|\^/| 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_0D2, > array_const_0D3, > #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, > 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_0D2, array_const_0D3, 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, 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_0D2, > array_const_0D3, > #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, > 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_0D2, array_const_0D3, 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, 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_0D2, > array_const_0D3, > #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, > 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_0D2, array_const_0D3, 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, 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_0D2, > array_const_0D3, > #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, > 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_0D2, array_const_0D3, 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, 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_0D2, > array_const_0D3, > #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, > 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_0D2, array_const_0D3, 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, 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_0D2, > array_const_0D3, > #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, > 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_0D2, array_const_0D3, 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, 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_0D2, > array_const_0D3, > #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, > 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_0D2, array_const_0D3, 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, 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_0D2, > array_const_0D3, > #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, > 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_0D2, array_const_0D3, 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, 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_0D2, > array_const_0D3, > #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, > 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_0D2[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D3[1]; > #emit pre exp 1 $eq_no = 1 > array_tmp3[1] := exp(array_x[1]); > #emit pre div LINEAR - FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp2[1] / 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_0D2[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre exp ID_LINEAR iii = 2 $eq_no = 1 > array_tmp3[2] := array_tmp3[1] * array_x[2] / 1; > #emit pre div LINEAR - FULL $eq_no = 1 i = 2 > array_tmp4[2] := (array_tmp2[2] - array_tmp4[1] * array_tmp3[2]) / 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 exp ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := array_tmp3[2] * array_x[2] / 2; > #emit pre div LINEAR FULL $eq_no = 1 i = 3 > array_tmp4[3] := - ats(3,array_tmp3,array_tmp4,2) / 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 exp ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := array_tmp3[3] * array_x[2] / 3; > #emit pre div LINEAR FULL $eq_no = 1 i = 4 > array_tmp4[4] := - ats(4,array_tmp3,array_tmp4,2) / 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 exp ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := array_tmp3[4] * array_x[2] / 4; > #emit pre div LINEAR FULL $eq_no = 1 i = 5 > array_tmp4[5] := - ats(5,array_tmp3,array_tmp4,2) / 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 exp LINEAR $eq_no = 1 > array_tmp3[kkk] := array_tmp3[kkk - 1] * array_x[2] / (kkk - 1); > #emit div LINEAR FULL $eq_no = 1 i = 1 > array_tmp4[kkk] := -ats(kkk,array_tmp3,array_tmp4,2) / 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_0D2, array_const_0D3, 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, 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_0D2[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D3[1]; array_tmp3[1] := exp(array_x[1]); array_tmp4[1] := array_tmp2[1]/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_0D2[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp3[1]*array_x[2]; array_tmp4[2] := (array_tmp2[2] - array_tmp4[1]*array_tmp3[2])/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] := 1/2*array_tmp3[2]*array_x[2]; array_tmp4[3] := -ats(3, array_tmp3, array_tmp4, 2)/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] := 1/3*array_tmp3[3]*array_x[2]; array_tmp4[4] := -ats(4, array_tmp3, array_tmp4, 2)/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] := 1/4*array_tmp3[4]*array_x[2]; array_tmp4[5] := -ats(5, array_tmp3, array_tmp4, 2)/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] := array_tmp3[kkk - 1]*array_x[2]/(kkk - 1); array_tmp4[kkk] := -ats(kkk, array_tmp3, array_tmp4, 2)/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(-(0.1 * (5.0 + 2.0*x))/exp(x)); > end; exact_soln_y := proc(x) return -0.1*(5.0 + 2.0*x)/exp(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, > #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, > 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/div_lin_exppostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 1.0;"); > omniout_str(ALWAYS,"## did poorly with x_start := -5.0;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"glob_display_interval := 0.1;"); > omniout_str(ALWAYS,"glob_max_minutes := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(-(0.1 * (5.0 + 2.0*x))/exp(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= 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[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 := 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_0D2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D2[1] := 0.2; > array_const_0D3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D3[1] := 0.3; > 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; > ## did poorly with x_start := -5.0; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > glob_display_interval := 0.1; > glob_max_minutes := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T00:38:12-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"div_lin_exp") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"div_lin_exp diffeq.mxt") > ; > logitem_str(html_log_file,"div_lin_exp 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_0D2, array_const_0D3, 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, 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/div_lin_exppostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 1.0;"); omniout_str(ALWAYS, "## did poorly with x_start := -5.0;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "glob_display_interval := 0.1;"); omniout_str(ALWAYS, "glob_max_minutes := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(-(0.1 * (5.0 + 2.0*x))/exp(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := 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[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 := 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_0D2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D2[term] := 0.; term := term + 1 end do; array_const_0D2[1] := 0.2; array_const_0D3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D3[term] := 0.; term := term + 1 end do; array_const_0D3[1] := 0.3; 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 ) = (0.2 * x + 0.3) / exp(x);"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T00:38:12-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "div_lin_exp"); logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "div_lin_exp diffeq.mxt"); logitem_str(html_log_file, "div_lin_exp 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/div_lin_exppostode.ode################# diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 1.0; ## did poorly with x_start := -5.0; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_display_interval := 0.1; glob_max_minutes := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(-(0.1 * (5.0 + 2.0*x))/exp(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 4 estimated_steps = 4000000 step_error = 2.5000000000000000000000000000000e-17 est_needed_step_err = 2.5000000000000000000000000000000e-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 = 4.1048661150121780371637913489201e-183 estimated_step_error = 4.1048661150121780371637913489201e-183 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.7547289652248410630600428198733e-175 estimated_step_error = 2.7547289652248410630600428198733e-175 best_h = 4.00e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.8486672433291175267476193880828e-167 estimated_step_error = 1.8486672433291175267476193880828e-167 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.2406194901562091326028780353513e-159 estimated_step_error = 1.2406194901562091326028780353513e-159 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 = 8.3256551758148895297327195118363e-152 estimated_step_error = 8.3256551758148895297327195118363e-152 best_h = 3.200000e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.5872508799883415175070451286084e-144 estimated_step_error = 5.5872508799883415175070451286084e-144 best_h = 6.4000000e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.7495382736895762263439532229913e-136 estimated_step_error = 3.7495382736895762263439532229913e-136 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.5162694259322292023918421138892e-128 estimated_step_error = 2.5162694259322292023918421138892e-128 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.6886356463423070720953376633391e-120 estimated_step_error = 1.6886356463423070720953376633391e-120 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1332185883198211555385793129102e-112 estimated_step_error = 1.1332185883198211555385793129102e-112 best_h = 0.001024 opt_iter = 11 bytes used=4000380, alloc=2883056, time=0.13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.6048259035613479009330536153264e-105 estimated_step_error = 7.6048259035613479009330536153264e-105 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.1034111978908212028075737625071e-97 estimated_step_error = 5.1034111978908212028075737625071e-97 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.4247056271197763495299671765467e-89 estimated_step_error = 3.4247056271197763495299671765467e-89 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.2980989921127089988834200403461e-81 estimated_step_error = 2.2980989921127089988834200403461e-81 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.5419838402869234539780683746088e-73 estimated_step_error = 1.5419838402869234539780683746088e-73 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0344801120150850060074101048472e-65 estimated_step_error = 1.0344801120150850060074101048472e-65 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 = 6.9378838760705646127052428579083e-58 estimated_step_error = 6.9378838760705646127052428579083e-58 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.6500474852119528547967616703486e-50 estimated_step_error = 4.6500474852119528547967616703486e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = -0.25751560882000962511686663911302 y[1] (numeric) = -0.25751560882000962511686663911302 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 275.1 Order of pole (three term test) = -7220 Radius of convergence (six term test) for eq 1 = 2.986e+10 Order of pole (six term test) = 1.274e+20 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = -0.25568172365920937046944649953742 y[1] (numeric) = -0.25568172365920937046944649953741 absolute error = 1e-32 relative error = 3.9111125570041545498429862060689e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 275 Order of pole (three term test) = -7217 Radius of convergence (six term test) for eq 1 = 3.338e+10 Order of pole (six term test) = 1.588e+20 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = -0.25385883788184712199006451079643 y[1] (numeric) = -0.25385883788184712199006451079642 absolute error = 1e-32 relative error = 3.9391971079038322681806815016270e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 274.8 Order of pole (three term test) = -7213 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = -0.25204691416181804305580601464985 y[1] (numeric) = -0.25204691416181804305580601464984 absolute error = 1e-32 relative error = 3.9675153465992621945747348720731e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 274.7 Order of pole (three term test) = -7209 Radius of convergence (six term test) for eq 1 = 2.073e+10 Order of pole (six term test) = 6.085e+19 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = -0.25024591482681634489201125183874 y[1] (numeric) = -0.25024591482681634489201125183873 absolute error = 1e-32 relative error = 3.9960692293101123157054887107081e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 274.5 Order of pole (three term test) = -7205 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = -0.24845580186892030181697720023953 y[1] (numeric) = -0.24845580186892030181697720023953 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 274.4 Order of pole (three term test) = -7201 Radius of convergence (six term test) for eq 1 = 3.380e+10 Order of pole (six term test) = 1.609e+20 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = -0.24667653695500089706889794384017 y[1] (numeric) = -0.24667653695500089706889794384016 absolute error = 1e-32 relative error = 4.0538918388594919188783360743280e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 274.2 Order of pole (three term test) = -7198 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = -0.24490808143695656104710871943071 y[1] (numeric) = -0.2449080814369565610471087194307 absolute error = 1e-32 relative error = 4.0831645657941129886244688697136e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 274.1 Order of pole (three term test) = -7194 Radius of convergence (six term test) for eq 1 = 3.904e+10 Order of pole (six term test) = 2.134e+20 TOP MAIN SOLVE Loop bytes used=8001332, alloc=3931440, time=0.27 x[1] = 1.08 y[1] (analytic) = -0.24315039636177643227001891411732 y[1] (numeric) = -0.24315039636177643227001891411731 absolute error = 1e-32 relative error = 4.1126809372423516984917616274223e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 273.9 Order of pole (three term test) = -7190 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = -0.24140344248143454020615485234121 y[1] (numeric) = -0.24140344248143454020615485234121 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 273.8 Order of pole (three term test) = -7186 Radius of convergence (six term test) for eq 1 = 2.675e+11 Order of pole (six term test) = 9.965e+21 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = -0.23966718026261727836796977263054 y[1] (numeric) = -0.23966718026261727836796977263054 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 273.6 Order of pole (three term test) = -7182 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = -0.23794156989628650566605335731524 y[1] (numeric) = -0.23794156989628650566605335731524 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 273.5 Order of pole (three term test) = -7179 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = -0.23622657130708058399967521238963 y[1] (numeric) = -0.23622657130708058399967521238962 absolute error = 1e-32 relative error = 4.2332240376975166366969932208546e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 273.3 Order of pole (three term test) = -7175 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = -0.23452214416255563040386515477689 y[1] (numeric) = -0.23452214416255563040386515477688 absolute error = 1e-32 relative error = 4.2639896695932665156928544449359e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 273.2 Order of pole (three term test) = -7171 Radius of convergence (six term test) for eq 1 = 2.020e+10 Order of pole (six term test) = 5.618e+19 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = -0.23282824788226923277915751934655 y[1] (numeric) = -0.23282824788226923277915751934654 absolute error = 1e-32 relative error = 4.2950114906403238408400497818399e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 273 Order of pole (three term test) = -7167 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = -0.23114484164670884929344596527355 y[1] (numeric) = -0.23114484164670884929344596527355 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 272.9 Order of pole (three term test) = -7163 Radius of convergence (six term test) for eq 1 = 2.054e+10 Order of pole (six term test) = 5.777e+19 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = -0.22947188440606708296189744676165 y[1] (numeric) = -0.22947188440606708296189744676164 absolute error = 1e-32 relative error = 4.3578323444210173123603705410133e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 272.7 Order of pole (three term test) = -7160 Radius of convergence (six term test) for eq 1 = 4.267e+10 Order of pole (six term test) = 2.488e+20 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = -0.22780933488886599467639555874577 y[1] (numeric) = -0.22780933488886599467639555874577 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 272.6 Order of pole (three term test) = -7156 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = -0.22615715161043259006640870493178 y[1] (numeric) = -0.22615715161043259006640870493178 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 272.4 Order of pole (three term test) = -7152 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = -0.22451529288122758802443914265516 y[1] (numeric) = -0.22451529288122758802443914265515 absolute error = 1e-32 relative error = 4.4540395763998892651095273761623e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 272.3 Order of pole (three term test) = -7148 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = -0.22288371681502955151728342924159 y[1] (numeric) = -0.22288371681502955151728342924158 absolute error = 1e-32 relative error = 4.4866444901845236345010370670291e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 272.1 Order of pole (three term test) = -7144 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = -0.22126238133697643442524790517897 y[1] (numeric) = -0.22126238133697643442524790517896 absolute error = 1e-32 relative error = 4.5195210950795467398970207916114e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 272 Order of pole (three term test) = -7141 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = -0.2196512441914665716012851395343 y[1] (numeric) = -0.21965124419146657160128513953429 absolute error = 1e-32 relative error = 4.5526716849749121423214317043861e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 271.8 Order of pole (three term test) = -7137 Radius of convergence (six term test) for eq 1 = 5.174e+10 Order of pole (six term test) = 3.598e+20 TOP MAIN SOLVE Loop bytes used=12002460, alloc=4193536, time=0.41 x[1] = 1.23 y[1] (analytic) = -0.21805026294992111311686451636277 y[1] (numeric) = -0.21805026294992111311686451636275 absolute error = 2e-32 relative error = 9.1721971482296878653891483953140e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 271.7 Order of pole (three term test) = -7133 Radius of convergence (six term test) for eq 1 = 4.477e+10 Order of pole (six term test) = 2.687e+20 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = -0.21645939501840987775742287432843 y[1] (numeric) = -0.21645939501840987775742287432842 absolute error = 1e-32 relative error = 4.6198040972763042754780955803771e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 271.5 Order of pole (three term test) = -7129 Radius of convergence (six term test) for eq 1 = 6.869e+10 Order of pole (six term test) = 6.308e+20 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = -0.21487859764514257524366406998588 y[1] (numeric) = -0.21487859764514257524366406998586 absolute error = 2e-32 relative error = 9.3075812198982436696814560791260e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 