 0.5351578127155115737441400098081 y[1] (numeric) = 0.53515781271551157374414000980845 absolute error = 3.5e-31 relative error = 6.5401268875067145954952564637133e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4747 Order of pole (three term test) = -15.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.69 y[1] (analytic) = 0.5387539850028933980264606845022 y[1] (numeric) = 0.53875398500289339802646068450255 absolute error = 3.5e-31 relative error = 6.4964716687547157942500738173212e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.473 Order of pole (three term test) = -15.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.68 y[1] (analytic) = 0.5424272812490720628176059159557 y[1] (numeric) = 0.542427281249072062817605915956 absolute error = 3.0e-31 relative error = 5.5306952723538592073492032188977e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.17 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4711 Order of pole (three term test) = -15.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.67 y[1] (analytic) = 0.5461783341191507146970578551619 y[1] (numeric) = 0.5461783341191507146970578551622 absolute error = 3.0e-31 relative error = 5.4927114691179593785019464249601e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.469 Order of pole (three term test) = -15.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.66 y[1] (analytic) = 0.5500077685026349072161829087698 y[1] (numeric) = 0.55000776850263490721618290877007 absolute error = 2.7e-31 relative error = 4.9090215713690690964071393434184e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4667 Order of pole (three term test) = -15.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.65 y[1] (analytic) = 0.5539162014509441710823954293201 y[1] (numeric) = 0.55391620145094417108239542932041 absolute error = 3.1e-31 relative error = 5.5965144039473300243140657435165e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4642 Order of pole (three term test) = -16.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.64 y[1] (analytic) = 0.5579042421157073864138892207397 y[1] (numeric) = 0.55790424211570738641388922073999 absolute error = 2.9e-31 relative error = 5.1980246448790223642466293818622e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.89 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4615 Order of pole (three term test) = -16.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.63 y[1] (analytic) = 0.5619724916878481274762910342229 y[1] (numeric) = 0.56197249168784812747629103422326 absolute error = 3.6e-31 relative error = 6.4060075061461322175257828154769e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4586 Order of pole (three term test) = -16.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.62 y[1] (analytic) = 0.5661215433374660713160003456393 y[1] (numeric) = 0.56612154333746607131600034563962 absolute error = 3.2e-31 relative error = 5.6524964252993888244003451227236e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4556 Order of pole (three term test) = -16.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.61 y[1] (analytic) = 0.5703519821545204820992534213452 y[1] (numeric) = 0.57035198215452048209925342134549 absolute error = 2.9e-31 relative error = 5.0845795065797252254859645155062e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4524 Order of pole (three term test) = -17.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6 y[1] (analytic) = 0.5746643850903217027590475010446 y[1] (numeric) = 0.57466438509032170275904750104494 absolute error = 3.4e-31 relative error = 5.9164968078987737058772375430894e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.449 Order of pole (three term test) = -17.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.59 y[1] (analytic) = 0.5790593208998365047520034775093 y[1] (numeric) = 0.57905932089983650475200347750964 absolute error = 3.4e-31 relative error = 5.8715918685438433072439330810279e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4454 Order of pole (three term test) = -17.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.58 y[1] (analytic) = 0.58353735008481306534211267195 y[1] (numeric) = 0.5835373500848130653421126719503 absolute error = 3.0e-31 relative error = 5.1410590934135938670980534979734e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4416 Order of pole (three term test) = -17.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.57 y[1] (analytic) = 0.588099024837731259866243636084 y[1] (numeric) = 0.58809902483773125986624363608431 absolute error = 3.1e-31 relative error = 5.2712211193605607661143243206936e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4377 Order of pole (three term test) = -18.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.56 y[1] (analytic) = 0.5927448889865838739054744961337 y[1] (numeric) = 0.592744888986583873905474496134 absolute error = 3.0e-31 relative error = 5.0611992709529743201355982587111e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4335 Order of pole (three term test) = -18.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.55 y[1] (analytic) = 0.5974754779404942571950182023822 y[1] (numeric) = 0.59747547794049425719501820238255 absolute error = 3.5e-31 relative error = 5.8579810037803484730923509462324e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4293 Order of pole (three term test) = -18.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.54 y[1] (analytic) = 0.6022913186361758574620312210822 y[1] (numeric) = 0.60229131863617585746203122108253 absolute error = 3.3e-31 relative error = 5.4790761511763050707392868628378e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4248 Order of pole (three term test) = -18.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.53 y[1] (analytic) = 0.6071929294852389881933049814358 y[1] (numeric) = 0.60719292948523898819330498143612 absolute error = 3.2e-31 relative error = 5.2701535946949672104743910799230e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4202 Order of pole (three term test) = -18.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.52 y[1] (analytic) = 0.6121808203223500996121524280115 y[1] (numeric) = 0.61218082032235009961215242801181 absolute error = 3.1e-31 relative error = 5.0638633179779516042784264219926e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4154 Order of pole (three term test) = -19.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.51 y[1] (analytic) = 0.6172554923542487368941915264245 y[1] (numeric) = 0.61725549235424873689419152642481 absolute error = 3.1e-31 relative error = 5.0222315368574814101096129482884e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4104 Order of pole (three term test) = -19.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=84030164, alloc=4521156, time=8.23 x[1] = -0.5 y[1] (analytic) = 0.6224174381096272838837184173962 y[1] (numeric) = 0.62241743810962728388371841739649 absolute error = 2.9e-31 relative error = 4.6592524926803525776201153290192e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4053 Order of pole (three term test) = -19.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.49 y[1] (analytic) = 0.6276671413898785042945318408633 y[1] (numeric) = 0.62766714138987850429453184086366 absolute error = 3.6e-31 relative error = 5.7355240741586669304738057247366e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4 Order of pole (three term test) = -19.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.48 y[1] (analytic) = 0.6330050772207158056000451688413 y[1] (numeric) = 0.63300507722071580560004516884158 absolute error = 2.8e-31 relative error = 4.4233452475511468768829754464755e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3945 Order of pole (three term test) = -19.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.47 y[1] (analytic) = 0.6384317118046710635459807234666 y[1] (numeric) = 0.63843171180467106354598072346693 absolute error = 3.3e-31 relative error = 5.1689161722117570791002669646844e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3889 Order of pole (three term test) = -20.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.46 y[1] (analytic) = 0.6439475024744747574636100964996 y[1] (numeric) = 0.64394750247447475746361009649992 absolute error = 3.2e-31 relative error = 4.9693491902732301432130128933261e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3832 Order of pole (three term test) = -20.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.45 y[1] (analytic) = 0.6495528976473230783311593885136 y[1] (numeric) = 0.64955289764732307833115938851388 absolute error = 2.8e-31 relative error = 4.3106573924026575269341662995083e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3773 Order of pole (three term test) = -20.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.44 y[1] (analytic) = 0.6552483367800365828344626110016 y[1] (numeric) = 0.65524833678003658283446261100196 absolute error = 3.6e-31 relative error = 5.4941001722962038561389599280165e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3712 Order of pole (three term test) = -20.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.43 y[1] (analytic) = 0.6610342503251148775240895223366 y[1] (numeric) = 0.66103425032511487752408952233688 absolute error = 2.8e-31 relative error = 4.2357865702463719058372052247176e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.365 Order of pole (three term test) = -20.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.42 y[1] (analytic) = 0.6669110596876917275639112103343 y[1] (numeric) = 0.66691105968769172756391121033466 absolute error = 3.6e-31 relative error = 5.3980211419583394784583302680468e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3586 Order of pole (three term test) = -21.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.41 y[1] (analytic) = 0.672879177183394894524357941723 y[1] (numeric) = 0.67287917718339489452435794172331 absolute error = 3.1e-31 relative error = 4.6070678141301544306237849735043e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3521 Order of pole (three term test) = -21.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4 y[1] (analytic) = 0.6789390059971149172014732679482 y[1] (numeric) = 0.67893900599711491720147326794853 absolute error = 3.3e-31 relative error = 4.8605249821425387614536155992507e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3455 Order of pole (three term test) = -21.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.39 y[1] (analytic) = 0.6850909401426869585493232471189 y[1] (numeric) = 0.68509094014268695854932324711923 absolute error = 3.3e-31 relative error = 4.8168787625664619352119352079167e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3387 Order of pole (three term test) = -21.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.38 y[1] (analytic) = 0.6913353644234897505074691922754 y[1] (numeric) = 0.69133536442348975050746919227577 absolute error = 3.7e-31 relative error = 5.3519611326197097523586351339047e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3318 Order of pole (three term test) = -21.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.37 y[1] (analytic) = 0.6976726543939655767961870955091 y[1] (numeric) = 0.69767265439396557679618709550945 absolute error = 3.5e-31 relative error = 5.0166793523536913994459866696166e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3247 Order of pole (three term test) = -21.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.36 y[1] (analytic) = 0.7041031763220651416490876318753 y[1] (numeric) = 0.70410317632206514164908763187559 absolute error = 2.9e-31 relative error = 4.1187145542338891731948439046362e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3175 Order of pole (three term test) = -22.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.35 y[1] (analytic) = 0.7106272871526210799649676426963 y[1] (numeric) = 0.71062728715262107996496764269666 absolute error = 3.6e-31 relative error = 5.0659467558931912152573404473207e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3102 Order of pole (three term test) = -22.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.34 y[1] (analytic) = 0.7172453344716537714973559399734 y[1] (numeric) = 0.71724533447165377149735593997375 absolute error = 3.5e-31 relative error = 4.8797807832074833539730898303516e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3028 Order of pole (three term test) = -22.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.33 y[1] (analytic) = 0.7239576564716130284705894216338 y[1] (numeric) = 0.72395765647161302847058942163412 absolute error = 3.2e-31 relative error = 4.4201480174904050012326663444191e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2952 Order of pole (three term test) = -22.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.32 y[1] (analytic) = 0.7307645819175591324246927262339 y[1] (numeric) = 0.73076458191755913242469272623423 absolute error = 3.3e-31 relative error = 4.5158182014523084403399452455591e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2876 Order of pole (three term test) = -22.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.31 y[1] (analytic) = 0.7376664301142866021571945637978 y[1] (numeric) = 0.73766643011428660215719456379811 absolute error = 3.1e-31 relative error = 4.2024414741493892343114956574891e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2798 Order of pole (three term test) = -22.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3 y[1] (analytic) = 0.744663510874393980357689772432 y[1] (numeric) = 0.74466351087439398035768977243227 absolute error = 2.7e-31 relative error = 3.6257987138776592270470204703967e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2719 Order of pole (three term test) = -22.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.29 y[1] (analytic) = 0.7517561244873028319298752220681 y[1] (numeric) = 0.75175612448730283192987522206846 absolute error = 3.6e-31 relative error = 4.7887870583764083908467628235558e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2639 Order of pole (three term test) = -23.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.28 y[1] (analytic) = 0.7589445616892290520754099464035 y[1] (numeric) = 0.75894456168922905207540994640385 absolute error = 3.5e-31 relative error = 4.6116675402612243672681368553172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2558 Order of pole (three term test) = -23.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=88030828, alloc=4521156, time=8.63 x[1] = -0.27 y[1] (analytic) = 0.7662291036341094869837672905078 y[1] (numeric) = 0.76622910363410948698376729050812 absolute error = 3.2e-31 relative error = 4.1762965995716958635980446773345e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2476 Order of pole (three term test) = -23.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.26 y[1] (analytic) = 0.7736100218654867744417823535499 y[1] (numeric) = 0.77361002186548677444178235355026 absolute error = 3.6e-31 relative error = 4.6535074498116549700455681648085e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2393 Order of pole (three term test) = -23.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.25 y[1] (analytic) = 0.7810875782893552158554045505058 y[1] (numeric) = 0.78108757828935521585540455050614 absolute error = 3.4e-31 relative error = 4.3529049680271118629650671560072e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2309 Order of pole (three term test) = -23.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.24 y[1] (analytic) = 0.7886620251479703950738247530366 y[1] (numeric) = 0.78866202514797039507382475303695 absolute error = 3.5e-31 relative error = 4.4378959407146841948627170498802e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2224 Order of pole (three term test) = -23.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.23 y[1] (analytic) = 0.7963336049946251630322693519284 y[1] (numeric) = 0.79633360499462516303226935192873 absolute error = 3.3e-31 relative error = 4.1439918889549729359955004626701e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2138 Order of pole (three term test) = -23.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.22 y[1] (analytic) = 0.8041025506693945105939770189553 y[1] (numeric) = 0.80410255066939451059397701895563 absolute error = 3.3e-31 relative error = 4.1039541501924544576208607852108e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2051 Order of pole (three term test) = -23.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.21 y[1] (analytic) = 0.8119690852758517550838614319006 y[1] (numeric) = 0.81196908527585175508386143190098 absolute error = 3.8e-31 relative error = 4.6799811334061062073447864777664e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1963 Order of pole (three term test) = -23.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2 y[1] (analytic) = 0.8199334221587583688758034832518 y[1] (numeric) = 0.81993342215875836887580348325216 absolute error = 3.6e-31 relative error = 4.3906003862139863403436123354170e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1875 Order of pole (three term test) = -24.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.19 y[1] (analytic) = 0.8279957648827296810321224958101 y[1] (numeric) = 0.82799576488272968103212249581042 absolute error = 3.2e-31 relative error = 3.8647540672544634841210001123910e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1786 Order of pole (three term test) = -24.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.18 y[1] (analytic) = 0.8361563072118785854072839753885 y[1] (numeric) = 0.8361563072118785854072839753888 absolute error = 3.0e-31 relative error = 3.5878459256061226846947496702530e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1696 Order of pole (three term test) = -24.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.17 y[1] (analytic) = 0.8444152330904392908280700097875 y[1] (numeric) = 0.84441523309043929082807000978783 absolute error = 3.3e-31 relative error = 3.9080299249487373293901254518597e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1606 Order of pole (three term test) = -24.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.16 y[1] (analytic) = 0.8527727166243730509590474759817 y[1] (numeric) = 0.852772716624373050959047475982 absolute error = 3.0e-31 relative error = 3.5179361880563442524397308994512e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1515 Order of pole (three term test) = -24.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.15 y[1] (analytic) = 0.8612289220639577132650190013457 y[1] (numeric) = 0.861228922063957713265019001346 absolute error = 3.0e-31 relative error = 3.4833943950818805178147265826072e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1423 Order of pole (three term test) = -24.