|\^/| 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_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > array_tmp4_g[1] := sin(array_tmp3[1]); > array_tmp4[1] := cos(array_tmp3[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/2.0; > #emit pre cos FULL $eq_no = 1 > array_tmp4_g[2] := (att(1,array_tmp4,array_tmp3,1)); > array_tmp4[2] := (-att(1,array_tmp4_g,array_tmp3,1)); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0.0; > array_tmp3[3] := -ats(3,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre cos FULL $eq_no = 1 > array_tmp4_g[3] := (att(2,array_tmp4,array_tmp3,1)); > array_tmp4[3] := (-att(2,array_tmp4_g,array_tmp3,1)); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0.0; > array_tmp3[4] := -ats(4,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre cos FULL $eq_no = 1 > array_tmp4_g[4] := (att(3,array_tmp4,array_tmp3,1)); > array_tmp4[4] := (-att(3,array_tmp4_g,array_tmp3,1)); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0.0; > array_tmp3[5] := -ats(5,array_tmp3,array_tmp3,2) / array_tmp3[1] / 2.0; > #emit pre cos FULL $eq_no = 1 > array_tmp4_g[5] := (att(4,array_tmp4,array_tmp3,1)); > array_tmp4[5] := (-att(4,array_tmp4_g,array_tmp3,1)); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0.0; > array_tmp3[kkk] := -ats(kkk,array_tmp3,array_tmp3,2) /array_tmp3[1] / 2.0; > #emit cos FULL $eq_no = 1 > array_tmp4[kkk] := -att(kkk-1,array_tmp4_g,array_tmp3,1); > array_tmp4_g[kkk] := att(kkk-1,array_tmp4,array_tmp3,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := array_const_2D0[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4_g[1] := sin(array_tmp3[1]); array_tmp4[1] := cos(array_tmp3[1]); array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_2D0[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*2.0); array_tmp4_g[2] := att(1, array_tmp4, array_tmp3, 1); array_tmp4[2] := -att(1, array_tmp4_g, array_tmp3, 1); array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp3[3] := 0.; array_tmp3[3] := -ats(3, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4_g[3] := att(2, array_tmp4, array_tmp3, 1); array_tmp4[3] := -att(2, array_tmp4_g, array_tmp3, 1); array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp3[4] := 0.; array_tmp3[4] := -ats(4, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4_g[4] := att(3, array_tmp4, array_tmp3, 1); array_tmp4[4] := -att(3, array_tmp4_g, array_tmp3, 1); array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp3[5] := 0.; array_tmp3[5] := -ats(5, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0) ; array_tmp4_g[5] := att(4, array_tmp4, array_tmp3, 1); array_tmp4[5] := -att(4, array_tmp4_g, array_tmp3, 1); array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp3[kkk] := 0.; array_tmp3[kkk] := -ats(kkk, array_tmp3, array_tmp3, 2)/(array_tmp3[1]*2.0); array_tmp4[kkk] := -att(kkk - 1, array_tmp4_g, array_tmp3, 1); array_tmp4_g[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1); array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp5[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0))); > end; exact_soln_y := proc(x) return cos(sqrt(2.0*x + 3.0)) + sqrt(2.0*x + 3.0)*sin(sqrt(2.0*x + 3.0)) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/cos_sqrt_linpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -1.0;"); > 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(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4_g:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_2D0[1] := 2.0; > array_const_3D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_3D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_3D0[1] := 3.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -1.0; > 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 ) = cos(sqrt(2.0*x + 3.0));"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T00:14:26-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"cos_sqrt_lin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"cos_sqrt_lin diffeq.mxt") > ; > logitem_str(html_log_file,"cos_sqrt_lin maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/cos_sqrt_linpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -1.0;"); 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(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(\ sqrt(2.0*x+3.0)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4_g := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_g[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_3D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3D0[term] := 0.; term := term + 1 end do; array_const_3D0[1] := 3.0; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := -1.0; 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 ) = cos(sqrt(2.0*x + 3.0));"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T00:14:26-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "cos_sqrt_lin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0));"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "cos_sqrt_lin diffeq.mxt"); logitem_str(html_log_file, "cos_sqrt_lin maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/cos_sqrt_linpostode.ode################# diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0)); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -1.0; 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(cos(sqrt(2.0*x+3.0))+sqrt(2.0*x+3.0)*sin(sqrt(2.0*x+3.0))); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 6 estimated_steps = 6000000 step_error = 1.6666666666666666666666666666667e-17 est_needed_step_err = 1.6666666666666666666666666666667e-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 = 4.6153837606897130647130647130647e-185 estimated_step_error = 4.6153837606897130647130647130647e-185 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0153834900287545787545787545788e-176 estimated_step_error = 1.0153834900287545787545787545788e-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 = 3.4461430199840252340252340252340e-169 estimated_step_error = 3.4461430199840252340252340252340e-169 best_h = 8.000e-06 opt_iter = 4 bytes used=4000484, alloc=3014104, time=0.29 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.9229686626617826617826617826617e-162 estimated_step_error = 4.9229686626617826617826617826617e-162 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 = 1.9938655263142043142043142043143e-153 estimated_step_error = 1.9938655263142043142043142043143e-153 best_h = 3.200000e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.4763760593813593813593813593814e-146 estimated_step_error = 1.4763760593813593813593813593814e-146 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 = 3.9270197737077737077737077737077e-139 estimated_step_error = 3.9270197737077737077737077737077e-139 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 = 5.1198997955229955229955229955230e-130 estimated_step_error = 5.1198997955229955229955229955230e-130 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0318459242328042328042328042328e-121 estimated_step_error = 1.0318459242328042328042328042328e-121 best_h = 0.000512 opt_iter = 10 bytes used=8001516, alloc=3996964, time=0.58 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.4985120872608872608872608872609e-114 estimated_step_error = 1.4985120872608872608872608872609e-114 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 = 5.4883035115995115995115995115995e-107 estimated_step_error = 5.4883035115995115995115995115995e-107 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 = 9.2254226129426129426129426129426e-100 estimated_step_error = 9.2254226129426129426129426129426e-100 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.5368150948310948310948310948311e-91 estimated_step_error = 1.5368150948310948310948310948311e-91 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.7703578412698412698412698412699e-82 estimated_step_error = 1.7703578412698412698412698412699e-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 = 2.0633558323158323158323158323159e-75 estimated_step_error = 2.0633558323158323158323158323159e-75 best_h = 0.032768 opt_iter = 16 bytes used=12002224, alloc=4193536, time=0.89 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.1276361090761090761090761090761e-67 estimated_step_error = 2.1276361090761090761090761090761e-67 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 = 6.7033032153032153032153032153020e-61 estimated_step_error = 6.7033032153032153032153032153020e-61 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 = 6.6997023361823361823361823361823e-52 estimated_step_error = 6.6997023361823361823361823361823e-52 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = 1.3817732906760362240534389290733 y[1] (numeric) = 1.3817732906760362240534389290733 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 = 0.02121 Order of pole (three term test) = -30.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = 1.3871342903544166154371007094768 y[1] (numeric) = 1.3871342903544166154371007094768 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 = 0.006395 Order of pole (three term test) = -6.024 Radius of convergence (six term test) for eq 1 = 0.1155 Order of pole (six term test) = -11.4 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = 1.3924114437413490976852412826912 y[1] (numeric) = 1.3924114437413490976852412826912 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=16003156, alloc=4259060, time=1.21 x[1] = -0.97 y[1] (analytic) = 1.3976050510761118950933993659855 y[1] (numeric) = 1.3976050510761118950933993659855 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 = 0.001765 Order of pole (three term test) = -24.79 Radius of convergence (six term test) for eq 1 = 0.06964 Order of pole (six term test) = -11.22 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (analytic) = 1.4027154119794318390745075888768 y[1] (numeric) = 1.4027154119794318390745075888768 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 = 0.009669 Order of pole (three term test) = -27.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = 1.407742825454382501814219222154 y[1] (numeric) = 1.4077428254543825018142192221541 absolute error = 1e-31 relative error = 7.1035702112509520306728117515007e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02477 Order of pole (three term test) = -96.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.94 y[1] (analytic) = 1.4126875898872813216838642202808 y[1] (numeric) = 1.4126875898872813216838642202808 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 = 0.004197 Order of pole (three term test) = -25.31 Radius of convergence (six term test) for eq 1 = 0.1493 Order of pole (six term test) = -12.43 TOP MAIN SOLVE Loop x[1] = -0.93 y[1] (analytic) = 1.4175500030485857213341443069425 y[1] (numeric) = 1.4175500030485857213341443069425 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 = 0.001429 Order of pole (three term test) = 0.1818 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=20004064, alloc=4324584, time=1.52 x[1] = -0.92 y[1] (analytic) = 1.4223303620937882193919630535745 y[1] (numeric) = 1.4223303620937882193919630535745 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 = 0.009884 Order of pole (three term test) = -23.69 Radius of convergence (six term test) for eq 1 = 0.1486 Order of pole (six term test) = -10.74 TOP MAIN SOLVE Loop x[1] = -0.91 y[1] (analytic) = 1.4270289635643105366820735985177 y[1] (numeric) = 1.4270289635643105366820735985176 absolute error = 1e-31 relative error = 7.0075662480058272858983638901397e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01149 Order of pole (three term test) = -19.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9 y[1] (analytic) = 1.4316461033883966978945138297226 y[1] (numeric) = 1.4316461033883966978945138297225 absolute error = 1e-31 relative error = 6.9849664496918356757024087441620e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4361820768820051296180865063764 y[1] (numeric) = 1.4361820768820051296180865063763 absolute error = 1e-31 relative error = 6.9629054428184366801611892091008e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4406371787496997556594299241749 y[1] (numeric) = 1.4406371787496997556594299241748 absolute error = 1e-31 relative error = 6.9413729893315680944873940506986e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01515 Order of pole (three term test) = -9.356 Radius of convergence (six term test) for eq 1 = 0.03444 Order of pole (six term test) = -11.64 TOP MAIN SOLVE Loop x[1] = -0.87 y[1] (analytic) = 1.4450117030855400905665133349323 y[1] (numeric) = 1.4450117030855400905665133349322 absolute error = 1e-31 relative error = 6.9203591767782602168071063399857e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01071 Order of pole (three term test) = -24.38 Radius of convergence (six term test) for eq 1 = 0.1019 Order of pole (six term test) = -11.84 TOP MAIN SOLVE Loop bytes used=24005104, alloc=4390108, time=1.85 x[1] = -0.86 y[1] (analytic) = 1.4493059433739703322746804135193 y[1] (numeric) = 1.4493059433739703322746804135192 absolute error = 1e-31 relative error = 6.8998544066686816552239827845285e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03455 Order of pole (three term test) = -40.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.85 y[1] (analytic) = 1.453520192490707454792653623479 y[1] (numeric) = 1.453520192490707454792653623479 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 Radius of convergence (six term test) for eq 1 = 0.07296 Order of pole (six term test) = -11.27 TOP MAIN SOLVE Loop x[1] = -0.84 y[1] (analytic) = 1.4576547427036283018452023667972 y[1] (numeric) = 1.4576547427036283018452023667971 absolute error = 1e-31 relative error = 6.8603351033950631233284877114839e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008074 Order of pole (three term test) = -34.03 Radius of convergence (six term test) for eq 1 = 0.1025 Order of pole (six term test) = -11 TOP MAIN SOLVE Loop x[1] = -0.83 y[1] (analytic) = 1.4617098856736556823884683129225 y[1] (numeric) = 1.4617098856736556823884683129224 absolute error = 1e-31 relative error = 6.8413028453941922020044391495495e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001616 Order of pole (three term test) = -0.7587 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.82 y[1] (analytic) = 1.4656859124556434689132322869684 y[1] (numeric) = 1.4656859124556434689132322869683 absolute error = 1e-31 relative error = 6.8227441602722188021590727741427e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=28005888, alloc=4390108, time=2.16 x[1] = -0.81 y[1] (analytic) = 1.469583113499260699450698556785 y[1] (numeric) = 1.4695831134992606994506985567849 absolute error = 1e-31 relative error = 6.8046508619636712245877710142776e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04456 Order of pole (three term test) = -26.43 Radius of convergence (six term test) for eq 1 = 0.1658 Order of pole (six term test) = -11.26 TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (analytic) = 1.4734017786498746841946642930075 y[1] (numeric) = 1.4734017786498746841946642930074 absolute error = 1e-31 relative error = 6.7870150185126834821965486944088e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1161 Order of pole (three term test) = -49.26 Radius of convergence (six term test) for eq 1 = 0.2445 Order of pole (six term test) = -12.18 TOP MAIN SOLVE Loop x[1] = -0.79 y[1] (analytic) = 1.4771421971494331176532343849659 y[1] (numeric) = 1.4771421971494331176532343849658 absolute error = 1e-31 relative error = 6.7698289435491384550747825882669e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0378 Order of pole (three term test) = -17.02 Radius of convergence (six term test) for eq 1 = 0.05663 Order of pole (six term test) = -11.75 TOP MAIN SOLVE Loop x[1] = -0.78 y[1] (analytic) = 1.4808046576373451972425346782169 y[1] (numeric) = 1.4808046576373451972425346782168 absolute error = 1e-31 relative error = 6.7530851881268452742161091100908e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008522 Order of pole (three term test) = 12.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.77 y[1] (analytic) = 1.4843894481513617492341700561392 y[1] (numeric) = 1.4843894481513617492341700561391 absolute error = 1e-31 relative error = 6.7367765329064166991973775982937e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4878968561284543629674676182464 y[1] (numeric) = 1.4878968561284543629674676182463 absolute error = 1e-31 relative error = 6.7208959806664660283635114722191e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=32007080, alloc=4390108, time=2.49 x[1] = -0.75 y[1] (analytic) = 1.4913271684056935342368395113354 y[1] (numeric) = 1.4913271684056935342368395113353 absolute error = 1e-31 relative error = 6.7054367491276385482201746742027e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07084 Order of pole (three term test) = -66.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.74 y[1] (analytic) = 1.4946806712211258187638947460211 y[1] (numeric) = 1.494680671221125818763894746021 absolute error = 1e-31 relative error = 6.6903922640748336356554281685461e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1034 Order of pole (three term test) = -63.1 Radius of convergence (six term test) for eq 1 = 0.1968 Order of pole (six term test) = -11.48 TOP MAIN SOLVE Loop x[1] = -0.73 y[1] (analytic) = 1.497957650214649996663224580334 y[1] (numeric) = 1.4979576502146499966632245803339 absolute error = 1e-31 relative error = 6.6757561527637640250275146899207e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0005345 Order of pole (three term test) = -0.9465 Radius of convergence (six term test) for eq 1 = 0.06329 Order of pole (six term test) = -11.7 TOP MAIN SOLVE Loop x[1] = -0.72 y[1] (analytic) = 1.5011583904288922488100817735946 y[1] (numeric) = 1.5011583904288922488100817735944 absolute error = 2e-31 relative error = 1.3323044475197483653963933475108e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5042831763100803460174702074492 y[1] (numeric) = 1.504283176310080346017470207449 absolute error = 2e-31 relative error = 1.3295369060138559550972647314177e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=36008024, alloc=4455632, time=2.81 x[1] = -0.7 y[1] (analytic) = 1.5073322917089168519294580364768 y[1] (numeric) = 1.5073322917089168519294580364766 absolute error = 2e-31 relative error = 1.3268474449867507590662687489916e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1321 Order of pole (six term test) = -11.5 TOP MAIN SOLVE Loop x[1] = -0.69 y[1] (analytic) = 1.5103060198814513405368246678763 y[1] (numeric) = 1.5103060198814513405368246678761 absolute error = 2e-31 relative error = 1.3242349389277984052690132006589e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1362 Order of pole (six term test) = -11.49 TOP MAIN SOLVE Loop x[1] = -0.68 y[1] (analytic) = 1.513204643489951629220449478141 y[1] (numeric) = 1.5132046434899516292204494781408 absolute error = 2e-31 relative error = 1.3216982967930476843959519303217e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3942 Order of pole (six term test) = -12 TOP MAIN SOLVE Loop x[1] = -0.67 y[1] (analytic) = 1.5160284446037740282271482540418 y[1] (numeric) = 1.5160284446037740282271482540417 absolute error = 1e-31 relative error = 6.5961823048864882899638059749342e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.0937 Order of pole (six term test) = -12.18 TOP MAIN SOLVE Loop x[1] = -0.66 y[1] (analytic) = 1.5187777047002326074819618953976 y[1] (numeric) = 1.5187777047002326074819618953975 absolute error = 1e-31 relative error = 6.5842420316367108282850429113757e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01629 Order of pole (three term test) = -4.658 Radius of convergence (six term test) for eq 1 = 0.142 Order of pole (six term test) = -9.57 TOP MAIN SOLVE Loop x[1] = -0.65 y[1] (analytic) = 1.5214527046654674816402009377242 y[1] (numeric) = 1.5214527046654674816402009377241 absolute error = 1e-31 relative error = 6.5726656959729618461001693380651e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007494 Order of pole (three term test) = -7.979 Radius of convergence (six term test) for eq 1 = 0.06819 Order of pole (six term test) = -12.03 TOP MAIN SOLVE Loop bytes used=40008980, alloc=4455632, time=3.14 x[1] = -0.64 y[1] (analytic) = 1.5240537247953121142818489436586 y[1] (numeric) = 1.5240537247953121142818489436585 absolute error = 1e-31 relative error = 6.5614484826268503212755576548993e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1475 Order of pole (six term test) = -12 TOP MAIN SOLVE Loop x[1] = -0.63 y[1] (analytic) = 1.5265810447961596421502277727575 y[1] (numeric) = 1.5265810447961596421502277727574 absolute error = 1e-31 relative error = 6.5505857249362569795936489216569e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02004 Order of pole (three term test) = -46.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.62 y[1] (analytic) = 1.5290349437858282203361281696052 y[1] (numeric) = 1.5290349437858282203361281696051 absolute error = 1e-31 relative error = 6.5400729006496133107757072332159e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2073 Order of pole (six term test) = -11.31 TOP MAIN SOLVE Loop x[1] = -0.61 y[1] (analytic) = 1.5314157002944253893079100098493 y[1] (numeric) = 1.5314157002944253893079100098492 absolute error = 1e-31 relative error = 6.5299056278954368780227167839947e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3824 Order of pole (three term test) = -91.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6 y[1] (analytic) = 1.5337235922652114646873779125413 y[1] (numeric) = 1.5337235922652114646873779125412 absolute error = 1e-31 relative error = 6.5200796613101848427102652096127e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04402 Order of pole (three term test) = -21 Radius of convergence (six term test) for eq 1 = 0.1877 Order of pole (six term test) = -11.24 TOP MAIN SOLVE Loop bytes used=44010524, alloc=4455632, time=3.47 x[1] = -0.59 y[1] (analytic) = 1.5359588970554619506705397647102 y[1] (numeric) = 1.5359588970554619506705397647101 absolute error = 1e-31 relative error = 6.5105908883178336310102773828795e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06107 Order of pole (three term test) = -52.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.58 y[1] (analytic) = 1.53812189143732897799165801017 y[1] (numeric) = 1.5381218914373289779916580101698 absolute error = 2e-31 relative error = 1.3002870651109839686426001890200e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01388 Order of pole (three term test) = -28.05 Radius of convergence (six term test) for eq 1 = 0.1427 Order of pole (six term test) = -11.05 TOP MAIN SOLVE Loop x[1] = -0.57 y[1] (analytic) = 1.5402128515987017673283063288728 y[1] (numeric) = 1.5402128515987017673283063288726 absolute error = 2e-31 relative error = 1.2985218230870173992616740967599e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02715 Order of pole (three term test) = -23.12 Radius of convergence (six term test) for eq 1 = 0.1476 Order of pole (six term test) = -11.16 TOP MAIN SOLVE Loop x[1] = -0.56 y[1] (analytic) = 1.5422320531440661190444475753984 y[1] (numeric) = 1.5422320531440661190444475753983 absolute error = 1e-31 relative error = 6.4841085228474755670574423365626e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04803 Order of pole (three term test) = -44.24 Radius of convergence (six term test) for eq 1 = 0.04255 Order of pole (six term test) = -11.62 TOP MAIN SOLVE Loop x[1] = -0.55 y[1] (analytic) = 1.5441797710953629301678525551331 y[1] (numeric) = 1.5441797710953629301678525551329 absolute error = 2e-31 relative error = 1.2951859863967142134158088987469e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03022 Order of pole (three term test) = 3.593 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.54 y[1] (analytic) = 1.5460562798928457394974833940672 y[1] (numeric) = 1.5460562798928457394974833940671 absolute error = 1e-31 relative error = 6.4680698432873874688029393575103e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1031 Order of pole (three term test) = -64.33 Radius of convergence (six term test) for eq 1 = 0.2158 Order of pole (six term test) = -11.13 TOP MAIN SOLVE Loop bytes used=48011676, alloc=4455632, time=3.79 x[1] = -0.53 y[1] (analytic) = 1.5478618533959373017357699026535 y[1] (numeric) = 1.5478618533959373017357699026535 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 = 0.001055 Order of pole (three term test) = -26.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.52 y[1] (analytic) = 1.5495967648840851915400124455322 y[1] (numeric) = 1.5495967648840851915400124455321 absolute error = 1e-31 relative error = 6.4532917379625738156096059866483e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5512612870576164383864504068832 y[1] (numeric) = 1.5512612870576164383864504068831 absolute error = 1e-31 relative error = 6.4463672776671202244279704799838e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1422 Order of pole (three term test) = -76.97 Radius of convergence (six term test) for eq 1 = 0.4931 Order of pole (six term test) = -13.44 TOP MAIN SOLVE Loop x[1] = -0.5 y[1] (analytic) = 1.5528556920385911931398413854228 y[1] (numeric) = 1.5528556920385911931398413854227 absolute error = 1e-31 relative error = 6.4397484268947010593729509663601e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5543802513716554272207027633469 y[1] (numeric) = 1.5543802513716554272207027633469 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 = 0.0111 Order of pole (three term test) = -26.