271.4 Order of pole (three term test) = -7125 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = -0.21330782792782732138203799037388 y[1] (numeric) = -0.21330782792782732138203799037387 absolute error = 1e-32 relative error = 4.6880604885177954321458883718389e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 271.2 Order of pole (three term test) = -7122 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = -0.21174704282089834538472159813669 y[1] (numeric) = -0.21174704282089834538472159813667 absolute error = 2e-32 relative error = 9.4452322608899748656749904232145e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 271.1 Order of pole (three term test) = -7118 Radius of convergence (six term test) for eq 1 = 2.751e+10 Order of pole (six term test) = 1.003e+20 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = -0.21019619914261476394268150194665 y[1] (numeric) = -0.21019619914261476394268150194664 absolute error = 1e-32 relative error = 4.7574599544567215110697333429111e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 270.9 Order of pole (three term test) = -7114 Radius of convergence (six term test) for eq 1 = 3.696e+10 Order of pole (six term test) = 1.806e+20 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = -0.20865525358203227228129601694921 y[1] (numeric) = -0.2086552535820322722812960169492 absolute error = 1e-32 relative error = 4.7925944007292995917093426154505e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 270.8 Order of pole (three term test) = -7110 Radius of convergence (six term test) for eq 1 = 5.424e+10 Order of pole (six term test) = 3.882e+20 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = -0.20712416270584957837297320734814 y[1] (numeric) = -0.20712416270584957837297320734814 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 270.6 Order of pole (three term test) = -7106 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = -0.20560288296513138272167978906589 y[1] (numeric) = -0.20560288296513138272167978906589 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 270.5 Order of pole (three term test) = -7102 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = -0.2040913707019096826667946600333 y[1] (numeric) = -0.2040913707019096826667946600333 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 270.3 Order of pole (three term test) = -7099 Radius of convergence (six term test) for eq 1 = 5.229e+10 Order of pole (six term test) = 3.578e+20 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = -0.20258958215566515697476124460871 y[1] (numeric) = -0.20258958215566515697476124460871 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 270.2 Order of pole (three term test) = -7095 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = -0.20109747346969036359321573543502 y[1] (numeric) = -0.20109747346969036359321573543502 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 270 Order of pole (three term test) = -7091 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = -0.19961500069733646083023411024789 y[1] (numeric) = -0.19961500069733646083023411024789 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 269.9 Order of pole (three term test) = -7087 Radius of convergence (six term test) for eq 1 = 2.973e+10 Order of pole (six term test) = 1.148e+20 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = -0.19814211980814513988772893629301 y[1] (numeric) = -0.19814211980814513988772893629301 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 269.7 Order of pole (three term test) = -7083 Radius of convergence (six term test) for eq 1 = 4.183e+11 Order of pole (six term test) = 2.267e+22 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = -0.19667878669386743461953547666174 y[1] (numeric) = -0.19667878669386743461953547666174 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 269.6 Order of pole (three term test) = -7080 NO COMPLEX POLE (six term test) for Equation 1 bytes used=16003232, alloc=4259060, time=0.55 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = -0.19522495717437105259809165153842 y[1] (numeric) = -0.19522495717437105259809165153842 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 269.4 Order of pole (three term test) = -7076 Radius of convergence (six term test) for eq 1 = 3.799e+10 Order of pole (six term test) = 1.860e+20 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = -0.19378058700343785005561186637287 y[1] (numeric) = -0.19378058700343785005561186637287 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 269.3 Order of pole (three term test) = -7072 Radius of convergence (six term test) for eq 1 = 2.229e+10 Order of pole (six term test) = 6.389e+19 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = -0.19234563187445305201309176707034 y[1] (numeric) = -0.19234563187445305201309176707034 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 269.1 Order of pole (three term test) = -7068 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = -0.19092004742598779792020765098168 y[1] (numeric) = -0.19092004742598779792020765098168 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 269 Order of pole (three term test) = -7064 Radius of convergence (six term test) for eq 1 = 2.075e+10 Order of pole (six term test) = 5.505e+19 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = -0.18950378924727657239807502829262 y[1] (numeric) = -0.18950378924727657239807502829262 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 268.8 Order of pole (three term test) = -7060 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = -0.18809681288359106020182619962463 y[1] (numeric) = -0.18809681288359106020182619962463 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 268.7 Order of pole (three term test) = -7057 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = -0.1866990738415119442980128237105 y[1] (numeric) = -0.18669907384151194429801282371051 absolute error = 1e-32 relative error = 5.3562129657316660224280823975774e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 268.5 Order of pole (three term test) = -7053 Radius of convergence (six term test) for eq 1 = 2.791e+10 Order of pole (six term test) = 9.883e+19 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = -0.18531052759410014597992764447817 y[1] (numeric) = -0.18531052759410014597992764447818 absolute error = 1e-32 relative error = 5.3963474875554650485931780703556e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 268.4 Order of pole (three term test) = -7049 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = -0.1839311295859689862190959999805 y[1] (numeric) = -0.18393112958596898621909599998051 absolute error = 1e-32 relative error = 5.4368175862944521517121084460640e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 268.2 Order of pole (three term test) = -7045 Radius of convergence (six term test) for eq 1 = 1.641e+10 Order of pole (six term test) = 3.401e+19 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = -0.18256083523825872797047304114329 y[1] (numeric) = -0.1825608352382587279704730411433 absolute error = 1e-32 relative error = 5.4776261222452656278440452391212e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 268 Order of pole (three term test) = -7041 Radius of convergence (six term test) for eq 1 = 2.353e+10 Order of pole (six term test) = 6.970e+19 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = -0.18119959995351493990939137501262 y[1] (numeric) = -0.18119959995351493990939137501263 absolute error = 1e-32 relative error = 5.5187759810537144293138035720066e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 267.9 Order of pole (three term test) = -7037 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = -0.17984737912047210307716439149093 y[1] (numeric) = -0.17984737912047210307716439149094 absolute error = 1e-32 relative error = 5.5602700739394293342217491904936e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 267.7 Order of pole (three term test) = -7034 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = -0.17850412811874386314662437661121 y[1] (numeric) = -0.17850412811874386314662437661122 absolute error = 1e-32 relative error = 5.6021113379225810282525693251491e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 267.6 Order of pole (three term test) = -7030 Radius of convergence (six term test) for eq 1 = 1.841e+10 Order of pole (six term test) = 4.237e+19 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = -0.17716980232342131248595608940911 y[1] (numeric) = -0.17716980232342131248595608940912 absolute error = 1e-32 relative error = 5.6443027360526835213021692566229e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 267.4 Order of pole (three term test) = -7026 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = -0.17584435710958066789620272820068 y[1] (numeric) = -0.1758443571095806678962027282007 absolute error = 2e-32 relative error = 1.1373694515279003002458299560795e-29 % Correct digits = 31 h = 0.01 bytes used=20004024, alloc=4259060, time=0.70 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 267.3 Order of pole (three term test) = -7022 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (analytic) = -0.17452774785670169182203122564831 y[1] (numeric) = -0.17452774785670169182203122564833 absolute error = 2e-32 relative error = 1.1459495836972160816574490589962e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 267.1 Order of pole (three term test) = -7018 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = -0.17321992995299818698403846064011 y[1] (numeric) = -0.17321992995299818698403846064013 absolute error = 2e-32 relative error = 1.1546015522247836393052937540208e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 267 Order of pole (three term test) = -7014 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = -0.17192085879966187675138154803958 y[1] (numeric) = -0.17192085879966187675138154803959 absolute error = 1e-32 relative error = 5.8166298550502979326822713735610e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 266.8 Order of pole (three term test) = -7011 Radius of convergence (six term test) for eq 1 = 3.807e+10 Order of pole (six term test) = 1.789e+20 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = -0.17063048981502096616317721615346 y[1] (numeric) = -0.17063048981502096616317721615348 absolute error = 2e-32 relative error = 1.1721234593935601137645161340924e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 266.7 Order of pole (three term test) = -7007 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = -0.16934877843861466131332146670224 y[1] (numeric) = -0.16934877843861466131332146670226 absolute error = 2e-32 relative error = 1.1809946422052034824621965010022e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 266.5 Order of pole (three term test) = -7003 Radius of convergence (six term test) for eq 1 = 3.392e+10 Order of pole (six term test) = 1.414e+20 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = -0.16807568013518490783354565347136 y[1] (numeric) = -0.16807568013518490783354565347138 absolute error = 2e-32 relative error = 1.1899401498130964010978926628039e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 266.4 Order of pole (three term test) = -6999 Radius of convergence (six term test) for eq 1 = 2.553e+10 Order of pole (six term test) = 7.987e+19 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (analytic) = -0.16681115039858659244109324873472 y[1] (numeric) = -0.16681115039858659244109324873474 absolute error = 2e-32 relative error = 1.1989606181727682635809992104166e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 266.2 Order of pole (three term test) = -6995 Radius of convergence (six term test) for eq 1 = 5.003e+10 Order of pole (six term test) = 3.060e+20 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = -0.16555514475561743495784699946755 y[1] (numeric) = -0.16555514475561743495784699946757 absolute error = 2e-32 relative error = 1.2080566888768572691839722820546e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 266.1 Order of pole (three term test) = -6991 Radius of convergence (six term test) for eq 1 = 2.349e+10 Order of pole (six term test) = 6.730e+19 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = -0.16430761876976878185456235273505 y[1] (numeric) = -0.16430761876976878185456235273507 absolute error = 2e-32 relative error = 1.2172290092052524816350081375460e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 265.9 Order of pole (three term test) = -6987 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = -0.16306852804489849622460239810636 y[1] (numeric) = -0.16306852804489849622460239810638 absolute error = 2e-32 relative error = 1.2264782321756959241276924575012e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 265.8 Order of pole (three term test) = -6984 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = -0.16183782822882712314378325339081 y[1] (numeric) = -0.16183782822882712314378325339083 absolute error = 2e-32 relative error = 1.2358050165948488463769139068093e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 265.6 Order of pole (three term test) = -6980 Radius of convergence (six term test) for eq 1 = 3.055e+10 Order of pole (six term test) = 1.130e+20 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = -0.16061547501685849362421627326992 y[1] (numeric) = -0.16061547501685849362421627326994 absolute error = 2e-32 relative error = 1.2452100271098263395675841313694e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 265.5 Order of pole (three term test) = -6976 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = -0.15940142415522591481799217667387 y[1] (numeric) = -0.15940142415522591481799217667389 absolute error = 2e-32 relative error = 1.2546939342602045150981462874005e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 265.3 Order of pole (three term test) = -6972 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = -0.15819563144446507876883736050089 y[1] (numeric) = -0.15819563144446507876883736050091 absolute error = 2e-32 relative error = 1.2642574145305045034183823251572e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 265.2 Order of pole (three term test) = -6968 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=24004972, alloc=4324584, time=0.85 x[1] = 1.67 y[1] (analytic) = -0.15699805274271480684415687584571 y[1] (numeric) = -0.15699805274271480684415687584573 absolute error = 2e-32 relative error = 1.2739011504031575700045602371299e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 265 Order of pole (three term test) = -6964 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = -0.15580864396894673200386144658671 y[1] (numeric) = -0.15580864396894673200386144658673 absolute error = 2e-32 relative error = 1.2836258304119556866084294896945e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 264.9 Order of pole (three term test) = -6960 Radius of convergence (six term test) for eq 1 = 2.019e+10 Order of pole (six term test) = 4.877e+19 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = -0.15462736110612500627378393582625 y[1] (numeric) = -0.15462736110612500627378393582628 absolute error = 3e-32 relative error = 1.9401482237939879060458923172745e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 264.7 Order of pole (three term test) = -6957 Radius of convergence (six term test) for eq 1 = 1.855e+10 Order of pole (six term test) = 4.105e+19 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = -0.15345416020429710618807670371751 y[1] (numeric) = -0.15345416020429710618807670371753 absolute error = 2e-32 relative error = 1.3033208075540951811406815864307e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 264.5 Order of pole (three term test) = -6953 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = -0.15228899738361679454452440312886 y[1] (numeric) = -0.15228899738361679454452440312888 absolute error = 2e-32 relative error = 1.3132925124997634337004399884705e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 264.4 Order of pole (three term test) = -6949 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = -0.15113182883730028257701184377505 y[1] (numeric) = -0.15113182883730028257701184377507 absolute error = 2e-32 relative error = 1.3233479773166004757455415812842e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 264.2 Order of pole (three term test) = -6945 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = -0.14998261083451662258828410634347 y[1] (numeric) = -0.1499826108345166225882841063435 absolute error = 3e-32 relative error = 2.0002318824213903537769846517050e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 264.1 Order of pole (three term test) = -6941 Radius of convergence (six term test) for eq 1 = 2.142e+10 Order of pole (six term test) = 5.421e+19 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = -0.14884129972321334720148186880219 y[1] (numeric) = -0.14884129972321334720148186880222 absolute error = 3e-32 relative error = 2.0155696070773553108268038336180e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 263.9 Order of pole (three term test) = -6937 Radius of convergence (six term test) for eq 1 = 2.617e+10 Order of pole (six term test) = 8.075e+19 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = -0.14770785193287835767860966986642 y[1] (numeric) = -0.14770785193287835767860966986644 absolute error = 2e-32 relative error = 1.3540241590601718674979999305512e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 263.8 Order of pole (three term test) = -6933 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (analytic) = -0.14658222397723905021600403622931 y[1] (numeric) = -0.14658222397723905021600403622933 absolute error = 2e-32 relative error = 1.3644219235686827816620517897769e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 263.6 Order of pole (three term test) = -6930 Radius of convergence (six term test) for eq 1 = 2.070e+10 Order of pole (six term test) = 5.029e+19 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = -0.14546437245689965575894191986325 y[1] (numeric) = -0.14546437245689965575894191986327 absolute error = 2e-32 relative error = 1.3749071103940517789499423690465e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 263.5 Order of pole (three term test) = -6926 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = -0.14435425406191775567772175258403 y[1] (numeric) = -0.14435425406191775567772175258405 absolute error = 2e-32 relative error = 1.3854804716334453064413718649642e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 263.3 Order of pole (three term test) = -6922 Radius of convergence (six term test) for eq 1 = 5.171e+10 Order of pole (six term test) = 3.124e+20 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = -0.14325182557432092261383751862116 y[1] (numeric) = -0.14325182557432092261383751862118 absolute error = 2e-32 relative error = 1.3961427660566697736499922440129e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 263.2 Order of pole (three term test) = -6918 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = -0.1421570438705644229352520595717 y[1] (numeric) = -0.14215704387056442293525205957173 absolute error = 3e-32 relative error = 2.1103421387487021222317525417539e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 263 Order of pole (three term test) = -6914 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (analytic) = -0.14106986592393090453228417382358 y[1] (numeric) = -0.1410698659239309045322841738236 absolute error = 2e-32 relative error = 1.4177372232553619082898006788851e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 262.9 Order of pole (three term test) = -6910 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=28006292, alloc=4324584, time=1.01 x[1] = 1.82 y[1] (analytic) = -0.13999024880687298113830282854031 y[1] (numeric) = -0.13999024880687298113830282854034 absolute error = 3e-32 relative error = 2.1430064062095670580082540437152e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 262.7 Order of pole (three term test) = -6906 Radius of convergence (six term test) for eq 1 = 2.787e+10 Order of pole (six term test) = 8.991e+19 