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.14 y[1] (analytic) = 0.8697840037873628281010517729886 y[1] (numeric) = 0.86978400378736282810105177298894 absolute error = 3.4e-31 relative error = 3.9090164744294403096760945440537e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1331 Order of pole (three term test) = -24.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.13 y[1] (analytic) = 0.8784381062852119604054878288482 y[1] (numeric) = 0.87843810628521196040548782884853 absolute error = 3.3e-31 relative error = 3.7566676313203487785390800606513e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1238 Order of pole (three term test) = -24.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.12 y[1] (analytic) = 0.8871913641461337477519018321424 y[1] (numeric) = 0.88719136414613374775190183214271 absolute error = 3.1e-31 relative error = 3.4941728755256272111395355221030e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1145 Order of pole (three term test) = -24.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.11 y[1] (analytic) = 0.8960439020433031496421603885802 y[1] (numeric) = 0.8960439020433031496421603885805 absolute error = 3.0e-31 relative error = 3.3480502385641132118434833311910e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1051 Order of pole (three term test) = -24.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1 y[1] (analytic) = 0.9049958347219742339044380121961 y[1] (numeric) = 0.90499583472197423390443801219648 absolute error = 3.8e-31 relative error = 4.1989143531996546479332527940719e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09566 Order of pole (three term test) = -24.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.09 y[1] (analytic) = 0.9140472669880057469071606281749 y[1] (numeric) = 0.91404726698800574690716062817521 absolute error = 3.1e-31 relative error = 3.3915095115542625690585362923833e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0862 Order of pole (three term test) = -24.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.08 y[1] (analytic) = 0.9231982936973806150222932253665 y[1] (numeric) = 0.92319829369738061502229322536684 absolute error = 3.4e-31 relative error = 3.6828490945137096710746771699238e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07671 Order of pole (three term test) = -24.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.07 y[1] (analytic) = 0.9324489997467204253790916100603 y[1] (numeric) = 0.93244899974672042537909161006061 absolute error = 3.1e-31 relative error = 3.3245786105642752110597901626678e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06719 Order of pole (three term test) = -24.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.06 y[1] (analytic) = 0.9417994600647958344523383128172 y[1] (numeric) = 0.94179946006479583445233831281751 absolute error = 3.1e-31 relative error = 3.2915712223775535993477243854044e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05764 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.05 y[1] (analytic) = 0.9512497396050337534371291888435 y[1] (numeric) = 0.95124973960503375343712918884383 absolute error = 3.3e-31 relative error = 3.4691205291369493717469202141237e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04807 Order of pole (three term test) = -24.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.04 y[1] (analytic) = 0.9607998933390220596854292418709 y[1] (numeric) = 0.96079989333902205968542924187122 absolute error = 3.2e-31 relative error = 3.3305582381771427676365391143713e-29 % Correct digits = 31 h = 0.01 bytes used=92032168, alloc=4521156, time=9.04 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03848 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.03 y[1] (analytic) = 0.9704499662510124837278412935334 y[1] (numeric) = 0.97044996625101248372784129353374 absolute error = 3.4e-31 relative error = 3.5035294123762897636969809494029e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02887 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.02 y[1] (analytic) = 0.9801999933334222215873044091625 y[1] (numeric) = 0.98019999333342222158730440916288 absolute error = 3.8e-31 relative error = 3.8767598712963897268175612222498e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01925 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.01 y[1] (analytic) = 0.9900499995833347222197420662478 y[1] (numeric) = 0.99004999958333472221974206624815 absolute error = 3.5e-31 relative error = 3.5351749926498506846263030500842e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009629 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1.0000000000000000000000000000004 absolute error = 4e-31 relative error = 4.0000000000000000000000000000000e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.0100499995833347222197420662478 y[1] (numeric) = 1.0100499995833347222197420662482 absolute error = 4e-31 relative error = 3.9601999917331595758832454903874e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.0201999933334222215873044091625 y[1] (numeric) = 1.0201999933334222215873044091629 absolute error = 4e-31 relative error = 3.9207998687887838451977249328033e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.0304499662510124837278412935334 y[1] (numeric) = 1.0304499662510124837278412935338 absolute error = 4e-31 relative error = 3.8817993410711800693723593731521e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.0407998933390220596854292418709 y[1] (numeric) = 1.0407998933390220596854292418713 absolute error = 4e-31 relative error = 3.8431979342037375868249268847858e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.0512497396050337534371291888435 y[1] (numeric) = 1.0512497396050337534371291888439 absolute error = 4e-31 relative error = 3.8049949971952854820517939498012e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.0617994600647958344523383128172 y[1] (numeric) = 1.0617994600647958344523383128176 absolute error = 4e-31 relative error = 3.7671897099626532106191761850193e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.0724489997467204253790916100603 y[1] (numeric) = 1.0724489997467204253790916100607 absolute error = 4e-31 relative error = 3.7297810907042454868088636650760e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.0831982936973806150222932253665 y[1] (numeric) = 1.0831982936973806150222932253669 absolute error = 4e-31 relative error = 3.6927680031201223272694388036797e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.0940472669880057469071606281749 y[1] (numeric) = 1.0940472669880057469071606281753 absolute error = 4e-31 relative error = 3.6561491634747192128508728617653e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1049958347219742339044380121961 y[1] (numeric) = 1.1049958347219742339044380121966 absolute error = 5e-31 relative error = 4.5249039343736891848674411342547e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1160439020433031496421603885802 y[1] (numeric) = 1.1160439020433031496421603885806 absolute error = 4e-31 relative error = 3.5840883971290205426062094584280e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1271913641461337477519018321424 y[1] (numeric) = 1.1271913641461337477519018321428 absolute error = 4e-31 relative error = 3.5486432270797840017805778290261e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1384381062852119604054878288482 y[1] (numeric) = 1.1384381062852119604054878288486 absolute error = 4e-31 relative error = 3.5135858312510520418366441301289e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1497840037873628281010517729886 y[1] (numeric) = 1.149784003787362828101051772989 absolute error = 4e-31 relative error = 3.4789142889656573233075677067550e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1612289220639577132650190013457 y[1] (numeric) = 1.1612289220639577132650190013461 absolute error = 4e-31 relative error = 3.4446265710385824867221561809515e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1727727166243730509590474759817 y[1] (numeric) = 1.1727727166243730509590474759821 absolute error = 4e-31 relative error = 3.4107205456768470788051994078045e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1844152330904392908280700097875 y[1] (numeric) = 1.1844152330904392908280700097879 absolute error = 4e-31 relative error = 3.3771939842102393587496199367991e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1961563072118785854072839753885 y[1] (numeric) = 1.1961563072118785854072839753889 absolute error = 4e-31 relative error = 3.3440445666533350207704731228620e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.2079957648827296810321224958101 y[1] (numeric) = 1.2079957648827296810321224958105 absolute error = 4e-31 relative error = 3.3112698870995741246236031210625e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=96035420, alloc=4521156, time=9.44 x[1] = 0.2 y[1] (analytic) = 1.2199334221587583688758034832518 y[1] (numeric) = 1.2199334221587583688758034832522 absolute error = 4e-31 relative error = 3.2788674589484706735556510215050e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.2319690852758517550838614319006 y[1] (numeric) = 1.231969085275851755083861431901 absolute error = 4e-31 relative error = 3.2468347199673074134240961887622e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.2441025506693945105939770189553 y[1] (numeric) = 1.2441025506693945105939770189556 absolute error = 3e-31 relative error = 2.4113767778916919846402610626919e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.2563336049946251630322693519284 y[1] (numeric) = 1.2563336049946251630322693519287 absolute error = 3e-31 relative error = 2.3879007837355704398336896603635e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.2686620251479703950738247530366 y[1] (numeric) = 1.2686620251479703950738247530369 absolute error = 3e-31 relative error = 2.3646959872154248492952609168657e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.2810875782893552158554045505058 y[1] (numeric) = 1.2810875782893552158554045505061 absolute error = 3e-31 relative error = 2.3417602752857224645285633970708e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.2936100218654867744417823535499 y[1] (numeric) = 1.2936100218654867744417823535502 absolute error = 3e-31 relative error = 2.3190914953439874303968170942753e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.3062291036341094869837672905078 y[1] (numeric) = 1.3062291036341094869837672905081 absolute error = 3e-31 relative error = 2.2966874583130833014727572814001e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.3189445616892290520754099464035 y[1] (numeric) = 1.3189445616892290520754099464038 absolute error = 3e-31 relative error = 2.2745459416108975157762907403833e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.3317561244873028319298752220681 y[1] (numeric) = 1.3317561244873028319298752220684 absolute error = 3e-31 relative error = 2.2526646920095335084003069030677e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.344663510874393980357689772432 y[1] (numeric) = 1.3446635108743939803576897724322 absolute error = 2e-31 relative error = 1.4873609522574614497622490683254e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.3576664301142866021571945637978 y[1] (numeric) = 1.357666430114286602157194563798 absolute error = 2e-31 relative error = 1.4731158962453263204234719758989e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.3707645819175591324246927262339 y[1] (numeric) = 1.3707645819175591324246927262341 absolute error = 2e-31 relative error = 1.4590397405820079045786375531878e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.3839576564716130284705894216338 y[1] (numeric) = 1.383957656471613028470589421634 absolute error = 2e-31 relative error = 1.4451309190333041741113914992709e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.3972453344716537714973559399734 y[1] (numeric) = 1.3972453344716537714973559399736 absolute error = 2e-31 relative error = 1.4313878534124920688140896278246e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4106272871526210799649676426963 y[1] (numeric) = 1.4106272871526210799649676426965 absolute error = 2e-31 relative error = 1.4178089550763187995045851770043e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4241031763220651416490876318753 y[1] (numeric) = 1.4241031763220651416490876318754 absolute error = 1e-31 relative error = 7.0219631317910005484778586053048e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4376726543939655767961870955091 y[1] (numeric) = 1.4376726543939655767961870955093 absolute error = 2e-31 relative error = 1.3911372619402551467025670834688e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4513353644234897505074691922754 y[1] (numeric) = 1.4513353644234897505074691922756 absolute error = 2e-31 relative error = 1.3780412501658118865890732787639e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4650909401426869585493232471189 y[1] (numeric) = 1.4650909401426869585493232471191 absolute error = 2e-31 relative error = 1.3651029742940172768328986313153e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4789390059971149172014732679482 y[1] (numeric) = 1.4789390059971149172014732679484 absolute error = 2e-31 relative error = 1.3523208136981827346013553587269e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.492879177183394894524357941723 y[1] (numeric) = 1.4928791771833948945243579417232 absolute error = 2e-31 relative error = 1.3396931450094886794552560462028e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5069110596876917275639112103343 y[1] (numeric) = 1.5069110596876917275639112103346 absolute error = 3e-31 relative error = 1.9908275148114925255568893347726e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=100037532, alloc=4586680, time=9.84 x[1] = 0.43 y[1] (analytic) = 1.5210342503251148775240895223366 y[1] (numeric) = 1.5210342503251148775240895223368 absolute error = 2e-31 relative error = 1.3148947826602248725026124028546e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5352483367800365828344626110016 y[1] (numeric) = 1.5352483367800365828344626110019 absolute error = 3e-31 relative error = 1.9540812571678599973274367642530e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5495528976473230783311593885136 y[1] (numeric) = 1.5495528976473230783311593885138 absolute error = 2e-31 relative error = 1.2906948856257750673292694945665e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5639475024744747574636100964996 y[1] (numeric) = 1.5639475024744747574636100964998 absolute error = 2e-31 relative error = 1.2788153034776447496392315387529e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5784317118046710635459807234666 y[1] (numeric) = 1.5784317118046710635459807234668 absolute error = 2e-31 relative error = 1.2670804730052822717197014020573e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5930050772207158056000451688413 y[1] (numeric) = 1.5930050772207158056000451688415 absolute error = 2e-31 relative error = 1.2554887794139112983064530201582e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.6076671413898785042945318408633 y[1] (numeric) = 1.6076671413898785042945318408636 absolute error = 3e-31 relative error = 1.8660579188092419497225301647710e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.6224174381096272838837184173962 y[1] (numeric) = 1.6224174381096272838837184173964 absolute error = 2e-31 relative error = 1.2327283675712436082043359375135e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.6372554923542487368941915264245 y[1] (numeric) = 1.6372554923542487368941915264247 absolute error = 2e-31 relative error = 1.2215564457347779487879078664748e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.6521808203223500996121524280115 y[1] (numeric) = 1.6521808203223500996121524280117 absolute error = 2e-31 relative error = 1.2105212549373308624223852400931e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.6671929294852389881933049814358 y[1] (numeric) = 1.667192929485238988193304981436 absolute error = 2e-31 relative error = 1.1996212103763649165895333718474e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.6822913186361758574620312210822 y[1] (numeric) = 1.6822913186361758574620312210824 absolute error = 2e-31 relative error = 1.1888547351129344171600444236643e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.6974754779404942571950182023822 y[1] (numeric) = 1.6974754779404942571950182023824 absolute error = 2e-31 relative error = 1.1782202606110996036406616760133e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.7127448889865838739054744961337 y[1] (numeric) = 1.7127448889865838739054744961339 absolute error = 2e-31 relative error = 1.1677162272446671584534724319817e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.728099024837731259866243636084 y[1] (numeric) = 1.7280990248377312598662436360842 absolute error = 2e-31 relative error = 1.1573410847725003951848584377773e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.74353735008481306534211267195 y[1] (numeric) = 1.7435373500848130653421126719502 absolute error = 2e-31 relative error = 1.1470932927836111463890603809184e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.7590593208998365047520034775093 y[1] (numeric) = 1.7590593208998365047520034775095 absolute error = 2e-31 relative error = 1.1369713211132139082189779826860e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.7746643850903217027590475010446 y[1] (numeric) = 1.7746643850903217027590475010448 absolute error = 2e-31 relative error = 1.1269736502308913022709737152081e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.7903519821545204820992534213452 y[1] (numeric) = 1.7903519821545204820992534213454 absolute error = 2e-31 relative error = 1.1170987716019884626572703487139e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.8061215433374660713160003456393 y[1] (numeric) = 1.8061215433374660713160003456395 absolute error = 2e-31 relative error = 1.1073451880233226196599835346854e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.8219724916878481274762910342229 y[1] (numeric) = 1.8219724916878481274762910342231 absolute error = 2e-31 relative error = 1.0977114139342629950914914187252e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 1.8379042421157073864138892207397 y[1] (numeric) = 1.8379042421157073864138892207398 absolute error = 1e-31 relative error = 5.4409798785210260365271911752267e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 1.8539162014509441710823954293201 y[1] (numeric) = 1.8539162014509441710823954293202 absolute error = 1e-31 relative error = 5.3939870594871687928198816706232e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 1.8700077685026349072161829087698 y[1] (numeric) = 1.8700077685026349072161829087699 absolute error = 1e-31 relative error = 