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=52012720, alloc=4521156, time=4.11 x[1] = -0.48 y[1] (analytic) = 1.5558352360248926652616742695672 y[1] (numeric) = 1.5558352360248926652616742695671 absolute error = 1e-31 relative error = 6.4274158139969035189305761624579e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5572209163906747521437675991053 y[1] (numeric) = 1.5572209163906747521437675991053 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.46 y[1] (analytic) = 1.5585375622865116553025770572386 y[1] (numeric) = 1.5585375622865116553025770572385 absolute error = 1e-31 relative error = 6.4162714085178163052030200810629e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05655 Order of pole (three term test) = -49.04 Radius of convergence (six term test) for eq 1 = 0.1377 Order of pole (six term test) = -11.8 TOP MAIN SOLVE Loop x[1] = -0.45 y[1] (analytic) = 1.559785442955900303193833568637 y[1] (numeric) = 1.5597854429559003031938335686369 absolute error = 1e-31 relative error = 6.4111381761899987482781103038629e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5609648270691724608069932280444 y[1] (numeric) = 1.5609648270691724608069932280442 absolute error = 2e-31 relative error = 1.2812588504989883237005477602691e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04575 Order of pole (three term test) = -25.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.43 y[1] (analytic) = 1.5620759827243416431148608697349 y[1] (numeric) = 1.5620759827243416431148608697348 absolute error = 1e-31 relative error = 6.4017372461994330339164628821696e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.234 Order of pole (three term test) = 54.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=56013664, alloc=4521156, time=4.44 x[1] = -0.42 y[1] (analytic) = 1.563119177447949067346558897768 y[1] (numeric) = 1.5631191774479490673465588977678 absolute error = 2e-31 relative error = 1.2794929707569266915039304972368e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3324 Order of pole (six term test) = -13.1 TOP MAIN SOLVE Loop x[1] = -0.41 y[1] (analytic) = 1.5640946781959086449704618476762 y[1] (numeric) = 1.5640946781959086449704618476761 absolute error = 1e-31 relative error = 6.3934748576310052529881399450183e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5650027513543510142730278423965 y[1] (numeric) = 1.5650027513543510142730278423964 absolute error = 1e-31 relative error = 6.3897651242759893699678125138307e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1702 Order of pole (six term test) = -11.69 TOP MAIN SOLVE Loop x[1] = -0.39 y[1] (analytic) = 1.5658436627404666144187692606989 y[1] (numeric) = 1.5658436627404666144187692606988 absolute error = 1e-31 relative error = 6.3863336027419659336519606949168e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01138 Order of pole (three term test) = -0.1104 Radius of convergence (six term test) for eq 1 = 0.1166 Order of pole (six term test) = -12.44 TOP MAIN SOLVE Loop x[1] = -0.38 y[1] (analytic) = 1.5666176776033478018759165548274 y[1] (numeric) = 1.5666176776033478018759165548273 absolute error = 1e-31 relative error = 6.3831783229321517414978631120714e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01085 Order of pole (three term test) = -5.79 Radius of convergence (six term test) for eq 1 = 0.1321 Order of pole (six term test) = -11.49 TOP MAIN SOLVE Loop bytes used=60014748, alloc=4521156, time=4.76 x[1] = -0.37 y[1] (analytic) = 1.56732506062483001009164123525 y[1] (numeric) = 1.5673250606248300100916412352499 absolute error = 1e-31 relative error = 6.3802973940921985352940756997870e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7601 Order of pole (six term test) = -14.57 TOP MAIN SOLVE Loop x[1] = -0.36 y[1] (analytic) = 1.5679660759203319533000165840625 y[1] (numeric) = 1.5679660759203319533000165840624 absolute error = 1e-31 relative error = 6.3776890033353617182185083736055e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009464 Order of pole (three term test) = -4.776 Radius of convergence (six term test) for eq 1 = 0.1476 Order of pole (six term test) = -11.8 TOP MAIN SOLVE Loop x[1] = -0.35 y[1] (analytic) = 1.5685409870396948753452076644143 y[1] (numeric) = 1.5685409870396948753452076644142 absolute error = 1e-31 relative error = 6.3753514142292102057325953115232e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00507 Order of pole (three term test) = -25.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.34 y[1] (analytic) = 1.5690500569680208444016956610648 y[1] (numeric) = 1.5690500569680208444016956610646 absolute error = 2e-31 relative error = 1.2746565930883889203572923921582e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1754 Order of pole (three term test) = -76.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.33 y[1] (analytic) = 1.56949354812651009447265551655 y[1] (numeric) = 1.5694935481265100944726555165498 absolute error = 2e-31 relative error = 1.2742964138892966256989665232726e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008479 Order of pole (three term test) = -25.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.32 y[1] (analytic) = 1.5698717223732974145469202181775 y[1] (numeric) = 1.5698717223732974145469202181773 absolute error = 2e-31 relative error = 1.2739894422561125889531248344484e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04442 Order of pole (three term test) = -35.93 Radius of convergence (six term test) for eq 1 = 0.117 Order of pole (six term test) = -11.47 TOP MAIN SOLVE Loop bytes used=64015808, alloc=4521156, time=5.08 x[1] = -0.31 y[1] (analytic) = 1.570184841004287586294279942891 y[1] (numeric) = 1.5701848410042875862942799428908 absolute error = 2e-31 relative error = 1.2737353894722377781518523195586e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05637 Order of pole (three term test) = -34.81 Radius of convergence (six term test) for eq 1 = 0.2139 Order of pole (six term test) = -11.91 TOP MAIN SOLVE Loop x[1] = -0.3 y[1] (analytic) = 1.5704331647539898711781795796907 y[1] (numeric) = 1.5704331647539898711781795796904 absolute error = 3e-31 relative error = 1.9103009713055527504981899095441e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0145 Order of pole (three term test) = -31.09 Radius of convergence (six term test) for eq 1 = 0.3684 Order of pole (six term test) = -9.11 TOP MAIN SOLVE Loop x[1] = -0.29 y[1] (analytic) = 1.5706169537963515478641939224803 y[1] (numeric) = 1.57061695379635154786419392248 absolute error = 3e-31 relative error = 1.9100774334242824637027242397487e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2288 Order of pole (six term test) = -11.72 TOP MAIN SOLVE Loop x[1] = -0.28 y[1] (analytic) = 1.5707364677455905008019760596691 y[1] (numeric) = 1.5707364677455905008019760596689 absolute error = 2e-31 relative error = 1.2732880665020229092520183665427e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02492 Order of pole (three term test) = -6.186 Radius of convergence (six term test) for eq 1 = 0.27 Order of pole (six term test) = -12.23 TOP MAIN SOLVE Loop x[1] = -0.27 y[1] (analytic) = 1.5707919656570268608576911803111 y[1] (numeric) = 1.5707919656570268608576911803108 absolute error = 3e-31 relative error = 1.9098646196252777778274638202427e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=68017264, alloc=4521156, time=5.41 x[1] = -0.26 y[1] (analytic) = 1.5707837060279136988732651697435 y[1] (numeric) = 1.5707837060279136988732651697433 absolute error = 2e-31 relative error = 1.2732497748257511459028728294887e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2552 Order of pole (six term test) = -11.11 TOP MAIN SOLVE Loop x[1] = -0.25 y[1] (analytic) = 1.570711946798266773028094980324 y[1] (numeric) = 1.5707119467982667730280949803238 absolute error = 2e-31 relative error = 1.2733079442585207003103249086572e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.04706 Order of pole (six term test) = -10.78 TOP MAIN SOLVE Loop x[1] = -0.24 y[1] (analytic) = 1.5705769453516933308781858346734 y[1] (numeric) = 1.5705769453516933308781858346732 absolute error = 2e-31 relative error = 1.2734173934739297954554759146006e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.006351 Order of pole (three term test) = -28.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.23 y[1] (analytic) = 1.5703789585162199669469988495613 y[1] (numeric) = 1.5703789585162199669469988495611 absolute error = 2e-31 relative error = 1.2735779406326925819533074590839e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.003493 Order of pole (three term test) = -1.362 Radius of convergence (six term test) for eq 1 = 0.1622 Order of pole (six term test) = -11.51 TOP MAIN SOLVE Loop x[1] = -0.22 y[1] (analytic) = 1.5701182425651195367416116579275 y[1] (numeric) = 1.5701182425651195367416116579273 absolute error = 2e-31 relative error = 1.2737894164789639550299805095617e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5697950532177371280671140542581 y[1] (numeric) = 1.5697950532177371280671140542579 absolute error = 2e-31 relative error = 1.2740516641968240739695185718579e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0281 Order of pole (three term test) = -35.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=72018268, alloc=4521156, time=5.74 x[1] = -0.2 y[1] (analytic) = 1.5694096456403150905114805943555 y[1] (numeric) = 1.5694096456403150905114805943552 absolute error = 3e-31 relative error = 1.9115468089123459745491492039572e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.306 Order of pole (three term test) = -395.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.19 y[1] (analytic) = 1.568962274446817123972482444179 y[1] (numeric) = 1.5689622744468171239724824441788 absolute error = 2e-31 relative error = 1.2747279093789285985622442657866e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1534 Order of pole (three term test) = -67.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.18 y[1] (analytic) = 1.5684531936997514270975215936278 y[1] (numeric) = 1.5684531936997514270975215936275 absolute error = 3e-31 relative error = 1.9127124813482251692220806901610e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009612 Order of pole (three term test) = -2.975 Radius of convergence (six term test) for eq 1 = 0.2505 Order of pole (six term test) = -11.57 TOP MAIN SOLVE Loop x[1] = -0.17 y[1] (analytic) = 1.5678826569109929065065918296025 y[1] (numeric) = 1.5678826569109929065065918296023 absolute error = 2e-31 relative error = 1.2756056655032813164985290793400e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5672509170426044476678925981676 y[1] (numeric) = 1.5672509170426044476678925981673 absolute error = 3e-31 relative error = 1.9141797700530217192783032514190e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=76019360, alloc=4521156, time=6.06 x[1] = -0.15 y[1] (analytic) = 1.566558226507657248294944077844 y[1] (numeric) = 1.5665582265076572482949440778437 absolute error = 3e-31 relative error = 1.9150261696227709089419427009447e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6403 Order of pole (six term test) = -11.25 TOP MAIN SOLVE Loop x[1] = -0.14 y[1] (analytic) = 1.565804837171050215133374434752 y[1] (numeric) = 1.5658048371710502151333744347517 absolute error = 3e-31 relative error = 1.9159475873251991704019464467339e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6477 Order of pole (six term test) = -13.76 TOP MAIN SOLVE Loop x[1] = -0.13 y[1] (analytic) = 1.5649910003503284250048733351949 y[1] (numeric) = 1.5649910003503284250048733351946 absolute error = 3e-31 relative error = 1.9169439308778389472354255736208e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3805 Order of pole (six term test) = -8.505 TOP MAIN SOLVE Loop x[1] = -0.12 y[1] (analytic) = 1.5641169668165006509751293520824 y[1] (numeric) = 1.5641169668165006509751293520822 absolute error = 2e-31 relative error = 1.2786767501606140119747897574538e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.563182986794855954511892918049 y[1] (numeric) = 1.5631829867948559545118929180487 absolute error = 3e-31 relative error = 1.9191611125138892485685397812971e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01422 Order of pole (three term test) = -9.259 Radius of convergence (six term test) for eq 1 = 0.1622 Order of pole (six term test) = -11.53 TOP MAIN SOLVE Loop x[1] = -0.1 y[1] (analytic) = 1.5621893099657793444986309499634 y[1] (numeric) = 1.5621893099657793444986309499632 absolute error = 2e-31 relative error = 1.2802545678947266324092177617816e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1466 Order of pole (six term test) = -11.31 TOP MAIN SOLVE Loop bytes used=80021236, alloc=4521156, time=6.39 x[1] = -0.09 y[1] (analytic) = 1.5611361854655665039685641964877 y[1] (numeric) = 1.5611361854655665039685641964875 absolute error = 2e-31 relative error = 1.2811182128890019114218485816895e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03973 Order of pole (three term test) = -7.028 Radius of convergence (six term test) for eq 1 = 0.2391 Order of pole (six term test) = -12.32 TOP MAIN SOLVE Loop x[1] = -0.08 y[1] (analytic) = 1.5600238618872375854232037421401 y[1] (numeric) = 1.5600238618872375854232037421399 absolute error = 2e-31 relative error = 1.2820316719902615097932067036532e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3464 Order of pole (six term test) = -12.38 TOP MAIN SOLVE Loop x[1] = -0.07 y[1] (analytic) = 1.5588525872813500755988289376984 y[1] (numeric) = 1.5588525872813500755988289376982 absolute error = 2e-31 relative error = 1.2829949517471784349888726599973e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004372 Order of pole (three term test) = -25.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.06 y[1] (analytic) = 1.5576226091568107305436753174596 y[1] (numeric) = 1.5576226091568107305436753174594 absolute error = 2e-31 relative error = 1.2840080698897031460183569633661e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5563341744816865818679278085896 y[1] (numeric) = 1.5563341744816865818679278085893 absolute error = 3e-31 relative error = 1.9276065829493876897115498219068e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1508 Order of pole (six term test) = -11.5 TOP MAIN SOLVE Loop bytes used=84022516, alloc=4521156, time=6.71 x[1] = -0.04 y[1] (analytic) = 1.554987529684015015027941736282 y[1] (numeric) = 1.5549875296840150150279417362817 absolute error = 3e-31 relative error = 1.9292759219809449039209354474528e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04881 Order of pole (three term test) = -28.63 Radius of convergence (six term test) for eq 1 = 0.2734 Order of pole (six term test) = -11.94 TOP MAIN SOLVE Loop x[1] = -0.03 y[1] (analytic) = 1.5535829206526129205054417804259 y[1] (numeric) = 1.5535829206526129205054417804257 absolute error = 2e-31 relative error = 1.2873467990751731782377081453074e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5521205927378849187417771446912 y[1] (numeric) = 1.552120592737884918741777144691 absolute error = 2e-31 relative error = 1.2885596707869663081097942529655e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5506007907526306596866397571081 y[1] (numeric) = 1.5506007907526306596866397571079 absolute error = 2e-31 relative error = 1.2898226364435425950316558387711e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009135 Order of pole (three term test) = -0.2586 Radius of convergence (six term test) for eq 1 = 0.4389 Order of pole (six term test) = -13.54 TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 1.5490237589728511978199813320776 y[1] (numeric) = 1.5490237589728511978199813320774 absolute error = 2e-31 relative error = 1.2911357804648448842103164184123e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02636 Order of pole (three term test) = -23.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (analytic) = 1.5473897411385544435051945870289 y[1] (numeric) = 1.5473897411385544435051945870287 absolute error = 2e-31 relative error = 1.2924991983780500538020687139928e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005831 Order of pole (three term test) = -1.77 Radius of convergence (six term test) for eq 1 = 0.124 Order of pole (six term test) = -11.93 TOP MAIN SOLVE Loop bytes used=88023740, alloc=4521156, time=7.04 x[1] = 0.02 y[1] (analytic) = 1.5456989804545596915309538223722 y[1] (numeric) = 1.5456989804545596915309538223719 absolute error = 3e-31 relative error = 1.9408694952478774107351010858161e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05453 Order of pole (three term test) = -3.876 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.03 y[1] (analytic) = 1.5439517195913012276984404407148 y[1] (numeric) = 1.5439517195913012276984404407145 absolute error = 3e-31 relative error = 1.9430659404259925073000847482923e-29 % Correct digits = 31 h = 0.01 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) = -27.41 Radius of convergence (six term test) for eq 1 = 0.5088 Order of pole (six term test) = -11.39 TOP MAIN SOLVE Loop x[1] = 0.04 y[1] (analytic) = 1.5421482006856310143100098002425 y[1] (numeric) = 1.5421482006856310143100098002422 absolute error = 3e-31 relative error = 1.9453383265410002164497270515287e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.540288665341620455414687067451 y[1] (numeric) = 1.5402886653416204554146870674508 absolute error = 2e-31 relative error = 1.2984579092234118451519576989307e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09621 Order of pole (three term test) = -34.84 Radius of convergence (six term test) for eq 1 = 0.4976 Order of pole (six term test) = -11.66 TOP MAIN SOLVE Loop x[1] = 0.06 y[1] (analytic) = 1.5383733546313612426652114557752 y[1] (numeric) = 1.538373354631361242665211455775 absolute error = 2e-31 relative error = 1.3000745196079256425699650082855e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08825 Order of pole (three term test) = -24.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=92024720, alloc=4521156, time=7.36 x[1] = 0.07 y[1] (analytic) = 1.5364025090957652826406804088408 y[1] (numeric) = 1.5364025090957652826406804088406 absolute error = 2e-31 relative error = 1.3017422115361426353847075857892e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02657 Order of pole (three term test) = -14.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.08 y[1] (analytic) = 1.5343763687453637064881779097844 y[1] (numeric) = 1.5343763687453637064881779097842 absolute error = 2e-31 relative error = 1.3034611590345135967570237105680e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007031 Order of pole (three term test) = -25.4 Radius of convergence (six term test) for eq 1 = 0.3884 Order of pole (six term test) = -10.52 TOP MAIN SOLVE Loop x[1] = 0.09 y[1] (analytic) = 1.5322951730611049627361041710849 y[1] (numeric) = 1.5322951730611049627361041710847 absolute error = 2e-31 relative error = 1.3052315475252390388666209601929e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2228 Order of pole (six term test) = -11.49 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.5301591609951519941312574823598 y[1] (numeric) = 1.5301591609951519941312574823597 absolute error = 1e-31 relative error = 6.5352678694524922149486840812907e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05358 Order of pole (three term test) = -34.77 Radius of convergence (six term test) for eq 1 = 0.2694 Order of pole (six term test) = -11.29 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 1.5279685709716784993510529663306 y[1] (numeric) = 1.5279685709716784993510529663304 absolute error = 2e-31 relative error = 1.3089274465430550989564128401877e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.5257236408876642804415974153874 y[1] (numeric) = 1.5257236408876642804415974153873 absolute error = 1e-31 relative error = 6.5542669275164481058731924537738e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.002151 Order of pole (three term test) = -24.62 Radius of convergence (six term test) for eq 1 = 0.2895 Order of pole (six term test) = -11.11 TOP MAIN SOLVE Loop bytes used=96025540, alloc=4586680, time=7.69 x[1] = 0.13 y[1] (analytic) = 1.5234246081136896768316742526236 y[1] (numeric) = 1.5234246081136896768316742526235 absolute error = 1e-31 relative error = 6.5641581124136094994257069699212e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2902 Order of pole (six term test) = -12 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 1.5210717094947290867720279815834 y[1] (numeric) = 1.5210717094947290867720279815832 absolute error = 2e-31 relative error = 1.3148624009740880172633684557286e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04193 Order of pole (three term test) = -20.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 1.5186651813509435770486732580231 y[1] (numeric) = 1.5186651813509435770486732580229 absolute error = 2e-31 relative error = 1.3169459763480455197718525009254e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03934 Order of pole (three term test) = -31.14 Radius of convergence (six term test) for eq 1 = 0.1964 Order of pole (six term test) = -12.15 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 1.5162052594784725818182899344495 y[1] (numeric) = 1.5162052594784725818182899344493 absolute error = 2e-31 relative error = 1.3190826159565874023337811244913e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4963 Order of pole (six term test) = -11.3 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 1.5136921791502246914131020937992 y[1] (numeric) = 1.5136921791502246914131020937989 absolute error = 3e-31 relative error = 1.9819088988648783573183426497567e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2455 Order of pole (three term test) = -110.3 Radius of convergence (six term test) for eq 1 = 0.2558 Order of pole (six term test) = -11.49 TOP MAIN SOLVE Loop bytes used=100026576, alloc=4586680, time=8.02 x[1] = 0.18 y[1] (analytic) = 1.5111261751166675319619762021087 y[1] (numeric) = 1.5111261751166675319619762021084 absolute error = 3e-31 relative error = 1.9852743267903376394270303046812e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04251 Order of pole (three term test) = -13.32 Radius of convergence (six term test) for eq 1 = 0.4041 Order of pole (six term test) = -11.84 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 1.5085074816066167366738110711143 y[1] (numeric) = 1.508507481606616736673811071114 absolute error = 3e-31 relative error = 1.9887206636886468054827083446556e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01508 Order of pole (three term test) = -27.41 Radius of convergence (six term test) for eq 1 = 0.1422 Order of pole (six term test) = -11.52 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 1.5058363323280240096286303301544 y[1] (numeric) = 1.5058363323280240096286303301541 absolute error = 3e-31 relative error = 1.9922483842330978482644945863831e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3119 Order of pole (six term test) = -11.68 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 1.5031129604687642829211265622632 y[1] (numeric) = 1.5031129604687642829211265622628 absolute error = 4e-31 relative error = 2.6611439760006797841329009013255e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02748 Order of pole (three term test) = -22.39 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 1.500337598697421968000745161669 y[1] (numeric) = 1.5003375986974219680007451616687 absolute error = 3e-31 relative error = 1.9995499696898683765592480067719e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01895 Order of pole (three term test) = -6.309 Radius of convergence (six term test) for eq 1 = 0.1365 Order of pole (six term test) = -11.03 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 1.4975104791640763020517353187854 y[1] (numeric) = 1.4975104791640763020517353187851 absolute error = 3e-31 relative error = 2.0033248793521810554139403291142e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008239 Order of pole (three term test) = -0.9703 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=104027792, alloc=4586680, time=8.35 x[1] = 0.24 y[1] (analytic) = 1.494631833501085790255935333935 y[1] (numeric) = 1.4946318335010857902559353339347 absolute error = 3e-31 relative error = 2.0071832626317607599460766750048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4917018928238717447803997022225 y[1] (numeric) = 1.4917018928238717447803997022222 absolute error = 3e-31 relative error = 2.0111256910191613325159987966009e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04514 Order of pole (three term test) = -23.57 Radius of convergence (six term test) for eq 1 = 0.2738 Order of pole (six term test) = -11.69 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 1.4887208877317009213313160988903 y[1] (numeric) = 1.48872088773170092133131609889 absolute error = 3e-31 relative error = 2.0151527561160031415120325162015e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01046 Order of pole (three term test) = -1.