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = -0.13891814969329961197034163770439 y[1] (numeric) = -0.13891814969329961197034163770442 absolute error = 3e-32 relative error = 2.1595450318214956017422749780507e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 262.6 Order of pole (three term test) = -6902 Radius of convergence (six term test) for eq 1 = 2.736e+10 Order of pole (six term test) = 8.647e+19 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = -0.13785352586080716325200088210822 y[1] (numeric) = -0.13785352586080716325200088210824 absolute error = 2e-32 relative error = 1.4508152675176628611087591191301e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 262.4 Order of pole (three term test) = -6899 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = -0.13679633469285602610270824316572 y[1] (numeric) = -0.13679633469285602610270824316574 absolute error = 2e-32 relative error = 1.4620274764601911964016602001463e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 262.3 Order of pole (three term test) = -6895 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = -0.13574653368089365335170060303866 y[1] (numeric) = -0.13574653368089365335170060303868 absolute error = 2e-32 relative error = 1.4733341218874160649123725442453e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 262.1 Order of pole (three term test) = -6891 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = -0.13470408042642486606012701260046 y[1] (numeric) = -0.13470408042642486606012701260048 absolute error = 2e-32 relative error = 1.4847360181434121544688858865787e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 261.9 Order of pole (three term test) = -6887 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = -0.13366893264303026890863805380436 y[1] (numeric) = -0.13366893264303026890863805380439 absolute error = 3e-32 relative error = 2.2443509802024481326375404593561e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 261.8 Order of pole (three term test) = -6883 Radius of convergence (six term test) for eq 1 = 2.541e+10 Order of pole (six term test) = 7.371e+19 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = -0.13264104815833360212892140943797 y[1] (numeric) = -0.132641048158333602128921409438 absolute error = 3e-32 relative error = 2.2617432850944455639410839966150e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 261.6 Order of pole (three term test) = -6879 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = -0.13162038491591884632409062081129 y[1] (numeric) = -0.13162038491591884632409062081132 absolute error = 3e-32 relative error = 2.2792821962315691191156354753498e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 261.5 Order of pole (three term test) = -6875 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = -0.1306069009771978853328776762566 y[1] (numeric) = -0.13060690097719788533287767625663 absolute error = 3e-32 relative error = 2.2969689790922743817961421492693e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 261.3 Order of pole (three term test) = -6871 Radius of convergence (six term test) for eq 1 = 3.170e+10 Order of pole (six term test) = 1.139e+20 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (analytic) = -0.12960055452322952124448469998359 y[1] (numeric) = -0.12960055452322952124448469998362 absolute error = 3e-32 relative error = 2.3148049103927884055248638573331e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 261.2 Order of pole (three term test) = -6868 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (analytic) = -0.12860130385649062476300039214676 y[1] (numeric) = -0.12860130385649062476300039214679 absolute error = 3e-32 relative error = 2.3327912781877967496430087699753e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 261 Order of pole (three term test) = -6864 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = -0.12760910740260019335078788544181 y[1] (numeric) = -0.12760910740260019335078788544184 absolute error = 3e-32 relative error = 2.3509293819720513855175230154987e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 260.9 Order of pole (three term test) = -6860 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = -0.12662392371199707894752706788881 y[1] (numeric) = -0.12662392371199707894752706788884 absolute error = 3e-32 relative error = 2.3692205327829078654913085169318e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 260.7 Order of pole (three term test) = -6856 Radius of convergence (six term test) for eq 1 = 2.239e+10 Order of pole (six term test) = 5.631e+19 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = -0.1256457114615721365639905432976 y[1] (numeric) = -0.12564571146157213656399054329763 absolute error = 3e-32 relative error = 2.3876660533038002258211105847809e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 260.6 Order of pole (three term test) = -6852 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=32007780, alloc=4390108, time=1.15 x[1] = 1.97 y[1] (analytic) = -0.12467442945625553468551203393797 y[1] (numeric) = -0.12467442945625553468551203393801 absolute error = 4e-32 relative error = 3.2083563706248828992741987042048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 260.4 Order of pole (three term test) = -6848 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = -0.12371003663055995818785213165665 y[1] (numeric) = -0.12371003663055995818785213165668 absolute error = 3e-32 relative error = 2.4250255530673031948144312789547e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 260.3 Order of pole (three term test) = -6844 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = -0.12275249205008042436618079563696 y[1] (numeric) = -0.12275249205008042436618079563699 absolute error = 3e-32 relative error = 2.4439422368517482777623065145370e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 260.1 Order of pole (three term test) = -6840 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = -0.12180175491295142270459954547524 y[1] (numeric) = -0.12180175491295142270459954547527 absolute error = 3e-32 relative error = 2.4630186996435500757434758201916e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 260 Order of pole (three term test) = -6837 Radius of convergence (six term test) for eq 1 = 4.829e+10 Order of pole (six term test) = 2.591e+20 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = -0.12085778455126207916745810743713 y[1] (numeric) = -0.12085778455126207916745810743716 absolute error = 3e-32 relative error = 2.4822563239420823555487022574385e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 259.8 Order of pole (three term test) = -6833 Radius of convergence (six term test) for eq 1 = 3.338e+10 Order of pole (six term test) = 1.235e+20 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = -0.11992054043243003607313785931741 y[1] (numeric) = -0.11992054043243003607313785931744 absolute error = 3e-32 relative error = 2.5016565045338237094482617291129e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 259.6 Order of pole (three term test) = -6829 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = -0.11898998216053472901445341435182 y[1] (numeric) = -0.11898998216053472901445341435185 absolute error = 3e-32 relative error = 2.5212206486026405684381952503762e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 259.5 Order of pole (three term test) = -6825 Radius of convergence (six term test) for eq 1 = 2.834e+10 Order of pole (six term test) = 8.868e+19 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = -0.11806606947761073281585761798056 y[1] (numeric) = -0.11806606947761073281585761798059 absolute error = 3e-32 relative error = 2.5409501758410786461261800313274e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 259.3 Order of pole (three term test) = -6821 Radius of convergence (six term test) for eq 1 = 4.090e+10 Order of pole (six term test) = 1.842e+20 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = -0.11714876226490183916473533023783 y[1] (numeric) = -0.11714876226490183916473533023786 absolute error = 3e-32 relative error = 2.5608465185626720273334057621685e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 259.2 Order of pole (three term test) = -6817 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = -0.11623802054407651932076635185884 y[1] (numeric) = -0.11623802054407651932076635185887 absolute error = 3e-32 relative error = 2.5809111218152792018178603338671e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 259 Order of pole (three term test) = -6813 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = -0.11533380447840541619217373726719 y[1] (numeric) = -0.11533380447840541619217373726721 absolute error = 2e-32 relative error = 1.7340969623303036204267299900101e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 258.9 Order of pole (three term test) = -6809 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = -0.11443607437390150106921363007176 y[1] (numeric) = -0.11443607437390150106921363007178 absolute error = 2e-32 relative error = 1.7477006363092472804017432156920e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 258.7 Order of pole (three term test) = -6805 Radius of convergence (six term test) for eq 1 = 5.407e+10 Order of pole (six term test) = 3.192e+20 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = -0.11354479068042352142208666220373 y[1] (numeric) = -0.11354479068042352142208666220375 absolute error = 2e-32 relative error = 1.7614194257745229139375687835386e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 258.6 Order of pole (three term test) = -6801 Radius of convergence (six term test) for eq 1 = 1.064e+11 Order of pole (six term test) = 1.234e+21 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = -0.11265991399274335740115558598682 y[1] (numeric) = -0.11265991399274335740115558598684 absolute error = 2e-32 relative error = 1.7752543288190543637934190022779e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 258.4 Order of pole (three term test) = -6798 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = -0.11178140505157789602055238104201 y[1] (numeric) = -0.11178140505157789602055238104204 absolute error = 3e-32 relative error = 2.6838095286203886164595077006259e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 258.3 Order of pole (three term test) = -6794 Radius of convergence (six term test) for eq 1 = 2.773e+10 Order of pole (six term test) = 8.341e+19 bytes used=36011760, alloc=4390108, time=1.30 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = -0.11090922474458602346058013925996 y[1] (numeric) = -0.11090922474458602346058013925999 absolute error = 3e-32 relative error = 2.7049147687297701095781329381320e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 258.1 Order of pole (three term test) = -6790 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = -0.11004333410733132748840626037928 y[1] (numeric) = -0.11004333410733132748840626037931 absolute error = 3e-32 relative error = 2.7261987510065213859954019291843e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 257.9 Order of pole (three term test) = -6786 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = -0.10918369432421109366906551679945 y[1] (numeric) = -0.10918369432421109366906551679948 absolute error = 3e-32 relative error = 2.7476630265795656732275826713502e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 257.8 Order of pole (three term test) = -6782 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = -0.10833026672935217081842176419004 y[1] (numeric) = -0.10833026672935217081842176419007 absolute error = 3e-32 relative error = 2.7693091603799657633032218104521e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 257.6 Order of pole (three term test) = -6778 Radius of convergence (six term test) for eq 1 = 6.266e+10 Order of pole (six term test) = 4.222e+20 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = -0.10748301280747427303516846429221 y[1] (numeric) = -0.10748301280747427303516846429225 absolute error = 4e-32 relative error = 3.7215183083534141132484920323651e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 257.5 Order of pole (three term test) = -6774 Radius of convergence (six term test) for eq 1 = 2.625e+10 Order of pole (six term test) = 7.392e+19 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = -0.10664189419472127763888913389901 y[1] (numeric) = -0.10664189419472127763888913389905 absolute error = 4e-32 relative error = 3.7508711095249826048147431557850e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 257.3 Order of pole (three term test) = -6770 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = -0.10580687267946107043437295382424 y[1] (numeric) = -0.10580687267946107043437295382427 absolute error = 3e-32 relative error = 2.8353545701028468995560921206215e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 257.2 Order of pole (three term test) = -6766 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = -0.1049779102030544819175267316456 y[1] (numeric) = -0.10497791020305448191752673164563 absolute error = 3e-32 relative error = 2.8577440665347810707690216730273e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 257 Order of pole (three term test) = -6762 Radius of convergence (six term test) for eq 1 = 3.477e+10 Order of pole (six term test) = 1.289e+20 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = -0.10415496886059385033409576029894 y[1] (numeric) = -0.10415496886059385033409576029897 absolute error = 3e-32 relative error = 2.8803234572662088063207799468794e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 256.9 Order of pole (three term test) = -6759 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = -0.10333801090161173989777110837224 y[1] (numeric) = -0.10333801090161173989777110837226 absolute error = 2e-32 relative error = 1.9353962617919970494310412682721e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 256.7 Order of pole (three term test) = -6755 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = -0.10252699873076033496790231405919 y[1] (numeric) = -0.10252699873076033496790231405922 absolute error = 3e-32 relative error = 2.9260585378863085674127576363602e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 256.6 Order of pole (three term test) = -6751 Radius of convergence (six term test) for eq 1 = 5.835e+10 Order of pole (six term test) = 3.606e+20 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = -0.10172189490846202357774950233917 y[1] (numeric) = -0.1017218949084620235777495023392 absolute error = 3e-32 relative error = 2.9492175727749213543530386663651e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 256.4 Order of pole (three term test) = -6747 Radius of convergence (six term test) for eq 1 = 2.912e+10 Order of pole (six term test) = 8.962e+19 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = -0.10092266215153167639080898000512 y[1] (numeric) = -0.10092266215153167639080898000515 absolute error = 3e-32 relative error = 2.9725731922287285781978510034853e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 256.2 Order of pole (three term test) = -6743 Radius of convergence (six term test) for eq 1 = 3.125e+10 Order of pole (six term test) = 1.030e+20 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = -0.10012926333377111994405680477866 y[1] (numeric) = -0.10012926333377111994405680477869 absolute error = 3e-32 relative error = 2.9961271062184818064895902245827e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 256.1 Order of pole (three term test) = -6739 Radius of convergence (six term test) for eq 1 = 6.081e+10 Order of pole (six term test) = 3.893e+20 TOP MAIN SOLVE Loop bytes used=40012452, alloc=4390108, time=1.46 x[1] = 2.26 y[1] (analytic) = -0.099341661486536295911814973424912 y[1] (numeric) = -0.099341661486536295911814973424939 absolute error = 2.7e-32 relative error = 2.7178929359520819594206933057040e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 255.9 Order of pole (three term test) = -6735 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = -0.098559819799277591091207751429108 y[1] (numeric) = -0.098559819799277591091207751429135 absolute error = 2.7e-32 relative error = 2.7394530605866530337973080347474e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 255.8 Order of pole (three term test) = -6731 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = -0.097783701620053815868707858622811 y[1] (numeric) = -0.097783701620053815868707858622838 absolute error = 2.7e-32 relative error = 2.7611963499715526909478568834632e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 255.6 Order of pole (three term test) = -6727 Radius of convergence (six term test) for eq 1 = 3.025e+10 Order of pole (six term test) = 9.569e+19 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = -0.097013270456020302075953723274113 y[1] (numeric) = -0.09701327045602030207595372327414 absolute error = 2.7e-32 relative error = 2.7831243986605004759439767062340e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 255.5 Order of pole (three term test) = -6723 Radius of convergence (six term test) for eq 1 = 3.025e+10 Order of pole (six term test) = 9.554e+19 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = -0.096248489973891584380743066046067 y[1] (numeric) = -0.096248489973891584380743066046094 absolute error = 2.7e-32 relative error = 2.8052388154166402081130792628806e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 255.3 Order of pole (three term test) = -6719 Radius of convergence (six term test) for eq 1 = 3.301e+10 Order of pole (six term test) = 1.135e+20 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = -0.095489324000379122684781018840141 y[1] (numeric) = -0.095489324000379122684781018840163 absolute error = 2.2e-32 relative error = 2.3039224782775353056694388396367e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 255.2 Order of pole (three term test) = -6715 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = -0.094735736522604516412302114226203 y[1] (numeric) = -0.094735736522604516412302114226225 absolute error = 2.2e-32 relative error = 2.3222493229627942678804217028392e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 255 Order of pole (three term test) = -6712 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = -0.093987691688488655072026890256781 y[1] (numeric) = -0.093987691688488655072026890256811 absolute error = 3.0e-32 relative error = 3.1919073083985862587696083031382e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 254.9 Order of pole (three term test) = -6708 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = -0.093245153807117243058000285592435 y[1] (numeric) = -0.093245153807117243058000285592461 absolute error = 2.6e-32 relative error = 2.7883486635436773211811613589161e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 254.7 Order of pole (three term test) = -6704 Radius of convergence (six term test) for eq 1 = 4.231e+10 Order of pole (six term test) = 1.849e+20 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = -0.092508087349083130321647698895804 y[1] (numeric) = -0.092508087349083130321647698895834 absolute error = 3.0e-32 relative error = 3.2429597086786312356398064553945e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 254.5 Order of pole (three term test) = -6700 Radius of convergence (six term test) for eq 1 = 2.828e+10 Order of pole (six term test) = 8.247e+19 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = -0.091776456946805874296845163117692 y[1] (numeric) = -0.091776456946805874296845163117716 absolute error = 2.4e-32 relative error = 2.6150497413416742014886405943464e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 254.4 Order of pole (three term test) = -6696 Radius of convergence (six term test) for eq 1 = 4.933e+10 Order of pole (six term test) = 2.503e+20 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = -0.09105022739482895229091436644959 y[1] (numeric) = -0.091050227394828952290914366449615 absolute error = 2.5e-32 relative error = 2.7457372392482167294484494964528e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 254.2 Order of pole (three term test) = -6692 Radius