|\^/| 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_g, > 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_g, 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_g, > 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_g, 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_g, > 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_g, 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_g, > 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_g, 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_g, > 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_g, 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_g, > 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_g, 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_g, > 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_g, 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_g, > 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_g, 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_g, > 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 sin 1 $eq_no = 1 > array_tmp3[1] := sin(array_x[1]); > array_tmp3_g[1] := cos(array_x[1]); > #emit pre mult 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 sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp3[2] := array_tmp3_g[1] * array_x[2] / 1; > array_tmp3_g[2] := -array_tmp3[1] * array_x[2] / 1; > #emit pre mult LINEAR FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[1] * array_tmp2[2] + array_tmp3[2] * array_tmp2[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 sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := array_tmp3_g[2] * array_x[2] / 2; > array_tmp3_g[3] := -array_tmp3[2] * array_x[2] / 2; > #emit pre mult LINEAR FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[2] * array_tmp2[2] + array_tmp3[3] * array_tmp2[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 sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := array_tmp3_g[3] * array_x[2] / 3; > array_tmp3_g[4] := -array_tmp3[3] * array_x[2] / 3; > #emit pre mult LINEAR FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[3] * array_tmp2[2] + array_tmp3[4] * array_tmp2[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 sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := array_tmp3_g[4] * array_x[2] / 4; > array_tmp3_g[5] := -array_tmp3[4] * array_x[2] / 4; > #emit pre mult LINEAR FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[4] * array_tmp2[2] + array_tmp3[5] * array_tmp2[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 sin LINEAR $eq_no = 1 > array_tmp3[kkk] := array_tmp3_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp3_g[kkk] := -array_tmp3[kkk - 1] * array_x[2] / (kkk - 1); > #emit mult LINEAR FULL $eq_no = 1 i = 1 > array_tmp4[kkk] := array_tmp3[kkk-1] * array_tmp2[2] + array_tmp3[kkk] * array_tmp2[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_g, 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] := sin(array_x[1]); array_tmp3_g[1] := cos(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_g[1]*array_x[2]; array_tmp3_g[2] := -array_tmp3[1]*array_x[2]; array_tmp4[2] := array_tmp3[1]*array_tmp2[2] + array_tmp3[2]*array_tmp2[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_g[2]*array_x[2]; array_tmp3_g[3] := -1/2*array_tmp3[2]*array_x[2]; array_tmp4[3] := array_tmp3[2]*array_tmp2[2] + array_tmp3[3]*array_tmp2[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_g[3]*array_x[2]; array_tmp3_g[4] := -1/3*array_tmp3[3]*array_x[2]; array_tmp4[4] := array_tmp3[3]*array_tmp2[2] + array_tmp3[4]*array_tmp2[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_g[4]*array_x[2]; array_tmp3_g[5] := -1/4*array_tmp3[4]*array_x[2]; array_tmp4[5] := array_tmp3[4]*array_tmp2[2] + array_tmp3[5]*array_tmp2[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_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp3_g[kkk] := -array_tmp3[kkk - 1]*array_x[2]/(kkk - 1); array_tmp4[kkk] := array_tmp3[kkk - 1]*array_tmp2[2] + array_tmp3[kkk]*array_tmp2[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(0.2 * sin(x) - 0.2 * cos(x) * x - 0.3 * cos(x)); > end; exact_soln_y := proc(x) return 0.2*sin(x) - 0.2*cos(x)*x - 0.3*cos(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_g, > 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/mult_lin_sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = (0.2 * x + 0.3) * sin(x);"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > 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,"#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(0.2 * sin(x) - 0.2 * cos(x) * x - 0.3 * cos(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_g:= 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_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_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_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_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 := 0.1; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > #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) * sin(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,"2013-05-26T04:17:59-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mult_lin_sin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = (0.2 * x + 0.3) * sin(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,"mult_lin_sin diffeq.mxt") > ; > logitem_str(html_log_file,"mult_lin_sin 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_g, 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/mult_lin_sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.2 * x + 0.3) * sin(x);") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); 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, "#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(0.2 * sin(x) - 0.2 * cos(x) * x - 