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 1.4856890483084672541150015269043 y[1] (numeric) = 1.4856890483084672541150015269039 absolute error = 4e-31 relative error = 2.6923534265492526747126136024798e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4826066041234726900461084661439 y[1] (numeric) = 1.4826066041234726900461084661435 absolute error = 4e-31 relative error = 2.6979510200987049764522500722470e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01556 Order of pole (three term test) = 2.227 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=108028908, alloc=4586680, time=8.69 x[1] = 0.29 y[1] (analytic) = 1.4794737842322071230425138861616 y[1] (numeric) = 1.4794737842322071230425138861612 absolute error = 4e-31 relative error = 2.7036639936650543328298707079280e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6141 Order of pole (six term test) = -13.06 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 1.4762908171771274292457064517528 y[1] (numeric) = 1.4762908171771274292457064517524 absolute error = 4e-31 relative error = 2.7094932471696560221645254128607e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03104 Order of pole (three term test) = -6.386 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 1.4730579309884356040048301622881 y[1] (numeric) = 1.4730579309884356040048301622877 absolute error = 4e-31 relative error = 2.7154397093642900457660938684891e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4697753531848560014618860216289 y[1] (numeric) = 1.4697753531848560014618860216284 absolute error = 5e-31 relative error = 3.4018804228588407874729443023668e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.006491 Order of pole (three term test) = -1.402 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 1.4664433107744116775749371352182 y[1] (numeric) = 1.4664433107744116775749371352177 absolute error = 5e-31 relative error = 3.4096101521712135480917798533903e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.002633 Order of pole (three term test) = -0.8072 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 1.4630620302551998374155068743454 y[1] (numeric) = 1.463062030255199837415506874345 absolute error = 4e-31 relative error = 2.7339920777673969614661358334898e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02072 Order of pole (three term test) = 0.5737 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=112029980, alloc=4586680, time=9.02 x[1] = 0.35 y[1] (analytic) = 1.4596317376161663875757044343603 y[1] (numeric) = 1.4596317376161663875757044343599 absolute error = 4e-31 relative error = 2.7404172551993825271378496600933e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3039 Order of pole (six term test) = -12.03 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 1.4561526583378795945199572434966 y[1] (numeric) = 1.4561526583378795945199572434962 absolute error = 4e-31 relative error = 2.7469647341548558087122862464810e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04471 Order of pole (three term test) = -21.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 1.4526250173933028497155752516978 y[1] (numeric) = 1.4526250173933028497155752516974 absolute error = 4e-31 relative error = 2.7536356266105716262600539112686e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07426 Order of pole (three term test) = -39.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 1.4490490392485665423757181441449 y[1] (numeric) = 1.4490490392485665423757181441445 absolute error = 4e-31 relative error = 2.7604310769732681156902343294427e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07885 Order of pole (three term test) = -21.19 Radius of convergence (six term test) for eq 1 = 0.3487 Order of pole (six term test) = -11.5 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 1.4454249478637390406476829818173 y[1] (numeric) = 1.4454249478637390406476829818168 absolute error = 5e-31 relative error = 3.4591903283458150140650936511041e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5556 Order of pole (six term test) = -12.17 TOP MAIN SOLVE Loop bytes used=116030972, alloc=4586680, time=9.35 x[1] = 0.4 y[1] (analytic) = 1.4417529666935967820787766710982 y[1] (numeric) = 1.4417529666935967820787766710977 absolute error = 5e-31 relative error = 3.4680004935010523969749618046562e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00567 Order of pole (three term test) = -26.14 Radius of convergence (six term test) for eq 1 = 0.2857 Order of pole (six term test) = -11.53 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 1.4380333186883934741913850059127 y[1] (numeric) = 1.4380333186883934741913850059122 absolute error = 5e-31 relative error = 3.4769708983936601137863533136497e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.208 Order of pole (three term test) = -43.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 1.4342662262946284059981978088856 y[1] (numeric) = 1.4342662262946284059981978088852 absolute error = 4e-31 relative error = 2.7888825147433374689009271014549e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 1.4304519114558138712878979222795 y[1] (numeric) = 1.4304519114558138712878979222791 absolute error = 4e-31 relative error = 2.7963190988567241434471615978741e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4752 Order of pole (six term test) = -11.62 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 1.4265905956132417045109704647401 y[1] (numeric) = 1.4265905956132417045109704647396 absolute error = 5e-31 relative error = 3.5048597792351728036661274799030e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3389 Order of pole (six term test) = -12.02 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 1.4226824997067489300946378758921 y[1] (numeric) = 1.4226824997067489300946378758916 absolute error = 5e-31 relative error = 3.5144875972190754072350079842357e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=120031912, alloc=4586680, time=9.68 x[1] = 0.46 y[1] (analytic) = 1.4187278441754825260152758173194 y[1] (numeric) = 1.418727844175482526015275817319 absolute error = 4e-31 relative error = 2.8194272893295239910383074341479e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4147268489586633024560149851678 y[1] (numeric) = 1.4147268489586633024560149851673 absolute error = 5e-31 relative error = 3.5342511550412331723835257085370e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.4106797334963488963765843162729 y[1] (numeric) = 1.4106797334963488963765843162724 absolute error = 5e-31 relative error = 3.5443906092048078164270786246936e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01493 Order of pole (three term test) = -28.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 1.4065867167301958828218019360697 y[1] (numeric) = 1.4065867167301958828218019360694 absolute error = 3e-31 relative error = 2.1328226438636590157173401310940e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02078 Order of pole (three term test) = 1.101 Radius of convergence (six term test) for eq 1 = 0.9311 Order of pole (six term test) = -14.13 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 1.4024480171042210037944715023227 y[1] (numeric) = 1.4024480171042210037944715023223 absolute error = 4e-31 relative error = 2.8521556244624398637090281669615e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=124032820, alloc=4586680, time=10.01 x[1] = 0.51 y[1] (analytic) = 1.3982638525655615155177933436685 y[1] (numeric) = 1.3982638525655615155177933436681 absolute error = 4e-31 relative error = 2.8606904145170618297143149369672e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5265 Order of pole (six term test) = -11.43 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 1.3940344405652346549117519758292 y[1] (numeric) = 1.3940344405652346549117519758288 absolute error = 4e-31 relative error = 2.8693695676400454515461583144037e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05104 Order of pole (three term test) = 1.801 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 1.3897599980588962261072942008533 y[1] (numeric) = 1.3897599980588962261072942008529 absolute error = 4e-31 relative error = 2.8781948002438369133891278651191e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09651 Order of pole (three term test) = -17.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 1.3854407415075983078214650556406 y[1] (numeric) = 1.3854407415075983078214650556402 absolute error = 4e-31 relative error = 2.8871678738473582052966232789852e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09349 Order of pole (three term test) = -50.12 Radius of convergence (six term test) for eq 1 = 0.2055 Order of pole (six term test) = -11.62 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 1.3810768868785460824160223750185 y[1] (numeric) = 1.3810768868785460824160223750181 absolute error = 4e-31 relative error = 2.8962905961308480281313443203927e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2057 Order of pole (six term test) = -11.69 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 1.3766686496458537874614046715186 y[1] (numeric) = 1.3766686496458537874614046715182 absolute error = 4e-31 relative error = 2.9055648220281581751764667662185e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1621 Order of pole (six term test) = -11.5 TOP MAIN SOLVE Loop bytes used=128033772, alloc=4586680, time=10.34 x[1] = 0.57 y[1] (analytic) = 1.3722162447912997906272814084825 y[1] (numeric) = 1.3722162447912997906272814084821 absolute error = 4e-31 relative error = 2.9149924548578416921807586591469e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3343 Order of pole (three term test) = -53.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 1.3677198868050807887202695549477 y[1] (numeric) = 1.3677198868050807887202695549473 absolute error = 4e-31 relative error = 2.9245754474944297856463638392864e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3418 Order of pole (six term test) = -11.6 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 1.3631797896865651316887555596704 y[1] (numeric) = 1.3631797896865651316887555596699 absolute error = 5e-31 relative error = 3.6678947544766975377099068875229e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.1536 Order of pole (six term test) = -11.79 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 1.3585961669450452724141175673624 y[1] (numeric) = 1.358596166945045272414117567362 absolute error = 4e-31 relative error = 2.9442155787870690828221323533926e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02282 Order of pole (three term test) = -27.81 Radius of convergence (six term test) for eq 1 = 0.4046 Order of pole (six term test) = -11.22 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 1.3539692316004893431069988225092 y[1] (numeric) = 1.3539692316004893431069988225089 absolute error = 3e-31 relative error = 2.2157076615794167642950163718098e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1196 Order of pole (three term test) = -24.09 Radius of convergence (six term test) for eq 1 = 0.9457 Order of pole (six term test) = -10.1 TOP MAIN SOLVE Loop bytes used=132034748, alloc=4586680, time=10.67 x[1] = 0.62 y[1] (analytic) = 1.3492991961842918591266397647154 y[1] (numeric) = 1.3492991961842918591266397647151 absolute error = 3e-31 relative error = 2.2233764079040108078809376904785e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04838 Order of pole (three term test) = -31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 1.3445862727400235510406333141538 y[1] (numeric) = 1.3445862727400235510406333141534 absolute error = 4e-31 relative error = 2.9748927838216908986492442764567e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.242 Order of pole (six term test) = -11.27 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 1.3398306728241803257418252760985 y[1] (numeric) = 1.3398306728241803257418252760981 absolute error = 4e-31 relative error = 2.9854518792054114862881266797137e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0885 Order of pole (three term test) = -31.65 Radius of convergence (six term test) for eq 1 = 0.3428 Order of pole (six term test) = -11.33 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 1.335032607506931357438439659449 y[1] (numeric) = 1.3350326075069313574384396594486 absolute error = 4e-31 relative error = 2.9961814996187142905239507650237e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04943 Order of pole (three term test) = -20.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 1.3301922873728663093328670053409 y[1] (numeric) = 1.3301922873728663093328670053406 absolute error = 3e-31 relative error = 2.2553130314151864824231228419976e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4464 Order of pole (six term test) = -11.53 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 1.325309922521741686803912558129 y[1] (numeric) = 1.3253099225217416868039125581286 absolute error = 4e-31 relative error = 3.0181619650058721022164240488903e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6102 Order of pole (six term test) = -11.95 TOP MAIN SOLVE Loop bytes used=136035784, alloc=4586680, time=11.00 x[1] = 0.68 y[1] (analytic) = 1.3203857225692263229066602819605 y[1] (numeric) = 1.3203857225692263229066602819601 absolute error = 4e-31 relative error = 3.0294177918076394117667707534036e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.3154198966476459970034683315745 y[1] (numeric) = 1.3154198966476459970034683315742 absolute error = 3e-31 relative error = 2.2806405830149860039874964045415e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01996 Order of pole (three term test) = -0.365 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 1.310412653406727187338971625603 y[1] (numeric) = 1.3104126534067271873389716256026 absolute error = 4e-31 relative error = 3.0524735773888135735530929121177e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.379 Order of pole (six term test) = -5.191 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 1.3053642010143399583713276442537 y[1] (numeric) = 1.3053642010143399583713276442533 absolute error = 4e-31 relative error = 3.0642789168660971788776695610444e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3796 Order of pole (six term test) = -10.81 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 1.3002747471572399836713024805746 y[1] (numeric) = 1.3002747471572399836713024805742 absolute error = 4e-31 relative error = 3.0762729251991593861764157301539e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3359 Order of pole (six term test) = -12 TOP MAIN SOLVE Loop bytes used=140036736, alloc=4586680, time=11.32 x[1] = 0.73 y[1] (analytic) = 1.2951444990418097052001555152551 y[1] (numeric) = 1.2951444990418097052001555152546 absolute error = 5e-31 relative error = 3.8605730894885965749099229895524e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1395 Order of pole (three term test) = -44.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 1.2899736633947986297766428588745 y[1] (numeric) = 1.289973663394798629776642858874 absolute error = 5e-31 relative error = 3.8760481255420340400296063887692e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01657 Order of pole (three term test) = -28.08 Radius of convergence (six term test) for eq 1 = 1.174 Order of pole (six term test) = -7.282 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 1.284762446464062763542821912393 y[1] (numeric) = 1.2847624464640627635428219123925 absolute error = 5e-31 relative error = 3.8917700418167223104849129815707e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1265 Order of pole (three term test) = -23.51 Radius of convergence (six term test) for eq 1 = 0.6244 Order of pole (six term test) = -11.83 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 1.2795110540193031852377020362348 y[1] (numeric) = 1.2795110540193031852377020362343 absolute error = 5e-31 relative error = 3.9077427149172312805299703370023e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.274219691352803759087149390288 y[1] (numeric) = 1.2742196913528037590871493902875 absolute error = 5e-31 relative error = 3.9239701237795489300635115097695e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.2688885632801679881178175112751 y[1] (numeric) = 1.2688885632801679881178175112746 absolute error = 5e-31 relative error = 3.9404563526639732754909080274852e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05553 Order of pole (three term test) = -34.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=144037616, alloc=4586680, time=11.65 x[1] = 0.79 y[1] (analytic) = 1.263517874141055008702239129979 y[1] (numeric) = 1.2635178741410550087022391299785 absolute error = 5e-31 relative error = 3.9572055942611986591215703335480e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3062 Order of pole (three term test) = -131.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 1.2581078277999147271415790984816 y[1] (numeric) = 1.2581078277999147271415790984812 absolute error = 4e-31 relative error = 3.1793777223331501750206208223820e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.2526586276467220990919130966288 y[1] (numeric) = 1.2526586276467220990919130966284 absolute error = 4e-31 relative error = 3.1932083583813306445458136255238e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.944 Order of pole (six term test) = -5.444 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 1.2471704765977105526392620171209 y[1] (numeric) = 1.2471704765977105526392620171205 absolute error = 4e-31 relative error = 3.2072600138130489585819824813602e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02099 Order of pole (three term test) = -25.8 Radius of convergence (six term test) for eq 1 = 0.2277 Order of pole (six term test) = -11.05 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 1.2416435770961045558279775896833 y[1] (numeric) = 1.2416435770961045558279775896828 absolute error = 5e-31 relative error = 4.0269205206970555544571074920928e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08069 Order of pole (three term test) = -26.09 Radius of convergence (six term test) for eq 1 = 0.3648 Order of pole (six term test) = -11.28 TOP MAIN SOLVE Loop bytes used=148038716, alloc=4586680, time=11.98 x[1] = 0.84 y[1] (analytic) = 1.2360781311128513294464408964378 y[1] (numeric) = 1.2360781311128513294464408964374 absolute error = 4e-31 relative error = 3.2360413952140444643190436166266e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09922 Order of pole (three term test) = -25.94 Radius of convergence (six term test) for eq 1 = 0.4291 Order of pole (six term test) = -11.86 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 1.2304743401473517058734019526235 y[1] (numeric) = 1.2304743401473517058734019526232 absolute error = 3e-31 relative error = 2.4380841616256249112204494489637e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2031 Order of pole (three term test) = -46.91 Radius of convergence (six term test) for eq 1 = 0.4579 Order of pole (six term test) = -11.63 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 1.2248324052281901347876554789341 y[1] (numeric) = 1.2248324052281901347876554789339 absolute error = 2e-31 relative error = 1.6328764584142380694629527690598e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.2191525269138638365431153737114 y[1] (numeric) = 1.2191525269138638365431153737112 absolute error = 2e-31 relative error = 1.6404838244995943668789789523262e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04949 Order of pole (three term test) = -11.48 Radius of convergence (six term test) for eq 1 = 0.5057 Order of pole (six term test) = -11.74 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 1.2134349052935111040107182047827 y[1] (numeric) = 1.2134349052935111040107182047825 absolute error = 2e-31 relative error = 1.6482136711867794718863880673918e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.2076797399876387536879542816159 y[1] (numeric) = 1.2076797399876387536879542816157 absolute error = 2e-31 relative error = 1.6560681890883348484382659350972e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9454 Order of pole (three term test) = -234.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=152039588, alloc=4586680, time=12.31 x[1] = 0.9 y[1] (analytic) = 1.2018872301488487268761935384199 y[1] (numeric) = 1.2018872301488487268761935384196 absolute error = 3e-31 relative error = 2.4960744442125926379888013397432e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5316 Order of pole (six term test) = -11.4 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 1.1960575744625638417253425575932 y[1] (numeric) = 1.196057574462563841725342557593 absolute error = 2e-31 relative error = 1.6721603062450228710835260346599e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1901909711477526969447385902606 y[1] (numeric) = 1.1901909711477526969447385902602 absolute error = 4e-31 relative error = 3.3608051959448379720511756086821e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1842876179576537279785563862737 y[1] (numeric) = 1.1842876179576537279785563862734 absolute error = 3e-31 relative error = 2.5331684250601277832525038463038e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06656 Order of pole (three term test) = -36.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 1.1783477121804984164433740297515 y[1] (numeric) = 1.1783477121804984164433740297512 absolute error = 3e-31 relative error = 2.5459378152893313853839539636477e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08047 Order of pole (three term test) = -37.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=156040720, alloc=4586680, time=12.64 x[1] = 0.95 y[1] (analytic) = 1.1723714506402336536249147877116 y[1] (numeric) = 1.1723714506402336536249147877113 absolute error = 3e-31 relative error = 2.5589159462742767186950549342695e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1663590296972432588303532183775 y[1] (numeric) = 1.1663590296972432588303532183772 absolute error = 3e-31 relative error = 2.5721068072656175816703739518532e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4415 Order of pole (six term test) = -11.44 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 1.1603106452490686533919454520502 y[1] (numeric) = 1.1603106452490686533919454520499 absolute error = 3e-31 relative error = 2.5855145018996437671107543234825e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1542264927311286911171156507711 y[1] (numeric) = 1.1542264927311286911171156507707 absolute error = 4e-31 relative error = 3.4655243361597142478939367622060e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 1.1481067671174386459795031731133 y[1] (numeric) = 1.1481067671174386459795031731129 absolute error = 4e-31 relative error = 3.4839965363524803300575666802736e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7517 Order of pole (six term test) = -11.35 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 1.1419516629213283578448479170698 y[1] (numeric) = 1.1419516629213283578448479170694 absolute error = 4e-31 relative error = 3.5027752311050043801472383705838e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3211 Order of pole (three term test) = -76.93 Radius of convergence (six term test) for eq 1 = 0.4715 Order of pole (six term test) = -11.62 TOP MAIN SOLVE Loop bytes used=160041736, alloc=4586680, time=12.96 x[1] = 1.01 y[1] (analytic) = 1.1357613741961595370249646868967 y[1] (numeric) = 1.1357613741961595370249646868964 absolute error = 3e-31 relative error = 2.6413999174107009340000119990293e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 1.1295360945360422284524312286767 y[1] (numeric) = 1.1295360945360422284524312286764 absolute error = 3e-31 relative error = 2.6559576223478296014872178657997e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03537 Order of pole (three term test) = -34.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = 1.1232760170765504362679888040208 y[1] (numeric) = 1.1232760170765504362679888040204 absolute error = 4e-31 relative error = 3.5610125554095249015964837557844e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1818 Order of pole (three term test) = -122.8 Radius of convergence (six term test) for eq 1 = 0.8903 Order of pole (six term test) = -10.48 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = 1.1169813344954369096120288214886 y[1] (numeric) = 1.1169813344954369096120288214884 absolute error = 2e-31 relative error = 1.7905402160578095110945376570194e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2259 Order of pole (three term test) = 27.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 1.1106522390133470904109141207111 y[1] (numeric) = 1.1106522390133470904109141207108 absolute error = 3e-31 relative error = 2.7011155198904235648380115656951e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9485 Order of pole (six term test) = -9.871 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 1.1042889223945322239482590045896 y[1] (numeric) = 1.1042889223945322239482590045893 absolute error = 3e-31 relative error = 2.7166803353372606463065546463095e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3734 Order of pole (six term test) = -11.27 bytes used=164042980, alloc=4586680, time=13.30 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = 1.0978915759475616330106680400931 y[1] (numeric) = 1.0978915759475616330106680400929 absolute error = 2e-31 relative error = 1.8216735093115657388157463333363e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04483 Order of pole (three term test) = -26.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 1.0914603905260341563968099977819 y[1] (numeric) = 1.0914603905260341563968099977816 absolute error = 3e-31 relative error = 2.7486109675076131241410537992569e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 1.0849955565292887525780800740422 y[1] (numeric) = 1.0849955565292887525780800740419 absolute error = 3e-31 relative error = 2.7649882821607822338786713677648e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07332 Order of pole (three term test) = 2.501 Radius of convergence (six term test) for eq 1 = 0.4233 Order of pole (six term test) = -12.24 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 1.078497263903114269298480737846 y[1] (numeric) = 1.0784972639031142692984807378457 absolute error = 3e-31 relative error = 2.7816482251822402591198094509418e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9232 Order of pole (six term test) = -9.981 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 1.0719657021404583799007291653952 y[1] (numeric) = 1.0719657021404583799007291653949 absolute error = 3e-31 relative error = 2.7985970017601492245670107749831e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03703 Order of pole (three term test) = -2.321 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=168043924, alloc=4586680, time=13.63 x[1] = 1.12 y[1] (analytic) = 1.0654010602821356871649772710374 y[1] (numeric) = 1.0654010602821356871649772710371 absolute error = 3e-31 relative error = 2.8158410122152035038066682623145e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5675 Order of pole (three term test) = -92.