of convergence (six term test) for eq 1 = 7.178e+10 Order of pole (six term test) = 5.290e+20 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = -0.090329363650095037466215141194639 y[1] (numeric) = -0.090329363650095037466215141194662 absolute error = 2.3e-32 relative error = 2.5462373552297023411320868603852e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 254.1 Order of pole (three term test) = -6688 Radius of convergence (six term test) for eq 1 = 3.549e+10 Order of pole (six term test) = 1.291e+20 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = -0.08961383083219974552842338090745 y[1] (numeric) = -0.089613830832199745528423380907472 absolute error = 2.2e-32 relative error = 2.4549781875963540114788549353806e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 253.9 Order of pole (three term test) = -6684 Radius of convergence (six term test) for eq 1 = 4.714e+10 Order of pole (six term test) = 2.272e+20 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = -0.088903594223624253307668775678096 y[1] (numeric) = -0.088903594223624253307668775678122 absolute error = 2.6e-32 relative error = 2.9245161826192004383488411633813e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 253.8 Order of pole (three term test) = -6680 Radius of convergence (six term test) for eq 1 = 4.765e+10 Order of pole (six term test) = 2.317e+20 TOP MAIN SOLVE Loop bytes used=44013492, alloc=4390108, time=1.60 x[1] = 2.41 y[1] (analytic) = -0.088198619269947184566493579309495 y[1] (numeric) = -0.088198619269947184566493579309519 absolute error = 2.4e-32 relative error = 2.7211310334171824016033454512726e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 253.6 Order of pole (three term test) = -6676 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = -0.087498871580036152593121672564968 y[1] (numeric) = -0.087498871580036152593121672564996 absolute error = 2.8e-32 relative error = 3.2000412684623139251923221316552e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 253.5 Order of pole (three term test) = -6672 Radius of convergence (six term test) for eq 1 = 3.874e+10 Order of pole (six term test) = 1.525e+20 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = -0.086804316926219343438848690815511 y[1] (numeric) = -0.086804316926219343438848690815534 absolute error = 2.3e-32 relative error = 2.6496378077082504675656200459420e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 253.3 Order of pole (three term test) = -6668 Radius of convergence (six term test) for eq 1 = 6.007e+10 Order of pole (six term test) = 3.660e+20 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = -0.086114921244437518033542432632324 y[1] (numeric) = -0.086114921244437518033542432632351 absolute error = 2.7e-32 relative error = 3.1353451422617459667299097485398e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 253.1 Order of pole (three term test) = -6664 Radius of convergence (six term test) for eq 1 = 6.684e+10 Order of pole (six term test) = 4.521e+20 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = -0.085430650634376805862352781350995 y[1] (numeric) = -0.085430650634376805862352781351018 absolute error = 2.3e-32 relative error = 2.6922421670923025100715782064731e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 253 Order of pole (three term test) = -6661 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = -0.084751471359582657408857581611753 y[1] (numeric) = -0.084751471359582657408857581611778 absolute error = 2.5e-32 relative error = 2.9498012953580783439977318953652e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 252.8 Order of pole (three term test) = -6657 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = -0.084077349847555317164111821258835 y[1] (numeric) = -0.08407734984755531716411182125886 absolute error = 2.5e-32 relative error = 2.9734524274764489156027045524756e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 252.7 Order of pole (three term test) = -6653 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = -0.083408252689827173666529330407187 y[1] (numeric) = -0.083408252689827173666529330407215 absolute error = 2.8e-32 relative error = 3.3569819648571776702988672837041e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 252.5 Order of pole (three term test) = -6649 Radius of convergence (six term test) for eq 1 = 9.208e+10 Order of pole (six term test) = 8.514e+20 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = -0.082744146642022337773326904860512 y[1] (numeric) = -0.082744146642022337773326904860536 absolute error = 2.4e-32 relative error = 2.9005072834736796139713184808845e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 252.4 Order of pole (three term test) = -6645 Radius of convergence (six term test) for eq 1 = 3.547e+10 Order of pole (six term test) = 1.261e+20 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = -0.08208499862389879516952867446716 y[1] (numeric) = -0.082084998623898795169528674467185 absolute error = 2.5e-32 relative error = 3.0456234901758683595175439877920e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 252.2 Order of pole (three term test) = -6641 Radius of convergence (six term test) for eq 1 = 5.675e+10 Order of pole (six term test) = 3.220e+20 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = -0.081430775719373473994402434001873 y[1] (numeric) = -0.081430775719373473994402434001897 absolute error = 2.4e-32 relative error = 2.9472886372480027871363876632457e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 252.1 Order of pole (three term test) = -6637 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = -0.080781445176530563406828561525371 y[1] (numeric) = -0.080781445176530563406828561525399 absolute error = 2.8e-32 relative error = 3.4661424958184384095236245918874e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 251.9 Order of pole (three term test) = -6633 Radius of convergence (six term test) for eq 1 = 6.342e+10 Order of pole (six term test) = 4.006e+20 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = -0.08013697440761341391964523592534 y[1] (numeric) = -0.080136974407613413919645235925364 absolute error = 2.4e-32 relative error = 2.9948722393641903955543594115487e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 251.7 Order of pole (three term test) = -6629 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = -0.079497330989000345407640125180843 y[1] (numeric) = -0.079497330989000345407640125180869 absolute error = 2.6e-32 relative error = 3.2705500520008013967039150343229e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 251.6 Order of pole (three term test) = -6625 Radius of convergence (six term test) for eq 1 = 1.724e+11 Order of pole (six term test) = 2.947e+21 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = -0.078862482661164683833747651948313 y[1] (numeric) = -0.078862482661164683833747651948341 absolute error = 2.8e-32 relative error = 3.5504842169758900718649020304662e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 251.4 Order of pole (three term test) = -6621 Radius of convergence (six term test) for eq 1 = 4.299e+10 Order of pole (six term test) = 1.829e+20 TOP MAIN SOLVE Loop bytes used=48014316, alloc=4390108, time=1.76 x[1] = 2.56 y[1] (analytic) = -0.078232397328619342942351248972236 y[1] (numeric) = -0.078232397328619342942351248972266 absolute error = 3.0e-32 relative error = 3.8347284532242320958044264303476e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 251.3 Order of pole (three term test) = -6617 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = -0.077607043059846262436580269093602 y[1] (numeric) = -0.077607043059846262436580269093629 absolute error = 2.7e-32 relative error = 3.4790656795387877657988107811072e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 251.1 Order of pole (three term test) = -6613 Radius of convergence (six term test) for eq 1 = 7.440e+10 Order of pole (six term test) = 5.459e+20 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = -0.076986388087211009487339556331622 y[1] (numeric) = -0.076986388087211009487339556331646 absolute error = 2.4e-32 relative error = 3.1174342109429190969876412294131e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 251 Order of pole (three term test) = -6609 Radius of convergence (six term test) for eq 1 = 4.775e+10 Order of pole (six term test) = 2.244e+20 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = -0.076370400806862845814733715220247 y[1] (numeric) = -0.076370400806862845814733715220277 absolute error = 3.0e-32 relative error = 3.9282234587020945433758615451679e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 250.8 Order of pole (three term test) = -6605 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = -0.075759049778620558036774781573376 y[1] (numeric) = -0.075759049778620558036774781573402 absolute error = 2.6e-32 relative error = 3.4319332246082740229560927318351e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 250.7 Order of pole (three term test) = -6601 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = -0.075152303725844344495027483586668 y[1] (numeric) = -0.075152303725844344495027483586696 absolute error = 2.8e-32 relative error = 3.7257673566660070984090908239523e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 250.5 Order of pole (three term test) = -6597 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = -0.074550131535294047341395902981914 y[1] (numeric) = -0.074550131535294047341395902981943 absolute error = 2.9e-32 relative error = 3.8899998434302716336315160301556e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 250.3 Order of pole (three term test) = -6594 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = -0.073952502256974014303843441863639 y[1] (numeric) = -0.073952502256974014303843441863663 absolute error = 2.4e-32 relative error = 3.2453262928958843716840546939768e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 250.2 Order of pole (three term test) = -6590 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = -0.073359385103964870240727832094713 y[1] (numeric) = -0.07335938510396487024072783209474 absolute error = 2.7e-32 relative error = 3.6805106751829528728327087600527e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 250 Order of pole (three term test) = -6586 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = -0.072770749452242474342896566532256 y[1] (numeric) = -0.072770749452242474342896566532284 absolute error = 2.8e-32 relative error = 3.8476998259274026462728729574866e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 249.9 Order of pole (three term test) = -6582 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = -0.072186564840484334649006375337096 y[1] (numeric) = -0.072186564840484334649006375337121 absolute error = 2.5e-32 relative error = 3.4632483281680235282484848621851e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 249.7 Order of pole (three term test) = -6578 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = -0.071606800969863747401992618097381 y[1] (numeric) = -0.071606800969863747401992618097409 absolute error = 2.8e-32 relative error = 3.9102431083025210696316724299481e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 249.6 Order of pole (three term test) = -6574 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = -0.071031427703831924692518628200816 y[1] (numeric) = -0.071031427703831924692518628200842 absolute error = 2.6e-32 relative error = 3.6603515993523217374827140854764e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 249.4 Order of pole (three term test) = -6570 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = -0.070460415067888369807887457414605 y[1] (numeric) = -0.070460415067888369807887457414634 absolute error = 2.9e-32 relative error = 4.1157861434762481634759817867533e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 249.3 Order of pole (three term test) = -6566 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = -0.069893733249339755731613768890206 y[1] (numeric) = -0.069893733249339755731613768890232 absolute error = 2.6e-32 relative error = 3.7199329312182085279672482548670e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 249.1 Order of pole (three term test) = -6562 Radius of convergence (six term test) for eq 1 = 5.487e+10 Order of pole (six term test) = 2.895e+20 bytes used=52015288, alloc=4390108, time=1.91 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = -0.069331352597047558318954677142431 y[1] (numeric) = -0.069331352597047558318954677142459 absolute error = 2.8e-32 relative error = 4.0385769137860965777893889654304e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 248.9 Order of pole (three term test) = -6558 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = -0.06877324362116469180651611804696 y[1] (numeric) = -0.068773243621164691806516118046989 absolute error = 2.9e-32 relative error = 4.2167561791538599910530624946472e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 248.8 Order of pole (three term test) = -6554 Radius of convergence (six term test) for eq 1 = 6.008e+10 Order of pole (six term test) = 3.457e+20 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = -0.068219376992861390498924862781868 y[1] (numeric) = -0.068219376992861390498924862781894 absolute error = 2.6e-32 relative error = 3.8112338672809473222804586606171e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 248.6 Order of pole (three term test) = -6550 Radius of convergence (six term test) for eq 1 = 1.978e+11 Order of pole (six term test) = 3.740e+21 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = -0.067669723544040576711832513748314 y[1] (numeric) = -0.06766972354404057671183251374834 absolute error = 2.6e-32 relative error = 3.8421909590156326607121823980954e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 248.5 Order of pole (three term test) = -6546 Radius of convergence (six term test) for eq 1 = 3.583e+10 Order of pole (six term test) = 1.225e+20 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = -0.067124254267042951337551526835848 y[1] (numeric) = -0.067124254267042951337551526835877 absolute error = 2.9e-32 relative error = 4.3203459489662569209158880317957e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 248.3 Order of pole (three term test) = -6542 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = -0.066582940314342039736777032691134 y[1] (numeric) = -0.06658294031434203973677703269116 absolute error = 2.6e-32 relative error = 3.9049041507107445884633143827874e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 248.2 Order of pole (three term test) = -6538 Radius of convergence (six term test) for eq 1 = 6.090e+10 Order of pole (six term test) = 3.525e+20 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = -0.066045752998229422046492180032814 y[1] (numeric) = -0.066045752998229422046492180032841 absolute error = 2.7e-32 relative error = 4.0880751258485652467329909346148e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 248 Order of pole (three term test) = -6534 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = -0.065512663790490373429666667710763 y[1] (numeric) = -0.06551266379049037342966666771079 absolute error = 2.7e-32 relative error = 4.1213405833024974618169396449059e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 247.8 Order of pole (three term test) = -6530 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = -0.064983644322070136276123323056813 y[1] (numeric) = -0.064983644322070136276123323056843 absolute error = 3.0e-32 relative error = 4.6165462575959624192672429524392e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 247.7 Order of pole (three term test) = -6526 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = -0.064458666382731042895358671474977 y[1] (numeric) = -0.064458666382731042895358671475006 absolute error = 2.9e-32 relative error = 4.4990071354888155308815326822342e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 247.5 Order of pole (three term test) = -6522 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = -0.063937701920700703820560384657685 y[1] (numeric) = -0.063937701920700703820560384657715 absolute error = 3.0e-32 relative error = 4.6920672934425706134475088950220e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 247.4 Order of pole (three term test) = -6518 Radius of convergence (six term test) for eq 1 = 4.222e+10 Order of pole (six term test) = 1.679e+20 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = -0.063420723042311473467974474582547 y[1] (numeric) = -0.063420723042311473467974474582577 absolute error = 3.0e-32 relative error = 4.7303150391371823485264661948761e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 247.2 Order of pole (three term test) = -6514 Radius of convergence (six term test) for eq 1 = 4.383e+10 Order of pole (six term test) = 1.805e+20 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = -0.062907702011631401566552439288916 y[1] (numeric) = -0.062907702011631401566552439288943 absolute error = 2.7e-32 relative error = 4.2920022726323399643887416410863e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 247.1 Order of pole (three term test) = -6510 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = -0.062398611250086875488874642174957 y[1] (numeric) = -0.062398611250086875488874642174987 absolute error = 3.0e-32 relative error = 4.8077993081870443083729701450169e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 246.9 Order of pole (three term test) = -6506 Radius of convergence (six term test) for eq 1 = 3.572e+10 Order of pole (six term test) = 1.195e+20 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = -0.061893423336077155375129370651819 y[1] (numeric) = -0.061893423336077155375129370651848 absolute error = 2.9e-32 relative error = 4.6854735829575844699088588023358e-29 % Correct digits = 31 h = 0.01 bytes used=56016980, alloc=4390108, time=2.06 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 246.7 Order of pole (three term test) = -6502 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = -0.061392111004581000746862516048042 y[1] (numeric) = -0.061392111004581000746862516048071 absolute error = 2.9e-32 relative error = 4.7237339660524227807304755526971e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 246.6 Order of pole (three term test) = -6498 Radius of convergence (six term test) for eq 1 = 3.861e+10 Order of pole (six term test) = 1.391e+20 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = -0.060894647146755584155742699869714 y[1] (numeric) = -0.060894647146755584155742699869742 absolute error = 2.8e-32 relative error = 4.5981053034957632675965867063230e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 246.4 Order of pole (three term test) = -6494 Radius of convergence (six term test) for eq 1 = 2.996e+11 Order of pole (six term test) = 8.357e+21 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = -0.060401004809527884304159729033937 y[1] (numeric) = -0.060401004809527884304159729033966 absolute error = 2.9e-32 relative error = 4.8012446301928787887905150797960e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 246.3 Order of pole (three term test) = -6491 Radius of convergence (six term test) for eq 1 = 3.606e+10 Order of pole (six term test) = 1.208e+20 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = -0.05991115719517874800854593487176 y[1] (numeric) = -0.059911157195178748008545934871789 absolute error = 2.9e-32 relative error = 4.8405007276897878676429444960029e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 246.1 Order of pole (three term test) = -6487 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = -0.059425077660919807352342253300909 y[1] (numeric) = -0.059425077660919807352342253300938 absolute error = 2.9e-32 relative error = 4.8800945899430441420149207467566e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 246 Order of pole (three term test) = -6483 Radius of convergence (six term test) for eq 1 = 4.930e+10 Order of pole (six term test) = 2.251e+20 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = -0.058942739718463435392992350814033 y[1] (numeric) = -0.058942739718463435392992350814062 