5.3475713675816794584693223570559e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=104038600, alloc=4586680, time=10.23 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 1.8861783341191507146970578551619 y[1] (numeric) = 1.886178334119150714697057855162 absolute error = 1e-31 relative error = 5.3017256211195009957716482215279e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 1.9024272812490720628176059159557 y[1] (numeric) = 1.9024272812490720628176059159558 absolute error = 1e-31 relative error = 5.2564427027320194179595473533944e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 1.9187539850028933980264606845022 y[1] (numeric) = 1.9187539850028933980264606845024 absolute error = 2e-31 relative error = 1.0423431120571635380846799465550e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 1.9351578127155115737441400098081 y[1] (numeric) = 1.9351578127155115737441400098083 absolute error = 2e-31 relative error = 1.0335074415421957659057646529434e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 1.9516381240094918334585420558604 y[1] (numeric) = 1.9516381240094918334585420558606 absolute error = 2e-31 relative error = 1.0247801451486059192860022639474e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 1.968194270859105020554513037748 y[1] (numeric) = 1.9681942708591050205545130377482 absolute error = 2e-31 relative error = 1.0161598525164957263172730413730e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 1.9848255976551296112098678414497 y[1] (numeric) = 1.9848255976551296112098678414498 absolute error = 1e-31 relative error = 5.0382260344757680676195228725394e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 2.0015314412704120902085754393012 y[1] (numeric) = 2.0015314412704120902085754393013 absolute error = 1e-31 relative error = 4.9961743262213256720957351513925e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 2.0183111311261791136881612469999 y[1] (numeric) = 2.018311131126179113688161247 absolute error = 1e-31 relative error = 4.9546374916042754721661583400640e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 2.035163989259094827660311633333 y[1] (numeric) = 2.0351639892590948276603116333331 absolute error = 1e-31 relative error = 4.9136089537632386511996943204996e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 2.0520893303890566366287094346757 y[1] (numeric) = 2.0520893303890566366287094346758 absolute error = 1e-31 relative error = 4.8730822054925333231550214744462e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 2.0690864619877226427837349762354 y[1] (numeric) = 2.0690864619877226427837349762356 absolute error = 2e-31 relative error = 9.6661016189659232241715582336039e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 2.086154684347763903087219138915 y[1] (numeric) = 2.0861546843477639030872191389152 absolute error = 2e-31 relative error = 9.5870167970085106209265114458075e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.83 Order of pole (ratio test) Not computed 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) = 2.1032932906528345790792500183577 y[1] (numeric) = 2.1032932906528345790792500183578 absolute error = 1e-31 relative error = 4.7544486755321372703828097218447e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 2.1205015670482529824503607593199 y[1] (numeric) = 2.12050156704825298245036075932 absolute error = 1e-31 relative error = 4.7158654138228445972888748163979e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.09 Order of pole (ratio test) Not computed 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) = 2.1377787927123864483334420215631 y[1] (numeric) = 2.1377787927123864483334420215632 absolute error = 1e-31 relative error = 4.6777524569378516601071284570458e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 2.1551242399287328978875370821356 y[1] (numeric) = 2.1551242399287328978875370821357 absolute error = 1e-31 relative error = 4.6401037187214258912212591381627e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed 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) = 2.1725371741586918820773289631291 y[1] (numeric) = 2.1725371741586918820773289631293 absolute error = 2e-31 relative error = 9.2058263664670946099209246753327e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.03 Order of pole (ratio test) Not computed 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) = 2.1900168541150178296045839705385 y[1] (numeric) = 2.1900168541150178296045839705387 absolute error = 2e-31 relative error = 9.1323498092812471779026019272560e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.69 Order of pole (ratio test) Not computed 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) = 2.2075625318359481537279693357761 y[1] (numeric) = 2.2075625318359481537279693357763 absolute error = 2e-31 relative error = 9.0597660141326729771707600522714e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 2.2251734527599988052223361945172 y[1] (numeric) = 2.2251734527599988052223361945173 absolute error = 1e-31 relative error = 4.4940316844048619762253849948990e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 2.2428488558014197919845013942779 y[1] (numeric) = 2.242848855801419791984501394278 absolute error = 1e-31 relative error = 4.4586152000986163348925404233071e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 2.2605879734263031197964469426198 y[1] (numeric) = 2.2605879734263031197964469426198 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 bytes used=108039896, alloc=4586680, time=10.64 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 2.2783900317293355435152838485929 y[1] (numeric) = 2.2783900317293355435152838485929 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 = 15.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 2.2962542505111884534788217738253 y[1] (numeric) = 2.2962542505111884534788217738254 absolute error = 1e-31 relative error = 4.3549184493719787226693862835167e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 2.3141798433565371582025952933256 y[1] (numeric) = 2.3141798433565371582025952933257 absolute error = 1e-31 relative error = 4.3211853342805807425956695437056e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 2.332166017712701761505092915567 y[1] (numeric) = 2.3321660177127017615050929155671 absolute error = 1e-31 relative error = 4.2878594079711414673498274497523e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 2.350211974968901770039010184776 y[1] (numeric) = 2.3502119749689017700390101847761 absolute error = 1e-31 relative error = 4.2549353447713247047942737756942e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 2.3683169105361165058338190262395 y[1] (numeric) = 2.3683169105361165058338190262397 absolute error = 2e-31 relative error = 8.4448157723421376388861782187524e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 2.3864800139275433378749491996481 y[1] (numeric) = 2.3864800139275433378749491996483 absolute error = 2e-31 relative error = 8.3805436807681667942523354634869e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 2.4047004688396456869634722451501 y[1] (numeric) = 2.4047004688396456869634722451503 absolute error = 2e-31 relative error = 8.3170441637792494244227154826572e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 2.4229774532337826991233417326401 y[1] (numeric) = 2.4229774532337826991233417326402 absolute error = 1e-31 relative error = 4.1271535509559456487278483669392e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 2.4413101394184124246568735913464 y[1] (numeric) = 2.4413101394184124246568735913465 absolute error = 1e-31 relative error = 4.0961612531467536080573862074283e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.459697694131860282599063392557 y[1] (numeric) = 2.4596976941318602825990633925571 absolute error = 1e-31 relative error = 4.0655402588119500479375523379615e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.4781392786256445337932686442208 y[1] (numeric) = 2.4781392786256445337932686442209 absolute error = 1e-31 relative error = 4.0352857025638675817383927304158e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.4966340487483504301103861919662 y[1] (numeric) = 2.4966340487483504301103861919663 absolute error = 1e-31 relative error = 4.0053927827401649648075939857164e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.5151811550300446524664977001626 y[1] (numeric) = 2.5151811550300446524664977001628 absolute error = 2e-31 relative error = 7.9517135217089734956793215062937e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.5337797427672215962655265790078 y[1] (numeric) = 2.533779742767221596265526579008 absolute error = 2e-31 relative error = 7.8933459220718856555575157491336e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.5524289521082730097091504271879 y[1] (numeric) = 2.5524289521082730097091504271881 absolute error = 2e-31 relative error = 7.8356735389168270345035348505222e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.5711279181394724380813624600436 y[1] (numeric) = 2.5711279181394724380813624600438 absolute error = 2e-31 relative error = 7.7786872675212760541174895678084e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.5898757709714658756349069318241 y[1] (numeric) = 2.5898757709714658756349069318243 absolute error = 2e-31 relative error = 7.7223781249159967131916256160218e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.608671635826259976086475211474 y[1] (numeric) = 2.6086716358262599760864752114742 absolute error = 2e-31 relative error = 7.6667372486937329175325768753999e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.6275146331246991229721029261249 y[1] (numeric) = 2.6275146331246991229721029261251 absolute error = 2e-31 relative error = 7.6117558958046802685553008327472e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.6464038785744226122286299482153 y[1] (numeric) = 2.6464038785744226122286299482155 absolute error = 2e-31 relative error = 7.5574254413403047228538695456551e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.6653384832582931513562624880664 y[1] (numeric) = 2.6653384832582931513562624880666 absolute error = 2e-31 relative error = 7.5037373773069992573493334878729e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=112042696, alloc=4586680, time=11.03 x[1] = 1.12 y[1] (analytic) = 2.6843175537232878323860112060389 y[1] (numeric) = 2.684317553723287832386011206039 absolute error = 1e-31 relative error = 3.7253416556954972565999868167199e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.7033401920698426896287841643465 y[1] (numeric) = 2.7033401920698426896287841643466 absolute error = 1e-31 relative error = 3.6991274828579336223317053126967e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.7224054960416419078248132591774 y[1] (numeric) = 2.7224054960416419078248132591776 absolute error = 2e-31 relative error = 7.3464441755939211668414078536552e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.7415125591158427018474232811901 y[1] (numeric) = 2.7415125591158427018474232811903 absolute error = 2e-31 relative error = 7.2952428882726483811775587498384e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.760660470593726845548360376606 y[1] (numeric) = 2.7606604705937268455483603766062 absolute error = 2e-31 relative error = 7.2446431616774158643615336436451e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.7798483156917697846673380649495 y[1] (numeric) = 2.7798483156917697846673380649497 absolute error = 2e-31 relative error = 7.1946371631514604417856829027846e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.7990751756331182269704005332872 y[1] (numeric) = 2.7990751756331182269704005332874 absolute error = 2e-31 relative error = 7.1452171681942171400074708855903e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.8183401277394670619343204416495 y[1] (numeric) = 2.8183401277394670619343204416497 absolute error = 2e-31 relative error = 7.0963755591989497351597096209791e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.8376422455233264223616266443769 y[1] (numeric) = 2.8376422455233264223616266443771 absolute error = 2e-31 relative error = 7.0481048241905985995520067724639e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.8569805987806696612969892863352 y[1] (numeric) = 2.8569805987806696612969892863354 absolute error = 2e-31 relative error = 7.0003975555647095127220834164902e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.8763542536839529795244770255648 y[1] (numeric) = 2.876354253683952979524477025565 absolute error = 2e-31 relative error = 6.9532464488282578640899848711977e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.8957622728754974017604527545023 y[1] (numeric) = 2.8957622728754974017604527545025 absolute error = 2e-31 relative error = 6.9066443013431355525618393481222e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.9152037155612237634223065843026 y[1] (numeric) = 2.9152037155612237634223065843028 absolute error = 2e-31 relative error = 6.8605840110730228065830708756034e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.934677637604731334552461447562 y[1] (numeric) = 2.9346776376047313345524614475621 absolute error = 1e-31 relative error = 3.4075292876671620155677217243391e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.9541830916217106731136575108235 y[1] (numeric) = 2.9541830916217106731136575108237 absolute error = 2e-31 relative error = 6.7700610895518055630879533063599e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.973719127074681266448862983912 y[1] (numeric) = 2.9737191270746812664488629839122 absolute error = 2e-31 relative error = 6.7255847460195338124003352507975e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 2.9932847903680444872206131064074 y[1] (numeric) = 2.9932847903680444872206131064076 absolute error = 2e-31 relative error = 6.6816228326676746153343081283485e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.0128791249434423586133939099388 y[1] (numeric) = 3.012879124943442358613393909939 absolute error = 2e-31 relative error = 6.6381687318356786605566010031208e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.0325011713754125930020158907071 y[1] (numeric) = 3.0325011713754125930020158907073 absolute error = 2e-31 relative error = 6.5952159190523435054002115626647e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.0521499674673303386618230213838 y[1] (numeric) = 3.052149967467330338661823021384 absolute error = 2e-31 relative error = 6.5527579618232099152066999797559e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.0718245483476270404260172705726 y[1] (numeric) = 3.0718245483476270404260172705728 absolute error = 2e-31 relative error = 6.5107885184257189732243696815366e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 3.0915239465662767924842150139894 y[1] (numeric) = 3.0915239465662767924842150139896 absolute error = 2e-31 relative error = 6.4693013367125265635683307736895e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.1112471921915405347673605076999 y[1] (numeric) = 3.1112471921915405347673605077 absolute error = 1e-31 relative error = 3.2141451264616716843814272662196e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=116043788, alloc=4586680, time=11.43 x[1] = 1.35 y[1] (analytic) = 3.1309933129069584185799778269894 y[1] (numeric) = 3.1309933129069584185799778269895 absolute error = 1e-31 relative error = 3.1938745952528206958835991867466e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.1507613341085806423240247476081 y[1] (numeric) = 3.1507613341085806423240247476083 absolute error = 2e-31 relative error = 6.3476721589445421573525862942933e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.1705502790024270343118016103547 y[1] (numeric) = 3.1705502790024270343118016103548 absolute error = 1e-31 relative error = 3.1540266263010885591313568261025e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.1903591687021656367908499264018 y[1] (numeric) = 3.1903591687021656367908499264019 absolute error = 1e-31 relative error = 3.1344433247833936692574419098358e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.210187022327000523403836782196 y[1] (numeric) = 3.210187022327000523403836782196 absolute 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] = 1.4 y[1] (analytic) = 3.2300328570997590613832519647964 y[1] (numeric) = 3.2300328570997590613832519647964 absolute 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] = 1.41 y[1] (analytic) = 3.2498956884451688098364374506391 y[1] (numeric) = 3.2498956884451688098364374506391 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 3.2697745300883142265130178970241 y[1] (numeric) = 3.2697745300883142265130178970241 absolute 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] = 1.43 y[1] (analytic) = 3.2896683941532633374661023754251 y[1] (numeric) = 3.2896683941532633374661023754251 absolute 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] = 1.44 y[1] (analytic) = 3.3095762912618545070224798438708 y[1] (numeric) = 3.3095762912618545070224798438709 absolute error = 1e-31 relative error = 3.0215348189442288609669342896970e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.329497230632633429467133372752 y[1] (numeric) = 3.3294972306326334294671333727521 absolute error = 1e-31 relative error = 3.0034564702430802241498993358272e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.3494302201799304488253518908766 y[1] (numeric) = 3.3494302201799304488253518908767 absolute error = 1e-31 relative error = 2.9855824252588259068786024264646e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.3693742666130682990930253985376 y[1] (numeric) = 3.3693742666130682990930253985377 absolute error = 1e-31 relative error = 2.9679101247639398893509571825398e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.3893283755356903442237734593522 y[1] (numeric) = 3.3893283755356903442237734593523 absolute error = 1e-31 relative error = 2.9504370459293367711104534924337e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.4092915515451993851316815154363 y[1] (numeric) = 3.4092915515451993851316815154364 absolute error = 1e-31 relative error = 2.9331607018084686500552124408106e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.4292627983322970899118101485657 y[1] (numeric) = 3.4292627983322970899118101485658 absolute error = 1e-31 relative error = 2.9160786408271634461358499057791e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.4492411187806140934184044850838 y[1] (numeric) = 3.4492411187806140934184044850839 absolute error = 1e-31 relative error = 2.8991884462792295401827650828570e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.4692255150664208032738707298473 y[1] (numeric) = 3.4692255150664208032738707298474 absolute error = 1e-31 relative error = 2.8824877358278459592037312632420e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.4892149887584089413110109929239 y[1] (numeric) = 3.489214988758408941311010992924 absolute error = 1e-31 relative error = 2.8659741610127520095134951287382e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.5092085409175338423775231929236 y[1] (numeric) = 3.5092085409175338423775231929237 absolute error = 1e-31 relative error = 2.8496454067632452246679701719753e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.5292051721969075263560872253044 y[1] (numeric) = 3.5292051721969075263560872253045 absolute error = 1e-31 relative error = 2.8334991909169917433705270053522e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 3.5492038829417325541760793362391 y[1] (numeric) = 3.5492038829417325541760793362392 absolute error = 1e-31 relative error = 2.8175332637446487507977111305229e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 3.5692036732892666745145914663546 y[1] (numeric) = 3.5692036732892666745145914663548 absolute error = 2e-31 relative error = 5.6034908149605887862940379994201e-30 % Correct digits = 32 h = 0.01 bytes used=120044488, alloc=4586680, time=11.83 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 3.5892035432688082648053890569827 y[1] (numeric) = 3.5892035432688082648053890569829 absolute error = 2e-31 relative error = 5.5722668717153131962072325404602e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008874 Order of pole (three term test) = -0.8949 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (analytic) = 3.6092024929016925680950273462434 y[1] (numeric) = 3.6092024929016925680950273462436 absolute error = 2e-31 relative error = 5.5413903873042569845522888160698e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01851 Order of pole (three term test) = -0.9018 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 3.6291995223012887262057704629465 y[1] (numeric) = 3.6291995223012887262057704629467 absolute error = 2e-31 relative error = 5.5108571124571091796495026724403e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02814 Order of pole (three term test) = -0.9135 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = 3.649193631772987609585327609601 y[1] (numeric) = 3.6491936317729876095853276096012 absolute error = 2e-31 relative error = 5.4806628581895372485661833721427e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03776 Order of pole (three term test) = -0.