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 1.0588035269175349954459088110772 y[1] (numeric) = 1.058803526917534995445908811077 absolute error = 2e-31 relative error = 1.8889245730249349400937875931230e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01143 Order of pole (three term test) = 1.072 Radius of convergence (six term test) for eq 1 = 0.1408 Order of pole (six term test) = -11.62 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = 1.052173290185325751893356928312 y[1] (numeric) = 1.0521732901853257518933569283118 absolute error = 2e-31 relative error = 1.9008275715188775615931481445208e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009298 Order of pole (three term test) = -0.5089 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = 1.0455105377741636575409648190359 y[1] (numeric) = 1.0455105377741636575409648190357 absolute error = 2e-31 relative error = 1.9129410252123270367972024601248e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5813 Order of pole (six term test) = -11.78 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 1.0388154569233954490467919406335 y[1] (numeric) = 1.0388154569233954490467919406333 absolute error = 2e-31 relative error = 1.9252697740205885543563215790625e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3567 Order of pole (three term test) = -149.1 Radius of convergence (six term test) for eq 1 = 2.254 Order of pole (six term test) = -10.09 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 1.0320882344237628518691483364618 y[1] (numeric) = 1.0320882344237628518691483364617 absolute error = 1e-31 relative error = 9.6890940778752467219107057732310e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1109 Order of pole (three term test) = -14.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=172044940, alloc=4586680, time=13.96 x[1] = 1.18 y[1] (analytic) = 1.0253290566181057056603202352588 y[1] (numeric) = 1.0253290566181057056603202352587 absolute error = 1e-31 relative error = 9.7529665578614361665681232133079e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 1.0185381094020642626602310845493 y[1] (numeric) = 1.0185381094020642626602310845492 absolute error = 1e-31 relative error = 9.8179929721731559627288028783214e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0984 Order of pole (three term test) = -26.8 Radius of convergence (six term test) for eq 1 = 0.9004 Order of pole (six term test) = -10.98 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 1.011715578224780659871463601209 y[1] (numeric) = 1.0117155782247806598714636012088 absolute error = 2e-31 relative error = 1.9768401743000981656925765091271e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6297 Order of pole (three term test) = -161.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 1.0048616480895995657964502672288 y[1] (numeric) = 1.0048616480895995657964502672286 absolute error = 2e-31 relative error = 1.9903237463608202674003399633547e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 0.9979765035547680025170219645519 y[1] (numeric) = 0.99797650355476800251702196455176 absolute error = 1.4e-31 relative error = 1.4028386389992490738919620862976e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=176045976, alloc=4586680, time=14.29 x[1] = 1.23 y[1] (analytic) = 0.99106032873413434389588712937858 y[1] (numeric) = 0.99106032873413434389588712937846 absolute error = 1.2e-31 relative error = 1.2108243718449925121030843579620e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005339 Order of pole (three term test) = -1.643 Radius of convergence (six term test) for eq 1 = 0.1755 Order of pole (six term test) = -12.01 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 0.98411330729784649067899691329815 y[1] (numeric) = 0.98411330729784649067899691329806 absolute error = 9e-32 relative error = 9.1452883862651680899418352135496e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07664 Order of pole (three term test) = -38.81 Radius of convergence (six term test) for eq 1 = 0.3456 Order of pole (six term test) = -12.19 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 0.97713562247304922327713536576483 y[1] (numeric) = 0.97713562247304922327713536576471 absolute error = 1.2e-31 relative error = 1.2280792680169611666678380211140e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.629 Order of pole (six term test) = -8.816 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = 0.97012745704458073300445759952675 y[1] (numeric) = 0.97012745704458073300445759952656 absolute error = 1.9e-31 relative error = 1.9585055408989299303930885355976e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1071 Order of pole (three term test) = -46.46 Radius of convergence (six term test) for eq 1 = 0.3996 Order of pole (six term test) = -12.49 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 0.96308899335566833255108326740178 y[1] (numeric) = 0.96308899335566833255108326740171 absolute error = 7e-32 relative error = 7.2682795134124257870626537932003e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06764 Order of pole (three term test) = -49.74 Radius of convergence (six term test) for eq 1 = 0.6447 Order of pole (six term test) = -11.62 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 0.95602041330862334646623746501355 y[1] (numeric) = 0.95602041330862334646623746501344 absolute error = 1.1e-31 relative error = 1.1506030464277304477987398731526e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3855 Order of pole (three term test) = -69.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=180046984, alloc=4586680, time=14.63 x[1] = 1.29 y[1] (analytic) = 0.94892189836553518242781637950302 y[1] (numeric) = 0.94892189836553518242781637950287 absolute error = 1.5e-31 relative error = 1.5807412628833479128972093463819e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8208 Order of pole (six term test) = -10.01 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0.94179362954896458407364062857779 y[1] (numeric) = 0.94179362954896458407364062857763 absolute error = 1.6e-31 relative error = 1.6988859871204031692296694059692e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.272 Order of pole (six term test) = -10.65 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 0.93463578744263606616904527728 y[1] (numeric) = 0.93463578744263606616904527727978 absolute error = 2.2e-31 relative error = 2.3538580798619660807078393192556e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08532 Order of pole (three term test) = 7.005 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 0.92744855219212953288484198131523 y[1] (numeric) = 0.92744855219212953288484198131508 absolute error = 1.5e-31 relative error = 1.6173403866495671093540388115168e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 0.92023210350557107995907558542752 y[1] (numeric) = 0.92023210350557107995907558542735 absolute error = 1.7e-31 relative error = 1.8473600231115042919148126504368e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4113 Order of pole (three term test) = -72.06 Radius of convergence (six term test) for eq 1 = 0.6806 Order of pole (six term test) = -12.43 TOP MAIN SOLVE Loop bytes used=184048020, alloc=4586680, time=14.96 x[1] = 1.34 y[1] (analytic) = 0.91298662065432298151538480287687 y[1] (numeric) = 0.91298662065432298151538480287678 absolute error = 9e-32 relative error = 9.8577567254488825130328313291163e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05499 Order of pole (three term test) = -6.814 Radius of convergence (six term test) for eq 1 = 0.6167 Order of pole (six term test) = -6.314 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 0.9057122824736728623101643173389 y[1] (numeric) = 0.90571228247367286231016431733873 absolute error = 1.7e-31 relative error = 1.8769757602899852462601868891452e-29 % Correct digits = 31 h = 0.01 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) = -43.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 0.89840926736352205618011378123045 y[1] (numeric) = 0.89840926736352205618011378123025 absolute error = 2.0e-31 relative error = 2.2261569116146960471081760047973e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.393 Order of pole (six term test) = -11.27 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 0.89107775328907315146114773434518 y[1] (numeric) = 0.89107775328907315146114773434502 absolute error = 1.6e-31 relative error = 1.7955784375653091659637836147205e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05318 Order of pole (three term test) = -29.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 0.88371791778151672414902943348432 y[1] (numeric) = 0.88371791778151672414902943348418 absolute error = 1.4e-31 relative error = 1.5842159266325124860781109272545e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.043 Order of pole (six term test) = -10.5 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 0.87632993793871725957148096726067 y[1] (numeric) = 0.87632993793871725957148096726056 absolute error = 1.1e-31 relative error = 1.2552349889898708903940940150239e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02494 Order of pole (three term test) = 1.108 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=188048888, alloc=4586680, time=15.29 x[1] = 1.4 y[1] (analytic) = 0.86891399042589826334091183017841 y[1] (numeric) = 0.86891399042589826334091183017826 absolute error = 1.5e-31 relative error = 1.7262928397145209706518069197060e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2198 Order of pole (three term test) = -38.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 0.86147025147632656235629834619829 y[1] (numeric) = 0.86147025147632656235629834619816 absolute error = 1.3e-31 relative error = 1.5090480463743841244263717725148e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03732 Order of pole (three term test) = -1.676 Radius of convergence (six term test) for eq 1 = 0.8305 Order of pole (six term test) = -12.24 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 0.85399889689199579662213696404437 y[1] (numeric) = 0.85399889689199579662213696404436 absolute error = 1e-32 relative error = 1.1709616998796531063686962497027e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5966 Order of pole (six term test) = -12.09 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 0.84650010204430910265178549423719 y[1] (numeric) = 0.84650010204430910265178549423705 absolute error = 1.4e-31 relative error = 1.6538686724537672450506967886651e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02169 Order of pole (three term test) = -27 Radius of convergence (six term test) for eq 1 = 0.5184 Order of pole (six term test) = -11.12 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 0.8389740418747609892218978210054 y[1] (numeric) = 0.83897404187476098922189782100522 absolute error = 1.8e-31 relative error = 2.1454775835230161867237075282033e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0147 Order of pole (three term test) = -29.4 Radius of convergence (six term test) for eq 1 = 0.5635 Order of pole (six term test) = -11.45 TOP MAIN SOLVE Loop bytes used=192049872, alloc=4586680, time=15.62 x[1] = 1.45 y[1] (analytic) = 0.83142089089561840624404950058915 y[1] (numeric) = 0.83142089089561840624404950058905 absolute error = 1.0e-31 relative error = 1.2027602516972911040053134918917e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1062 Order of pole (three term test) = -23.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 0.82384082319060100751904395073818 y[1] (numeric) = 0.82384082319060100751904395073804 absolute error = 1.4e-31 relative error = 1.6993574008362787422415233367840e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3733 Order of pole (three term test) = 79.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = 0.81623401241556060813878164419837 y[1] (numeric) = 0.81623401241556060813878164419822 absolute error = 1.5e-31 relative error = 1.8377082762832980686009939245553e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07827 Order of pole (three term test) = -37.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = 0.80860063179915983729996784141234 y[1] (numeric) = 0.80860063179915983729996784141228 absolute error = 6e-32 relative error = 7.4202267028283494320434427685618e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 0.80094085414354998729332793428085 y[1] (numeric) = 0.80094085414354998729332793428079 absolute error = 6e-32 relative error = 7.4911898537324951983093537737109e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02839 Order of pole (three term test) = -4.239 Radius of convergence (six term test) for eq 1 = 1.342 Order of pole (six term test) = -9.226 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 0.7932548518250480594313934234041 y[1] (numeric) = 0.79325485182504805943139342340404 absolute error = 6e-32 relative error = 7.5637734659873178385498442660554e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=196052084, alloc=4652204, time=15.95 x[1] = 1.51 y[1] (analytic) = 0.78554279679481300767731591549317 y[1] (numeric) = 0.78554279679481300767731591549299 absolute error = 1.8e-31 relative error = 2.2914092107322414467134933493185e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.11 Order of pole (six term test) = -19.4 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = 0.77780486057952118073656130535769 y[1] (numeric) = 0.77780486057952118073656130535766 absolute error = 3e-32 relative error = 3.8570085532311817248357762887789e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (analytic) = 0.77004121428204096337273149780351 y[1] (numeric) = 0.77004121428204096337273149780339 absolute error = 1.2e-31 relative error = 1.5583581472568806776463323156092e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = 0.76225202858210661770815662864271 y[1] (numeric) = 0.76225202858210661770815662864263 absolute error = 8e-32 relative error = 1.0495216411402797963619429008969e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2528 Order of pole (three term test) = -92.18 Radius of convergence (six term test) for eq 1 = 0.4904 Order of pole (six term test) = -11.89 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 0.75443747373699132526929676061439 y[1] (numeric) = 0.7544374737369913252692967606144 absolute error = 1e-32 relative error = 1.3254908919710099168071190657738e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=200053164, alloc=4652204, time=16.28 x[1] = 1.56 y[1] (analytic) = 0.74659771958217943053638845904851 y[1] (numeric) = 0.7465977195821794305363884590483 absolute error = 2.1e-31 relative error = 2.8127597297983027219379145320353e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.73873293553203788675616849336738 y[1] (numeric) = 0.73873293553203788675616849336736 absolute error = 2e-32 relative error = 2.7073383408302940093102779237895e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.537 Order of pole (six term test) = -9.985 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 0.73084329058048690477590416374714 y[1] (numeric) = 0.73084329058048690477590416374711 absolute error = 3e-32 relative error = 4.1048471521400846166023051394772e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1103 Order of pole (three term test) = -45.83 Radius of convergence (six term test) for eq 1 = 0.5605 Order of pole (six term test) = -11.18 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (analytic) = 0.72292895330166980565635741719035 y[1] (numeric) = 0.72292895330166980565635741719014 absolute error = 2.1e-31 relative error = 2.9048497648477699522672979661850e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.71499009185062207782070799368926 y[1] (numeric) = 0.71499009185062207782070799368913 absolute error = 1.3e-31 relative error = 1.8182070140792943825226877710776e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05913 Order of pole (three term test) = -32.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = 0.70702687396393963949585933079012 y[1] (numeric) = 0.70702687396393963949585933079012 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 = 0.01143 Order of pole (three term test) = -24.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=204053976, alloc=4652204, time=16.61 x[1] = 1.62 y[1] (analytic) = 0.69903946696044630720194985348533 y[1] (numeric) = 0.69903946696044630720194985348524 absolute error = 9e-32 relative error = 1.2874809542776854774479278693488e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04814 Order of pole (three term test) = 2.583 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 0.69102803774186047104529158571374 y[1] (numeric) = 0.69102803774186047104529158571366 absolute error = 8e-32 relative error = 1.1576954281250841988110889452117e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6997 Order of pole (six term test) = -10.83 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = 0.68299275279346097756935773958471 y[1] (numeric) = 0.68299275279346097756935773958464 absolute error = 7e-32 relative error = 1.0249010654022006352625153950378e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4685 Order of pole (six term test) = -11.97 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = 0.67493377818475222091784106851159 y[1] (numeric) = 0.67493377818475222091784106851161 absolute error = 2e-32 relative error = 2.9632536770926470093102591734562e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.6668512795701284430632053105147 y[1] (numeric) = 0.66685127957012844306320531051454 absolute error = 1.6e-31 relative error = 2.3993355775389770869608641350315e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007384 Order of pole (three term test) = -26.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=208055036, alloc=4652204, time=16.94 x[1] = 1.67 y[1] (analytic) = 0.65874542218953724385355299776381 y[1] (numeric) = 0.65874542218953724385355299776374 absolute error = 7e-32 relative error = 1.0626259802661562943706844292878e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.65061637086914230163003426775646 y[1] (numeric) = 0.65061637086914230163003426775628 absolute error = 1.8e-31 relative error = 2.7666072982384758703543847690027e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1231 Order of pole (three term test) = -22.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 0.6424642900219853051664230800898 y[1] (numeric) = 0.64246429002198530516642308008984 absolute error = 4e-32 relative error = 6.2260269747648058337770241745515e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03164 Order of pole (three term test) = -28.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 0.6342893436486470976818894203837 y[1] (numeric) = 0.63428934364864709768188942038364 absolute error = 6e-32 relative error = 9.4594053330392848566706586950238e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.62609169533790803367739865924558 y[1] (numeric) = 0.62609169533790803367739865924561 absolute error = 3e-32 relative error = 4.7916303990917330307888263827871e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05504 Order of pole (three term test) = -19.29 Radius of convergence (six term test) for eq 1 = 0.407 Order of pole (six term test) = -11.47 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 0.6178715082674075493455722290549 y[1] (numeric) = 0.61787150826740754934557222905483 absolute error = 7e-32 relative error = 1.1329216360257353082378768065729e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009527 Order of pole (three term test) = -27.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=212055908, alloc=4652204, time=17.27 x[1] = 1.73 y[1] (analytic) = 0.6096289452043029473032471844726 y[1] (numeric) = 0.6096289452043029473032471844725 absolute error = 1.0e-31 relative error = 1.6403420603082966844586655042344e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7098 Order of pole (six term test) = -10.73 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = 0.60136416850592739639537602376926 y[1] (numeric) = 0.60136416850592739639537602376925 absolute error = 1e-32 relative error = 1.6628859056974948717395141481739e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05416 Order of pole (three term test) = -0.1739 Radius of convergence (six term test) for eq 1 = 0.4421 Order of pole (six term test) = -12.45 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 0.59307734012044714731831236701554 y[1] (numeric) = 0.59307734012044714731831236701547 absolute error = 7e-32 relative error = 1.1802845137496537926990647983756e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04427 Order of pole (three term test) = -16.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (analytic) = 0.58476862158751796480993271368091 y[1] (numeric) = 0.58476862158751796480993271368083 absolute error = 8e-32 relative error = 1.3680624617445721779639788911071e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.57643817403894077715344953598403 y[1] (numeric) = 0.57643817403894077715344953598394 absolute error = 9e-32 relative error = 1.5613122803681653575275518619014e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07294 Order of pole (three term test) = -20.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 0.56808615819931654374117640517919 y[1] (numeric) = 0.56808615819931654374117640517908 absolute error = 1.1e-31 relative error = 1.9363260028843339526483012487479e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 bytes used=216057272, alloc=4652204, time=17.60 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5545 Order of pole (six term test) = -11.52 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = 0.55971273438670034144391169561953 y[1] (numeric) = 0.55971273438670034144391169561942 absolute error = 1.1e-31 relative error = 1.9652938595462082045034520377371e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2666 Order of pole (three term test) = -46.73 Radius of convergence (six term test) for eq 1 = 1.137 Order of pole (six term test) = -13.64 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0.55131806251325467053101366565145 y[1] (numeric) = 0.55131806251325467053101366565138 absolute error = 7e-32 relative error = 1.2696845026425571722296672526613e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.54290230208590198088564637492838 y[1] (numeric) = 0.54290230208590198088564637492823 absolute error = 1.5e-31 relative error = 2.7629280521316688159435529791654e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.002078 Order of pole (three term test) = -0.9762 Radius of convergence (six term test) for eq 1 = 0.2453 Order of pole (six term test) = -11.79 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = 0.53446561220697641925908296433907 y[1] (numeric) = 0.53446561220697641925908296433885 absolute error = 2.2e-31 relative error = 4.1162610835063996974239987277911e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1638 Order of pole (three term test) = -81.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = 0.52600815157487479830736029718629 y[1] (numeric) = 0.52600815157487479830736029718619 absolute error = 1.0e-31 relative error = 1.9011112223375015143042329373672e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=220058036, alloc=4652204, time=17.93 x[1] = 1.84 y[1] (analytic) = 0.51753007848470678815298683827532 y[1] (numeric) = 0.51753007848470678815298683827532 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] = 1.85 y[1] (analytic) = 0.5090315508289443312138139309396 y[1] (numeric) = 0.5090315508289443312138139309396 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] = 1.86 y[1] (analytic) = 0.50051272609807028104058932050237 y[1] (numeric) = 0.50051272609807028104058932050225 absolute error = 1.2e-31 relative error = 2.3975414358692498811265881921661e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.022 Order of pole (six term test) = -12.95 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = 0.49197376138122626590412086599556 y[1] (numeric) = 0.49197376138122626590412086599562 absolute error = 6e-32 relative error = 1.2195772358173897091387096811855e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7843 Order of pole (six term test) = -11.7 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = 0.4834148133668597778723878798992 y[1] (numeric) = 0.48341481336685977787238787989908 absolute error = 1.2e-31 relative error = 2.4823401493270526739406458691012e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01863 Order of pole (three term test) = -23.6 Radius of convergence (six term test) for eq 1 = 0.1426 Order of pole (six term test) = -11.84 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 0.4748360383433704881173474379656 y[1] (numeric) = 0.47483603834337048811734743796539 absolute error = 2.1e-31 relative error = 4.4225792282459757438620056533270e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3611 Order of pole (six term test) = -11.18 TOP MAIN SOLVE Loop bytes used=224060616, alloc=4652204, time=18.25 x[1] = 1.9 y[1] (analytic) = 0.4662375921997557891905933076416 y[1] (numeric) = 0.46623759219975578919059330764162 absolute error = 2e-32 relative error = 4.2896583919022898148622616975946e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4813 Order of pole (six term test) = -12.12 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 0.45761963042625556500643585391184 y[1] (numeric) = 0.45761963042625556500643585391175 absolute error = 9e-32 relative error = 1.9666988480404209743603521296969e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1599 Order of pole (three term test) = -35.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (analytic) = 0.44898230811499618927038239535099 y[1] (numeric) = 0.44898230811499618927038239535096 absolute error = 3e-32 relative error = 6.6817777577810950633350432510092e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8479 Order of pole (six term test) = -11.76 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (analytic) = 0.44032577996063375309040900054392 y[1] (numeric) = 0.44032577996063375309040900054393 absolute error = 1e-32 relative error = 2.2710457699964843042455152455477e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07316 Order of pole (three term test) = -20.