absolute error = 2.9e-32 relative error = 4.9200291907903859939548292122113e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 245.8 Order of pole (three term test) = -6479 Radius of convergence (six term test) for eq 1 = 3.565e+11 Order of pole (six term test) = 1.174e+22 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = -0.058464117033585920845713629427383 y[1] (numeric) = -0.058464117033585920845713629427411 absolute error = 2.8e-32 relative error = 4.7892624434770512426285461863034e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 245.7 Order of pole (three term test) = -6475 Radius of convergence (six term test) for eq 1 = 2.591e+11 Order of pole (six term test) = 6.195e+21 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = -0.057989183425684039265544837310934 y[1] (numeric) = -0.057989183425684039265544837310964 absolute error = 3.0e-32 relative error = 5.1733785902411369557709212875411e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 245.5 Order of pole (three term test) = -6471 Radius of convergence (six term test) for eq 1 = 5.785e+10 Order of pole (six term test) = 3.081e+20 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = -0.05751791286732519538779382717967 y[1] (numeric) = -0.057517912867325195387793827179699 absolute error = 2.9e-32 relative error = 5.0419075648473911255947663033030e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 245.3 Order of pole (three term test) = -6467 Radius of convergence (six term test) for eq 1 = 6.568e+10 Order of pole (six term test) = 3.965e+20 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = -0.05705027948379130846499949777876 y[1] (numeric) = -0.057050279483791308464999497778787 absolute error = 2.7e-32 relative error = 4.7326674372683896601843058079009e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 245.2 Order of pole (three term test) = -6463 Radius of convergence (six term test) for eq 1 = 5.446e+10 Order of pole (six term test) = 2.721e+20 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = -0.056586257552616609655379007825856 y[1] (numeric) = -0.056586257552616609655379007825883 absolute error = 2.7e-32 relative error = 4.7714765329539788310926787271342e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 245 Order of pole (three term test) = -6459 Radius of convergence (six term test) for eq 1 = 9.751e+10 Order of pole (six term test) = 8.707e+20 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = -0.056125821503119517772960904431163 y[1] (numeric) = -0.05612582150311951777296090443119 absolute error = 2.7e-32 relative error = 4.8106200099893982911212570566120e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 244.9 Order of pole (three term test) = -6455 Radius of convergence (six term test) for eq 1 = 4.111e+10 Order of pole (six term test) = 1.545e+20 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = -0.055668945915928757002718781136344 y[1] (numeric) = -0.055668945915928757002718781136371 absolute error = 2.7e-32 relative error = 4.8501008157717590745127351087899e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 244.7 Order of pole (three term test) = -6451 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = -0.055215605522503877514536309949837 y[1] (numeric) = -0.055215605522503877514536309949865 absolute error = 2.8e-32 relative error = 5.0710301435684185112597349135654e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 244.6 Order of pole (three term test) = -6447 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=60018832, alloc=4455632, time=2.21 x[1] = 3 y[1] (analytic) = -0.054765775204650337277276657215067 y[1] (numeric) = -0.054765775204650337277276657215096 absolute error = 2.9e-32 relative error = 5.2952779161131124044266123634807e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 244.4 Order of pole (three term test) = -6443 Radius of convergence (six term test) for eq 1 = 5.170e+10 Order of pole (six term test) = 2.430e+20 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = -0.054319429994029300778126850819468 y[1] (numeric) = -0.054319429994029300778126850819497 absolute error = 2.9e-32 relative error = 5.3387894540107712109425059620763e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 244.2 Order of pole (three term test) = -6439 Radius of convergence (six term test) for eq 1 = 4.690e+10 Order of pole (six term test) = 1.996e+20 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = -0.053876545071662307792275780226237 y[1] (numeric) = -0.053876545071662307792275780226266 absolute error = 2.9e-32 relative error = 5.3826762576231456059410457290410e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 244.1 Order of pole (three term test) = -6435 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = -0.053437095767430962823403986271071 y[1] (numeric) = -0.0534370957674309628234039862711 absolute error = 2.9e-32 relative error = 5.4269416373625279228306605358215e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 243.9 Order of pole (three term test) = -6431 Radius of convergence (six term test) for eq 1 = 6.901e+10 Order of pole (six term test) = 4.306e+20 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = -0.053001057559571793345960614651822 y[1] (numeric) = -0.053001057559571793345960614651849 absolute error = 2.7e-32 relative error = 5.0942379724504007915321184138301e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 243.8 Order of pole (three term test) = -6427 Radius of convergence (six term test) for eq 1 = 9.029e+10 Order of pole (six term test) = 7.358e+20 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = -0.052568406074166422525329754966104 y[1] (numeric) = -0.052568406074166422525329754966133 absolute error = 2.9e-32 relative error = 5.5166215157988986340375964155613e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 243.6 Order of pole (three term test) = -6423 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = -0.052139117084627199671302200085871 y[1] (numeric) = -0.052139117084627199671302200085899 absolute error = 2.8e-32 relative error = 5.3702482062657665024111262843118e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 243.4 Order of pole (three term test) = -6419 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = -0.051713166511178429293332153328767 y[1] (numeric) = -0.051713166511178429293332153328797 absolute error = 3.0e-32 relative error = 5.8012305228911355638131562710304e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 243.3 Order of pole (three term test) = -6415 Radius of convergence (six term test) for eq 1 = 6.242e+10 Order of pole (six term test) = 3.497e+20 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = -0.051290530420333337272439615438391 y[1] (numeric) = -0.051290530420333337272439615438419 absolute error = 2.8e-32 relative error = 5.4590973753899478462618178430373e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 243.1 Order of pole (three term test) = -6411 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = -0.050871185024366910343891386852752 y[1] (numeric) = -0.05087118502436691034389138685278 absolute error = 2.8e-32 relative error = 5.5040982407994256796351429401602e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 243 Order of pole (three term test) = -6407 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = -0.050455106680784742796535303239736 y[1] (numeric) = -0.050455106680784742796535303239765 absolute error = 2.9e-32 relative error = 5.7476838139447086494643862237183e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 242.8 Order of pole (three term test) = -6403 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = -0.050042271891788022038457095912319 y[1] (numeric) = -0.050042271891788022038457095912349 absolute error = 3.0e-32 relative error = 5.9949316579535679845117216501235e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 242.7 Order of pole (three term test) = -6399 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = -0.049632657303734782454065817198494 y[1] (numeric) = -0.049632657303734782454065817198524 absolute error = 3.0e-32 relative error = 6.0444073780717248314478570500760e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 242.5 Order of pole (three term test) = -6395 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = -0.04922623970659755478438578971336 y[1] (numeric) = -0.049226239706597554784385789713388 absolute error = 2.8e-32 relative error = 5.6880233320456722688075659275997e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 242.3 Order of pole (three term test) = -6391 Radius of convergence (six term test) for eq 1 = 1.323e+11 Order of pole (six term test) = 1.556e+21 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = -0.048822996033417536099839176219681 y[1] (numeric) = -0.04882299603341753609983917621971 absolute error = 2.9e-32 relative error = 5.9398239264445328080921405391883e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 242.2 Order of pole (three term test) = -6387 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=64021228, alloc=4455632, time=2.36 x[1] = 3.15 y[1] (analytic) = -0.048422903359755403302747066360455 y[1] (numeric) = -0.048422903359755403302747066360483 absolute error = 2.8e-32 relative error = 5.7823876837734157898640924937865e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 242 Order of pole (three term test) = -6383 Radius of convergence (six term test) for eq 1 = 6.786e+10 Order of pole (six term test) = 4.076e+20 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (analytic) = -0.048025938903138890994766817864003 y[1] (numeric) = -0.04802593890313889099476681786403 absolute error = 2.7e-32 relative error = 5.6219619265445172657696340087248e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 241.9 Order of pole (three term test) = -6379 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (analytic) = -0.047632080022507252472132432586239 y[1] (numeric) = -0.047632080022507252472132432586268 absolute error = 2.9e-32 relative error = 6.0883337419438398519541285331987e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 241.7 Order of pole (three term test) = -6375 Radius of convergence (six term test) for eq 1 = 6.625e+10 Order of pole (six term test) = 3.870e+20 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = -0.047241304217652720568490875210256 y[1] (numeric) = -0.047241304217652720568490875210284 absolute error = 2.8e-32 relative error = 5.9270167205792771069779411500704e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 241.6 Order of pole (three term test) = -6371 Radius of convergence (six term test) for eq 1 = 1.533e+11 Order of pole (six term test) = 2.069e+21 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = -0.046853589128659083050953005632225 y[1] (numeric) = -0.046853589128659083050953005632253 absolute error = 2.8e-32 relative error = 5.9760629912710681627469134647875e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 241.4 Order of pole (three term test) = -6367 Radius of convergence (six term test) for eq 1 = 5.150e+11 Order of pole (six term test) = 2.330e+22 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = -0.046468912535337485289330358844645 y[1] (numeric) = -0.046468912535337485289330358844672 absolute error = 2.7e-32 relative error = 5.8103360993153720471590098303073e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 241.2 Order of pole (three term test) = -6363 Radius of convergence (six term test) for eq 1 = 2.029e+11 Order of pole (six term test) = 3.611e+21 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = -0.046087252356659570961040090634769 y[1] (numeric) = -0.046087252356659570961040090634796 absolute error = 2.7e-32 relative error = 5.8584529602790524523232131180407e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 241.1 Order of pole (three term test) = -6359 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = -0.045708586650188069624466240332695 y[1] (numeric) = -0.045708586650188069624466240332723 absolute error = 2.8e-32 relative error = 6.1257636807470162704099487730361e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 240.9 Order of pole (three term test) = -6355 Radius of convergence (six term test) for eq 1 = 1.352e+11 Order of pole (six term test) = 1.599e+21 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (analytic) = -0.04533289361150493809130672120713 y[1] (numeric) = -0.045332893611504938091306721207157 absolute error = 2.7e-32 relative error = 5.9559401240488491031882491097717e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 240.8 Order of pole (three term test) = -6351 Radius of convergence (six term test) for eq 1 = 6.965e+11 Order of pole (six term test) = 4.233e+22 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (analytic) = -0.044960151573637160653257211739887 y[1] (numeric) = -0.044960151573637160653257211739914 absolute error = 2.7e-32 relative error = 6.0053178325652538334867935244729e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 240.6 Order of pole (three term test) = -6347 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = -0.044590339006480311369934810557736 y[1] (numeric) = -0.044590339006480311369934810557763 absolute error = 2.7e-32 relative error = 6.0551232849061971861318513658537e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 240.5 Order of pole (three term test) = -6343 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = -0.044223434516219979802879653366151 y[1] (numeric) = -0.044223434516219979802879653366179 absolute error = 2.8e-32 relative error = 6.3314847221398746333157398568906e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 240.3 Order of pole (three term test) = -6339 Radius of convergence (six term test) for eq 1 = 6.600e+10 Order of pole (six term test) = 3.781e+20 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = -0.043859416844751159784449635604978 y[1] (numeric) = -0.043859416844751159784449635605006 absolute error = 2.8e-32 relative error = 6.3840338094579288369292572829824e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 240.1 Order of pole (three term test) = -6335 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (analytic) = -0.043498264869095699040104098021788 y[1] (numeric) = -0.043498264869095699040104098021816 absolute error = 2.8e-32 relative error = 6.4370383702116856409005810481142e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 240 Order of pole (three term test) = -6331 Radius of convergence (six term test) for eq 1 = 5.364e+10 Order of pole (six term test) = 2.489e+20 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = -0.04313995760081790573762311711766 y[1] (numeric) = -0.043139957600817905737623117117688 absolute error = 2.8e-32 relative error = 6.4905024383865268522096745753988e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 239.8 Order of pole (three term test) = -6327 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=68023752, alloc=4455632, time=2.52 x[1] = 3.3 y[1] (analytic) = -0.042784474185438406316900297500158 y[1] (numeric) = -0.042784474185438406316900297500185 absolute error = 2.7e-32 relative error = 6.3107004384289910390008279911745e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 239.7 Order of pole (three term test) = -6323 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = -0.04243179390184634725875313500178 y[1] (numeric) = -0.042431793901846347258753135001808 absolute error = 2.8e-32 relative error = 6.5988254149164378549684300827249e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 239.5 Order of pole (three term test) = -6319 Radius of convergence (six term test) for eq 1 = 6.481e+10 Order of pole (six term test) = 3.615e+20 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = -0.042081896161710031780394553883857 y[1] (numeric) = -0.042081896161710031780394553883884 absolute error = 2.7e-32 relative error = 6.4160606965631639043504681106394e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 239.3 Order of pole (three term test) = -6315 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (analytic) = -0.041734760508886080798484516553766 y[1] (numeric) = -0.041734760508886080798484516553794 absolute error = 2.8e-32 relative error = 6.7090357434873255425402760862263e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 239.2 Order of pole (three term test) = -6311 Radius of convergence (six term test) for eq 1 = 6.896e+10 Order of pole (six term test) = 4.079e+20 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = -0.041390366618827205877717963286282 y[1] (numeric) = -0.04139036661882720587771796328631 absolute error = 2.8e-32 relative error = 6.7648591417075441947235525964452e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 239 Order of pole (three term test) = -6307 Radius of convergence (six term test) for eq 1 = 5.667e+10 Order of pole (six term test) = 2.749e+20 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = -0.041048694297988680283394924794674 y[1] (numeric) = -0.041048694297988680283394924794701 absolute error = 2.7e-32 relative error = 6.5775539177924488546250522361823e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 238.9 Order of pole (three term test) = -6303 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = -0.040709723483233592680054437771227 y[1] (numeric) = -0.040709723483233592680054437771254 absolute error = 2.7e-32 relative error = 6.6323221308835520418968931633249e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 238.7 Order of pole (three term test) = -6299 Radius of convergence (six term test) for eq 1 = 6.195e+10 Order of pole (six term test) = 3.275e+20 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = -0.040373434241236966464733626417377 y[1] (numeric) = -0.040373434241236966464733626417405 absolute error = 2.8e-32 relative error = 6.9352534720470022624127011002412e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 238.6 Order of pole (three term test) = -6295 Radius of convergence (six term test) for eq 1 = 6.002e+10 Order of pole (six term test) = 3.068e+20 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = -0.04003980676788882619243845861026 y[1] (numeric) = -0.040039806767888826192438458610287 absolute error = 2.7e-32 relative error = 6.7432892862144113618524894667034e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 238.4 Order of pole (three term test) = -6291 Radius of convergence (six term test) for eq 1 = 8.806e+10 Order of pole (six term test) = 6.594e+20 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (analytic) = -0.039708821387696291042688390025546 y[1] (numeric) = -0.039708821387696291042688390025574 absolute error = 2.8e-32 relative error = 7.0513299114628849445686438630769e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 238.2 Order of pole (three term test) = -6287 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = -0.039380458553184773789232155135719 y[1] (numeric) = -0.039380458553184773789232155135746 absolute error = 2.7e-32 relative error = 6.8561923837264352576304604399212e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 238.1 Order of pole (three term test) = -6283 Radius of convergence (six term test) for eq 1 = 3.238e+11 Order of pole (six term test) = 8.884e+21 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = -0.039054698844298362269938724810878 y[1] (numeric) = -0.039054698844298362269938724810906 absolute error = 2.8e-32 relative error = 7.1694318042572104708023934521923e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 237.9 Order of pole (three term test) = -6279 Radius of convergence (six term test) for eq 1 = 3.757e+10 Order of pole (six term test) = 1.194e+20 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (analytic) = -0.03873152296779945891016185029374 y[1] (numeric) = -0.038731522967799458910161850293767 absolute error = 2.7e-32 relative error = 6.9710659254084094439323776207608e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 237.8 Order of pole (three term test) = -6275 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = -0.038410911756667752430278084209698 y[1] (numeric) = -0.038410911756667752430278084209725 absolute error = 2.7e-32 relative error = 