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = 3.6691838219141704451437442747123 y[1] (numeric) = 3.6691838219141704451437442747125 absolute error = 2e-31 relative error = 5.4508034949217215963125584525344e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04737 Order of pole (three term test) = -0.9513 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 3.6891690937141482452979716974198 y[1] (numeric) = 3.68916909371414824529797169742 absolute error = 2e-31 relative error = 5.4212749516082986457002411776486e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05696 Order of pole (three term test) = -0.9775 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = 3.7091484486540620443644927074566 y[1] (numeric) = 3.7091484486540620443644927074568 absolute error = 2e-31 relative error = 5.3920732148796568116523086883085e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06652 Order of pole (three term test) = -1.008 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = 3.7291208888067339523596145973413 y[1] (numeric) = 3.7291208888067339523596145973415 absolute error = 2e-31 relative error = 5.3631943281945246078445079277772e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07606 Order of pole (three term test) = -1.044 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = 3.7490854169364590411852579316506 y[1] (numeric) = 3.7490854169364590411852579316508 absolute error = 2e-31 relative error = 5.3346343910037853864481525529072e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08556 Order of pole (three term test) = -1.085 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (analytic) = 3.7690410365987280840947823424486 y[1] (numeric) = 3.7690410365987280840947823424488 absolute error = 2e-31 relative error = 5.3063895579254487975075305055350e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09503 Order of pole (three term test) = -1.13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = 3.7889867522398711762480047341728 y[1] (numeric) = 3.788986752239871176248004734173 absolute error = 2e-31 relative error = 5.2784560379307049478456923121808e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1045 Order of pole (three term test) = -1.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 3.8089215692966122720763904698331 y[1] (numeric) = 3.8089215692966122720763904698333 absolute error = 2e-31 relative error = 5.2508300935409834257124665417666e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1139 Order of pole (three term test) = -1.235 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 3.8288444942955246840876428573349 y[1] (numeric) = 3.8288444942955246840876428573351 absolute error = 2e-31 relative error = 5.2235080400359358226364984222393e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1232 Order of pole (three term test) = -1.294 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = 3.8487545349523775976426897830511 y[1] (numeric) = 3.8487545349523775976426897830513 absolute error = 2e-31 relative error = 5.1964862446722571146741137166385e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1325 Order of pole (three term test) = -1.358 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 3.8686507002713636671363782803312 y[1] (numeric) = 3.8686507002713636671363782803314 absolute error = 2e-31 relative error = 5.1697611259132582485808518162862e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1417 Order of pole (three term test) = -1.427 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = 3.8885320006441977709049483513426 y[1] (numeric) = 3.8885320006441977709049483513428 absolute error = 2e-31 relative error = 5.1433291526690995020280479409107e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1509 Order of pole (three term test) = -1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = 3.9083974479490770150673773153451 y[1] (numeric) = 3.9083974479490770150673773153453 absolute error = 2e-31 relative error = 5.1171868435475916390301023050363e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1601 Order of pole (three term test) = -1.578 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 3.9282460556494920903826769439426 y[1] (numeric) = 3.9282460556494920903826769439428 absolute error = 2e-31 relative error = 5.0913307661154695509230334101008e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1691 Order of pole (three term test) = -1.661 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (analytic) = 3.9480768388928801010698001765041 y[1] (numeric) = 3.9480768388928801010698001765043 absolute error = 2e-31 relative error = 5.0657575361700409487089602369058e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1781 Order of pole (three term test) = -1.748 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = 3.9678888146091090003894858417304 y[1] (numeric) = 3.9678888146091090003894858417306 absolute error = 2e-31 relative error = 5.0404638170211107439854031563491e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.187 Order of pole (three term test) = -1.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 3.9876810016087837846265532903126 y[1] (numeric) = 3.9876810016087837846265532903128 absolute error = 2e-31 relative error = 5.0154463187830800130895229252158e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1959 Order of pole (three term test) = -1.936 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = 4.0074524206813646149351702644646 y[1] (numeric) = 4.0074524206813646149351702644648 absolute error = 2e-31 relative error = 4.9907017976771168730106767543832e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2047 Order of pole (three term test) = -2.036 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=124045520, alloc=4586680, time=12.23 x[1] = 1.8 y[1] (analytic) = 4.0272020946930870553166743065306 y[1] (numeric) = 4.0272020946930870553166743065308 absolute error = 2e-31 relative error = 4.9662270553432951989764527093339e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2133 Order of pole (three term test) = -2.141 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (analytic) = 4.046929048684674634787749850842 y[1] (numeric) = 4.0469290486846746347877498508422 absolute error = 2e-31 relative error = 4.9420189381625958737093681204272e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2219 Order of pole (three term test) = -2.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = 4.0666323099688339625641710448309 y[1] (numeric) = 4.0666323099688339625641710448311 absolute error = 2e-31 relative error = 4.9180743365886641688749853956743e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2305 Order of pole (three term test) = -2.363 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = 4.0863109082275226468298375836185 y[1] (numeric) = 4.0863109082275226468298375836188 absolute error = 3e-31 relative error = 7.3415852767338238683796584892151e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2389 Order of pole (three term test) = -2.481 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = 4.1059638756089802903802829832816 y[1] (numeric) = 4.1059638756089802903802829832819 absolute error = 3e-31 relative error = 7.3064451877454764231015399638634e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2472 Order of pole (three term test) = -2.603 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = 4.1255902468245128601219498354748 y[1] (numeric) = 4.1255902468245128601219498354751 absolute error = 3e-31 relative error = 7.2716867660551475781749117379148e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2554 Order of pole (three term test) = -2.729 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = 4.1451890592450207520709354882891 y[1] (numeric) = 4.1451890592450207520709354882894 absolute error = 3e-31 relative error = 7.2373056020426763213697628610061e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2636 Order of pole (three term test) = -2.859 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = 4.1647593529972608991251480648099 y[1] (numeric) = 4.1647593529972608991251480648102 absolute error = 3e-31 relative error = 7.2032973473989171825424504900983e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2716 Order of pole (three term test) = -2.993 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = 4.1843001710598332954793137595222 y[1] (numeric) = 4.1843001710598332954793137595225 absolute error = 3e-31 relative error = 7.1696577142077639323118880459170e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2795 Order of pole (three term test) = -3.131 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 4.2038105593588823391103824155512 y[1] (numeric) = 4.2038105593588823391103824155515 absolute error = 3e-31 relative error = 7.1363824740416611063870708411036e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2873 Order of pole (three term test) = -3.273 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 4.2232895668635034222788336950803 y[1] (numeric) = 4.2232895668635034222788336950806 absolute error = 3e-31 relative error = 7.1034674570704374810498970794793e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.295 Order of pole (three term test) = -3.419 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 4.2427362456808452294663389393975 y[1] (numeric) = 4.2427362456808452294663389393978 absolute error = 3e-31 relative error = 7.0709085511832955444380000411119e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3025 Order of pole (three term test) = -3.569 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (analytic) = 4.262149651150898232599236603159 y[1] (numeric) = 4.2621496511508982325992366031593 absolute error = 3e-31 relative error = 7.0387017011237910551506300965896e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.31 Order of pole (three term test) = -3.723 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (analytic) = 4.2815288419409599047872890647119 y[1] (numeric) = 4.2815288419409599047872890647121 absolute error = 2e-31 relative error = 4.6712286050917579645268582029270e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3173 Order of pole (three term test) = -3.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = 4.3008728801397672061350676858407 y[1] (numeric) = 4.300872880139767206135067685841 absolute error = 3e-31 relative error = 6.9753282266331661171739644960904e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3245 Order of pole (three term test) = -4.041 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = 4.3201808313512869284558284591307 y[1] (numeric) = 4.320180831351286928455828459131 absolute error = 3e-31 relative error = 6.9441537683542880272526850696273e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3315 Order of pole (three term test) = -4.205 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 4.3394517647881545199315652154474 y[1] (numeric) = 4.3394517647881545199315652154478 absolute error = 4e-31 relative error = 9.2177542620876993609824879572565e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3385 Order of pole (three term test) = -4.373 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = 4.3586847533647520459146398138793 y[1] (numeric) = 4.3586847533647520459146398138797 absolute error = 4e-31 relative error = 9.1770803036676144730842142645247e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3453 Order of pole (three term test) = -4.545 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 4.3778788737899159781524738599072 y[1] (numeric) = 4.3778788737899159781524738599076 absolute error = 4e-31 relative error = 9.1368448404265981322976269103643e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3519 Order of pole (three term test) = -4.719 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = 4.3970332066592655417336357161303 y[1] (numeric) = 4.3970332066592655417336357161307 absolute error = 4e-31 relative error = 9.0970429651111970796046353309662e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3584 Order of pole (three term test) = -4.898 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 4.4161468365471423869975682295008 y[1] (numeric) = 4.4161468365471423869975682295012 absolute error = 4e-31 relative error = 9.0576698376439956092971696560713e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3648 Order of pole (three term test) = -5.079 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 4.4352188520981523925173823401654 y[1] (numeric) = 4.4352188520981523925173823401659 absolute error = 5e-31 relative error = 1.1273400855145329981624090967995e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.371 Order of pole (three term test) = -5.263 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=128047424, alloc=4586680, time=12.62 x[1] = 2.02 y[1] (analytic) = 4.4542483461183004450517028740902 y[1] (numeric) = 4.4542483461183004450517028740907 absolute error = 5e-31 relative error = 1.1225238494744686445074159845607e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3771 Order of pole (three term test) = -5.451 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = 4.4732344156657090830635167316961 y[1] (numeric) = 4.4732344156657090830635167316966 absolute error = 5e-31 relative error = 1.1177594410186744902421728311570e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.383 Order of pole (three term test) = -5.641 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = 4.4921761621409119320172702052914 y[1] (numeric) = 4.4921761621409119320172702052919 absolute error = 5e-31 relative error = 1.1130462874850985189849784899410e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3888 Order of pole (three term test) = -5.835 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = 4.5110726913767129021859299941674 y[1] (numeric) = 4.5110726913767129021859299941679 absolute error = 5e-31 relative error = 1.1083838239977626449925596631372e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3944 Order of pole (three term test) = -6.031 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = 4.5299231137276021631231096264879 y[1] (numeric) = 4.5299231137276021631231096264884 absolute error = 5e-31 relative error = 1.1037714933500447414425866953352e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3999 Order of pole (three term test) = -6.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = 4.5487265441587199532773271390117 y[1] (numeric) = 4.5487265441587199532773271390122 absolute error = 5e-31 relative error = 1.0992087458897229411490324609242e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4052 Order of pole (three term test) = -6.432 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 4.5674821023343593284415688497724 y[1] (numeric) = 4.5674821023343593284415688497728 absolute error = 4e-31 relative error = 8.7575603152460537029177822258328e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4103 Order of pole (three term test) = -6.636 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = 4.5861889127059989988370663118704 y[1] (numeric) = 4.5861889127059989988370663118709 absolute error = 5e-31 relative error = 1.0902298390167794346522674911372e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4153 Order of pole (three term test) = -6.843 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 4.6048461045998574516209385237192 y[1] (numeric) = 4.6048461045998574516209385237196 absolute error = 4e-31 relative error = 8.6865009364902192798089829732544e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4201 Order of pole (three term test) = -7.053 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = 4.6234528123039596034784101570717 y[1] (numeric) = 4.6234528123039596034784101570721 absolute error = 4e-31 relative error = 8.6515428239154440133531478055951e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4247 Order of pole (three term test) = -7.265 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = 4.6420081751547072767069018829839 y[1] (numeric) = 4.6420081751547072767069018829843 absolute error = 4e-31 relative error = 8.6169602660527183461385014115370e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4292 Order of pole (three term test) = -7.479 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 4.6605113376229448418165262096097 y[1] (numeric) = 4.6605113376229448418165262096101 absolute error = 4e-31 relative error = 8.5827492097469434073781494608967e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4335 Order of pole (three term test) = -7.695 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = 4.6789614493995114201544499120086 y[1] (numeric) = 4.678961449399511420154449912009 absolute error = 4e-31 relative error = 8.5489056562185440140218004870022e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4376 Order of pole (three term test) = -7.913 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = 4.697357665480271091404153882264 y[1] (numeric) = 4.6973576654802710914041538822644 absolute error = 4e-31 relative error = 8.5154256602494175253272042620319e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4415 Order of pole (three term test) = -8.133 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 4.7156991462506126030096987439834 y[1] (numeric) = 4.7156991462506126030096987439837 absolute error = 3e-31 relative error = 6.3617289970359085618416062732457e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4453 Order of pole (three term test) = -8.356 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 4.7339850575694101316244699944165 y[1] (numeric) = 4.7339850575694101316244699944168 absolute error = 3e-31 relative error = 6.3371556173443070050238286468646e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4489 Order of pole (three term test) = -8.