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = 0.43165020026099652250782663553908 y[1] (numeric) = 0.43165020026099652250782663553902 absolute error = 6e-32 relative error = 1.3900144136090081084458968692982e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02511 Order of pole (three term test) = -18.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=228061404, alloc=4652204, time=18.59 x[1] = 1.95 y[1] (analytic) = 0.42295572291772662668395689644434 y[1] (numeric) = 0.42295572291772662668395689644425 absolute error = 9e-32 relative error = 2.1278823083215924602234213276199e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05966 Order of pole (three term test) = -30.64 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 0.41424250143692097747824528737794 y[1] (numeric) = 0.41424250143692097747824528737784 absolute error = 1.0e-31 relative error = 2.4140449049317929365746642990835e-29 % Correct digits = 31 h = 0.01 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) = -23.66 Radius of convergence (six term test) for eq 1 = 0.5394 Order of pole (six term test) = -11.59 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = 0.4055106889297714211528531325236 y[1] (numeric) = 0.40551068892977142115285313252354 absolute error = 6e-32 relative error = 1.4796157447378934837222135106302e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5188 Order of pole (six term test) = -12.29 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 0.39676043811320412293818274176717 y[1] (numeric) = 0.3967604381132041229381827417672 absolute error = 3e-32 relative error = 7.5612377440314165417365528569349e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.38799190131051818519320438206401 y[1] (numeric) = 0.38799190131051818519320438206402 absolute error = 1e-32 relative error = 2.5773733849142348307707731958681e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0688 Order of pole (three term test) = -32.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0.37920523045202349989386794106468 y[1] (numeric) = 0.37920523045202349989386794106468 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 = 0.153 Order of pole (three term test) = -29.23 Radius of convergence (six term test) for eq 1 = 0.683 Order of pole (six term test) = -11.21 TOP MAIN SOLVE Loop bytes used=232062464, alloc=4652204, time=18.92 x[1] = 2.01 y[1] (analytic) = 0.37040057707567783618229690537076 y[1] (numeric) = 0.37040057707567783618229690537076 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 0.36157809232772316370887741285511 y[1] (numeric) = 0.36157809232772316370887741285489 absolute error = 2.2e-31 relative error = 6.0844394245157648058020952678573e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.309 Order of pole (three term test) = -311.8 Radius of convergence (six term test) for eq 1 = 0.6927 Order of pole (six term test) = -11.48 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = 0.35273792696332121249877067652739 y[1] (numeric) = 0.35273792696332121249877067652724 absolute error = 1.5e-31 relative error = 4.2524488730580272094606302157033e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5828 Order of pole (six term test) = -11.23 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = 0.34388023134718827007379301621636 y[1] (numeric) = 0.34388023134718827007379301621626 absolute error = 1.0e-31 relative error = 2.9079892033409162712200218486568e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = 0.33500515545422921656002407361727 y[1] (numeric) = 0.33500515545422921656002407361728 absolute error = 1e-32 relative error = 2.9850286890185697505995074208792e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5354 Order of pole (six term test) = -11.86 TOP MAIN SOLVE Loop bytes used=236063688, alloc=4652204, time=19.25 x[1] = 2.06 y[1] (analytic) = 0.32611284887017079851092052580639 y[1] (numeric) = 0.32611284887017079851092052580631 absolute error = 8e-32 relative error = 2.4531385462781597379052510527128e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1064 Order of pole (three term test) = -16.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = 0.31720346079219414217512975187826 y[1] (numeric) = 0.31720346079219414217512975187809 absolute error = 1.7e-31 relative error = 5.3593362309300322005008711271210e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.478 Order of pole (six term test) = -5.972 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 0.30827714002956650693761544670587 y[1] (numeric) = 0.30827714002956650693761544670586 absolute error = 1e-32 relative error = 3.2438344273730161986665631018336e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06195 Order of pole (three term test) = -75.45 Radius of convergence (six term test) for eq 1 = 0.3818 Order of pole (six term test) = -12.01 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = 0.29933403500427227966212511469582 y[1] (numeric) = 0.29933403500427227966212511469567 absolute error = 1.5e-31 relative error = 5.0111241108235188704049102902376e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3191 Order of pole (three term test) = -77.69 Radius of convergence (six term test) for eq 1 = 0.8767 Order of pole (six term test) = -11.07 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 0.2903742937516432106624477145795 y[1] (numeric) = 0.29037429375164321066244771457936 absolute error = 1.4e-31 relative error = 4.8213634268790278692134293975251e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1187 Order of pole (three term test) = -19.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = 0.28139806392098789202932846351791 y[1] (numeric) = 0.28139806392098789202932846351774 absolute error = 1.7e-31 relative error = 6.0412640240386764187072641190626e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06051 Order of pole (three term test) = -4.203 Radius of convergence (six term test) for eq 1 = 1.993 Order of pole (six term test) = -9.351 TOP MAIN SOLVE Loop bytes used=240064608, alloc=4652204, time=19.58 x[1] = 2.12 y[1] (analytic) = 0.27240549277622047903932694482916 y[1] (numeric) = 0.27240549277622047903932694482916 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 0.26339672719648865537132419827793 y[1] (numeric) = 0.26339672719648865537132419827795 absolute error = 2e-32 relative error = 7.5931087727906363359866739811625e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.077 Order of pole (six term test) = -12.22 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = 0.25437191367680084285580440481315 y[1] (numeric) = 0.25437191367680084285580440481301 absolute error = 1.4e-31 relative error = 5.5037522805242095170769083801516e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01906 Order of pole (three term test) = -20.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = 0.24533119832865265648145710869903 y[1] (numeric) = 0.24533119832865265648145710869904 absolute error = 1e-32 relative error = 4.0761224288334153719016565401677e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1471 Order of pole (three term test) = -18.17 Radius of convergence (six term test) for eq 1 = 0.997 Order of pole (six term test) = -12.17 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 0.23627472688065260538306664889203 y[1] (numeric) = 0.23627472688065260538306664889203 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 = 0.01854 Order of pole (three term test) = 2.268 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=244065648, alloc=4652204, time=19.91 x[1] = 2.17 y[1] (analytic) = 0.22720264467914704053407659803758 y[1] (numeric) = 0.22720264467914704053407659803753 absolute error = 5e-32 relative error = 2.2006786087639703510285757621221e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01748 Order of pole (three term test) = -2.061 Radius of convergence (six term test) for eq 1 = 0.1765 Order of pole (six term test) = -11.38 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 0.21811509668884434986663853137507 y[1] (numeric) = 0.218115096688844349866638531375 absolute error = 7e-32 relative error = 3.2093147637487762793276333828097e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.326 Order of pole (six term test) = -11.46 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 0.20901222749343840154137636887588 y[1] (numeric) = 0.20901222749343840154137636887574 absolute error = 1.4e-31 relative error = 6.6981727183590286352236471886084e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09824 Order of pole (three term test) = -30.07 Radius of convergence (six term test) for eq 1 = 0.7745 Order of pole (six term test) = -12.22 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 0.19989418129623123608851985188585 y[1] (numeric) = 0.19989418129623123608851985188584 absolute error = 1e-32 relative error = 5.0026468680349416202748132665377e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.486 Order of pole (three term test) = 445.4 Radius of convergence (six term test) for eq 1 = 0.431 Order of pole (six term test) = -12.41 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = 0.19076110192075500814148343015091 y[1] (numeric) = 0.19076110192075500814148343015088 absolute error = 3e-32 relative error = 1.5726476570921908953041476234324e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1193 Order of pole (three term test) = -12.05 Radius of convergence (six term test) for eq 1 = 0.767 Order of pole (six term test) = -12.02 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = 0.18161313281139317848338994612652 y[1] (numeric) = 0.18161313281139317848338994612639 absolute error = 1.3e-31 relative error = 7.1580726562878100444828613475707e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2437 Order of pole (six term test) = -12.01 TOP MAIN SOLVE Loop bytes used=248066908, alloc=4652204, time=20.25 x[1] = 2.23 y[1] (analytic) = 0.17245041703400095712646201068961 y[1] (numeric) = 0.17245041703400095712646201068942 absolute error = 1.9e-31 relative error = 1.1017659641990828162965352909623e-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 = 0.2149 Order of pole (three term test) = -17.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 0.16327309727652499814362786752253 y[1] (numeric) = 0.16327309727652499814362786752257 absolute error = 4e-32 relative error = 2.4498830895732080295118267092756e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1128 Order of pole (three term test) = -8.154 Radius of convergence (six term test) for eq 1 = 0.8648 Order of pole (six term test) = -11.78 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 0.15408131584962234697111284230509 y[1] (numeric) = 0.15408131584962234697111284230502 absolute error = 7e-32 relative error = 4.5430556984804961914850769442398e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2104 Order of pole (three term test) = -34.23 Radius of convergence (six term test) for eq 1 = 4.72 Order of pole (six term test) = 7.863 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 0.14487521468727864090021216717645 y[1] (numeric) = 0.14487521468727864090021216717624 absolute error = 2.1e-31 relative error = 1.4495233049579729560592785310661e-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 = 0.07006 Order of pole (three term test) = -29.16 Radius of convergence (six term test) for eq 1 = 0.6907 Order of pole (six term test) = -11.23 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = 0.13565493534742556347586606050004 y[1] (numeric) = 0.13565493534742556347586606049988 absolute error = 1.6e-31 relative error = 1.1794631694764686868605772377683e-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 = 0.08655 Order of pole (three term test) = 2.051 Radius of convergence (six term test) for eq 1 = 2.646 Order of pole (six term test) = -12.81 TOP MAIN SOLVE Loop bytes used=252068960, alloc=4652204, time=20.57 x[1] = 2.28 y[1] (analytic) = 0.12642061901255755351908342650922 y[1] (numeric) = 0.12642061901255755351908342650918 absolute error = 4e-32 relative error = 3.1640408275509819167351453167487e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1214 Order of pole (three term test) = -29.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 0.11717240649034776948968641872355 y[1] (numeric) = 0.11717240649034776948968641872358 absolute error = 3e-32 relative error = 2.5603297652226071935831211042982e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01134 Order of pole (three term test) = -1.149 Radius of convergence (six term test) for eq 1 = 0.8377 Order of pole (six term test) = -11.57 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 0.10791043821426330990527438485121 y[1] (numeric) = 0.10791043821426330990527438485102 absolute error = 1.9e-31 relative error = 1.7607193812218836287647409582074e-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 = 2.879 Order of pole (three term test) = -643 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = 0.09863485424417969053173237899442 y[1] (numeric) = 0.098634854244179690531732378994331 absolute error = 8.9e-32 relative error = 9.0231795527037816592554109013264e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3264 Order of pole (three term test) = -46.72 Radius of convergence (six term test) for eq 1 = 0.5514 Order of pole (six term test) = -11.07 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 0.08934579426699457906003648912541 y[1] (numeric) = 0.089345794266994579060036489125365 absolute error = 4.5e-32 relative error = 5.0366108857374102766756161342998e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.006761 Order of pole (three term test) = -26.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = 0.08004339759724078798353568373989 y[1] (numeric) = 0.080043397597240787983535683739891 absolute error = 1e-33 relative error = 1.2493222801857569455288232283254e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04146 Order of pole (three term test) = -1.158 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=256069976, alloc=4652204, time=20.90 x[1] = 2.34 y[1] (analytic) = 0.0707278031776985263893177311225 y[1] (numeric) = 0.070727803177698526389317731122432 absolute error = 6.8e-32 relative error = 9.6143237800211160533358106448234e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.349 Order of pole (three term test) = -210.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 0.06139914958000691137669498749622 y[1] (numeric) = 0.061399149580006911376694987496052 absolute error = 1.68e-31 relative error = 2.7361942494184801236921563614911e-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 = 0.02138 Order of pole (three term test) = -28.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = 0.05205757500527473981527448627069 y[1] (numeric) = 0.052057575005274739815274486270619 absolute error = 7.1e-32 relative error = 1.3638745176433192821361444320778e-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 = 0.472 Order of pole (three term test) = -71.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = 0.0427032172846905211545057893973 y[1] (numeric) = 0.042703217284690521154505789397376 absolute error = 7.6e-32 relative error = 1.7797253891511042704503152855900e-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 = 0.005635 Order of pole (three term test) = -25.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = 0.03333621388013177199602948325097 y[1] (numeric) = 0.03333621388013177199602948325101 absolute error = 4.0e-32 relative error = 1.1998963092758357137195783125150e-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 Radius of convergence (six term test) for eq 1 = 0.8968 Order of pole (six term test) = -11.15 TOP MAIN SOLVE Loop bytes used=260071008, alloc=4652204, time=21.23 x[1] = 2.39 y[1] (analytic) = 0.02395670188477357313957901525618 y[1] (numeric) = 0.023956701884773573139579015256198 absolute error = 1.8e-32 relative error = 7.5135551156315301243492714756292e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0808 Order of pole (three term test) = -23.75 Radius of convergence (six term test) for eq 1 = 1.264 Order of pole (six term test) = -10.4 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 0.01456481802369638981261877341731 y[1] (numeric) = 0.014564818023696389812618773417324 absolute error = 1.4e-32 relative error = 9.6122038581069444479113801318287e-29 % Correct digits = 31 h = 0.01 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) = -42.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 0.00516069865449315579333190876149 y[1] (numeric) = 0.0051606986544931557933319087613674 absolute error = 1.226e-31 relative error = 2.3756473339759620373168664449967e-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] = 2.42 y[1] (analytic) = -0.00425552023212437786399760977137 y[1] (numeric) = -0.004255520232124377863997609771433 absolute error = 6.30e-32 relative error = 1.4804300429456558329107550641054e-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 Radius of convergence (six term test) for eq 1 = 1.258 Order of pole (six term test) = -11.59 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = -0.0136837030117200287927328374927 y[1] (numeric) = -0.013683703011720028792732837492705 absolute error = 5e-33 relative error = 3.6539816712753287326197516219171e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -0.02312371442552830325885395052728 y[1] (numeric) = -0.023123714425528303258853950527358 absolute error = 7.8e-32 relative error = 3.3731604950928184764505047204631e-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 Radius of convergence (six term test) for eq 1 = 1.26 Order of pole (six term test) = -10.88 TOP MAIN SOLVE Loop bytes used=264072064, alloc=4652204, time=21.56 x[1] = 2.45 y[1] (analytic) = -0.03257541957985024937981079098334 y[1] (numeric) = -0.032575419579850249379810790983368 absolute error = 2.8e-32 relative error = 8.5954380207951621470538241583011e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.794 Order of pole (six term test) = -10.7 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = -0.04203868394545004291048550108396 y[1] (numeric) = -0.042038683945450042910485501083959 absolute error = 1e-33 relative error = 2.3787614314891811079035421989401e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07062 Order of pole (three term test) = -10.89 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = -0.05151337335695230489005994226394 y[1] (numeric) = -0.051513373356952304890059942264116 absolute error = 1.76e-31 relative error = 3.4165885192654896270773515399498e-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 = 0.03042 Order of pole (three term test) = -1.554 Radius of convergence (six term test) for eq 1 = 2.82 Order of pole (six term test) = -6.346 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = -0.06099935401224015044414926062277 y[1] (numeric) = -0.06099935401224015044414926062275 absolute error = 2.0e-32 relative error = 3.2787232461489335477619586835563e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8935 Order of pole (six term test) = -10.72 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = -0.070496492471853968037129235488 y[1] (numeric) = -0.070496492471853968037129235487999 absolute error = 1e-33 relative error = 1.4185102902804055956385827600976e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08574 Order of pole (three term test) = -12.92 Radius of convergence (six term test) for eq 1 = 1.47 Order of pole (six term test) = -10.36 TOP MAIN SOLVE Loop bytes used=268073184, alloc=4652204, time=21.89 x[1] = 2.5 y[1] (analytic) = -0.08000465565839092847015093343133 y[1] (numeric) = -0.080004655658390928470150933431384 absolute error = 5.4e-32 relative error = 6.7496072016824501983725112796738e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -0.08952371085590522292090168609172 y[1] (numeric) = -0.089523710855905222920901686091873 absolute error = 1.53e-31 relative error = 1.7090444368002615210958671135652e-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 = 0.09898 Order of pole (three term test) = -18.42 Radius of convergence (six term test) for eq 1 = 1.175 Order of pole (six term test) = -11.1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = -0.09905352570930902932173651687829 y[1] (numeric) = -0.099053525709309029321736516878398 absolute error = 1.08e-31 relative error = 1.0903195946497256576031380006151e-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 = 0.0617 Order of pole (three term test) = -8.636 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = -0.10859396822377420637336885924381 y[1] (numeric) = -0.10859396822377420637336885924377 absolute error = 4e-32 relative error = 3.6834458353684970004146445471164e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 76.21 Order of pole (six term test) = -24.02 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = -0.11814490676413471449187373799895 y[1] (numeric) = -0.11814490676413471449187373799907 absolute error = 1.2e-31 relative error = 1.0157018468817179407140042536044e-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) = -0.12770621005428976298732052529978 y[1] (numeric) = -0.12770621005428976298732052529999 absolute error = 2.1e-31 relative error = 1.6443992810586576234217992030891e-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 = 0.03252 Order of pole (three term test) = -16.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=272074064, alloc=4652204, time=22.22 x[1] = 2.56 y[1] (analytic) = -0.13727774717660768277291593471962 y[1] (numeric) = -0.13727774717660768277291593471973 absolute error = 1.1e-31 relative error = 8.0129520087829756818361590100732e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6287 Order of pole (three term test) = 59.3 Radius of convergence (six term test) for eq 1 = 2.107 Order of pole (six term test) = -10.97 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = -0.1468593875713305239041010804611 y[1] (numeric) = -0.1468593875713305239041010804613 absolute error = 2.0e-31 relative error = 1.3618468884248802138813455481964e-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 = 0.3519 Order of pole (three term test) = -18.36 Radius of convergence (six term test) for eq 1 = 5.303 Order of pole (six term test) = -11.43 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = -0.15645100103597937724760920448954 y[1] (numeric) = -0.15645100103597937724760920448964 absolute error = 1.0e-31 relative error = 6.3917775749483879834563872978601e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1465 Order of pole (three term test) = -28.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = -0.1660524577247604195810530624148 y[1] (numeric) = -0.16605245772476041958105306241498 absolute error = 1.8e-31 relative error = 1.0839947957792848376060318929641e-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 = 0.1594 Order of pole (three term test) = -15.97 Radius of convergence (six term test) for eq 1 = 0.458 Order of pole (six term test) = -11.14 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = -0.17566362814797168142417295956683 y[1] (numeric) = -0.17566362814797168142417295956704 absolute error = 2.1e-31 relative error = 1.1954665983734822859985526156940e-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) = -0.18528438317141053690343804209945 y[1] (numeric) = -0.18528438317141053690343804209954 absolute error = 9e-32 relative error = 4.8573980418381553166022265099050e-29 % Correct digits = 31 h = 0.01 bytes used=276075216, alloc=4652204, time=22.55 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01051 Order of pole (three term test) = -26.19 Radius of convergence (six term test) for eq 1 = 0.6704 Order of pole (six term test) = -11.15 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = -0.1949145940157819149522546743886 y[1] (numeric) = -0.19491459401578191495225467438856 absolute error = 4e-32 relative error = 2.0521808642384810658864456073803e-29 % Correct digits = 31 h = 0.01 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) = -25.56 Radius of convergence (six term test) for eq 1 = 0.8348 Order of pole (six term test) = -10.87 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = -0.20455413225610723114959657367169 y[1] (numeric) = -0.20455413225610723114959657367176 absolute error = 7e-32 relative error = 3.4220770427828919329396583024865e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -0.21420286982113403950043182604996 y[1] (numeric) = -0.21420286982113403950043182605007 absolute error = 1.1e-31 relative error = 5.1353186860593124137570113345014e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -0.22386067899274640346188197487397 y[1] (numeric) = -0.22386067899274640346188197487409 absolute error = 1.2e-31 relative error = 5.3604769064373414892179234438156e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9858 Order of pole (six term test) = -11 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = -0.23352743240537598551960805339605 y[1] (numeric) = -0.2335274324053759855196080533961 absolute error = 5e-32 relative error = 2.1410760819399545883377410786912e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8631 Order of pole (three term test) = 77.01 Radius of convergence (six term test) for eq 1 = 1.376 Order of pole (six term test) = -10.82 TOP MAIN SOLVE Loop bytes used=280076536, alloc=4652204, time=22.88 x[1] = 2.67 y[1] (analytic) = -0.24320300304541385461947772861921 y[1] (numeric) = -0.24320300304541385461947772861924 absolute error = 3e-32 relative error = 1.2335373997992134655419116834120e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -0.25288726425062301076012663275029 y[1] (numeric) = -0.25288726425062301076012663275041 absolute error = 1.2e-31 relative error = 4.7451974442285252051134885551883e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03315 Order of pole (three term test) = -34.