7.0292525652721764441029699785521e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 237.6 Order of pole (three term test) = -6271 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = -0.038092846169498594466329608519083 y[1] (numeric) = -0.03809284616949859446632960851911 absolute error = 2.7e-32 relative error = 7.0879450382521505051543178739402e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 237.4 Order of pole (three term test) = -6267 NO COMPLEX POLE (six term test) for Equation 1 bytes used=72024960, alloc=4455632, time=2.66 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (analytic) = -0.037777307289900852451490929142885 y[1] (numeric) = -0.037777307289900852451490929142912 absolute error = 2.7e-32 relative error = 7.1471478347579341774374560781832e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 237.3 Order of pole (three term test) = -6263 Radius of convergence (six term test) for eq 1 = 9.100e+10 Order of pole (six term test) = 6.960e+20 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = -0.037464276325894308745152223607566 y[1] (numeric) = -0.037464276325894308745152223607593 absolute error = 2.7e-32 relative error = 7.2068654857049300596892913156926e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 237.1 Order of pole (three term test) = -6259 Radius of convergence (six term test) for eq 1 = 5.796e+10 Order of pole (six term test) = 2.818e+20 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (analytic) = -0.03715373460930667465550490141511 y[1] (numeric) = -0.037153734609306674655504901415138 absolute error = 2.8e-32 relative error = 7.5362545096573557145864246247316e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 237 Order of pole (three term test) = -6255 Radius of convergence (six term test) for eq 1 = 5.662e+10 Order of pole (six term test) = 2.685e+20 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = -0.036845663595170286680363110870559 y[1] (numeric) = -0.036845663595170286680363110870586 absolute error = 2.7e-32 relative error = 7.3278636793338003774360529484176e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 236.8 Order of pole (three term test) = -6250 Radius of convergence (six term test) for eq 1 = 1.534e+11 Order of pole (six term test) = 1.967e+21 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = -0.036540044861118550989298119352908 y[1] (numeric) = -0.036540044861118550989298119352935 absolute error = 2.7e-32 relative error = 7.3891534897183718195905866825155e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 236.6 Order of pole (three term test) = -6246 Radius of convergence (six term test) for eq 1 = 6.182e+10 Order of pole (six term test) = 3.190e+20 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (analytic) = -0.036236860106782200887743550836343 y[1] (numeric) = -0.036236860106782200887743550836371 absolute error = 2.8e-32 relative error = 7.7269387903615398751524248484242e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 236.5 Order of pole (three term test) = -6242 Radius of convergence (six term test) for eq 1 = 9.336e+10 Order of pole (six term test) = 7.263e+20 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (analytic) = -0.035936091153185430740294416559987 y[1] (numeric) = -0.035936091153185430740294416560015 absolute error = 2.8e-32 relative error = 7.7916097999206117504227683598956e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 236.3 Order of pole (three term test) = -6238 Radius of convergence (six term test) for eq 1 = 1.627e+11 Order of pole (six term test) = 2.203e+21 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = -0.035637719942141968585720903201987 y[1] (numeric) = -0.035637719942141968585720903202015 absolute error = 2.8e-32 relative error = 7.8568438288022218330444205960535e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 236.2 Order of pole (three term test) = -6234 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = -0.035341728535651148450001280697606 y[1] (numeric) = -0.035341728535651148450001280697634 absolute error = 2.8e-32 relative error = 7.9226458807058227384143244793415e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 236 Order of pole (three term test) = -6230 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = -0.03504809911529404215570242667988 y[1] (numeric) = -0.035048099115294042155702426679908 absolute error = 2.8e-32 relative error = 7.9890210045033676583713308632399e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 235.9 Order of pole (three term test) = -6226 Radius of convergence (six term test) for eq 1 = 1.022e+11 Order of pole (six term test) = 8.655e+20 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = -0.034756813981629709236059742249032 y[1] (numeric) = -0.03475681398162970923605974224906 absolute error = 2.8e-32 relative error = 8.0559742946517074372691465250293e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 235.7 Order of pole (three term test) = -6222 Radius of convergence (six term test) for eq 1 = 1.032e+11 Order of pole (six term test) = 8.805e+20 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (analytic) = -0.034467855553591622389892062091893 y[1] (numeric) = -0.034467855553591622389892062091921 absolute error = 2.8e-32 relative error = 8.1235108916087881306316385616100e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 235.5 Order of pole (three term test) = -6218 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = -0.034181206367884324758795914620488 y[1] (numeric) = -0.034181206367884324758795914620516 absolute error = 2.8e-32 relative error = 8.1916359822536843199373196504001e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 235.4 Order of pole (three term test) = -6214 Radius of convergence (six term test) for eq 1 = 7.986e+10 Order of pole (six term test) = 5.254e+20 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = -0.033896849078380374170664469168011 y[1] (numeric) = -0.033896849078380374170664469168039 absolute error = 2.8e-32 relative error = 8.2603548003105037866268433960144e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 235.2 Order of pole (three term test) = -6210 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.59 bytes used=76027044, alloc=4455632, time=2.81 y[1] (analytic) = -0.033614766455517628373239917409908 y[1] (numeric) = -0.033614766455517628373239917409936 absolute error = 2.8e-32 relative error = 8.3296726267761994810676356414238e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 235.1 Order of pole (three term test) = -6206 Radius of convergence (six term test) for eq 1 = 2.235e+11 Order of pole (six term test) = 4.100e+21 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = -0.033334941385696924177906936171374 y[1] (numeric) = -0.033334941385696924177906936171403 absolute error = 2.9e-32 relative error = 8.6995803185791938100430181235766e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 234.9 Order of pole (three term test) = -6202 Radius of convergence (six term test) for eq 1 = 6.112e+10 Order of pole (six term test) = 3.062e+20 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = -0.033057356870680202347045156623923 y[1] (numeric) = -0.033057356870680202347045156623952 absolute error = 2.9e-32 relative error = 8.7726311917336552525659084337669e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 234.7 Order of pole (three term test) = -6198 Radius of convergence (six term test) for eq 1 = 1.505e+11 Order of pole (six term test) = 1.854e+21 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = -0.032781996026989128987758901638798 y[1] (numeric) = -0.032781996026989128987758901638827 absolute error = 2.9e-32 relative error = 8.8463191735257838100775773098569e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 234.6 Order of pole (three term test) = -6194 Radius of convergence (six term test) for eq 1 = 5.559e+10 Order of pole (six term test) = 2.525e+20 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = -0.032508842085304263160474289527232 y[1] (numeric) = -0.032508842085304263160474289527261 absolute error = 2.9e-32 relative error = 8.9206499339173794770863963886895e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 234.4 Order of pole (three term test) = -6190 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = -0.032237878389864819372521306020379 y[1] (numeric) = -0.032237878389864819372521306020407 absolute error = 2.8e-32 relative error = 8.6854350839672021780517718964864e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 234.3 Order of pole (three term test) = -6186 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = -0.031969088397869072604188478655587 y[1] (numeric) = -0.031969088397869072604188478655616 absolute error = 2.9e-32 relative error = 9.0712627270075740495492004469674e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 234.1 Order of pole (three term test) = -6182 Radius of convergence (six term test) for eq 1 = 6.311e+10 Order of pole (six term test) = 3.238e+20 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = -0.031702455678875452507639872093658 y[1] (numeric) = -0.031702455678875452507639872093687 absolute error = 2.9e-32 relative error = 9.1475563577000121387213147854864e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 233.9 Order of pole (three term test) = -6178 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = -0.031437963914204372427310412600276 y[1] (numeric) = -0.031437963914204372427310412600304 absolute error = 2.8e-32 relative error = 8.9064292065520745302675138243746e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 233.8 Order of pole (three term test) = -6174 Radius of convergence (six term test) for eq 1 = 5.669e+10 Order of pole (six term test) = 2.605e+20 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (analytic) = -0.031175596896340837913740796745567 y[1] (numeric) = -0.031175596896340837913740796745596 absolute error = 2.9e-32 relative error = 9.3021474765744762810643424653121e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 233.6 Order of pole (three term test) = -6170 Radius of convergence (six term test) for eq 1 = 6.258e+10 Order of pole (six term test) = 3.169e+20 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = -0.03091533852833787844107476239294 y[1] (numeric) = -0.030915338528337878441074762392968 absolute error = 2.8e-32 relative error = 9.0569928497902113405926865791974e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 233.5 Order of pole (three term test) = -6166 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = -0.030657172823220845091419154899419 y[1] (numeric) = -0.030657172823220845091419154899448 absolute error = 2.9e-32 relative error = 9.4594502132415671398220281284850e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 233.3 Order of pole (three term test) = -6162 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = -0.030401083903392616036763369913487 y[1] (numeric) = -0.030401083903392616036763369913515 absolute error = 2.8e-32 relative error = 9.2101979287900762908332361499110e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 233.1 Order of pole (three term test) = -6158 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = -0.030147056000039750730974234095278 y[1] (numeric) = -0.030147056000039750730974234095306 absolute error = 2.8e-32 relative error = 9.2878057479188283901543664350113e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 233 Order of pole (three term test) = -6154 Radius of convergence (six term test) for eq 1 = 3.454e+10 Order of pole (six term test) = 9.587e+19 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = -0.029895073452539632820332480736991 y[1] (numeric) = -0.029895073452539632820332480737019 absolute error = 2.8e-32 relative error = 9.3660917222537737589642866963533e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 232.8 Order of pole (three term test) = -6150 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=80027828, alloc=4455632, time=2.96 x[1] = 3.74 y[1] (analytic) = -0.029645120707868640890967389881705 y[1] (numeric) = -0.029645120707868640890967389881733 absolute error = 2.8e-32 relative error = 9.4450618959928943634718386203728e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 232.7 Order of pole (three term test) = -6146 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = -0.029397182320011385295188981375541 y[1] (numeric) = -0.029397182320011385295188981375568 absolute error = 2.7e-32 relative error = 9.1845537120135611399919252862665e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 232.5 Order of pole (three term test) = -6141 Radius of convergence (six term test) for eq 1 = 4.638e+10 Order of pole (six term test) = 1.721e+20 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = -0.029151242949371048435926822903941 y[1] (numeric) = -0.029151242949371048435926822903968 absolute error = 2.7e-32 relative error = 9.2620407462188631999255404079188e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 232.3 Order of pole (three term test) = -6137 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = -0.028907287362180865039077822987969 y[1] (numeric) = -0.028907287362180865039077822987996 absolute error = 2.7e-32 relative error = 9.3402053474321664161841803876036e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 232.2 Order of pole (three term test) = -6133 Radius of convergence (six term test) for eq 1 = 5.480e+10 Order of pole (six term test) = 2.395e+20 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = -0.028665300429916778107361403631793 y[1] (numeric) = -0.02866530042991677810736140363182 absolute error = 2.7e-32 relative error = 9.4190535578065061801951245835308e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 232 Order of pole (three term test) = -6129 Radius of convergence (six term test) for eq 1 = 5.643e+10 Order of pole (six term test) = 2.535e+20 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = -0.028425267128711305426100546560153 y[1] (numeric) = -0.02842526712871130542610054656018 absolute error = 2.7e-32 relative error = 9.4985914741776705791141099643286e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 231.9 Order of pole (three term test) = -6125 Radius of convergence (six term test) for eq 1 = 3.429e+10 Order of pole (six term test) = 9.347e+19 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = -0.028187172538768650681014986401437 y[1] (numeric) = -0.028187172538768650681014986401464 absolute error = 2.7e-32 relative error = 9.5788252485644620794766775847995e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 231.7 Order of pole (three term test) = -6121 Radius of convergence (six term test) for eq 1 = 1.249e+11 Order of pole (six term test) = 1.238e+21 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = -0.027951001843781092450454110242328 y[1] (numeric) = -0.027951001843781092450454110242355 absolute error = 2.7e-32 relative error = 9.6597610886735768707754470073982e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 231.6 Order of pole (three term test) = -6117 Radius of convergence (six term test) for eq 1 = 5.426e+10 Order of pole (six term test) = 2.333e+20 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = -0.027716740330346683549339936304052 y[1] (numeric) = -0.027716740330346683549339936304079 absolute error = 2.7e-32 relative error = 9.7414052584091447902761370023715e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 231.4 Order of pole (three term test) = -6113 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = -0.027484373387388292429265073364723 y[1] (numeric) = -0.027484373387388292429265073364751 absolute error = 2.8e-32 relative error = 1.0187607192401305490780486005600e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 231.2 Order of pole (three term test) = -6109 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = -0.027253886505574017578529136859446 y[1] (numeric) = -0.027253886505574017578529136859473 absolute error = 2.7e-32 relative error = 9.9068439264535382066041613020524e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 231.1 Order of pole (three term test) = -6105 Radius of convergence (six term test) for eq 1 = 1.453e+11 Order of pole (six term test) = 1.666e+21 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = -0.027025265276739005117234162991433 y[1] (numeric) = -0.02702526527673900511723416299146 absolute error = 2.7e-32 relative error = 9.9906512382097683728379752638690e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 230.9 Order of pole (three term test) = -6101 Radius of convergence (six term test) for eq 1 = 6.414e+10 Order of pole (six term test) = 3.239e+20 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = -0.026798495393308699045731654620683 y[1] (numeric) = -0.026798495393308699045731654620711 absolute error = 2.8e-32 relative error = 1.0448347785596688368866062316006e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 230.8 Order of pole (three term test) = -6097 Radius of convergence (six term test) for eq 1 = 5.071e+10 Order of pole (six term test) = 2.022e+20 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = -0.026573562647723552879559613167534 y[1] (numeric) = -0.026573562647723552879559613167562 absolute error = 2.8e-32 relative error = 1.0536788149630604424880040737197e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 230.6 Order of pole (three term test) = -6093 Radius of convergence (six term test) for eq 1 = 6.232e+10 Order of pole (six term test) = 3.048e+20 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = -0.026350452931865230690367900440014 y[1] (numeric) = -0.026350452931865230690367900440041 absolute error = 2.7e-32 relative error = 1.0246503189077741130986306405578e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 230.4 Order of pole (three term test) = -6089 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=84029016, alloc=4455632, time=3.11 x[1] = 3.89 y[1] (analytic) = -0.026129152236484324870047189866362 y[1] (numeric) = -0.026129152236484324870047189866389 absolute error = 2.7e-32 relative error = 1.0333285885295468591047777723355e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 230.3 Order of pole (three term test) = -6085 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = -0.025909646650629617244195255991877 y[1] (numeric) = -0.025909646650629617244195255991904 absolute error = 2.7e-32 relative error = 1.0420829108197771052762188567289e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 230.1 Order of pole (three term test) = -6081 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = -0.025691922361078909481021029343645 y[1] (numeric) = -0.025691922361078909481021029343672 absolute error = 2.7e-32 relative error = 1.0509139651185742941539920983134e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 230 Order of pole (three term test) = -6077 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = -0.025475965651771448072650269329411 y[1] (numeric) = -0.025475965651771448072650269329438 absolute error = 2.7e-32 relative error = 1.0598224369219378181554080409185e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 229.8 Order of pole (three term test) = -6073 Radius of convergence (six term test) for eq 1 = 4.186e+10 Order of pole (six term test) = 1.365e+20 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = -0.025261762903241968507407359071699 y[1] (numeric) = -0.025261762903241968507407359071726 absolute error = 2.7e-32 relative error = 1.0688090179381326876206088809018e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 229.6 Order of pole (three term test) = -6068 Radius of convergence (six term test) for eq 1 = 4.147e+10 Order of pole (six term test) = 1.337e+20 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = -0.025049300592056382603857978028571 y[1] (numeric) = -0.025049300592056382603857978028599 absolute error = 2.8e-32 relative error = 1.1177956804462373377612443001773e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 229.5 Order of pole (three term test) = -6064 Radius of convergence (six term test) for eq 1 = 6.253e+10 Order of pole (six term test) = 3.036e+20 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = -0.024838565290249132340061509709132 