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 4.7522145708524367005782248676625 y[1] (numeric) = 4.7522145708524367005782248676628 absolute error = 3e-31 relative error = 6.3128462641405306240914271349692e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4523 Order of pole (three term test) = -8.806 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 4.770386863155221912090205163797 y[1] (numeric) = 4.7703868631552219120902051637973 absolute error = 3e-31 relative error = 6.2887981332728738753035744375104e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4555 Order of pole (three term test) = -9.033 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 4.7885011172553457085241426126549 y[1] (numeric) = 4.7885011172553457085241426126553 absolute error = 4e-31 relative error = 8.3533446104586153116054743106842e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.83 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4586 Order of pole (three term test) = -9.262 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = 4.8065565217341599333776091775186 y[1] (numeric) = 4.806556521734159933377609177519 absolute error = 4e-31 relative error = 8.3219660102048233021032852778555e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.12 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4615 Order of pole (three term test) = -9.493 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = 4.8245522710579295199177144375002 y[1] (numeric) = 4.8245522710579295199177144375005 absolute error = 3e-31 relative error = 6.2181935886501628558382109349965e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4641 Order of pole (three term test) = -9.725 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = 4.8424875656583851934119039106856 y[1] (numeric) = 4.842487565658385193411903910686 absolute error = 4e-31 relative error = 8.2602173898533480645410870243168e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4666 Order of pole (three term test) = -9.958 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 4.8603616120126796317507622663104 y[1] (numeric) = 4.8603616120126796317507622663108 absolute error = 4e-31 relative error = 8.2298403273405757973223307385540e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4689 Order of pole (three term test) = -10.19 NO COMPLEX POLE (six term test) for Equation 1 bytes used=132048936, alloc=4586680, time=13.02 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 4.8781736227227390889133890573964 y[1] (numeric) = 4.8781736227227390889133890573968 absolute error = 4e-31 relative error = 8.1997901455738081847442288604866e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.34 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4711 Order of pole (three term test) = -10.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 4.8959228165940025461791265687448 y[1] (numeric) = 4.8959228165940025461791265687452 absolute error = 4e-31 relative error = 8.1700634381787936902142551086115e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.473 Order of pole (three term test) = -10.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = 4.9136084187135405172361343481243 y[1] (numeric) = 4.9136084187135405172361343481247 absolute error = 4e-31 relative error = 8.1406568434838006876067453202577e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4747 Order of pole (three term test) = -10.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = 4.9312296605275456953713983504607 y[1] (numeric) = 4.9312296605275456953713983504611 absolute error = 4e-31 relative error = 8.1115670438518529115310877974827e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = -11.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 4.948785779918187693742031018189 y[1] (numeric) = 4.9487857799181876937420310181894 absolute error = 4e-31 relative error = 8.0827907650230258609996141705351e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4776 Order of pole (three term test) = -11.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 4.966276021279824193317880571166 y[1] (numeric) = 4.9662760212798241933178805711665 absolute error = 5e-31 relative error = 1.0067905969333305474309446029007e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4788 Order of pole (three term test) = -11.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = 4.983699635594560877444164323471 y[1] (numeric) = 4.9836996355945608774441643234715 absolute error = 5e-31 relative error = 1.0032707357179029652852486405455e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4798 Order of pole (three term test) = -11.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 5.0010558805071525970936361660082 y[1] (numeric) = 5.0010558805071525970936361660087 absolute error = 5e-31 relative error = 9.9978886848449981302803960453132e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4806 Order of pole (three term test) = -12.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = 5.018344020399238276754180427816 y[1] (numeric) = 5.0183440203992382767541804278165 absolute error = 5e-31 relative error = 9.9634460684148574894060049364143e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -12.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 5.0355633264629021375231055720614 y[1] (numeric) = 5.0355633264629021375231055720619 absolute error = 5e-31 relative error = 9.9293756742646653345081889991443e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -12.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 5.0527130767735538813471291122589 y[1] (numeric) = 5.0527130767735538813471291122595 absolute error = 6e-31 relative error = 1.1874808461974537780776583256921e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = 5.0697925563621205484503630346451 y[1] (numeric) = 5.0697925563621205484503630346457 absolute error = 6e-31 relative error = 1.1834803758332390113720908858196e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = 5.0868010572865428288247166088224 y[1] (numeric) = 5.0868010572865428288247166088229 absolute error = 5e-31 relative error = 9.8293602279526827020444407001071e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -13.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = 5.1037378787025686782111476073675 y[1] (numeric) = 5.1037378787025686782111476073681 absolute error = 6e-31 relative error = 1.1756089639786265614490399376508e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.07 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -13.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 5.1206023269338371592691582926181 y[1] (numeric) = 5.1206023269338371592691582926186 absolute error = 5e-31 relative error = 9.7644762876830301236243711949094e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4807 Order of pole (three term test) = -13.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 5.1373937155412454996088222273348 y[1] (numeric) = 5.1373937155412454996088222273353 absolute error = 5e-31 relative error = 9.7325614442871826728610430004272e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4799 Order of pole (three term test) = -14.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 5.154111365391592430037344395568 y[1] (numeric) = 5.1541113653915924300373443955685 absolute error = 5e-31 relative error = 9.7009933343186821975931571884783e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.96 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.479 Order of pole (three term test) = -14.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = 5.1707546047254909387435325689107 y[1] (numeric) = 5.1707546047254909387435325689113 absolute error = 6e-31 relative error = 1.1603722200463103757817947580115e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4779 Order of pole (three term test) = -14.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 5.1873227692245436502013552441779 y[1] (numeric) = 5.1873227692245436502013552441785 absolute error = 6e-31 relative error = 1.1566660234826575120764993601939e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4765 Order of pole (three term test) = -14.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = 5.2038152020777741113106750925374 y[1] (numeric) = 5.203815202077774111310675092538 absolute error = 6e-31 relative error = 1.1530002060035348721895389410414e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.475 Order of pole (three term test) = -14.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = 5.2202312540473073417019030673365 y[1] (numeric) = 5.2202312540473073417019030673371 absolute error = 6e-31 relative error = 1.1493743682998964233271930475686e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4733 Order of pole (three term test) = -15.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = 5.2365702835332930802042763146862 y[1] (numeric) = 5.2365702835332930802042763146868 absolute error = 6e-31 relative error = 1.1457881161009825648707047141117e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.23 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4714 Order of pole (three term test) = -15.46 bytes used=136049756, alloc=4586680, time=13.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = 5.2528316566380652352072155840616 y[1] (numeric) = 5.2528316566380652352072155840621 absolute error = 5e-31 relative error = 9.5186755008252379595590801366444e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4693 Order of pole (three term test) = -15.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = 5.2690147472295311230231920335903 y[1] (numeric) = 5.2690147472295311230231920335909 absolute error = 6e-31 relative error = 1.1387328158750786995944673579507e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.467 Order of pole (three term test) = -15.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = 5.2851189370037841553810913325716 y[1] (numeric) = 5.2851189370037841553810913325721 absolute error = 5e-31 relative error = 9.4605250318823997930574202641041e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4646 Order of pole (three term test) = -16.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 5.3011436155469337148335027904674 y[1] (numeric) = 5.3011436155469337148335027904679 absolute error = 5e-31 relative error = 9.4319270757657753225032609443157e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.94 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4619 Order of pole (three term test) = -16.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = 5.3170881803961460351419175078784 y[1] (numeric) = 5.317088180396146035141917507879 absolute error = 6e-31 relative error = 1.1284371814862348370245587444141e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4591 Order of pole (three term test) = -16.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 5.3329520370998899826026642604518 y[1] (numeric) = 5.3329520370998899826026642604524 absolute error = 6e-31 relative error = 1.1250804354248153038243455082444e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4561 Order of pole (three term test) = -16.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = 5.348734599277381713785655172555 y[1] (numeric) = 5.3487345992773817137856551725555 absolute error = 5e-31 relative error = 9.3480054154780907717603323282814e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4529 Order of pole (three term test) = -17.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 5.3644352886772222652697043558066 y[1] (numeric) = 5.3644352886772222652697043558071 absolute error = 5e-31 relative error = 9.3206455683295496385974544388261e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4495 Order of pole (three term test) = -17.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = 5.3800535352352222116643104758323 y[1] (numeric) = 5.3800535352352222116643104758328 absolute error = 5e-31 relative error = 9.2935878188829103758994224441513e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.446 Order of pole (three term test) = -17.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = 5.3955887771314076095002881233824 y[1] (numeric) = 5.395588777131407609500288123383 absolute error = 6e-31 relative error = 1.1120195122041770408596823686963e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4422 Order of pole (three term test) = -17.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 5.4110404608462015264423637215671 y[1] (numeric) = 5.4110404608462015264423637215677 absolute error = 6e-31 relative error = 1.1088440464297867170863082493253e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4383 Order of pole (three term test) = -17.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = 5.4264080412157755377176324945692 y[1] (numeric) = 5.4264080412157755377176324945698 absolute error = 6e-31 relative error = 1.1057038015622047408914129713823e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4342 Order of pole (three term test) = -18.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = 5.4416909814865656546563597454083 y[1] (numeric) = 5.4416909814865656546563597454089 absolute error = 6e-31 relative error = 1.1025984423615533980041834046820e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.43 Order of pole (three term test) = -18.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 5.4568887533689472337977021516452 y[1] (numeric) = 5.4568887533689472337977021516458 absolute error = 6e-31 relative error = 1.0995276376663807570934489747305e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4255 Order of pole (three term test) = -18.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = 5.4720008370900634991141674487226 y[1] (numeric) = 5.4720008370900634991141674487232 absolute error = 6e-31 relative error = 1.0964910603322786330851343940970e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4209 Order of pole (three term test) = -18.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = 5.4870267214458023945466136767484 y[1] (numeric) = 5.4870267214458023945466136767489 absolute error = 5e-31 relative error = 9.1124032264281128915581344354873e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4161 Order of pole (three term test) = -19.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = 5.5019659038519165692078483901949 y[1] (numeric) = 5.5019659038519165692078483901955 absolute error = 6e-31 relative error = 1.0905192988926759149042300698159e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4112 Order of pole (three term test) = -19.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = 5.516817890394281383298907316266 y[1] (numeric) = 5.5168178903942813832989073162666 absolute error = 6e-31 relative error = 1.0875834800432729312069967184656e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4061 Order of pole (three term test) = -19.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = 5.5315821958782859089793023660538 y[1] (numeric) = 5.5315821958782859089793023660544 absolute error = 6e-31 relative error = 1.0846806189503508401962666323263e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4008 Order of pole (three term test) = -19.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = 5.5462583438773519871323110038826 y[1] (numeric) = 5.5462583438773519871323110038832 absolute error = 6e-31 relative error = 1.0818104076640325171263926501914e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3954 Order of pole (three term test) = -19.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 5.5608458667805764881600628584297 y[1] (numeric) = 5.5608458667805764881600628584304 absolute error = 7e-31 relative error = 1.2588012988845192536083495735855e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3898 Order of pole (three term test) = -20.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 5.5753443058394920126220458186207 y[1] (numeric) = 5.5753443058394920126220458186213 absolute error = 6e-31 relative error = 1.0761667209890038591042806479222e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3841 Order of pole (three term test) = -20.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=140050904, alloc=4586680, time=13.81 x[1] = 2.69 y[1] (analytic) = 5.5897532112139413556859348843289 y[1] (numeric) = 5.5897532112139413556859348843295 absolute error = 6e-31 relative error = 1.0733926478118994226458716176547e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3782 Order of pole (three term test) = -20.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 5.6040721420170611479825272819433 y[1] (numeric) = 5.604072142017061147982527281944 absolute error = 7e-31 relative error = 1.2490917002150699761029029391128e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3722 Order of pole (three term test) = -20.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = 5.6183006663593701745381845937161 y[1] (numeric) = 5.6183006663593701745381845937167 absolute error = 6e-31 relative error = 1.0679385736555763618488650709381e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.366 Order of pole (three term test) = -20.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = 5.6324383613919579629896287999871 y[1] (numeric) = 5.6324383613919579629896287999877 absolute error = 6e-31 relative error = 1.0652579957425766928744069341141e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3596 Order of pole (three term test) = -21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 5.6464848133487693222582611248928 y[1] (numeric) = 5.6464848133487693222582611248934 absolute error = 6e-31 relative error = 1.0626080115925382059414514481686e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3532 Order of pole (three term test) = -21.