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = -0.262580089709551626052585482796 y[1] (numeric) = -0.26258008970955162605258548279604 absolute error = 4e-32 relative error = 1.5233447457591053623565660643602e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05141 Order of pole (three term test) = -17.39 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = -0.2722813534609470015537027278625 y[1] (numeric) = -0.27228135346094700155370272786245 absolute error = 5e-32 relative error = 1.8363358108975847278130392344774e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 565.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.0659 Order of pole (three term test) = -3.842 Radius of convergence (six term test) for eq 1 = 4.887 Order of pole (six term test) = -11.13 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = -0.28199092989317023918065021786787 y[1] (numeric) = -0.28199092989317023918065021786803 absolute error = 1.6e-31 relative error = 5.6739413590577037293048784651590e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -0.29170869374361162801435675687512 y[1] (numeric) = -0.29170869374361162801435675687506 absolute error = 6e-32 relative error = 2.0568464803018573060047144786700e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8868 Order of pole (six term test) = -11.08 bytes used=284079624, alloc=4652204, time=23.21 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = -0.30143452009810674430027138933691 y[1] (numeric) = -0.30143452009810674430027138933697 absolute error = 6e-32 relative error = 1.9904820450050654018537981675530e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -0.31116828439035326445541486846486 y[1] (numeric) = -0.31116828439035326445541486846497 absolute error = 1.1e-31 relative error = 3.5350646424494726999842129711599e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.005866 Order of pole (three term test) = -0.8046 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = -0.3209098624013284903912339728774 y[1] (numeric) = -0.32090986240132849039123397287743 absolute error = 3e-32 relative error = 9.3484194519650285281629278369413e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.9903 Order of pole (six term test) = -11 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = -0.33065913025870758646232917093895 y[1] (numeric) = -0.33065913025870758646232917093907 absolute error = 1.2e-31 relative error = 3.6291149712428035021911210199427e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.31 Order of pole (six term test) = -10.97 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = -0.34041596443628252735168158195616 y[1] (numeric) = -0.34041596443628252735168158195609 absolute error = 7e-32 relative error = 2.0563077914373864080555943567223e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08384 Order of pole (three term test) = -9.134 Radius of convergence (six term test) for eq 1 = 1.231 Order of pole (six term test) = -11.03 TOP MAIN SOLVE Loop bytes used=288080520, alloc=4652204, time=23.54 x[1] = 2.78 y[1] (analytic) = -0.35018024175338175620356024989981 y[1] (numeric) = -0.35018024175338175620356024989987 absolute error = 6e-32 relative error = 1.7134033519302797373930045566835e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.05299 Order of pole (three term test) = 1.833 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = -0.35995183937429055231584542881732 y[1] (numeric) = -0.35995183937429055231584542881731 absolute error = 1e-32 relative error = 2.7781494372644805759981751194358e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.201 Order of pole (six term test) = -11.01 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = -0.36973063480767210770405787978151 y[1] (numeric) = -0.36973063480767210770405787978169 absolute error = 1.8e-31 relative error = 4.8684091350351070253499897342651e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2559 Order of pole (six term test) = -10.94 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = -0.37951650590598931184993809737539 y[1] (numeric) = -0.37951650590598931184993809737551 absolute error = 1.2e-31 relative error = 3.1619178120733807277066274200997e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04598 Order of pole (three term test) = -22.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = -0.38930933086492724394797291950733 y[1] (numeric) = -0.38930933086492724394797291950732 absolute error = 1e-32 relative error = 2.5686515085017441788224887315402e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9085 Order of pole (three term test) = 363.6 Radius of convergence (six term test) for eq 1 = 3.712 Order of pole (six term test) = -11.21 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = -0.39910898822281637196382012807913 y[1] (numeric) = -0.39910898822281637196382012807912 absolute error = 1e-32 relative error = 2.5055812560195098259054523430164e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.337 Order of pole (six term test) = -11.11 TOP MAIN SOLVE Loop bytes used=292081412, alloc=4652204, time=23.87 x[1] = 2.84 y[1] (analytic) = -0.40891535686005645781913441987036 y[1] (numeric) = -0.40891535686005645781913441987046 absolute error = 1.0e-31 relative error = 2.4454938735456469419063261052193e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1153 Order of pole (three term test) = -21.03 Radius of convergence (six term test) for eq 1 = 1.423 Order of pole (six term test) = -11.01 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = -0.41872831599854116801785051722084 y[1] (numeric) = -0.41872831599854116801785051722098 absolute error = 1.4e-31 relative error = 3.3434567152723379270753013598673e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.03184 Order of pole (three term test) = -0.1266 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = -0.42854774520108338902953119690498 y[1] (numeric) = -0.42854774520108338902953119690496 absolute error = 2e-32 relative error = 4.6669245665067237533163363818007e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.339 Order of pole (six term test) = -10.95 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = -0.43837352437084124674593964323076 y[1] (numeric) = -0.4383735243708412467459396432308 absolute error = 4e-32 relative error = 9.1246386417629720493394626531175e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 484.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.05 Order of pole (three term test) = -11.27 Radius of convergence (six term test) for eq 1 = 1.817 Order of pole (six term test) = -10.94 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = -0.44820553375074482932754677809521 y[1] (numeric) = -0.4482055337507448293275467780952 absolute error = 1e-32 relative error = 2.2311192626999514303517599794305e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=296082192, alloc=4652204, time=24.20 x[1] = 2.89 y[1] (analytic) = -0.45804365392292361275723508670654 y[1] (numeric) = -0.45804365392292361275723508670658 absolute error = 4e-32 relative error = 8.7327920946877523276432279929421e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1675 Order of pole (three term test) = -28.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = -0.46788776580813458841901094319542 y[1] (numeric) = -0.46788776580813458841901094319543 absolute error = 1e-32 relative error = 2.1372646884083461355110141148255e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -0.47773775066519109202008754558054 y[1] (numeric) = -0.47773775066519109202008754558051 absolute error = 3e-32 relative error = 6.2795958573984759926806910428998e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.084 Order of pole (six term test) = -11.09 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = -0.48759349009039233317525029478961 y[1] (numeric) = -0.48759349009039233317525029478962 absolute error = 1e-32 relative error = 2.0508887430277532651940554862913e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -0.49745486601695362497296579787143 y[1] (numeric) = -0.4974548660169536249729657978714 absolute error = 3e-32 relative error = 6.0306978681715374154521898357095e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.502 Order of pole (six term test) = -11.19 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = -0.50732176071443731284324464141016 y[1] (numeric) = -0.50732176071443731284324464141019 absolute error = 3e-32 relative error = 5.9134068993516884926806144689551e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.593 Order of pole (six term test) = -11.03 TOP MAIN SOLVE Loop bytes used=300083280, alloc=4652204, time=24.53 x[1] = 2.95 y[1] (analytic) = -0.51719405678818440204781666769916 y[1] (numeric) = -0.51719405678818440204781666769918 absolute error = 2e-32 relative error = 3.8670204611788399789712273177069e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 575.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1285 Order of pole (three term test) = -18.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = -0.52707163717874688311372569366704 y[1] (numeric) = -0.52707163717874688311372569366716 absolute error = 1.2e-31 relative error = 2.2767303633017185932724311497151e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = -0.53695438516132075453199844112039 y[1] (numeric) = -0.53695438516132075453199844112048 absolute error = 9e-32 relative error = 1.6761200296922932329230231069792e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03671 Order of pole (three term test) = -24.01 Radius of convergence (six term test) for eq 1 = 0.8032 Order of pole (six term test) = -10.99 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = -0.5468421843451797420435898967836 y[1] (numeric) = -0.54684218434517974204358989678378 absolute error = 1.8e-31 relative error = 3.2916260879826296576384914607638e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5759 Order of pole (six term test) = -11.01 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = -0.55673491867310971383535439212944 y[1] (numeric) = -0.55673491867310971383535439212958 absolute error = 1.4e-31 relative error = 2.5146617412406612422337492347562e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.185 Order of pole (three term test) = -9.692 Radius of convergence (six term test) for eq 1 = 7.447 Order of pole (six term test) = -12.59 TOP MAIN SOLVE Loop bytes used=304084724, alloc=4652204, time=24.86 x[1] = 3 y[1] (analytic) = -0.56663247242084379096933838630693 y[1] (numeric) = -0.566632472420843790969338386307 absolute error = 7e-32 relative error = 1.2353686632348574059827596372599e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2361 Order of pole (three term test) = -61.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = -0.57653473019649815236923725084239 y[1] (numeric) = -0.57653473019649815236923725084259 absolute error = 2.0e-31 relative error = 3.4690017708358134148573330379124e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06106 Order of pole (three term test) = -4.651 Radius of convergence (six term test) for eq 1 = 0.3848 Order of pole (six term test) = -11.05 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = -0.58644157694000853368840429242015 y[1] (numeric) = -0.58644157694000853368840429242014 absolute error = 1e-32 relative error = 1.7051996981828889499901231435802e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -0.59635289792256741938434581017999 y[1] (numeric) = -0.59635289792256741938434581018005 absolute error = 6e-32 relative error = 1.0061156776300366587918574286217e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -0.60626857874606192732518116684082 y[1] (numeric) = -0.60626857874606192732518116684104 absolute error = 2.2e-31 relative error = 3.6287547749055934395522622706765e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.111 Order of pole (three term test) = -4.968 Radius of convergence (six term test) for eq 1 = 2.834 Order of pole (six term test) = -11.05 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = -0.61618850534251238525409165876576 y[1] (numeric) = -0.61618850534251238525409165876578 absolute error = 2e-32 relative error = 3.2457599949682394710708207035368e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1102 Order of pole (three term test) = -18.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=308085940, alloc=4652204, time=25.19 x[1] = 3.06 y[1] (analytic) = -0.6261125639735115984383263990955 y[1] (numeric) = -0.62611256397351159843832639909571 absolute error = 2.1e-31 relative error = 3.3540294842076398259712688801892e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.06077 Order of pole (three term test) = -8.177 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = -0.63604064122966480782987748049712 y[1] (numeric) = -0.63604064122966480782987748049731 absolute error = 1.9e-31 relative error = 2.9872304957222667195198867344151e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1279 Order of pole (three term test) = -4.516 Radius of convergence (six term test) for eq 1 = 1.029 Order of pole (six term test) = -11.19 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = -0.64597262403003033806548036011992 y[1] (numeric) = -0.64597262403003033806548036012002 absolute error = 1.0e-31 relative error = 1.5480532189759042149297003340295e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1505 Order of pole (three term test) = -33.62 Radius of convergence (six term test) for eq 1 = 0.3266 Order of pole (six term test) = -10.97 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = -0.65590839962156093463413870929279 y[1] (numeric) = -0.6559083996215609346341387092928 absolute error = 1e-32 relative error = 1.5246031314387334940603591564932e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.3566 Order of pole (six term test) = -11 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = -0.66584785557854578954091589451004 y[1] (numeric) = -0.66584785557854578954091589451021 absolute error = 1.7e-31 relative error = 2.5531358038585166434928194023709e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08592 Order of pole (three term test) = -7.861 Radius of convergence (six term test) for eq 1 = 1.811 Order of pole (six term test) = -11.03 TOP MAIN SOLVE Loop bytes used=312086848, alloc=4652204, time=25.52 x[1] = 3.11 y[1] (analytic) = -0.67579087980205325479627780460661 y[1] (numeric) = -0.67579087980205325479627780460665 absolute error = 4e-32 relative error = 5.9189907995971253173334154319017e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -0.68573736051937424306081391191724 y[1] (numeric) = -0.68573736051937424306081391191741 absolute error = 1.7e-31 relative error = 2.4790832436378091122975501525947e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1506 Order of pole (three term test) = -13.15 Radius of convergence (six term test) for eq 1 = 0.3889 Order of pole (six term test) = -11.02 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = -0.69568718628346631477570525290438 y[1] (numeric) = -0.69568718628346631477570525290431 absolute error = 7e-32 relative error = 1.0061993577020928140862811761874e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1406 Order of pole (three term test) = -12.43 Radius of convergence (six term test) for eq 1 = 1.255 Order of pole (six term test) = -11 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = -0.70564024597239845110984943640911 y[1] (numeric) = -0.70564024597239845110984943640926 absolute error = 1.5e-31 relative error = 2.1257290929217682624716612281315e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = -0.71559642878879651205509383561824 y[1] (numeric) = -0.71559642878879651205509383561844 absolute error = 2.0e-31 relative error = 2.7948714101119230014675442465834e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660.2 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] = 3.16 y[1] (analytic) = -0.7255556242592893790015687931998 y[1] (numeric) = -0.72555562425928937900156879319987 absolute error = 7e-32 relative error = 9.6477785657663560291523500294735e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=316087880, alloc=4652204, time=25.85 x[1] = 3.17 y[1] (analytic) = -0.73551772223395578112565296814446 y[1] (numeric) = -0.73551772223395578112565296814451 absolute error = 5e-32 relative error = 6.7979327334407645140441914405381e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04464 Order of pole (three term test) = -2.684 Radius of convergence (six term test) for eq 1 = 1.079 Order of pole (six term test) = -11.01 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = -0.7454826128857718049236428778232 y[1] (numeric) = -0.74548261288577180492364287782318 absolute error = 2e-32 relative error = 2.6828258170341182065691724386916e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.132 Order of pole (three term test) = -16.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = -0.75545018671005908622473823989437 y[1] (numeric) = -0.75545018671005908622473823989441 absolute error = 4e-32 relative error = 5.2948560611517796932901285592268e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.287 Order of pole (six term test) = -11 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = -0.76542033452393368401749389618871 y[1] (numeric) = -0.76542033452393368401749389618881 absolute error = 1.0e-31 relative error = 1.3064716926053018510855675321853e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = -0.77539294746575563542442790478019 y[1] (numeric) = -0.77539294746575563542442790478012 absolute error = 7e-32 relative error = 9.0276807686713544573659702952235e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07524 Order of pole (three term test) = -8.989 Radius of convergence (six term test) for eq 1 = 1.152 Order of pole (six term test) = -11 TOP MAIN SOLVE Loop bytes used=320088948, alloc=4652204, time=26.19 x[1] = 3.22 y[1] (analytic) = -0.78536791699457919116001381735737 y[1] (numeric) = -0.7853679169945791911600138173576 absolute error = 2.3e-31 relative error = 2.9285637345634978162480563329301e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07305 Order of pole (three term test) = -35.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (analytic) = -0.79534513488960373080782321696572 y[1] (numeric) = -0.79534513488960373080782321696567 absolute error = 5e-32 relative error = 6.2865789713971342320767899831656e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1848 Order of pole (three term test) = -45.66 Radius of convergence (six term test) for eq 1 = 1.432 Order of pole (six term test) = -11.01 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (analytic) = -0.8053244932496253572531222764 y[1] (numeric) = -0.80532449324962535725312227640018 absolute error = 1.8e-31 relative error = 2.2351238725357585824889087608169e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1069 Order of pole (three term test) = -28.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = -0.81530588449248916960776341027239 y[1] (numeric) = -0.81530588449248916960776341027255 absolute error = 1.6e-31 relative error = 1.9624536390976332471642915017131e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03042 Order of pole (three term test) = -29.18 Radius of convergence (six term test) for eq 1 = 2.177 Order of pole (six term test) = -10.99 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = -0.82528920135454221396475003419928 y[1] (numeric) = -0.82528920135454221396475003419924 absolute error = 4e-32 relative error = 4.8467858217880762311468741109456e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.923 Order of pole (six term test) = -10.99 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = -0.83527433689008711132038901296983 y[1] (numeric) = -0.83527433689008711132038901296982 absolute error = 1e-32 relative error = 1.1972114499808809148504992573962e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.688 Order of pole (three term test) = -417.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=324089808, alloc=4652204, time=26.52 x[1] = 3.28 y[1] (analytic) = -0.8452611844708363620024815761181 y[1] (numeric) = -0.84526118447083636200248157611829 absolute error = 1.9e-31 relative error = 2.2478259204454866121032803904500e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07326 Order of pole (three term test) = -2.109 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = -0.85524963778536732594353930429454 y[1] (numeric) = -0.8552496377853673259435393042945 absolute error = 4e-32 relative error = 4.6769970114899205314017997547324e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 615 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1632 Order of pole (three term test) = -22.48 Radius of convergence (six term test) for eq 1 = 1.854 Order of pole (six term test) = -10.96 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = -0.86523959083857787813854724343072 y[1] (numeric) = -0.86523959083857787813854724343088 absolute error = 1.6e-31 relative error = 1.8491987848698680173978703143152e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 590.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.09809 Order of pole (three term test) = 3.206 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = -0.8752309379511427386273312861491 y[1] (numeric) = -0.87523093795114273862733128614925 absolute error = 1.5e-31 relative error = 1.7138333838054216561318433900770e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.01249 Order of pole (three term test) = -0.7965 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = -0.88522357375897047634212167137868 y[1] (numeric) = -0.88522357375897047634212167137877 absolute error = 9e-32 relative error = 1.0166923099192711548444031072896e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 579.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=328091080, alloc=4652204, time=26.85 x[1] = 3.33 y[1] (analytic) = -0.89521739321266118616143879398318 y[1] (numeric) = -0.89521739321266118616143879398337 absolute error = 1.9e-31 relative error = 2.1223895049463701945539791874776e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 641.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.436 Order of pole (six term test) = -10.99 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = -0.90521229157696483851196148655062 y[1] (numeric) = -0.90521229157696483851196148655082 absolute error = 2.0e-31 relative error = 2.2094264722320685018676705498542e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 660 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.2 Order of pole (six term test) = -11.07 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = -0.91520816443024030086057153560008 y[1] (numeric) = -0.91520816443024030086057153560002 absolute error = 6e-32 relative error = 6.5558855713828551679754907259441e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1398 Order of pole (three term test) = -35.89 Radius of convergence (six term test) for eq 1 = 1.525 Order of pole (six term test) = -11 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = -0.92520490766391503043930142454326 y[1] (numeric) = -0.92520490766391503043930142454326 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 = 660 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2273 Order of pole (three term test) = -35.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = -0.9352024174819454375464451560199 y[1] (numeric) = -0.93520241748194543754644515602007 absolute error = 1.7e-31 relative error = 1.8177882864944790117010738123379e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.115 Order of pole (six term test) = -11.01 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = -0.94520059040027791876762449692352 y[1] (numeric) = -0.94520059040027791876762449692374 absolute error = 2.2e-31 relative error = 2.3275482710694603165928342474328e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 642.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.07203 Order of pole (three term test) = 4.242 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=332091944, alloc=4652204, time=27.17 x[1] = 3.39 y[1] (analytic) = -0.95519932324631055946113511079392 y[1] (numeric) = -0.95519932324631055946113511079417 absolute error = 2.5e-31 relative error = 2.6172547856331997311291575629792e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.729 Order of pole (six term test) = -11.01 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = -0.96519851315835550485242879447624 y[1] (numeric) = -0.9651985131583555048524287944763 absolute error = 6e-32 relative error = 6.2163377980832101526987098529174e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.068 Order of pole (six term test) = -10.98 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = -0.97519805758510199908311941926515 y[1] (numeric) = -0.97519805758510199908311941926534 absolute error = 1.9e-31 relative error = 1.9483221743745053430879702229017e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1229 Order of pole (three term test) = -7.696 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (analytic) = -0.98519785428508009156043119140224 y[1] (numeric) = -0.98519785428508009156043119140245 absolute error = 2.1e-31 relative error = 2.1315515364412650180473762840706e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.545 Order of pole (six term test) = -10.98 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = -0.99519780132612500995353849297114 y[1] (numeric) = -0.99519780132612500995353849297114 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 = 659.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.688 Order of pole (six term test) = -10.97 TOP MAIN SOLVE Loop bytes used=336092968, alloc=4652204, time=27.50 x[1] = 3.44 y[1] (analytic) = -1.0051977970848421991837768421992 y[1] (numeric) = -1.0051977970848421991837768421993 absolute error = 1e-31 relative error = 9.9482908030646680079704274938162e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3011 Order of pole (three term test) = -96.