y[1] (numeric) = -0.02483856529024913234006150970916 absolute error = 2.8e-32 relative error = 1.1272792801358760876738583580121e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 229.3 Order of pole (three term test) = -6060 Radius of convergence (six term test) for eq 1 = 8.678e+10 Order of pole (six term test) = 5.838e+20 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = -0.024629543664762232884456092621648 y[1] (numeric) = -0.024629543664762232884456092621676 absolute error = 2.8e-32 relative error = 1.1368460732002890160588872812061e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 229.2 Order of pole (three term test) = -6056 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = -0.024422222476886026917941151330309 y[1] (numeric) = -0.024422222476886026917941151330337 absolute error = 2.8e-32 relative error = 1.1464968033314779705602264309272e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 229 Order of pole (three term test) = -6052 Radius of convergence (six term test) for eq 1 = 7.806e+10 Order of pole (six term test) = 4.709e+20 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = -0.024216588581701671729891786202869 y[1] (numeric) = -0.024216588581701671729891786202896 absolute error = 2.7e-32 relative error = 1.1149382130727325245015194591379e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 228.8 Order of pole (three term test) = -6048 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = -0.024012628927525379973898074805517 y[1] (numeric) = -0.024012628927525379973898074805544 absolute error = 2.7e-32 relative error = 1.1244083303619552235270194450302e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 228.7 Order of pole (three term test) = -6044 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4 y[1] (analytic) = -0.023810330555354434381833427655214 y[1] (numeric) = -0.023810330555354434381833427655241 absolute error = 2.7e-32 relative error = 1.1339615776114572731607515788286e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 228.5 Order of pole (three term test) = -6040 Radius of convergence (six term test) for eq 1 = 1.047e+11 Order of pole (six term test) = 8.438e+20 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = -0.023609680598314996157284670523026 y[1] (numeric) = -0.023609680598314996157284670523054 absolute error = 2.8e-32 relative error = 1.1859542056658884827874981190340e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 228.3 Order of pole (three term test) = -6036 Radius of convergence (six term test) for eq 1 = 6.394e+10 Order of pole (six term test) = 3.141e+20 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = -0.023410666281111726201289239559235 y[1] (numeric) = -0.023410666281111726201289239559263 absolute error = 2.8e-32 relative error = 1.1960360146857954110645773354417e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 228.2 Order of pole (three term test) = -6032 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = -0.023213274919479237764590218685376 y[1] (numeric) = -0.023213274919479237764590218685404 absolute error = 2.8e-32 relative error = 1.2062063667071818199054845995742e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 228 Order of pole (three term test) = -6028 Radius of convergence (six term test) for eq 1 = 8.130e+10 Order of pole (six term test) = 5.061e+20 TOP MAIN SOLVE Loop bytes used=88029900, alloc=4455632, time=3.27 x[1] = 4.04 y[1] (analytic) = -0.023017493919635398571108044482309 y[1] (numeric) = -0.023017493919635398571108044482337 absolute error = 2.8e-32 relative error = 1.2164660539397038433741432549529e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.48 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 227.9 Order of pole (three term test) = -6024 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = -0.02282331077773649991691033432962 y[1] (numeric) = -0.022823310777736499916910334329648 absolute error = 2.8e-32 relative error = 1.2268158757805294117265203046568e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 227.7 Order of pole (three term test) = -6020 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (analytic) = -0.022630713079334309717511879425232 y[1] (numeric) = -0.02263071307933430971751187942526 absolute error = 2.8e-32 relative error = 1.2372566388802287674731317867139e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 227.5 Order of pole (three term test) = -6016 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (analytic) = -0.022439688498835025953730424700265 y[1] (numeric) = -0.022439688498835025953730424700293 absolute error = 2.8e-32 relative error = 1.2477891572092741832563937485163e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 227.4 Order of pole (three term test) = -6011 Radius of convergence (six term test) for eq 1 = 5.346e+10 Order of pole (six term test) = 2.175e+20 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = -0.022250224798960146452437070590735 y[1] (numeric) = -0.022250224798960146452437070590763 absolute error = 2.8e-32 relative error = 1.2584142521251545523430438617742e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 227.2 Order of pole (three term test) = -6007 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = -0.022062309830209270433251194618407 y[1] (numeric) = -0.022062309830209270433251194618435 absolute error = 2.8e-32 relative error = 1.2691327524401105756315805005542e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 227.1 Order of pole (three term test) = -6003 Radius of convergence (six term test) for eq 1 = 1.735e+11 Order of pole (six term test) = 2.283e+21 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = -0.021875931530324846755418481470155 y[1] (numeric) = -0.021875931530324846755418481470183 absolute error = 2.8e-32 relative error = 1.2799454944894963226739713271420e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 226.9 Order of pole (three term test) = -5999 Radius of convergence (six term test) for eq 1 = 6.755e+10 Order of pole (six term test) = 3.456e+20 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = -0.021691077923758883310658287677234 y[1] (numeric) = -0.021691077923758883310658287677262 absolute error = 2.8e-32 relative error = 1.2908533222007729983144935875283e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 226.7 Order of pole (three term test) = -5995 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = -0.021507737121141631527555992470023 y[1] (numeric) = -0.021507737121141631527555992470051 absolute error = 2.8e-32 relative error = 1.3018570871631408011612496745797e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 226.6 Order of pole (three term test) = -5991 Radius of convergence (six term test) for eq 1 = 1.266e+11 Order of pole (six term test) = 1.211e+21 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = -0.021325897318752259480991545218319 y[1] (numeric) = -0.021325897318752259480991545218347 absolute error = 2.8e-32 relative error = 1.3129576486978148152324655336941e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 226.4 Order of pole (three term test) = -5987 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = -0.021145546797991526636022942942347 y[1] (numeric) = -0.021145546797991526636022942942374 absolute error = 2.7e-32 relative error = 1.2768645927172026842019481352487e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 226.3 Order of pole (three term test) = -5983 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = -0.020966673924856472799470157044775 y[1] (numeric) = -0.020966673924856472799470157044803 absolute error = 2.8e-32 relative error = 1.3354526378552278543413058316783e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 226.1 Order of pole (three term test) = -5979 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = -0.02078926714941713340405982458783 y[1] (numeric) = -0.020789267149417133404059824587858 absolute error = 2.8e-32 relative error = 1.3468488234220912971890913792920e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 225.9 Order of pole (three term test) = -5975 Radius of convergence (six term test) for eq 1 = 8.449e+10 Order of pole (six term test) = 5.360e+20 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = -0.020613315005295292809284005921241 y[1] (numeric) = -0.020613315005295292809284005921269 absolute error = 2.8e-32 relative error = 1.3583453215946665437381222633898e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 225.8 Order of pole (three term test) = -5971 Radius of convergence (six term test) for eq 1 = 1.575e+11 Order of pole (six term test) = 1.860e+21 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (analytic) = -0.020438806109145286869989081455812 y[1] (numeric) = -0.02043880610914528686998908145584 absolute error = 2.8e-32 relative error = 1.3699430314313455902895363173985e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 225.6 Order of pole (three term test) = -5967 NO COMPLEX POLE (six term test) for Equation 1 bytes used=92031748, alloc=4455632, time=3.42 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = -0.020265729160136865598036407199233 y[1] (numeric) = -0.020265729160136865598036407199262 absolute error = 2.9e-32 relative error = 1.4309872480208428421786504715186e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 225.5 Order of pole (three term test) = -5963 Radius of convergence (six term test) for eq 1 = 7.785e+10 Order of pole (six term test) = 4.530e+20 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = -0.020094072939440126324059042706496 y[1] (numeric) = -0.020094072939440126324059042706525 absolute error = 2.9e-32 relative error = 1.4432116419304694833624106753476e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 225.3 Order of pole (three term test) = -5958 Radius of convergence (six term test) for eq 1 = 4.790e+10 Order of pole (six term test) = 1.712e+20 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = -0.019923826309712527355274440914421 y[1] (numeric) = -0.01992382630971252735527444091445 absolute error = 2.9e-32 relative error = 1.4555437067759917145604015263479e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 225.1 Order of pole (three term test) = -5954 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = -0.019754978214587991721398528012411 y[1] (numeric) = -0.019754978214587991721398528012439 absolute error = 2.8e-32 relative error = 1.4173642560295764824905934131820e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 225 Order of pole (three term test) = -5950 Radius of convergence (six term test) for eq 1 = 5.003e+10 Order of pole (six term test) = 1.863e+20 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = -0.01958751767816811020384051417679 y[1] (numeric) = -0.019587517678168110203840514176819 absolute error = 2.9e-32 relative error = 1.4805347199417142502521058782976e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 224.8 Order of pole (three term test) = -5946 Radius of convergence (six term test) for eq 1 = 6.080e+10 Order of pole (six term test) = 2.746e+20 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = -0.019421433804515452453439787555739 y[1] (numeric) = -0.019421433804515452453439787555767 absolute error = 2.8e-32 relative error = 1.4417061212797813391886674938225e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 224.7 Order of pole (three term test) = -5942 Radius of convergence (six term test) for eq 1 = 9.409e+10 Order of pole (six term test) = 6.568e+20 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = -0.019256715777148994618937376905602 y[1] (numeric) = -0.01925671577714899461893737690563 absolute error = 2.8e-32 relative error = 1.4540381820053777976655501036020e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 224.5 Order of pole (three term test) = -5938 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = -0.019093352858541671532057027098704 y[1] (numeric) = -0.019093352858541671532057027098732 absolute error = 2.8e-32 relative error = 1.4664789472779171167768607718208e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 224.3 Order of pole (three term test) = -5934 Radius of convergence (six term test) for eq 1 = 4.471e+10 Order of pole (six term test) = 1.478e+20 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = -0.018931334389620061125408486772067 y[1] (numeric) = -0.018931334389620061125408486772095 absolute error = 2.8e-32 relative error = 1.4790293924210770207014569345015e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 224.2 Order of pole (three term test) = -5930 Radius of convergence (six term test) for eq 1 = 6.717e+10 Order of pole (six term test) = 3.333e+20 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = -0.018770649789266208396322979640463 y[1] (numeric) = -0.018770649789266208396322979640491 absolute error = 2.8e-32 relative error = 1.4916905016261874419307494324906e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 224 Order of pole (three term test) = -5926 Radius of convergence (six term test) for eq 1 = 4.722e+10 Order of pole (six term test) = 1.645e+20 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (analytic) = -0.018611288553821595873094076641628 y[1] (numeric) = -0.018611288553821595873094076641656 absolute error = 2.8e-32 relative error = 1.5044632680336660184477616015002e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 223.9 Order of pole (three term test) = -5922 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = -0.018453240256593267189833581355044 y[1] (numeric) = -0.018453240256593267189833581355072 absolute error = 2.8e-32 relative error = 1.5173486938152075834774519358664e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 223.7 Order of pole (three term test) = -5918 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = -0.018296494547362110032170067351987 y[1] (numeric) = -0.018296494547362110032170067352016 absolute error = 2.9e-32 relative error = 1.5850030684801894848936268818877e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 223.5 Order of pole (three term test) = -5913 Radius of convergence (six term test) for eq 1 = 8.172e+10 Order of pole (six term test) = 4.903e+20 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = -0.018141041151893304378227034880409 y[1] (numeric) = -0.018141041151893304378227034880438 absolute error = 2.9e-32 relative error = 1.5985852056221917357387472533123e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 223.4 Order of pole (three term test) = -5909 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = -0.017986869871448941627629132798142 y[1] (numeric) = -0.017986869871448941627629132798171 absolute error = 2.9e-32 relative error = 1.6122871965640061621908502385988e-28 % Correct digits = 30 h = 0.01 bytes used=96032732, alloc=4455632, time=3.57 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 223.2 Order of pole (three term test) = -5905 Radius of convergence (six term test) for eq 1 = 1.308e+11 Order of pole (six term test) = 1.253e+21 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (analytic) = -0.01783397058230281988561052837111 y[1] (numeric) = -0.017833970582302819885610528371139 absolute error = 2.9e-32 relative error = 1.6261101175515879585526225183671e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 223 Order of pole (three term test) = -5901 Radius of convergence (six term test) for eq 1 = 6.318e+10 Order of pole (six term test) = 2.918e+20 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = -0.017682333235257420349552457792092 y[1] (numeric) = -0.017682333235257420349552457792121 absolute error = 2.9e-32 relative error = 1.6400550546223102244659088195521e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 222.9 Order of pole (three term test) = -5897 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = -0.017531947855163069431371542193595 y[1] (numeric) = -0.017531947855163069431371542193625 absolute error = 3.0e-32 relative error = 1.7111618314085478332132263438029e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 222.7 Order of pole (three term test) = -5893 Radius of convergence (six term test) for eq 1 = 5.654e+10 Order of pole (six term test) = 2.330e+20 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = -0.017382804540439290941032014524905 y[1] (numeric) = -0.017382804540439290941032014524934 absolute error = 2.9e-32 relative error = 1.6683153706603850572253184486884e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 222.6 Order of pole (three term test) = -5889 Radius of convergence (six term test) for eq 1 = 8.640e+10 Order of pole (six term test) = 5.434e+20 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = -0.017234893462598352353980084014123 y[1] (numeric) = -0.017234893462598352353980084014152 absolute error = 2.9e-32 relative error = 1.6826329714734382035273392568965e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 222.4 Order of pole (three term test) = -5885 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = -0.017088204865771008888414870576956 y[1] (numeric) = -0.017088204865771008888414870576986 absolute error = 3.0e-32 relative error = 1.7555969299087882372813807981306e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 222.2 Order of pole (three term test) = -5881 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = -0.016942729066234448826936353006427 y[1] (numeric) = -0.016942729066234448826936353006457 absolute error = 3.0e-32 relative error = 1.7706710579340895096608872114388e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 222.1 Order of pole (three term test) = -5877 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = -0.016798456451942443231166338333738 y[1] (numeric) = -0.016798456451942443231166338333767 absolute error = 2.9e-32 relative error = 1.7263490894514099774068787823057e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 221.9 Order of pole (three term test) = -5873 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = -0.016655377482057702917344373215563 y[1] (numeric) = -0.016655377482057702917344373215592 absolute error = 2.9e-32 relative error = 1.7411793897340818534317773007065e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 221.8 Order of pole (three term test) = -5868 Radius of convergence (six term test) for eq 1 = 8.961e+10 Order of pole (six term test) = 5.802e+20 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = -0.016513482686486445285578617995082 y[1] (numeric) = -0.016513482686486445285578617995112 absolute error = 3.0e-32 relative error = 1.8166973357201045692073897441053e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 221.6 Order of pole (three term test) = -5864 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = -0.016372762665415173325304852386465 y[1] (numeric) = -0.016372762665415173325304852386495 absolute error = 3.0e-32 relative error = 1.8323114194631412361578645914531e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 221.4 Order of pole (three term test) = -5860 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = -0.01623320808884966885449885381994 y[1] (numeric) = -0.01623320808884966885449885381997 absolute error = 3.0e-32 relative error = 1.8480635396158397331605444702810e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 221.3 Order of pole (three term test) = -5856 Radius of convergence (six term test) for eq 1 = 8.403e+10 Order of pole (six term test) = 5.080e+20 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = -0.016094809696156201790223261198965 y[1] (numeric) = -0.016094809696156201790223261198995 absolute error = 3.0e-32 relative error = 1.8639549374208920687992314774935e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 221.1 Order of pole (three term test) = -5852 Radius of convergence (six term test) for eq 1 = 5.146e+10 Order of pole (six term test) = 1.903e+20 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = -0.015957558295604956993095572196783 y[1] (numeric) = -0.015957558295604956993095572196812 absolute error = 2.9e-32 relative error = 1.8173206365780410374621925928330e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 220.9 Order of pole (three term test) = -5848 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=100033952, alloc=4521156, time=3.72 x[1] = 4.48 