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = 5.6604396175879806032653732517793 y[1] (numeric) = 5.6604396175879806032653732517799 absolute error = 6e-31 relative error = 1.0599883410745952695074385513995e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3465 Order of pole (three term test) = -21.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = 5.6743023786324635440966594895267 y[1] (numeric) = 5.6743023786324635440966594895273 absolute error = 6e-31 relative error = 1.0573987073008314514001900529008e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3398 Order of pole (three term test) = -21.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 5.6880727102093326532652331971401 y[1] (numeric) = 5.6880727102093326532652331971407 absolute error = 6e-31 relative error = 1.0548388365765436545504743384565e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3329 Order of pole (three term test) = -21.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = 5.7017502352885721763677772078291 y[1] (numeric) = 5.7017502352885721763677772078297 absolute error = 6e-31 relative error = 1.0523084583511808384155535193662e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3258 Order of pole (three term test) = -21.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 5.7153345861207387834693516691176 y[1] (numeric) = 5.7153345861207387834693516691182 absolute error = 6e-31 relative error = 1.0498073051699457483164297690758e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3187 Order of pole (three term test) = -22.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 5.7288254042737362069795396196241 y[1] (numeric) = 5.7288254042737362069795396196247 absolute error = 6e-31 relative error = 1.0473351126260482660772073012945e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3114 Order of pole (three term test) = -22.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 5.7422223406686581525867881173662 y[1] (numeric) = 5.7422223406686581525867881173668 absolute error = 6e-31 relative error = 1.0448916193135991840010067034444e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.304 Order of pole (three term test) = -22.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = 5.7555250556146958989897204783588 y[1] (numeric) = 5.7555250556146958989897204783595 absolute error = 7e-31 relative error = 1.2162226612446556221054529212872e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2965 Order of pole (three term test) = -22.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = 5.76873321884310709569453606376 y[1] (numeric) = 5.7687332188431070956945360637607 absolute error = 7e-31 relative error = 1.2134379827333769114805728207064e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2888 Order of pole (three term test) = -22.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = 5.7818465095402423620270251127245 y[1] (numeric) = 5.7818465095402423620270251127252 absolute error = 7e-31 relative error = 1.2106858922058486270898541462432e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.281 Order of pole (three term test) = -22.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = 5.7948646163796263847268194935862 y[1] (numeric) = 5.7948646163796263847268194935869 absolute error = 7e-31 relative error = 1.2079660981576630154156208883957e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2732 Order of pole (three term test) = -22.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 5.8077872375530903060408541071749 y[1] (numeric) = 5.8077872375530903060408541071756 absolute error = 7e-31 relative error = 1.2052783123214422686630745381620e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2652 Order of pole (three term test) = -23.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = 5.8206140808009522891031731663928 y[1] (numeric) = 5.8206140808009522891031731663934 absolute error = 6e-31 relative error = 1.0308190710995158616239398844146e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2571 Order of pole (three term test) = -23.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 5.8333448634412432425696937587379 y[1] (numeric) = 5.8333448634412432425696937587386 absolute error = 7e-31 relative error = 1.1999976280967753844082366196992e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2489 Order of pole (three term test) = -23.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = 5.8459793123979747819598179047655 y[1] (numeric) = 5.8459793123979747819598179047662 absolute error = 7e-31 relative error = 1.1974041689053899506789942030679e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2406 Order of pole (three term test) = -23.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = 5.8585171642284466009323155072093 y[1] (numeric) = 5.85851716422844660093231550721 absolute error = 7e-31 relative error = 1.1948415962218801649465593819491e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2322 Order of pole (three term test) = -23.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 5.8709581651495905217811066693455 y[1] (numeric) = 5.8709581651495905217811066693462 absolute error = 7e-31 relative error = 1.1923096372160304397679543007626e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2237 Order of pole (three term test) = -23.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=144051740, alloc=4586680, time=14.22 x[1] = 2.91 y[1] (analytic) = 5.8833020710633485907678471066028 y[1] (numeric) = 5.8833020710633485907678471066034 absolute error = 6e-31 relative error = 1.0198354474285151593723610356741e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2151 Order of pole (three term test) = -23.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = 5.8955486475810826805029317351583 y[1] (numeric) = 5.8955486475810826805029317351589 absolute error = 6e-31 relative error = 1.0177169859266233421047697200669e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2065 Order of pole (three term test) = -23.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = 5.9076976700470131584350196046763 y[1] (numeric) = 5.907697670047013158435019604677 absolute error = 7e-31 relative error = 1.1848947578159148342169609048149e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1977 Order of pole (three term test) = -23.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = 5.9197489235606842776017633813283 y[1] (numeric) = 5.919748923560684277601763381329 absolute error = 7e-31 relative error = 1.1824825833642878314637817168566e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1889 Order of pole (three term test) = -24.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 5.931702202998454043121389404702 y[1] (numeric) = 5.9317022029984540431213894047026 absolute error = 6e-31 relative error = 1.0115140299806388909966759659008e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.18 Order of pole (three term test) = -24.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 5.9435573130340064054563873229762 y[1] (numeric) = 5.9435573130340064054563873229768 absolute error = 6e-31 relative error = 1.0094964486743009647932032360861e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1711 Order of pole (three term test) = -24.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = 5.9553140681578837292470763748061 y[1] (numeric) = 5.9553140681578837292470763748068 absolute error = 7e-31 relative error = 1.1754207955929454065792219615426e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.162 Order of pole (three term test) = -24.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 5.9669722926960375844844419643954 y[1] (numeric) = 5.9669722926960375844844419643961 absolute error = 7e-31 relative error = 1.1731242674896371746980507968586e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1529 Order of pole (three term test) = -24.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = 5.9785318208273960049585841872108 y[1] (numeric) = 5.9785318208273960049585841872115 absolute error = 7e-31 relative error = 1.1708560244864998314850785249997e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1438 Order of pole (three term test) = -24.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 5.9899924966004454572715727947313 y[1] (numeric) = 5.9899924966004454572715727947319 absolute error = 6e-31 relative error = 1.0016707038289670966232004590796e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1345 Order of pole (three term test) = -24.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = 6.0013541739488258622316255741824 y[1] (numeric) = 6.0013541739488258622316255741831 absolute error = 7e-31 relative error = 1.1664034144803815221431257894128e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1253 Order of pole (three term test) = -24.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = 6.012616716705937109139466533263 y[1] (numeric) = 6.0126167167059371091394665332637 absolute error = 7e-31 relative error = 1.1642185640323019240497577511034e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1159 Order of pole (three term test) = -24.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = 6.0237799986185556023276073087084 y[1] (numeric) = 6.0237799986185556023276073087091 absolute error = 7e-31 relative error = 1.1620610317118690758978186782808e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1066 Order of pole (three term test) = -24.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = 6.0348439033594594783092449548432 y[1] (numeric) = 6.0348439033594594783092449548439 absolute error = 7e-31 relative error = 1.1599305818172463769499148958433e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09716 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = 6.0458083245390612310255822015649 y[1] (numeric) = 6.0458083245390612310255822015656 absolute error = 7e-31 relative error = 1.1578269809825119362015906614432e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08771 Order of pole (three term test) = -24.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = 6.0566731657160465819387392717932 y[1] (numeric) = 6.0566731657160465819387392717938 absolute error = 6e-31 relative error = 9.9064285554702761798498312011953e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07822 Order of pole (three term test) = -24.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = 6.0674383404070185310921136627268 y[1] (numeric) = 6.0674383404070185310921136627274 absolute error = 6e-31 relative error = 9.8888520383340317504025971408931e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06871 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = 6.0781037720951456247411185373598 y[1] (numeric) = 6.0781037720951456247411185373604 absolute error = 6e-31 relative error = 9.8714997719293249978865242738171e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05916 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = 6.0886693942378135747347435180858 y[1] (numeric) = 6.0886693942378135747347435180864 absolute error = 6e-31 relative error = 9.8543698327228468143892069709907e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04959 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = 6.0991351502732794644923760545415 y[1] (numeric) = 6.0991351502732794644923760545421 absolute error = 6e-31 relative error = 9.8374603155517260693921536627372e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04001 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = 6.1095009936263278761608308367168 y[1] (numeric) = 6.1095009936263278761608308367175 absolute error = 7e-31 relative error = 1.1457564222188810131966887600518e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0304 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = 6.1197668877129283733435849739756 y[1] (numeric) = 6.1197668877129283733435849739763 absolute error = 7e-31 relative error = 1.1438344186041424928168417410157e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02079 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = 6.1299328059438938736578272391392 y[1] (numeric) = 6.1299328059438938736578272391399 absolute error = 7e-31 relative error = 1.1419374765759984887403078850120e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01116 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 bytes used=148052816, alloc=4586680, time=14.61 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = 6.139998731727539545285114306345 y[1] (numeric) = 6.1399987317275395452851143063457 absolute error = 7e-31 relative error = 1.1400653820706070354940355848301e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001534 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = 6.1499646584713419616281946567947 y[1] (numeric) = 6.1499646584713419616281946567954 absolute error = 7e-31 relative error = 1.1382179229855844370641918637210e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.159830589582598348159917094274 y[1] (numeric) = 6.1598305895825983481599170942746 absolute error = 6e-31 relative error = 9.7405276212418874849121974398188e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.1695965384680858555400883501353 y[1] (numeric) = 6.1695965384680858555400883501359 absolute error = 6e-31 relative error = 9.7251091908350351100685226442574e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.1792625285327208930726841538603 y[1] (numeric) = 6.1792625285327208930726841538609 absolute error = 6e-31 relative error = 9.7098965649946464340044728061698e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.1888285931772186565689508296995 y[1] (numeric) = 6.1888285931772186565689508297001 absolute error = 6e-31 relative error = 9.6948879899737570539030106781788e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.1982947757947530846616607222836 y[1] (numeric) = 6.1982947757947530846616607222842 absolute error = 6e-31 relative error = 9.6800817273661730919208754266490e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.2076611297666175775721066652042 y[1] (numeric) = 6.2076611297666175775721066652049 absolute error = 7e-31 relative error = 1.1276388729458837408851874264871e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.2169277184568869122543427374759 y[1] (numeric) = 6.2169277184568869122543427374765 absolute error = 6e-31 relative error = 9.6510692607654591305151904689145e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.226094615206080887720708494585 y[1] (numeric) = 6.2260946152060808877207084945856 absolute error = 6e-31 relative error = 9.6368596541178691046344642994991e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.2351619033238303341788238437425 y[1] (numeric) = 6.2351619033238303341788238437431 absolute error = 6e-31 relative error = 9.6228455540208657687665843061944e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.2441296760805462193730292251716 y[1] (numeric) = 6.2441296760805462193730292251722 absolute error = 6e-31 relative error = 9.6090252945646911226420541140092e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = 6.2529980366980926852126945671717 y[1] (numeric) = 6.2529980366980926852126945671723 absolute error = 6e-31 relative error = 9.5953972235185783427217890202532e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.2617670983394649473759617404947 y[1] (numeric) = 6.2617670983394649473759617404954 absolute error = 7e-31 relative error = 1.1178952985741523871825247375517e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.2704369840974730900903584161317 y[1] (numeric) = 6.2704369840974730900903584161324 absolute error = 7e-31 relative error = 1.1163496288620362526321805961156e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.2790078269824328877013751255395 y[1] (numeric) = 6.2790078269824328877013751255402 absolute error = 7e-31 relative error = 1.1148258121162530397073276163568e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.2874797699088648839365910511028 y[1] (numeric) = 6.2874797699088648839365910511036 absolute error = 8e-31 relative error = 1.2723698990312548677073200885862e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.2958529656812030589463380705855 y[1] (numeric) = 6.2958529656812030589463380705863 absolute error = 8e-31 relative error = 1.2706777054051500486627228547154e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.3041275769785145132422895847312 y[1] (numeric) = 6.304127576978514513242289584732 absolute error = 8e-31 relative error = 1.2690098514526406283035140694785e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.3123037763382316965528467148593 y[1] (numeric) = 6.3123037763382316965528467148601 absolute error = 8e-31 relative error = 1.2673661286689217480630160936511e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.3203817461388988083588799010699 y[1] (numeric) = 6.3203817461388988083588799010707 absolute error = 8e-31 relative error = 1.2657463300989967359899757411978e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.3283616785819340954553943752715 y[1] (numeric) = 6.3283616785819340954553943752723 absolute error = 8e-31 relative error = 1.2641502503050123342790778874002e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=152054320, alloc=4586680, time=15.00 x[1] = 3.36 y[1] (analytic) = 6.3362437756724098702941653077783 y[1] (numeric) = 6.3362437756724098702941653077791 absolute error = 8e-31 relative error = 1.2625776853339311905448751248805e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.3440282491988521720894917659708 y[1] (numeric) = 6.3440282491988521720894917659716 absolute error = 8e-31 relative error = 1.2610284326855370150313265905185e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.3517153207120620907041253499906 y[1] (numeric) = 6.3517153207120620907041253499913 absolute error = 7e-31 relative error = 1.1020645048706719501671530512257e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.3593052215029608711653360746725 y[1] (numeric) = 6.3593052215029608711653360746732 absolute error = 7e-31 relative error = 1.1007491787515770559867861644950e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.3667981925794610142822015397657 y[1] (numeric) = 6.3667981925794610142822015397664 absolute error = 7e-31 relative error = 1.0994537267034063121390196195710e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.374194484642365686234783640953 y[1] (numeric) = 6.3741944846423656862347836409537 absolute error = 7e-31 relative error = 1.0981779763490768554677503069687e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.3814943580602988471741501456014 y[1] (numeric) = 6.3814943580602988471741501456021 absolute error = 7e-31 relative error = 1.0969217564469806090277519867778e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.3886980828436686057994896412256 y[1] (numeric) = 6.3886980828436686057994896412262 absolute error = 6e-31 relative error = 9.3915848302684926784742907843063e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.3958059386176664035551650129725 