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (analytic) = -1.0151977402460730257562344221173 y[1] (numeric) = -1.0151977402460730257562344221174 absolute error = 1e-31 relative error = 9.8502977336967943132630015273744e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1111 Order of pole (three term test) = -23.92 Radius of convergence (six term test) for eq 1 = 1.239 Order of pole (six term test) = -11 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = -1.0251975298023611467807631686836 y[1] (numeric) = -1.0251975298023611467807631686837 absolute error = 1e-31 relative error = 9.7542178061312851790175961250932e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.9 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] = 3.47 y[1] (analytic) = -1.0351970650534195430309775840861 y[1] (numeric) = -1.0351970650534195430309775840861 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 = 659.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1044 Order of pole (three term test) = -37.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = -1.0451962456055982153903382481896 y[1] (numeric) = -1.0451962456055982153903382481896 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 = 659.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.08764 Order of pole (three term test) = -28.91 Radius of convergence (six term test) for eq 1 = 3.366 Order of pole (six term test) = -10.79 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = -1.0551949713713525440349454412415 y[1] (numeric) = -1.0551949713713525440349454412415 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 = 0.1749 Order of pole (three term test) = 4.761 Radius of convergence (six term test) for eq 1 = 3.051 Order of pole (six term test) = -10.97 TOP MAIN SOLVE Loop bytes used=340094176, alloc=4652204, time=27.84 x[1] = 3.5 y[1] (analytic) = -1.0651931425687123097031963641976 y[1] (numeric) = -1.0651931425687123097031963641977 absolute error = 1e-31 relative error = 9.3879688108815730378988590381405e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2128 Order of pole (three term test) = -17.85 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (analytic) = -1.0751906597207513764029871496127 y[1] (numeric) = -1.0751906597207513764029871496129 absolute error = 2e-31 relative error = 1.8601352066427364576988877773435e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = -1.0851874236550580349076681961711 y[1] (numeric) = -1.0851874236550580349076681961713 absolute error = 2e-31 relative error = 1.8429996113148173633749526510430e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1045 Order of pole (three term test) = 4.027 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = -1.0951833355032060063924883338409 y[1] (numeric) = -1.095183335503206006392488333841 absolute error = 1e-31 relative error = 9.1308913090841367208640841182552e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3993 Order of pole (three term test) = -19.27 Radius of convergence (six term test) for eq 1 = 1.937 Order of pole (six term test) = -11.03 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = -1.1051782967002261055637899345408 y[1] (numeric) = -1.1051782967002261055637899345409 absolute error = 1e-31 relative error = 9.0483137696943466641582620863522e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2383 Order of pole (three term test) = 51.09 Radius of convergence (six term test) for eq 1 = 4.531 Order of pole (six term test) = -10.91 TOP MAIN SOLVE Loop bytes used=344095164, alloc=4652204, time=28.17 x[1] = 3.55 y[1] (analytic) = -1.1151722089840785626337433253337 y[1] (numeric) = -1.1151722089840785626337433253337 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 = 659.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.895 Order of pole (six term test) = -11.04 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (analytic) = -1.125164974395126003493934737724 y[1] (numeric) = -1.1251649743951260034939347377241 absolute error = 1e-31 relative error = 8.8875855786178106088204759364928e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1315 Order of pole (three term test) = 1.305 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = -1.1351564952756070874416475378731 y[1] (numeric) = -1.1351564952756070874416475378731 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 = 659.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1594 Order of pole (three term test) = -43.72 Radius of convergence (six term test) for eq 1 = 1.627 Order of pole (six term test) = -10.99 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = -1.1451466742691108018132016286544 y[1] (numeric) = -1.1451466742691108018132016286544 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 = 659.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.464 Order of pole (six term test) = -10.98 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = -1.1551354143200514128792406957032 y[1] (numeric) = -1.1551354143200514128792406957034 absolute error = 2e-31 relative error = 1.7313987392354879245788113783901e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2783 Order of pole (three term test) = -57.82 Radius of convergence (six term test) for eq 1 = 2.587 Order of pole (six term test) = -11 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = -1.1651226186731440723573813861608 y[1] (numeric) = -1.165122618673144072357381386161 absolute error = 2e-31 relative error = 1.7165575261749055466322702423029e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.0372 Order of pole (three term test) = -24.02 Radius of convergence (six term test) for eq 1 = 1.744 Order of pole (six term test) = -11.01 TOP MAIN SOLVE Loop bytes used=348096408, alloc=4652204, time=28.50 x[1] = 3.61 y[1] (analytic) = -1.1751081908728810788981625609214 y[1] (numeric) = -1.1751081908728810788981625609213 absolute error = 1e-31 relative error = 8.5098547330964554159971694166802e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.028 Order of pole (six term test) = -10.97 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = -1.1850920347630087939007564490647 y[1] (numeric) = -1.1850920347630087939007564490648 absolute error = 1e-31 relative error = 8.4381632030796413839369871431732e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = -1.195074054486005211015426857032 y[1] (numeric) = -1.1950740544860052110154268570322 absolute error = 2e-31 relative error = 1.6735364578391663088234580368048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3442 Order of pole (three term test) = -37.3 Radius of convergence (six term test) for eq 1 = 2.235 Order of pole (six term test) = -11 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = -1.2050541544825581786902425451768 y[1] (numeric) = -1.2050541544825581786902425451769 absolute error = 1e-31 relative error = 8.2983822451480863304885911695150e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = -1.2150322394910442751200764808554 y[1] (numeric) = -1.2150322394910442751200764808555 absolute error = 1e-31 relative error = 8.2302342892471930280758700376140e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.08016 Order of pole (three term test) = -4.581 Radius of convergence (six term test) for eq 1 = 1.152 Order of pole (six term test) = -11.04 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = -1.2250082145470083349564439103938 y[1] (numeric) = -1.2250082145470083349564439103938 absolute error = 0 bytes used=352097440, alloc=4652204, time=28.83 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7227 Order of pole (three term test) = -87.86 Radius of convergence (six term test) for eq 1 = 1.383 Order of pole (six term test) = -11.02 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = -1.2349819849826436271372540623215 y[1] (numeric) = -1.2349819849826436271372540623218 absolute error = 3e-31 relative error = 2.4291852322381543441246242068641e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1351 Order of pole (three term test) = -22.57 Radius of convergence (six term test) for eq 1 = 1.336 Order of pole (six term test) = -11.02 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (analytic) = -1.244953456426272683196071801424 y[1] (numeric) = -1.2449534564262726831960718014244 absolute error = 4e-31 relative error = 3.2129715206239790613272963173488e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.385 Order of pole (six term test) = -10.98 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = -1.2549225348018287754110066976287 y[1] (numeric) = -1.254922534801828775411006697629 absolute error = 3e-31 relative error = 2.3905858065364531180136908959159e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2694 Order of pole (three term test) = -36.4 Radius of convergence (six term test) for eq 1 = 4.998 Order of pole (six term test) = -10.88 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = -1.2648891263283380441538677557636 y[1] (numeric) = -1.2648891263283380441538677557638 absolute error = 2e-31 relative error = 1.5811662527335561623725777951586e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.6 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] = 3.71 y[1] (analytic) = -1.2748531375194022738007424719941 y[1] (numeric) = -1.2748531375194022738007424719943 absolute error = 2e-31 relative error = 1.5688081561234433206342993449112e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.019 Order of pole (six term test) = -11.02 TOP MAIN SOLVE Loop bytes used=356098364, alloc=4652204, time=29.16 x[1] = 3.72 y[1] (analytic) = -1.2848144751826823165656789404977 y[1] (numeric) = -1.2848144751826823165656789404978 absolute error = 1e-31 relative error = 7.7832248882299854592364385583616e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2486 Order of pole (three term test) = -35.41 Radius of convergence (six term test) for eq 1 = 2.694 Order of pole (six term test) = -10.91 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = -1.294773046419382163619669429891 y[1] (numeric) = -1.2947730464193821636196694298912 absolute error = 2e-31 relative error = 1.5446722539760006774533004225131e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 9.762 Order of pole (six term test) = -12.3 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (analytic) = -1.3047287586237336628576531833007 y[1] (numeric) = -1.3047287586237336628576531833008 absolute error = 1e-31 relative error = 7.6644282835830909714422979488800e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.148 Order of pole (six term test) = -11.03 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = -1.314681519482481882676775168978 y[1] (numeric) = -1.3146815194824818826767751689781 absolute error = 1e-31 relative error = 7.6064049367153592928323932449889e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.31 Order of pole (three term test) = -66.03 Radius of convergence (six term test) for eq 1 = 4.447 Order of pole (six term test) = -11.04 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = -1.3246312369743711211296561202402 y[1] (numeric) = -1.3246312369743711211296561202402 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 = 659.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6126 Order of pole (three term test) = -45.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = -1.3345778193696315598169474544683 y[1] (numeric) = -1.3345778193696315598169474544685 absolute error = 2e-31 relative error = 1.4986012587446350171855955985413e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.42 Order of pole (six term test) = -11.04 bytes used=360100668, alloc=4652204, time=29.49 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = -1.3445211752294665618839625511538 y[1] (numeric) = -1.3445211752294665618839625511539 absolute error = 1e-31 relative error = 7.4375920470671064918438403149204e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1025 Order of pole (three term test) = -48.87 Radius of convergence (six term test) for eq 1 = 3.863 Order of pole (six term test) = -11.01 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = -1.3544612134055406134866933987487 y[1] (numeric) = -1.3544612134055406134866933987488 absolute error = 1e-31 relative error = 7.3830094956036882835232561687462e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.06695 Order of pole (three term test) = -31.78 Radius of convergence (six term test) for eq 1 = 2.117 Order of pole (six term test) = -10.96 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = -1.3643978430394679080930387895985 y[1] (numeric) = -1.3643978430394679080930387895985 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 = 659.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3461 Order of pole (three term test) = -62.35 Radius of convergence (six term test) for eq 1 = 1.348 Order of pole (six term test) = -11.03 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = -1.3743309735623015729855870516918 y[1] (numeric) = -1.374330973562301572985587051692 absolute error = 2e-31 relative error = 1.4552535295162183987686370503251e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.158 Order of pole (six term test) = -11.01 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = -1.3842605146940235373328127556177 y[1] (numeric) = -1.3842605146940235373328127556179 absolute error = 2e-31 relative error = 1.4448147431569839325515794412461e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.216 Order of pole (six term test) = -11.01 TOP MAIN SOLVE Loop bytes used=364101388, alloc=4652204, time=29.82 x[1] = 3.83 y[1] (analytic) = -1.3941863764430350411960629251505 y[1] (numeric) = -1.3941863764430350411960629251507 absolute error = 2e-31 relative error = 1.4345284344999607397715570834679e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = -1.4041084691056477848402240105472 y[1] (numeric) = -1.4041084691056477848402240105472 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 = 659.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.05474 Order of pole (three term test) = -9.845 Radius of convergence (six term test) for eq 1 = 4.207 Order of pole (six term test) = -10.6 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = -1.4140267032655757177164762551204 y[1] (numeric) = -1.4140267032655757177164762551204 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 = 659.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8396 Order of pole (three term test) = 4.159 Radius of convergence (six term test) for eq 1 = 4.363 Order of pole (six term test) = -10.39 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = -1.4239409897934274664860570981963 y[1] (numeric) = -1.4239409897934274664860570981962 absolute error = 1e-31 relative error = 7.0227629316652440288708133381893e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.03944 Order of pole (three term test) = -9.464 Radius of convergence (six term test) for eq 1 = 2.839 Order of pole (six term test) = -10.82 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = -1.4338512398461994014544699113681 y[1] (numeric) = -1.4338512398461994014544699113682 absolute error = 1e-31 relative error = 6.9742241887468325198226120388754e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.519 Order of pole (six term test) = -11.12 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = -1.443757364866769340786088660261 y[1] (numeric) = -1.4437573648667693407860886602611 absolute error = 1e-31 relative error = 6.9263715935556838204388542362174e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=368102176, alloc=4652204, time=30.15 x[1] = 3.89 y[1] (analytic) = -1.4536592765833908918696230210185 y[1] (numeric) = -1.4536592765833908918696230210187 absolute error = 2e-31 relative error = 1.3758382257916046279796284266394e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.963 Order of pole (six term test) = -11.09 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = -1.4635568870091884292054220596594 y[1] (numeric) = -1.4635568870091884292054220596596 absolute error = 2e-31 relative error = 1.3665338312110608794088527895351e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 5.666 Order of pole (three term test) = -798.8 Radius of convergence (six term test) for eq 1 = 11.98 Order of pole (six term test) = -10.6 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = -1.4734501084416527081861078035146 y[1] (numeric) = -1.4734501084416527081861078035147 absolute error = 1e-31 relative error = 6.7867924015263601690740007541453e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.002636 Order of pole (three term test) = -0.8334 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = -1.4833388534621371141425428973935 y[1] (numeric) = -1.4833388534621371141425428973936 absolute error = 1e-31 relative error = 6.7415479454743847983228675473199e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = -1.4932230349353545460276490431345 y[1] (numeric) = -1.4932230349353545460276490431348 absolute error = 3e-31 relative error = 2.0090769629266251523730236294235e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.03359 Order of pole (three term test) = 2.091 Radius of convergence (six term test) for eq 1 = 1.954 Order of pole (six term test) = -10.81 TOP MAIN SOLVE Loop bytes used=372103136, alloc=4652204, time=30.48 x[1] = 3.94 y[1] (analytic) = -1.5031025660088749341111050700025 y[1] (numeric) = -1.5031025660088749341111050700025 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 = 659.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2253 Order of pole (three term test) = 26.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = -1.5129773601126233910584652752119 y[1] (numeric) = -1.512977360112623391058465275212 absolute error = 1e-31 relative error = 6.6094842286705582118027707948557e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.979 Order of pole (six term test) = -10.65 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = -1.522847330958378995768750108915 y[1] (numeric) = -1.5228473309583789957687501089153 absolute error = 3e-31 relative error = 1.9699939311132385113280936672837e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.02625 Order of pole (three term test) = -23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = -1.5327123925392742093450723564781 y[1] (numeric) = -1.5327123925392742093450723564784 absolute error = 3e-31 relative error = 1.9573143758757258338326752333109e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.523 Order of pole (six term test) = -11.24 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = -1.542572459129294922573372693046 y[1] (numeric) = -1.5425724591292949225733726930462 absolute error = 2e-31 relative error = 1.2965355294420983430167393667161e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.07894 Order of pole (three term test) = -12.02 Radius of convergence (six term test) for eq 1 = 4.138 Order of pole (six term test) = -10.76 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = -1.5524274452827811342848488514365 y[1] (numeric) = -1.5524274452827811342848488514366 absolute error = 1e-31 relative error = 6.4415248715075752157364253694672e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3193 Order of pole (three term test) = -29.72 Radius of convergence (six term test) for eq 1 = 5.136 Order of pole (six term test) = -10.9 TOP MAIN SOLVE Loop bytes used=376104264, alloc=4652204, time=30.82 x[1] = 4 y[1] (analytic) = -1.5622772658339282599781726545535 y[1] (numeric) = -1.5622772658339282599781726545536 absolute error = 1e-31 relative error = 6.4009124492137432589179742324456e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1457 Order of pole (three term test) = -14.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = -1.5721218358962890700780988179698 y[1] (numeric) = -1.5721218358962890700780988179699 absolute error = 1e-31 relative error = 6.3608301670200118075943621940925e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.08211 Order of pole (three term test) = -30.54 Radius of convergence (six term test) for eq 1 = 3.617 Order of pole (six term test) = -10.77 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = -1.5819610708622762572075787273268 y[1] (numeric) = -1.5819610708622762572075787273268 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 = 659.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = -1.5917948864026656318510013389437 y[1] (numeric) = -1.5917948864026656318510013389436 absolute error = 1e-31 relative error = 6.2822164371938856379091153649324e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3299 Order of pole (three term test) = -35.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = -1.6016231984660999457866919407409 y[1] (numeric) = -1.6016231984660999457866919407409 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 = 659.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.154 Order of pole (six term test) = -11.43 TOP MAIN SOLVE Loop bytes used=380106168, alloc=4652204, time=31.14 x[1] = 4.05 y[1] (analytic) = -1.611445923278593342667307744475 y[1] (numeric) = -1.6114459232785933426673077444749 absolute error = 1e-31 relative error = 6.2056069369391796960466051640211e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (analytic) = -1.6212629773430364351272771595745 y[1] (numeric) = -1.6212629773430364351272771595744 absolute error = 1e-31 relative error = 6.1680308128593876465246107099776e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.2 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] = 4.07 y[1] (analytic) = -1.6310742774387020077969371237776 y[1] (numeric) = -1.6310742774387020077969371237775 absolute error = 1e-31 relative error = 6.1309286390704016334506092841796e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.108 Order of pole (six term test) = -11.07 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = -1.6408797406207513456035300365047 y[1] (numeric) = -1.6408797406207513456035300365048 absolute error = 1e-31 relative error = 6.0942918316591319148086940915722e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.07236 Order of pole (three term test) = -5.683 Radius of convergence (six term test) for eq 1 = 6.942 Order of pole (six term test) = -10.32 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = -1.6506792842197411867397286576904 y[1] (numeric) = -1.6506792842197411867397286576904 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 = 659.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2153 Order of pole (three term test) = -16.34 Radius of convergence (six term test) for eq 1 = 9.087 Order of pole (six term test) = -10.56 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = -1.6604728258411312996808637978402 y[1] (numeric) = -1.6604728258411312996808637978403 absolute error = 1e-31 relative error = 6.0223810015887413520063598282793e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.753 Order of pole (six term test) = -11.04 TOP MAIN SOLVE Loop bytes used=384106840, alloc=4652204, time=31.47 x[1] = 4.11 y[1] (analytic) = -1.6702602833647926836325357346123 y[1] (numeric) = -1.6702602833647926836325357346121 absolute error = 2e-31 relative error = 1.1974181628571902137129275550267e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 20.86 Order of pole (three term test) = -1951 Radius of convergence (six term test) for eq 1 = 4.823 Order of pole (six term test) = -10.98 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = -1.680041574944516391790796047431 y[1] (numeric) = -1.680041574944516391790796047431 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 = 659.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1533 Order of pole (three term test) = -41.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = -1.6898166190075229767975919647854 y[1] (numeric) = -1.6898166190075229767975919647852 absolute error = 2e-31 relative error = 1.1835603801640064842571400075087e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.261 Order of pole (six term test) = -11.14 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = -1.6995853342539725577746703690964 y[1] (numeric) = -1.6995853342539725577746703690965 absolute error = 1e-31 relative error = 5.8837881208179919970712299201678e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8397 Order of pole (three term test) = -85.11 Radius of convergence (six term test) for eq 1 = 17.37 Order of pole (six term test) = -10.06 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = -1.7093476396564755083196433016555 y[1] (numeric) = -1.7093476396564755083196433016555 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 = 659.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1602 Order of pole (three term test) = -19.37 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=388108020, alloc=4652204, time=31.81 x[1] = 4.16 y[1] (analytic) = -1.7191034544596037648484211552572 y[1] (numeric) = -1.7191034544596037648484211552574 absolute error = 2e-31 relative error = 1.1633971154043753702715531703423e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.01783 Order of pole (three term test) = -25.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = -1.728852698179402754668723735093 y[1] (numeric) = -1.728852698179402754668723735093 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 = 659.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.02851 Order of pole (three term test) = -29.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (analytic) = -1.7385952906029039431698830093492 y[1] (numeric) = -1.7385952906029039431698830093492 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 = 659.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.89 Order of pole (six term test) = -11.46 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = -1.7483311517876379995146546600768 y[1] (numeric) = -1.7483311517876379995146546600768 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 = 659.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 17.96 Order of pole (six term test) = -13.69 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = -1.7580602020611485802192584823961 y[1] (numeric) = -1.7580602020611485802192584823963 absolute error = 2e-31 relative error = 1.1376174704684181838092891503221e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.453 Order of pole (six term test) = -10.85 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = -1.7677823620205067300083702662566 y[1] (numeric) = -1.7677823620205067300083702662566 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 = 659.