y[1] (analytic) = -0.015821444763915679978165961256329 y[1] (numeric) = -0.015821444763915679978165961256358 absolute error = 2.9e-32 relative error = 1.8329552346661123687887156475396e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 220.8 Order of pole (three term test) = -5844 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = -0.01568646004580554253941995203708 y[1] (numeric) = -0.015686460045805542539419952037109 absolute error = 2.9e-32 relative error = 1.8487281333913454560251504950110e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 220.6 Order of pole (three term test) = -5840 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = -0.015552595153539229094600388001703 y[1] (numeric) = -0.015552595153539229094600388001731 absolute error = 2.8e-32 relative error = 1.8003426260104362710023091349115e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 220.5 Order of pole (three term test) = -5836 Radius of convergence (six term test) for eq 1 = 1.834e+11 Order of pole (six term test) = 2.402e+21 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (analytic) = -0.015419841166481244321205314129138 y[1] (numeric) = -0.015419841166481244321205314129167 absolute error = 2.9e-32 relative error = 1.8806938208312104204458480264222e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 220.3 Order of pole (three term test) = -5831 Radius of convergence (six term test) for eq 1 = 6.098e+10 Order of pole (six term test) = 2.652e+20 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (analytic) = -0.015288189230650442423293935846499 y[1] (numeric) = -0.015288189230650442423293935846528 absolute error = 2.9e-32 relative error = 1.8968891320274548195296070175555e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 220.1 Order of pole (three term test) = -5827 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = -0.015157630558276778142053299633143 y[1] (numeric) = -0.015157630558276778142053299633172 absolute error = 2.9e-32 relative error = 1.9132277890335991897465626369579e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 220 Order of pole (three term test) = -5823 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = -0.015028156427360279400876190406069 y[1] (numeric) = -0.015028156427360279400876190406098 absolute error = 2.9e-32 relative error = 1.9297110820062110634770182742681e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 219.8 Order of pole (three term test) = -5819 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = -0.014899758181232241257909305138172 y[1] (numeric) = -0.014899758181232241257909305138202 absolute error = 3.0e-32 relative error = 2.0134554960622144182200340198433e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 219.7 Order of pole (three term test) = -5815 Radius of convergence (six term test) for eq 1 = 7.392e+10 Order of pole (six term test) = 3.876e+20 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = -0.014772427228118640625584264824498 y[1] (numeric) = -0.014772427228118640625584264824528 absolute error = 3.0e-32 relative error = 2.0308104779759124479641578021605e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 219.5 Order of pole (three term test) = -5811 Radius of convergence (six term test) for eq 1 = 5.050e+10 Order of pole (six term test) = 1.806e+20 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (analytic) = -0.014646155040705771007477564796187 y[1] (numeric) = -0.014646155040705771007477564796217 absolute error = 3.0e-32 relative error = 2.0483191606685569895714658922348e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 219.3 Order of pole (three term test) = -5807 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = -0.014520933155708096297895094806434 y[1] (numeric) = -0.014520933155708096297895094806463 absolute error = 2.9e-32 relative error = 1.9971168305116992301071356496545e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 219.2 Order of pole (three term test) = -5803 Radius of convergence (six term test) for eq 1 = 1.021e+11 Order of pole (six term test) = 7.358e+20 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = -0.01439675317343832248877919429881 y[1] (numeric) = -0.014396753173438322488779194298839 absolute error = 2.9e-32 relative error = 2.0143430710130066721717250627696e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 219 Order of pole (three term test) = -5799 Radius of convergence (six term test) for eq 1 = 7.182e+10 Order of pole (six term test) = 3.638e+20 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = -0.014273606757379685931828993950801 y[1] (numeric) = -0.01427360675737968593182899395083 absolute error = 2.9e-32 relative error = 2.0317219391662538403719489796756e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 218.8 Order of pole (three term test) = -5795 Radius of convergence (six term test) for eq 1 = 5.645e+11 Order of pole (six term test) = 2.244e+22 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (analytic) = -0.014151485633760456611046510750785 y[1] (numeric) = -0.014151485633760456611046510750814 absolute error = 2.9e-32 relative error = 2.0492548097435241647474368357527e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 218.7 Order of pole (three term test) = -5790 Radius of convergence (six term test) for eq 1 = 6.578e+10 Order of pole (six term test) = 3.043e+20 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (analytic) = -0.014030381591130654692210908615478 y[1] (numeric) = -0.014030381591130654692210908615507 absolute error = 2.9e-32 relative error = 2.0669430700539486267323027378104e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 218.5 Order of pole (three term test) = -5786 Radius of convergence (six term test) for eq 1 = 1.825e+11 Order of pole (six term test) = 2.340e+21 TOP MAIN SOLVE Loop bytes used=104034748, alloc=4521156, time=3.87 x[1] = 4.63 y[1] (analytic) = -0.013910286479940978430981617088102 y[1] (numeric) = -0.01391028647994097843098161708813 absolute error = 2.8e-32 relative error = 2.0128988745398437293615450163318e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 218.4 Order of pole (three term test) = -5782 Radius of convergence (six term test) for eq 1 = 6.361e+10 Order of pole (six term test) = 2.838e+20 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = -0.013791192212123941340378523185078 y[1] (numeric) = -0.013791192212123941340378523185107 absolute error = 2.9e-32 relative error = 2.1027913724896010621099190884388e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 218.2 Order of pole (three term test) = -5778 Radius of convergence (six term test) for eq 1 = 1.304e+11 Order of pole (six term test) = 1.190e+21 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = -0.013673090760677216341225911229106 y[1] (numeric) = -0.013673090760677216341225911229136 absolute error = 3.0e-32 relative error = 2.1940906065128851662167423097464e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 218 Order of pole (three term test) = -5774 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (analytic) = -0.013555974159249184445718696953557 y[1] (numeric) = -0.013555974159249184445718696953586 absolute error = 2.9e-32 relative error = 2.1392782000999479145931000154506e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 217.9 Order of pole (three term test) = -5770 Radius of convergence (six term test) for eq 1 = 9.364e+10 Order of pole (six term test) = 6.123e+20 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (analytic) = -0.013439834501726685354518029175181 y[1] (numeric) = -0.01343983450172668535451802917521 absolute error = 2.9e-32 relative error = 2.1577646656492845468690026221946e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 217.7 Order of pole (three term test) = -5766 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = -0.013324663941824967181652518632892 y[1] (numeric) = -0.01332466394182496718165251863292 absolute error = 2.8e-32 relative error = 2.1013663175481989254465604104886e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 217.6 Order of pole (three term test) = -5762 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = -0.013210454692679832358935953237933 y[1] (numeric) = -0.013210454692679832358935953237961 absolute error = 2.8e-32 relative error = 2.1195334037605336806735498372937e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 217.4 Order of pole (three term test) = -5757 Radius of convergence (six term test) for eq 1 = 9.632e+10 Order of pole (six term test) = 6.452e+20 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = -0.013097199026441976612557866979598 y[1] (numeric) = -0.013097199026441976612557866979628 absolute error = 3.0e-32 relative error = 2.2905660927525728933276812594869e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 217.2 Order of pole (three term test) = -5753 Radius of convergence (six term test) for eq 1 = 6.012e+10 Order of pole (six term test) = 2.510e+20 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = -0.012984889273873517748905972756003 y[1] (numeric) = -0.012984889273873517748905972756032 absolute error = 2.9e-32 relative error = 2.2333652130827158148985070599445e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 217.1 Order of pole (three term test) = -5749 Radius of convergence (six term test) for eq 1 = 1.395e+11 Order of pole (six term test) = 1.349e+21 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = -0.012873517823946710834486196633319 y[1] (numeric) = -0.012873517823946710834486196633348 absolute error = 2.9e-32 relative error = 2.2526865147967222626139050420824e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 216.9 Order of pole (three term test) = -5745 Radius of convergence (six term test) for eq 1 = 9.500e+10 Order of pole (six term test) = 6.250e+20 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = -0.012763077123444846205964525113938 y[1] (numeric) = -0.012763077123444846205964525113968 absolute error = 3.0e-32 relative error = 2.3505303391838146692212518493419e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 216.7 Order of pole (three term test) = -5741 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = -0.012653559676565326600813465055423 y[1] (numeric) = -0.012653559676565326600813465055452 absolute error = 2.9e-32 relative error = 2.2918451993954431439024823618192e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 216.6 Order of pole (three term test) = -5737 Radius of convergence (six term test) for eq 1 = 7.974e+10 Order of pole (six term test) = 4.392e+20 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = -0.012544958044524919556753680738013 y[1] (numeric) = -0.012544958044524919556753680738042 absolute error = 2.9e-32 relative error = 2.3116856905437531626682853427306e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 216.4 Order of pole (three term test) = -5733 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = -0.01243726484516718108908806397543 y[1] (numeric) = -0.012437264845167181089088063975459 absolute error = 2.9e-32 relative error = 2.3317023767704597318336101781536e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 216.3 Order of pole (three term test) = -5729 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = -0.012330472752572046519081539157613 y[1] (numeric) = -0.012330472752572046519081539157641 absolute error = 2.8e-32 relative error = 2.2707969566016359423227961258738e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 216.1 Order of pole (three term test) = -5724 Radius of convergence (six term test) for eq 1 = 1.419e+11 Order of pole (six term test) = 1.385e+21 TOP MAIN SOLVE Loop bytes used=108037256, alloc=4521156, time=4.01 x[1] = 4.78 y[1] (analytic) = -0.012224574496667584193696403546793 y[1] (numeric) = -0.012224574496667584193696403546822 absolute error = 2.9e-32 relative error = 2.3722707083101659207200893117204e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 215.9 Order of pole (three term test) = -5720 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = -0.012119562862843907707201713226515 y[1] (numeric) = -0.012119562862843907707201713226544 absolute error = 2.9e-32 relative error = 2.3928255769775367046237010096440e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 215.8 Order of pole (three term test) = -5716 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = -0.012015430691569242108388559078469 y[1] (numeric) = -0.012015430691569242108388559078498 absolute error = 2.9e-32 relative error = 2.4135630877008983164071201182455e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 215.6 Order of pole (three term test) = -5712 Radius of convergence (six term test) for eq 1 = 8.787e+10 Order of pole (six term test) = 5.288e+20 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = -0.011912170878008139453294092111419 y[1] (numeric) = -0.011912170878008139453294092111448 absolute error = 2.9e-32 relative error = 2.4344848891933587173605047447278e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 215.4 Order of pole (three term test) = -5708 Radius of convergence (six term test) for eq 1 = 1.117e+11 Order of pole (six term test) = 8.537e+20 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = -0.011809776371641838942419547171497 y[1] (numeric) = -0.011809776371641838942419547171527 absolute error = 3.0e-32 relative error = 2.5402682536849161909158155582476e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 215.3 Order of pole (three term test) = -5704 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = -0.011708240175890766763375600986895 y[1] (numeric) = -0.011708240175890766763375600986925 absolute error = 3.0e-32 relative error = 2.5622979670142947108717638071974e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 215.1 Order of pole (three term test) = -5700 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = -0.011607555347739170644657127860712 y[1] (numeric) = -0.011607555347739170644657127860742 absolute error = 3.0e-32 relative error = 2.5845235367189669857046016205843e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 215 Order of pole (three term test) = -5696 Radius of convergence (six term test) for eq 1 = 2.272e+11 Order of pole (six term test) = 3.516e+21 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = -0.011507714997361884013794340265994 y[1] (numeric) = -0.011507714997361884013794340266024 absolute error = 3.0e-32 relative error = 2.6069467315516093201554691876630e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 214.8 Order of pole (three term test) = -5691 Radius of convergence (six term test) for eq 1 = 3.142e+11 Order of pole (six term test) = 6.716e+21 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = -0.01140871228775321454340458344703 y[1] (numeric) = -0.011408712287753214543404583447059 absolute error = 2.9e-32 relative error = 2.5419170252132935683069550665493e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 214.6 Order of pole (three term test) = -5687 Radius of convergence (six term test) for eq 1 = 1.148e+11 Order of pole (six term test) = 8.956e+20 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = -0.011310540434357951761635451765616 y[1] (numeric) = -0.011310540434357951761635451765646 absolute error = 3.0e-32 relative error = 2.6523931525737889598075771882682e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 214.5 Order of pole (three term test) = -5683 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = -0.011213192704704488299102758818536 y[1] (numeric) = -0.011213192704704488299102758818566 absolute error = 3.0e-32 relative error = 2.6754199976794760626678051035973e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 214.3 Order of pole (three term test) = -5679 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = -0.011116662418040049242644154694593 y[1] (numeric) = -0.011116662418040049242644154694623 absolute error = 3.0e-32 relative error = 2.6986517060476884081821215287243e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 214.1 Order of pole (three term test) = -5675 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = -0.01102094294496802396698934870179 y[1] (numeric) = -0.01102094294496802396698934870182 absolute error = 3.0e-32 relative error = 2.7220901287486922602714586711017e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 214 Order of pole (three term test) = -5671 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = -0.010926027707087394718750038925556 y[1] (numeric) = -0.010926027707087394718750038925586 absolute error = 3.0e-32 relative error = 2.7457371337745992662099910316373e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 213.8 Order of pole (three term test) = -5667 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = -0.010831910176634256132916406215345 y[1] (numeric) = -0.010831910176634256132916406215375 absolute error = 3.0e-32 relative error = 2.7695946061954647836740266151244e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 213.7 Order of pole (three term test) = -5663 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=112037948, alloc=4521156, time=4.16 x[1] = 4.93 y[1] (analytic) = -0.010738583876125419770272588360867 y[1] (numeric) = -0.010738583876125419770272588360897 absolute error = 3.0e-32 relative error = 2.7936644483168368229890617865817e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 213.5 Order of pole (three term test) = -5658 Radius of convergence (six term test) for eq 1 = 2.955e+11 Order of pole (six term test) = 5.876e+21 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = -0.010646042378004097674771645595919 y[1] (numeric) = -0.010646042378004097674771645595949 absolute error = 3.0e-32 relative error = 2.8179485798387691673714846206516e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 213.3 Order of pole (three term test) = -5654 Radius of convergence (six term test) for eq 1 = 6.037e+10 Order of pole (six term test) = 2.450e+20 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = -0.010554279304287658862902436070549 y[1] (numeric) = -0.010554279304287658862902436070579 absolute error = 3.0e-32 relative error = 2.8424489380163123614292395268143e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 213.2 Order of pole (three term test) = -5650 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = -0.010463288326217452572398347251641 y[1] (numeric) = -0.010463288326217452572398347251672 absolute error = 3.1e-32 relative error = 2.9627397270822129330854487928443e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 213 Order of pole (three term test) = -5646 Radius of convergence (six term test) for eq 1 = 2.033e+11 Order of pole (six term test) = 2.771e+21 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = -0.010373063163910692015243310046742 y[1] (numeric) = -0.010373063163910692015243310046772 absolute error = 3.0e-32 relative error = 2.8921061721068189741462992135910e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 212.8 Order of pole (three term test) = -5642 Radius of convergence (six term test) for eq 1 = 1.886e+11 Order of pole (six term test) = 2.382e+21 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = -0.010283597586014392299786809817067 y[1] (numeric) = -0.010283597586014392299786809817098 absolute error = 3.1e-32 relative error = 3.0145092454959287512544943648609e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 212.7 Order of pole (three term test) = -5638 Radius of convergence (six term test) for eq 1 = 1.360e+11 Order of pole (six term test) = 1.236e+21 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = -0.010194885409361356108850068090735 y[1] (numeric) = -0.010194885409361356108850068090766 absolute error = 3.1e-32 relative error = 3.0407404061191846476027022169111e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 212.5 Order of pole (three term test) = -5634 Radius of convergence (six term test) for eq 1 = 1.261e+11 Order of pole (six term test) = 1.062e+21 Finished! diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x); Iterations = 400 Total Elapsed Time = 4 Seconds Elapsed Time(since restart) = 4 Seconds Time to Timeout = 2 Minutes 55 Seconds Percent Done = 100.2 % > quit bytes used=113934428, alloc=4521156, time=4.23