y[1] (numeric) = 6.3958059386176664035551650129731 absolute error = 6e-31 relative error = 9.3811476733091554059918116770827e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.4028182145943047285067851399478 y[1] (numeric) = 6.4028182145943047285067851399484 absolute error = 6e-31 relative error = 9.3708735730211136563300654462530e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.409735209543496155101605375782 y[1] (numeric) = 6.4097352095434961551016053757827 absolute error = 7e-31 relative error = 1.0920887948035130664622661755733e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.4165572317631766018851800535267 y[1] (numeric) = 6.4165572317631766018851800535274 absolute error = 7e-31 relative error = 1.0909276964520274077361088414900e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.4232845990484757948235981473823 y[1] (numeric) = 6.423284599048475794823598147383 absolute error = 7e-31 relative error = 1.0897851234922638992897875559120e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.4299176386599380191592786727668 y[1] (numeric) = 6.4299176386599380191592786727675 absolute error = 7e-31 relative error = 1.0886609119084880063994030354996e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.4364566872907963376986576266718 y[1] (numeric) = 6.4364566872907963376986576266725 absolute error = 7e-31 relative error = 1.0875548986171159514610601140938e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.4429020910333035480826663057576 y[1] (numeric) = 6.4429020910333035480826663057583 absolute error = 7e-31 relative error = 1.0864669214424380419537117762961e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.4492542053441232459162165122722 y[1] (numeric) = 6.449254205344123245916216512273 absolute error = 8e-31 relative error = 1.2404535075343849177021409604574e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = 6.455513395008784454621539014684 y[1] (numeric) = 6.4555133950087844546215390146848 absolute error = 8e-31 relative error = 1.2392507784408545647161621935690e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.4616800341052033765227688861298 y[1] (numeric) = 6.4616800341052033765227688861306 absolute error = 8e-31 relative error = 1.2380681119732693737795873277175e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.4677545059662759129562708227105 y[1] (numeric) = 6.4677545059662759129562708227113 absolute error = 8e-31 relative error = 1.2369053266663540712473276419981e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.4737372031415446941235206131037 y[1] (numeric) = 6.4737372031415446941235206131045 absolute error = 8e-31 relative error = 1.2357622419578288852348217632396e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.4796285273579444519516134360367 y[1] (numeric) = 6.4796285273579444519516134360376 absolute error = 9e-31 relative error = 1.3889685129325973823468682822584e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.485428889479629661391400854549 y[1] (numeric) = 6.4854288894796296613914008545499 absolute error = 9e-31 relative error = 1.3877262635011532114160827963532e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO 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=156055400, alloc=4586680, time=15.40 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = 6.4911387094668884673556498393478 y[1] (numeric) = 6.4911387094668884673556498393487 absolute error = 9e-31 relative error = 1.3865055736482886084231549349128e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.4967584163341470058702917252659 y[1] (numeric) = 6.4967584163341470058702917252668 absolute error = 9e-31 relative error = 1.3853062440142770527099755996948e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5022884481070683189716496935384 y[1] (numeric) = 6.5022884481070683189716496935393 absolute error = 9e-31 relative error = 1.3841280761114281058804984271214e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.507729251778750153422404272068 y[1] (numeric) = 6.5077292517787501534224042720689 absolute error = 9e-31 relative error = 1.3829708722962069063835754536572e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.513081283265026023429923544398 y[1] (numeric) = 6.5130812832650260234299235443989 absolute error = 9e-31 relative error = 1.3818344357416455590789007912365e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5183450073588740072234372441341 y[1] (numeric) = 6.518345007358874007223437244135 absolute error = 9e-31 relative error = 1.3807185704100451879915553997366e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5235208976839378365724044745283 y[1] (numeric) = 6.5235208976839378365724044745292 absolute error = 9e-31 relative error = 1.3796230810259675595974019706955e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5286094366471649270983909201599 y[1] (numeric) = 6.5286094366471649270983909201609 absolute error = 1.0e-30 relative error = 1.5317197478327948029909724297528e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5336111153905660855379561864798 y[1] (numeric) = 6.5336111153905660855379561864808 absolute error = 1.0e-30 relative error = 1.5305471696110000546357637658596e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5385264337421017179456248685362 y[1] (numeric) = 6.5385264337421017179456248685372 absolute error = 1.0e-30 relative error = 1.5293965851992193309992981261971e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5433559001656994501751930283722 y[1] (numeric) = 6.5433559001656994501751930283732 absolute error = 1.0e-30 relative error = 1.5282677807188765124352199299757e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5481000317104081588356701063544 y[1] (numeric) = 6.5481000317104081588356701063554 absolute error = 1.0e-30 relative error = 1.5271605429930996560253662156172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5527593539586934972763891726098 y[1] (numeric) = 6.5527593539586934972763891726107 absolute error = 9e-31 relative error = 1.3734671935667627336420960842630e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5573344009738800870056000894897 y[1] (numeric) = 6.5573344009738800870056000894906 absolute error = 9e-31 relative error = 1.3725089265942180540849739392544e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5618257152467456302796056979216 y[1] (numeric) = 6.5618257152467456302796056979226 absolute error = 1.0e-30 relative error = 1.5239661085122203709780173907720e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5662338476412722844066773562025 y[1] (numeric) = 6.5662338476412722844066773562035 absolute error = 1.0e-30 relative error = 1.5229430190933891135182381074923e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5705593573395607225831124022907 y[1] (numeric) = 6.5705593573395607225831124022917 absolute error = 1.0e-30 relative error = 1.5219404400980908457580854596675e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5748028117859123898094451375631 y[1] (numeric) = 6.5748028117859123898094451375641 absolute error = 1.0e-30 relative error = 1.5209581619807852418522517891263e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 6.5789647866300855456146217461962 y[1] (numeric) = 6.5789647866300855456146217461972 absolute error = 1.0e-30 relative error = 1.5199959757076396223036756876048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = 6.5830458656697307679365802592377 y[1] (numeric) = 6.5830458656697307679365802592387 absolute error = 1.0e-30 relative error = 1.5190536727306612829174343830844e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = 6.5870466407920116745608772518402 y[1] (numeric) = 6.5870466407920116745608772518411 absolute error = 9e-31 relative error = 1.3663179404659354651220452662081e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = 6.5909677119144166999965681743507 y[1] (numeric) = 6.5909677119144166999965681743517 absolute error = 1.0e-30 relative error = 1.5172278847494753694879102810814e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=160056764, alloc=4586680, time=15.79 x[1] = 3.81 y[1] (analytic) = 6.594809686924767846562330374365 y[1] (numeric) = 6.5948096869247678465623303743659 absolute error = 9e-31 relative error = 1.3647095863651523809316685428644e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = 6.5985731816204324087577276566562 y[1] (numeric) = 6.5985731816204324087577276566571 absolute error = 9e-31 relative error = 1.3639312245666178457682329253390e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = 6.6022588196467437496965225270235 y[1] (numeric) = 6.6022588196467437496965225270244 absolute error = 9e-31 relative error = 1.3631698250329344496855065557594e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = 6.6058672324346372874730769402477 y[1] (numeric) = 6.6058672324346372874730769402486 absolute error = 9e-31 relative error = 1.3624252022217813786241967606206e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = 6.6093990591375079278112350739528 y[1] (numeric) = 6.6093990591375079278112350739537 absolute error = 9e-31 relative error = 1.3616971708732704383868850151680e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.14 Order of pole (ratio test) Not computed 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) = 6.6128549465672952571998046093648 y[1] (numeric) = 6.6128549465672952571998046093657 absolute error = 9e-31 relative error = 1.3609855459890075977848236065440e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed 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) = 6.6162355491298028879420608093273 y[1] (numeric) = 6.6162355491298028879420608093281 absolute error = 8e-31 relative error = 1.2091467936101815552582158338978e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.84 Order of pole (ratio test) Not computed 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) = 6.6195415287592584231308680770413 y[1] (numeric) = 6.6195415287592584231308680770421 absolute error = 8e-31 relative error = 1.2085429127143023512740401468205e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = 6.6227735548521205854983883026317 y[1] (numeric) = 6.6227735548521205854983883026325 absolute error = 8e-31 relative error = 1.2079531232256711818992587404898e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = 6.6259323042001401293723304846144 y[1] (numeric) = 6.6259323042001401293723304846152 absolute error = 8e-31 relative error = 1.2073772614502635822118315078252e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = 6.6290184609226812295917636138744 y[1] (numeric) = 6.6290184609226812295917636138752 absolute error = 8e-31 relative error = 1.2068151638374671686674500728326e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = 6.6320327163983101151872025842926 y[1] (numeric) = 6.6320327163983101151872025842934 absolute error = 8e-31 relative error = 1.2062666669630964143958312356770e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = 6.634975769195657788904589839527 y[1] (numeric) = 6.6349757691956577889045898395278 absolute error = 8e-31 relative error = 1.2057316075126858868957673711255e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = 6.6378483250035637462436061494356 y[1] (numeric) = 6.6378483250035637462436061494364 absolute error = 8e-31 relative error = 1.2052098222650643253471968481604e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.51 Order of pole (ratio test) Not computed 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) = 6.6406510965605076795801933116402 y[1] (numeric) = 6.640651096560507679580193311641 absolute error = 8e-31 relative error = 1.2047011480762120369806893898286e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = 6.6433848035833362241440698087515 y[1] (numeric) = 6.6433848035833362241440698087523 absolute error = 8e-31 relative error = 1.2042054218634041927732640944202e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = 6.6460501726952918731172474893193 y[1] (numeric) = 6.6460501726952918731172474893201 absolute error = 8e-31 relative error = 1.2037224805896427021071076775141e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed 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) = 6.6486479373533512589020637166748 y[1] (numeric) = 6.6486479373533512589020637166756 absolute error = 8e-31 relative error = 1.2032521612483794438650024967289e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = 6.6511788377748800666700509520101 y[1] (numeric) = 6.6511788377748800666700509520109 absolute error = 8e-31 relative error = 1.2027943008485337276713088721814e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.74 Order of pole (ratio test) Not computed NO 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) = 6.6536436208636119146391681830978 y[1] (numeric) = 6.6536436208636119146391681830985 absolute error = 7e-31 relative error = 1.0520551443498310843528550626720e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = 6.656043040134958603129682414685 y[1] (numeric) = 6.6560430401349586031296824146858 absolute error = 8e-31 relative error = 1.2019153048982975310464247582668e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.08 Order of pole (ratio test) Not computed NO 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) = 6.6583778556406592013115533807654 y[1] (numeric) = 6.6583778556406592013115533807661 absolute error = 7e-31 relative error = 1.0513071128983668087003418103383e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=164059104, alloc=4586680, time=16.19 x[1] = 4.03 y[1] (analytic) = 6.6606488338927755066718545218524 y[1] (numeric) = 6.6606488338927755066718545218532 absolute error = 8e-31 relative error = 1.2010841885691260635470654333809e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = 6.6628567477870414775929465791727 y[1] (numeric) = 6.6628567477870414775929465791734 absolute error = 7e-31 relative error = 1.0506004053478915212545911940267e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = 6.6650023765255743040342707284824 y[1] (numeric) = 6.6650023765255743040342707284831 absolute error = 7e-31 relative error = 1.0502621911515443366485633907526e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.82 Order of pole (ratio test) Not computed NO 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) = 6.6670865055389548451462858477893 y[1] (numeric) = 6.6670865055389548451462858477901 absolute error = 8e-31 relative error = 1.1999244337618347600268080842785e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (analytic) = 6.6691099264076852257078557730396 y[1] (numeric) = 6.6691099264076852257078557730404 absolute error = 8e-31 relative error = 1.1995603743645590882448118699640e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = 6.6710734367830314455619910182479 y[1] (numeric) = 6.6710734367830314455619910182487 absolute error = 8e-31 relative error = 1.1992073053625103236164545735095e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.92 Order of pole (ratio test) Not computed NO 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) = 6.6729778403072589177230371136443 y[1] (numeric) = 6.6729778403072589177230371136451 absolute error = 8e-31 relative error = 1.1988650631622115529454265875397e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6748239465332689115350286796598 y[1] (numeric) = 6.6748239465332689115350286796606 absolute error = 8e-31 relative error = 1.1985334840411773391703889134589e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6766125708436439371699239938745 y[1] (numeric) = 6.6766125708436439371699239938753 absolute error = 8e-31 relative error = 1.1982124041367185949818050624207e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6783445343691101668598082727593 y[1] (numeric) = 6.6783445343691101668598082727601 absolute error = 8e-31 relative error = 1.1979016594350869287757345046195e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6800206639064250465529946920705 y[1] (numeric) = 6.6800206639064250465529946920713 absolute error = 8e-31 relative error = 1.1976010857609624702574370770699e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6816417918356983091644307735973 y[1] (numeric) = 6.6816417918356983091644307735981 absolute error = 8e-31 relative error = 1.1973105187672892451114323615062e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6832087560371546572501861716627 y[1] (numeric) = 6.6832087560371546572501861716635 absolute error = 8e-31 relative error = 1.1970297939254622272176767039585e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6847223998073464387683902107092 y[1] (numeric) = 6.68472239980734643876839021071 absolute error = 8e-31 relative error = 1.1967587465158702528098040074679e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6861835717748246945892205427578 y[1] (numeric) = 6.6861835717748246945892205427586 absolute error = 8e-31 relative error = 1.1964972116187990336334440521569e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6875931258152770105789180330467 y[1] (numeric) = 6.6875931258152770105789180330475 absolute error = 8e-31 relative error = 1.1962450241056985554615660535336e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6889519209661406604019012514924 y[1] (numeric) = 6.6889519209661406604019012514932 absolute error = 8e-31 relative error = 1.1960020186308191941493299505356e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6902608213406995776555448813771 y[1] (numeric) = 6.6902608213406995776555448813779 absolute error = 8e-31 relative error = 1.1957680296232209236515452662351e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6915206960416737475688229494868 y[1] (numeric) = 6.6915206960416737475688229494876 absolute error = 8e-31 relative error = 1.1955428912791600289688667720628e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6927324190743096592536384131552 y[1] (numeric) = 6.692732419074309659253638413156 absolute error = 8e-31 relative error = 1.1953264375548577717205808739156e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6938968692589805093911895895448 y[1] (numeric) = 6.6938968692589805093911895895456 absolute error = 8e-31 relative error = 1.1951185021596554868476054656160e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6950149301433048972601718697059 y[1] (numeric) = 6.6950149301433048972601718697067 absolute error = 8e-31 relative error = 1.1949189185495606157136709383535e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6960874899137927991640777205448 y[1] (numeric) = 6.6960874899137927991640777205456 absolute error = 8e-31 relative error = 1.1947275199211882034794096167754e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO 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=168061272, alloc=4586680, time=16.58 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = 6.697115441307027657586524135486 y[1] (numeric) = 6.6971154413070276575865241354867 absolute error = 