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.286 Order of pole (six term test) = -11.18 TOP MAIN SOLVE Loop bytes used=392108820, alloc=4652204, time=32.15 x[1] = 4.22 y[1] (analytic) = -1.7774975525318258993322900299476 y[1] (numeric) = -1.7774975525318258993322900299477 absolute error = 1e-31 relative error = 5.6258867899740475695352191825358e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.09645 Order of pole (three term test) = -31.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = -1.7872056947297775779340133586105 y[1] (numeric) = -1.7872056947297775779340133586105 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 = 659.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 9.461 Order of pole (six term test) = -10.92 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = -1.7969067100171075438544341343024 y[1] (numeric) = -1.7969067100171075438544341343026 absolute error = 2e-31 relative error = 1.1130238363798857960233787436379e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4144 Order of pole (three term test) = -55.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = -1.8066005200641527272644081269767 y[1] (numeric) = -1.8066005200641527272644081269767 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 = 659 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.09054 Order of pole (three term test) = -30.18 Radius of convergence (six term test) for eq 1 = 6.12 Order of pole (six term test) = -10.41 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = -1.8162870468083586885129077482284 y[1] (numeric) = -1.8162870468083586885129077482283 absolute error = 1e-31 relative error = 5.5057376627622488277292853492848e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.06978 Order of pole (three term test) = -4.653 Radius of convergence (six term test) for eq 1 = 4.07 Order of pole (six term test) = -10.69 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = -1.8259662124537977097809987520794 y[1] (numeric) = -1.8259662124537977097809987520792 bytes used=396110256, alloc=4652204, time=32.48 absolute error = 2e-31 relative error = 1.0953105190880446559647558348611e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 9.802 Order of pole (six term test) = -11.64 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = -1.8356379394706874997318697996024 y[1] (numeric) = -1.8356379394706874997318697996024 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 = 659 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.06934 Order of pole (three term test) = -0.441 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (analytic) = -1.8453021505949105105476455870719 y[1] (numeric) = -1.8453021505949105105476455870719 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 = 659 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.481 Order of pole (six term test) = -11.39 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = -1.8549587688275338667442136707527 y[1] (numeric) = -1.8549587688275338667442136707526 absolute error = 1e-31 relative error = 5.3909554045347933192656850702162e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = -1.8646077174343299051557942056431 y[1] (numeric) = -1.8646077174343299051557942056432 absolute error = 1e-31 relative error = 5.3630583561886349163981286999367e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 3.128 Order of pole (three term test) = -544.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = -1.8742489199452973254814805506658 y[1] (numeric) = -1.8742489199452973254814805506658 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 = 659 Order of pole (ratio test) 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=400111548, alloc=4652204, time=32.81 x[1] = 4.33 y[1] (analytic) = -1.883882300154182950786477079166 y[1] (numeric) = -1.8838823001541829507864770791659 absolute error = 1e-31 relative error = 5.3081872467200143166977909220458e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.06083 Order of pole (three term test) = -37.5 Radius of convergence (six term test) for eq 1 = 6.172 Order of pole (six term test) = -10.32 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (analytic) = -1.8935077821180040973512585713662 y[1] (numeric) = -1.8935077821180040973512585713661 absolute error = 1e-31 relative error = 5.2812035389758943929467712465932e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 659 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2185 Order of pole (three term test) = -35.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = -1.903125290156571553262373254814 y[1] (numeric) = -1.9031252901565715532623732548138 absolute error = 2e-31 relative error = 1.0509029596445846669823941127045e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.01435 Order of pole (three term test) = -0.7876 Radius of convergence (six term test) for eq 1 = 6.123 Order of pole (six term test) = -7.637 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = -1.9127347488520131651391089000926 y[1] (numeric) = -1.9127347488520131651391089000924 absolute error = 2e-31 relative error = 1.0456232894813887657703572201584e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.9 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] = 4.37 y[1] (analytic) = -1.9223360830482980323907383723393 y[1] (numeric) = -1.9223360830482980323907383723394 absolute error = 1e-31 relative error = 5.2020040034533094919513412527668e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.52 Order of pole (six term test) = -11.72 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = -1.9319292178507613083995576846453 y[1] (numeric) = -1.9319292178507613083995576846454 absolute error = 1e-31 relative error = 5.1761730748732251417254141123782e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1666 Order of pole (three term test) = -28.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=404112952, alloc=4652204, time=33.14 x[1] = 4.39 y[1] (analytic) = -1.9415140786256296080254258974095 y[1] (numeric) = -1.9415140786256296080254258974093 absolute error = 2e-31 relative error = 1.0301238718885684051232107033611e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.392 Order of pole (six term test) = -11.22 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = -1.9510905909995470208280121584055 y[1] (numeric) = -1.9510905909995470208280121584054 absolute error = 1e-31 relative error = 5.1253386419525415422672134401091e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1347 Order of pole (three term test) = -13.79 Radius of convergence (six term test) for eq 1 = 8.73 Order of pole (six term test) = -10.28 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = -1.9606586808591017294034507818954 y[1] (numeric) = -1.9606586808591017294034507818954 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 = 658.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.0451 Order of pole (three term test) = -1.789 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = -1.9702182743503532322326005217996 y[1] (numeric) = -1.9702182743503532322326005217994 absolute error = 2e-31 relative error = 1.0151159523984553424085876277709e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 9.877 Order of pole (six term test) = -14.65 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = -1.9797692978783601704385991039411 y[1] (numeric) = -1.9797692978783601704385991039411 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 = 658.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.05423 Order of pole (three term test) = -33.52 Radius of convergence (six term test) for eq 1 = 8.061 Order of pole (six term test) = -7.668 TOP MAIN SOLVE Loop bytes used=408114448, alloc=4652204, time=33.49 x[1] = 4.44 y[1] (analytic) = -1.9893116781067087578518986459106 y[1] (numeric) = -1.9893116781067087578518986459102 absolute error = 4e-31 relative error = 2.0107457489049314366807678663107e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.00962 Order of pole (three term test) = -24.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = -1.9988453419570418137814618103582 y[1] (numeric) = -1.9988453419570418137814618103582 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 = 658.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3475 Order of pole (three term test) = -46.97 Radius of convergence (six term test) for eq 1 = 22.88 Order of pole (six term test) = -8.303 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = -2.0083702166085883978912924087664 y[1] (numeric) = -2.0083702166085883978912924087663 absolute error = 1e-31 relative error = 4.9791616691500168995387341797010e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.03951 Order of pole (three term test) = -0.3071 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = -2.0178862294976940465819676981146 y[1] (numeric) = -2.0178862294976940465819676981144 absolute error = 2e-31 relative error = 9.9113615562848337174095716120042e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -12.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (analytic) = -2.0273933083173516102773327926444 y[1] (numeric) = -2.0273933083173516102773327926444 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 = 658.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = -2.0368913810167326910170104472626 y[1] (numeric) = -2.0368913810167326910170104472626 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 = 658.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.889 Order of pole (six term test) = -11.59 TOP MAIN SOLVE Loop bytes used=412115324, alloc=4652204, time=33.82 x[1] = 4.5 y[1] (analytic) = -2.0463803758007196797558719582775 y[1] (numeric) = -2.0463803758007196797558719582776 absolute error = 1e-31 relative error = 4.8866770412060570725983013120751e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.02762 Order of pole (three term test) = -24.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (analytic) = -2.0558602211294383927721070713289 y[1] (numeric) = -2.0558602211294383927721070713289 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 = 658.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1034 Order of pole (three term test) = -8.572 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (analytic) = -2.0653308457177913065860225857425 y[1] (numeric) = -2.0653308457177913065860225857424 absolute error = 1e-31 relative error = 4.8418392727411040346611613040221e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.03821 Order of pole (three term test) = 1.271 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = -2.0747921785349913907921907993594 y[1] (numeric) = -2.0747921785349913907921907993593 absolute error = 1e-31 relative error = 4.8197598311079954267454342085948e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.827 Order of pole (six term test) = -11.55 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = -2.0842441488040965382080600483396 y[1] (numeric) = -2.0842441488040965382080600483397 absolute error = 1e-31 relative error = 4.7979023982088797453781266852731e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.828 Order of pole (six term test) = -11.59 TOP MAIN SOLVE Loop bytes used=416116256, alloc=4652204, time=34.16 x[1] = 4.55 y[1] (analytic) = -2.0936866860015445917426303627453 y[1] (numeric) = -2.0936866860015445917426303627454 absolute error = 1e-31 relative error = 4.7762638349187184076691217577543e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = -2.1031197198566889673892876810772 y[1] (numeric) = -2.1031197198566889673892876810774 absolute error = 2e-31 relative error = 9.5096821218351004595591058418337e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1366 Order of pole (three term test) = -18.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (analytic) = -2.1125431803513348727473801455827 y[1] (numeric) = -2.112543180351334872747380145583 absolute error = 3e-31 relative error = 1.4200893159973530580682170251660e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = -2.1219569977192761204776097352735 y[1] (numeric) = -2.1219569977192761204776097352736 absolute error = 1e-31 relative error = 4.7126308453697269569593188407296e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.07939 Order of pole (three term test) = -40.07 Radius of convergence (six term test) for eq 1 = 13.26 Order of pole (six term test) = -8.354 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = -2.1313611024458325360968018854121 y[1] (numeric) = -2.1313611024458325360968018854122 absolute error = 1e-31 relative error = 4.6918375251028796232714773445166e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1163 Order of pole (three term test) = -28.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = -2.1407554252673879595181047909527 y[1] (numeric) = -2.1407554252673879595181047909527 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 = 658.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.01602 Order of pole (three term test) = -17.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=420117508, alloc=4652204, time=34.49 x[1] = 4.61 y[1] (analytic) = -2.1501398971709288397431587972472 y[1] (numeric) = -2.1501398971709288397431587972473 absolute error = 1e-31 relative error = 4.6508601664280609681393103856475e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.03599 Order of pole (three term test) = -19.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (analytic) = -2.1595144493935834221132646444976 y[1] (numeric) = -2.1595144493935834221132646444979 absolute error = 3e-31 relative error = 1.3892011701252726600572718099474e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.636 Order of pole (six term test) = -11.64 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (analytic) = -2.1688790134221615275270673531188 y[1] (numeric) = -2.1688790134221615275270673531188 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 = 658.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.53 Order of pole (six term test) = -25.91 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = -2.1782335209926949230327602156121 y[1] (numeric) = -2.1782335209926949230327602156124 absolute error = 3e-31 relative error = 1.3772628008372574350646183099126e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2198 Order of pole (three term test) = -26.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = -2.1875779040899782832033006969447 y[1] (numeric) = -2.1875779040899782832033006969447 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 = 658.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.96 Order of pole (six term test) = -11.4 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (analytic) = -2.1969120949471107417036170399549 y[1] (numeric) = -2.1969120949471107417036170399551 absolute error = 2e-31 relative error = 9.1036869640801386963517303945314e-30 % Correct digits = 32 h = 0.01 bytes used=424118400, alloc=4652204, time=34.82 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3219 Order of pole (three term test) = -26.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (analytic) = -2.2062360260450380324592710252519 y[1] (numeric) = -2.206236026045038032459271025252 absolute error = 1e-31 relative error = 4.5326066123243788950208304426628e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.141 Order of pole (six term test) = -11.4 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = -2.2155496301120952198365286465438 y[1] (numeric) = -2.2155496301120952198365286465439 absolute error = 1e-31 relative error = 4.5135526932403009715505549371908e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.732 Order of pole (three term test) = -209.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = -2.224852840123550017244276432638 y[1] (numeric) = -2.2248528401235500172442764326383 absolute error = 3e-31 relative error = 1.3484037891842791222964816994054e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = -2.2341455893011466935687067766265 y[1] (numeric) = -2.2341455893011466935687067766267 absolute error = 2e-31 relative error = 8.9519680793300997413097118876640e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.791 Order of pole (three term test) = 68.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = -2.2434278111126505668521809212603 y[1] (numeric) = -2.2434278111126505668521809212605 absolute error = 2e-31 relative error = 8.9149291548101113280099240047534e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.6 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 bytes used=428119668, alloc=4652204, time=35.15 x[1] = 4.72 y[1] (analytic) = -2.252699439271393084628163197426 y[1] (numeric) = -2.2526994392713930846281631974264 absolute error = 4e-31 relative error = 1.7756474433596649744335950118109e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3492 Order of pole (three term test) = -19.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = -2.261960407735817490324604720157 y[1] (numeric) = -2.2619604077358174903246047201573 absolute error = 3e-31 relative error = 1.3262831611641457227736590713437e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.605 Order of pole (six term test) = -11.62 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = -2.2712106507090250751486390139724 y[1] (numeric) = -2.2712106507090250751486390139727 absolute error = 3e-31 relative error = 1.3208814422666880045382047026011e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.008831 Order of pole (three term test) = -25.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = -2.2804501026383220148659359667396 y[1] (numeric) = -2.2804501026383220148659359667399 absolute error = 3e-31 relative error = 1.3155297704296221370789902986744e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2821 Order of pole (three term test) = -37.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = -2.2896786982147667908885440988956 y[1] (numeric) = -2.2896786982147667908885440988956 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 = 658.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1977 Order of pole (three term test) = -36.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = -2.2988963723727181950855343829676 y[1] (numeric) = -2.2988963723727181950855343829678 absolute error = 2e-31 relative error = 8.6998266822082819405355763612840e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.103 Order of pole (six term test) = -11.59 TOP MAIN SOLVE Loop bytes used=432120676, alloc=4652204, time=35.49 x[1] = 4.78 y[1] (analytic) = -2.3081030602893839177312417571066 y[1] (numeric) = -2.3081030602893839177312417571067 absolute error = 1e-31 relative error = 4.3325621684961615994159361255001e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2069 Order of pole (three term test) = -44.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = -2.3172986973843697180063830459698 y[1] (numeric) = -2.3172986973843697180063830459701 absolute error = 3e-31 relative error = 1.2946108343245621730406814951083e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3343 Order of pole (three term test) = -32.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = -2.3264832193192291764678122330291 y[1] (numeric) = -2.3264832193192291764678122330293 absolute error = 2e-31 relative error = 8.5966663476955400646096805418557e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.71 Order of pole (six term test) = -25.71 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = -2.3356565619970140289031559203648 y[1] (numeric) = -2.335656561997014028903155920365 absolute error = 2e-31 relative error = 8.5629027509505777160227142518630e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1009 Order of pole (three term test) = -31.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = -2.3448186615618250809870533655252 y[1] (numeric) = -2.3448186615618250809870533655254 absolute error = 2e-31 relative error = 8.5294442286119047162792780724604e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3495 Order of pole (three term test) = -95.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=436121868, alloc=4652204, time=35.83 x[1] = 4.83 y[1] (analytic) = -2.3539694543983637031562067002198 y[1] (numeric) = -2.35396945439836370315620670022 absolute error = 2e-31 relative error = 8.4962869686478895405800813199450e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 8.487 Order of pole (six term test) = -11.65 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = -2.3631088771314839051209278127357 y[1] (numeric) = -2.3631088771314839051209278127361 absolute error = 4e-31 relative error = 1.6926854444622523872059195360495e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.06631 Order of pole (three term test) = -24.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = -2.3722368666257449894313489151934 y[1] (numeric) = -2.3722368666257449894313489151937 absolute error = 3e-31 relative error = 1.2646291954256580622054106101135e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.5419 Order of pole (three term test) = -78.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = -2.3813533599849647835169440183069 y[1] (numeric) = -2.3813533599849647835169440183072 absolute error = 3e-31 relative error = 1.2597878376264752169587444312907e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 100 Order of pole (six term test) = 5.757 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = -2.3904582945517734496184884004058 y[1] (numeric) = -2.3904582945517734496184884004062 absolute error = 4e-31 relative error = 1.6733192999503997360069289841123e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 143.8 Order of pole (six term test) = -17.77 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = -2.399551607907167872032062684288 y[1] (numeric) = -2.3995516079071678720320626842882 absolute error = 2e-31 relative error = 8.3348905412555501183138485535313e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2607 Order of pole (three term test) = -34.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=440122940, alloc=4652204, time=36.16 x[1] = 4.89 y[1] (analytic) = -2.4086332378700666210851873252424 y[1] (numeric) = -2.4086332378700666210851873252427 absolute error = 3e-31 relative error = 1.2455196386199809533437363184111e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 8.519 Order of pole (six term test) = -11.71 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = -2.4177031224968654932656521664999 y[1] (numeric) = -2.4177031224968654932656521665004 absolute error = 5e-31 relative error = 2.0680785632754967855586030235508e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.09546 Order of pole (three term test) = -32.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = -2.4267612000809936269240842346364 y[1] (numeric) = -2.4267612000809936269240842346366 absolute error = 2e-31 relative error = 8.2414371876938266983589700634699e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.05029 Order of pole (three term test) = -26.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = -2.4358074091524701929717751272934 y[1] (numeric) = -2.4358074091524701929717751272938 absolute error = 4e-31 relative error = 1.6421659548986200821449788215509e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.262 Order of pole (three term test) = -20.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (analytic) = -2.4448416884774616599957671891963 y[1] (numeric) = -2.4448416884774616599957671891968 absolute error = 5e-31 relative error = 2.0451221948500792096901999262420e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.01916 Order of pole (three term test) = -25.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=444123960, alloc=4652204, time=36.48 x[1] = 4.94 y[1] (analytic) = -2.4538639770578396332136751800153 y[1] (numeric) = -2.4538639770578396332136751800157 absolute error = 4e-31 relative error = 1.6300822039842498748305361919755e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.002 Order of pole (six term test) = -11.68 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = -2.4628742141307392666911973093993 y[1] (numeric) = -2.4628742141307392666911973093998 absolute error = 5e-31 relative error = 2.0301483410368678676736063082738e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 8.012 Order of pole (six term test) = -12.07 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = -2.4718723391681182482457463506563 y[1] (numeric) = -2.4718723391681182482457463506567 absolute error = 4e-31 relative error = 1.6182065459521896248682922112781e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.002133 Order of pole (three term test) = -25.28 Radius of convergence (six term test) for eq 1 = 3.105 Order of pole (six term test) = -12.71 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = -2.4808582918763163564601080453001 y[1] (numeric) = -2.4808582918763163564601080453007 absolute error = 6e-31 relative error = 2.4185178249186072803517097633935e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.27 Order of pole (six term test) = -12.2 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = -2.4898320121956155892305101762396 y[1] (numeric) = -2.4898320121956155892305101762401 absolute error = 5e-31 relative error = 2.0081676095050428284850271171829e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 8.834 Order of pole (six term test) = -12.14 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = -2.4987934402998008632739615179273 y[1] (numeric) = -2.4987934402998008632739615179277 absolute error = 4e-31 relative error = 1.6007725710693745863556143250935e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 658.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.04 Order of pole (six term test) = -12.28 Finished! diff ( y , x , 1 ) = cos(sqrt(2.0*x + 3.0)); Iterations = 600 Total Elapsed Time = 36 Seconds Elapsed Time(since restart) = 35 Seconds Time to Timeout = 2 Minutes 23 Seconds Percent Done = 100.2 % > quit bytes used=447920036, alloc=4652204, time=36.77