7e-31 relative error = 1.0452261218053396060869633176112e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6980996815203934667916773220943 y[1] (numeric) = 6.698099681520393466791677322095 absolute error = 7e-31 relative error = 1.0450725329323672514539525017506e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.699041112122355782086820736836 y[1] (numeric) = 6.6990411121223557820868207368367 absolute error = 7e-31 relative error = 1.0449256666499686504438413945327e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.6999406389623056245713746337792 y[1] (numeric) = 6.6999406389623056245713746337799 absolute error = 7e-31 relative error = 1.0447853760513567637009055858207e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.700799172079975296906762396336 y[1] (numeric) = 6.7007991720799752969067623963367 absolute error = 7e-31 relative error = 1.0446515139816002957512935096870e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7016176256144351684500600968442 y[1] (numeric) = 6.7016176256144351684500600968449 absolute error = 7e-31 relative error = 1.0445239330344825158919505562058e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7023969177126805299970801594301 y[1] (numeric) = 6.7023969177126805299970801594307 absolute error = 6e-31 relative error = 8.9520213047120063170100515722140e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7031379704378176593732374506629 y[1] (numeric) = 6.7031379704378176593732374506635 absolute error = 6e-31 relative error = 8.9510316309483751059300320853354e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7038417096768582791891273544237 y[1] (numeric) = 6.7038417096768582791891273544243 absolute error = 6e-31 relative error = 8.9500919917890108010384856773236e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7045090650481316272382025774359 y[1] (numeric) = 6.7045090650481316272382025774365 absolute error = 6e-31 relative error = 8.9492011149319343023151523229693e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7051409698083233982523525669634 y[1] (numeric) = 6.7051409698083233982523525669641 absolute error = 7e-31 relative error = 1.0439750680141338763450663560220e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = 6.7057383607591508530437426924228 y[1] (numeric) = 6.7057383607591508530437426924235 absolute error = 7e-31 relative error = 1.0438820638996025548353714775846e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7063021781536834274442285238441 y[1] (numeric) = 6.7063021781536834274442285238448 absolute error = 7e-31 relative error = 1.0437943018438776520854049206779e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7068333656023182089033853667557 y[1] (numeric) = 6.7068333656023182089033853667565 absolute error = 8e-31 relative error = 1.1928132941292402056158628064802e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7073328699784196831191397422177 y[1] (numeric) = 6.7073328699784196831191397422185 absolute error = 8e-31 relative error = 1.1927244636698251971319784708926e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7078016413236331866477064664906 y[1] (numeric) = 6.7078016413236331866477064664914 absolute error = 8e-31 relative error = 1.1926411107203493044988378540420e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7082406327528815340686651434932 y[1] (numeric) = 6.708240632752881534068665143494 absolute error = 8e-31 relative error = 1.1925630635460694802404053379466e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7086508003590543199632903489336 y[1] (numeric) = 6.7086508003590543199632903489344 absolute error = 8e-31 relative error = 1.1924901501165974028767398500019e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7090331031173994266965123561634 y[1] (numeric) = 6.7090331031173994266965123561641 absolute error = 7e-31 relative error = 1.0433694233446844609892608766170e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7093885027896262987720567297445 y[1] (numeric) = 6.7093885027896262987720567297452 absolute error = 7e-31 relative error = 1.0433141555433171583096137989326e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7097179638277305733534136011127 y[1] (numeric) = 6.7097179638277305733534136011134 absolute error = 7e-31 relative error = 1.0432629266590917332061502204449e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7100224532775496844074386553302 y[1] (numeric) = 6.7100224532775496844074386553309 absolute error = 7e-31 relative error = 1.0432155851551300082618773049272e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=172063444, alloc=4586680, time=16.98 x[1] = 4.48 y[1] (analytic) = 6.7103029406820590848298014068488 y[1] (numeric) = 6.7103029406820590848298014068496 absolute error = 8e-31 relative error = 1.1921965477145584002096572456019e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7105603979844187568494820065161 y[1] (numeric) = 6.7105603979844187568494820065168 absolute error = 7e-31 relative error = 1.0431319569230786159834060030643e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7107957994307797059804818247938 y[1] (numeric) = 6.7107957994307797059804818247945 absolute error = 7e-31 relative error = 1.0430953659167741403899583822582e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7110101214728601577903583217408 y[1] (numeric) = 6.7110101214728601577903583217414 absolute error = 6e-31 relative error = 8.9405318892339633054961232001077e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7112043426703011997847211181989 y[1] (numeric) = 6.7112043426703011997847211181995 absolute error = 6e-31 relative error = 8.9402731516481850821950567227514e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7113794435928116327621307913814 y[1] (numeric) = 6.711379443592811632762130791382 absolute error = 6e-31 relative error = 8.9400398985458227429839652280392e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7115364067221118170727192195978 y[1] (numeric) = 6.7115364067221118170727192195984 absolute error = 6e-31 relative error = 8.9398308172634596186712826253404e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7116762163536863193141924250079 y[1] (numeric) = 6.7116762163536863193141924250085 absolute error = 6e-31 relative error = 8.9396445933735385675810873678962e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7117998584983551841186737926099 y[1] (numeric) = 6.7117998584983551841186737926105 absolute error = 6e-31 relative error = 8.9394799107469100940456764820418e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7119083207836736738211853143746 y[1] (numeric) = 6.7119083207836736738211853143752 absolute error = 6e-31 relative error = 8.9393354516192912100309417317310e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7120025923551703359536334006823 y[1] (numeric) = 6.7120025923551703359536334006829 absolute error = 6e-31 relative error = 8.9392098966616516196128782245027e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7120836637774332746752485243965 y[1] (numeric) = 6.7120836637774332746752485243971 absolute error = 6e-31 relative error = 8.9391019250545424433201122712815e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7121525269350545174299078212292 y[1] (numeric) = 6.7121525269350545174299078212298 absolute error = 6e-31 relative error = 8.9390102145663812821284531668749e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7122101749334423823111288281727 y[1] (numeric) = 6.7122101749334423823111288281733 absolute error = 6e-31 relative error = 8.9389334416357059490549481676365e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7122576019995117648153417756158 y[1] (numeric) = 6.7122576019995117648153417756164 absolute error = 6e-31 relative error = 8.9388702814574076698229948641963e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7122958033822622748720072874026 y[1] (numeric) = 6.7122958033822622748720072874032 absolute error = 6e-31 relative error = 8.9388194080729529729874426057137e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7123257752532541662540252007601 y[1] (numeric) = 6.7123257752532541662540252007607 absolute error = 6e-31 relative error = 8.9387794944646018543104443385323e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = 6.7123485146069920106925570161771 y[1] (numeric) = 6.7123485146069920106925570161777 absolute error = 6e-31 relative error = 8.9387492126536281102186618906116e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.712365019161226078245837166796 y[1] (numeric) = 6.7123650191612260782458371667966 absolute error = 6e-31 relative error = 8.9387272338025459910681825668344e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7123762872571813937008543201053 y[1] (numeric) = 6.7123762872571813937008543201059 absolute error = 6e-31 relative error = 8.9387122283213455269793111978944e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7123833177597244460191203679446 y[1] (numeric) = 6.7123833177597244460191203679452 absolute error = 6e-31 relative error = 8.9387028659777370275314895579108e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.712387109957477534072388396442 y[1] (numeric) = 6.7123871099574775340723883964426 absolute error = 6e-31 relative error = 8.9386978160114033520510948531199e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 6.7123886634628907371505082963271 y[1] (numeric) = 6.7123886634628907371505082963277 absolute error = 6e-31 relative error = 8.9386957472522565900755692510175e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=176064156, alloc=4586680, time=17.38 x[1] = 4.71 y[1] (analytic) = 6.7123889781122815029610961477247 y[1] (numeric) = 6.7123889781122815029610961477253 absolute error = 6e-31 relative error = 8.9386953282426937824033805086090e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = 6.7123890538658518490789173468254 y[1] (numeric) = 6.712389053865851849078917346826 absolute error = 6e-31 relative error = 8.9386952273638442525828548613374e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007339 Order of pole (three term test) = -0.8943 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = 6.7123898907076931760415198150572 y[1] (numeric) = 6.7123898907076931760415198150578 absolute error = 6e-31 relative error = 8.9386941129657990074726720015665e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01698 Order of pole (three term test) = -0.9004 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = 6.712392488545788691526478682781 y[1] (numeric) = 6.7123924885457886915264786827816 absolute error = 6e-31 relative error = 8.9386906535018105044195505925279e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02661 Order of pole (three term test) = -0.9113 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = 6.7123978471120234452845036876267 y[1] (numeric) = 6.7123978471120234452845036876273 absolute error = 6e-31 relative error = 8.9386835176664488725206513542164e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03623 Order of pole (three term test) = -0.927 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = 6.7124069658622119737415912835895 y[1] (numeric) = 6.7124069658622119737415912835901 absolute error = 6e-31 relative error = 8.9386713745376984173265764297248e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04584 Order of pole (three term test) = -0.9476 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = 6.7124208438761535514224512272127 y[1] (numeric) = 6.7124208438761535514224512272134 absolute error = 7e-31 relative error = 1.0428428376010138588773828390023e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05543 Order of pole (three term test) = -0.973 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = 6.7124404797577250435867782853404 y[1] (numeric) = 6.7124404797577250435867782853411 absolute error = 7e-31 relative error = 1.0428397869760558329651806975687e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.065 Order of pole (three term test) = -1.003 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = 6.7124668715350213507098497586524 y[1] (numeric) = 6.7124668715350213507098497586531 absolute error = 7e-31 relative error = 1.0428356867851811022052131907088e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07454 Order of pole (three term test) = -1.038 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = 6.7125010165605534306797847423505 y[1] (numeric) = 6.7125010165605534306797847423512 absolute error = 7e-31 relative error = 1.0428303821079731292352425395064e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08405 Order of pole (three term test) = -1.078 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = 6.7125439114115138788260773604616 y[1] (numeric) = 6.7125439114115138788260773604623 absolute error = 7e-31 relative error = 1.0428237181584470035370447784612e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09353 Order of pole (three term test) = -1.122 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = 6.7125965517901200391382893808302 y[1] (numeric) = 6.7125965517901200391382893808309 absolute error = 7e-31 relative error = 1.0428155403043305208289920926047e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.103 Order of pole (three term test) = -1.172 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = 6.7126599324240446122807332110462 y[1] (numeric) = 6.7126599324240446122807332110468 absolute error = 6e-31 relative error = 8.9383345207438623160264802762551e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1124 Order of pole (three term test) = -1.226 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = 6.7127350469669437172593695902673 y[1] (numeric) = 6.7127350469669437172593695902679 absolute error = 6e-31 relative error = 8.9382345020618932834371134099344e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1217 Order of pole (three term test) = -1.284 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = 6.7128228878990923538518602815347 y[1] (numeric) = 6.7128228878990923538518602815353 absolute error = 6e-31 relative error = 8.9381175404105082061563582955048e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.131 Order of pole (three term test) = -1.348 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = 6.7129244464281372021717292540146 y[1] (numeric) = 6.7129244464281372021717292540152 absolute error = 6e-31 relative error = 8.9379823173676930815231473622822e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1403 Order of pole (three term test) = -1.416 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = 6.713040712389976684003970214372 y[1] (numeric) = 6.7130407123899766840039702143726 absolute error = 6e-31 relative error = 8.9378275167109482089542889606290e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1495 Order of pole (three term test) = -1.488 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = 6.7131726741497781978233672529684 y[1] (numeric) = 6.713172674149778197823367252969 absolute error = 6e-31 relative error = 8.9376518246045244831338304190418e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1586 Order of pole (three term test) = -1.566 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = 6.7133213185031424256895414102862 y[1] (numeric) = 6.7133213185031424256895414102868 absolute error = 6e-31 relative error = 8.9374539297901646706606889420661e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1677 Order of pole (three term test) = -1.648 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = 6.7134876305774245955056708558781 y[1] (numeric) = 6.7134876305774245955056708558787 absolute error = 6e-31 relative error = 8.9372325237812975794543108969916e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1767 Order of pole (three term test) = -1.734 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = 6.7136725937332225664324268004806 y[1] (numeric) = 6.7136725937332225664324268004812 absolute error = 6e-31 relative error = 8.9369863010606302242962064255757e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1856 Order of pole (three term test) = -1.825 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = 6.7138771894660415885664907591882 y[1] (numeric) = 6.7138771894660415885664907591888 absolute error = 6e-31 relative error = 8.9367139592810802649092531888351e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1945 Order of pole (three term test) = -1.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=180065184, alloc=4586680, time=17.79 x[1] = 4.93 y[1] (analytic) = 6.7141023973081455703257395535142 y[1] (numeric) = 6.7141023973081455703257395535148 absolute error = 6e-31 relative error = 8.9364141994699881473727966489161e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2033 Order of pole (three term test) = -2.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = 6.7143491947306046683325691959603 y[1] (numeric) = 6.7143491947306046683325691959608 absolute error = 5e-31 relative error = 7.4467381051971212649582896327818e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.212 Order of pole (three term test) = -2.124 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = 6.7146185570455489949547425883653 y[1] (numeric) = 6.7146185570455489949547425883658 absolute error = 5e-31 relative error = 7.4464393733186446692974688498724e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2206 Order of pole (three term test) = -2.232 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = 6.7149114573086382180515519770647 y[1] (numeric) = 6.7149114573086382180515519770652 absolute error = 5e-31 relative error = 7.4461145642626519698394091102960e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2291 Order of pole (three term test) = -2.345 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = 6.7152288662217568058840464859875 y[1] (numeric) = 6.715228866221756805884046485988 absolute error = 5e-31 relative error = 7.4457626085545319471403524696402e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2375 Order of pole (three term test) = -2.462 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = 6.7155717520359446475837466793192 y[1] (numeric) = 6.7155717520359446475837466793198 absolute error = 6e-31 relative error = 8.9344589285059661771094116778846e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2459 Order of pole (three term test) = -2.583 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = 6.715941080454572756036908402303 y[1] (numeric) = 6.7159410804545727560369084023036 absolute error = 6e-31 relative error = 8.9339675975744060170977802669305e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2541 Order of pole (three term test) = -2.709 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin(x) + 1,0; Iterations = 1000 Total Elapsed Time = 17 Seconds Elapsed Time(since restart) = 17 Seconds Time to Timeout = 2 Minutes 42 Seconds Percent Done = 100.1 % > quit bytes used=181265812, alloc=4586680, time=17.90