0.3 * cos(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_g := 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_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3_g[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_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 := 0.1; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; 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) * sin(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, "2013-05-26T04:17:59-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mult_lin_sin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.2 * x + 0.3) * sin(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, "mult_lin_sin diffeq.mxt"); logitem_str(html_log_file, "mult_lin_sin 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/mult_lin_sinpostode.ode################# diff ( y , x , 1 ) = (0.2 * x + 0.3) * sin(x); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; #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(0.2 * sin(x) - 0.2 * cos(x) * x - 0.3 * cos(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 = 4.9 estimated_steps = 4900000 step_error = 2.0408163265306122448979591836735e-17 est_needed_step_err = 2.0408163265306122448979591836735e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.0272398256655853672790613613475e-183 estimated_step_error = 2.0272398256655853672790613613475e-183 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.3604577760145916504440233217750e-175 estimated_step_error = 1.3604577760145916504440233217750e-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 = 9.1298797135753698593918328550059e-168 estimated_step_error = 9.1298797135753698593918328550059e-168 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.1269614148153851521950329314236e-160 estimated_step_error = 6.1269614148153851521950329314236e-160 best_h = 1.60000e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.1117380344035638218934284077541e-152 estimated_step_error = 4.1117380344035638218934284077541e-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 = 2.7593458276969199544605293480668e-144 estimated_step_error = 2.7593458276969199544605293480668e-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 = 1.8517725404784173777571690213999e-136 estimated_step_error = 1.8517725404784173777571690213999e-136 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.2427127790539337260994802451798e-128 estimated_step_error = 1.2427127790539337260994802451798e-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 = 8.3398286175596256090304655743014e-121 estimated_step_error = 8.3398286175596256090304655743014e-121 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.5969311168309886751906393611954e-113 estimated_step_error = 5.5969311168309886751906393611954e-113 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.7562608627160730336762134263172e-105 estimated_step_error = 3.7562608627160730336762134263172e-105 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.5210846017253889554697292707233e-97 estimated_step_error = 2.5210846017253889554697292707233e-97 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.6922747020726020527533081864218e-89 estimated_step_error = 1.6922747020726020527533081864218e-89 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1362078404729793677322811073354e-81 estimated_step_error = 1.1362078404729793677322811073354e-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 = 7.6322295313205153728640394191345e-74 estimated_step_error = 7.6322295313205153728640394191345e-74 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.1316564811428693933954633444084e-66 estimated_step_error = 5.1316564811428693933954633444084e-66 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.4568859755031296958284519568513e-58 estimated_step_error = 3.4568859755031296958284519568513e-58 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.3374403360497583696904236406275e-50 estimated_step_error = 2.3374403360497583696904236406275e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = -0.29843464955960261468921699641511 y[1] (numeric) = -0.29843464955960261468921699641511 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1492 Order of pole (three term test) = -1.538 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = -0.29809820337462142408223445686051 y[1] (numeric) = -0.2980982033746214240822344568605 absolute error = 1e-32 relative error = 3.3545992182425040101192516269766e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1583 Order of pole (three term test) = -1.621 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = -0.29772755655886879373491368353168 y[1] (numeric) = -0.29772755655886879373491368353168 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1673 Order of pole (three term test) = -1.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = -0.29732234882708192899956980565382 y[1] (numeric) = -0.29732234882708192899956980565383 absolute error = 1e-32 relative error = 3.3633529532675140568481738084892e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1763 Order of pole (three term test) = -1.803 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = -0.29688222382889769603925734811866 y[1] (numeric) = -0.29688222382889769603925734811867 absolute error = 1e-32 relative error = 3.3683390911822682216983126493768e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1851 Order of pole (three term test) = -1.901 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=4001796, alloc=3079628, time=0.14 x[1] = 0.15 y[1] (analytic) = -0.2964068292241741103229986418184 y[1] (numeric) = -0.29640682922417411032299864181841 absolute error = 1e-32 relative error = 3.3737414303760677402800464801878e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1939 Order of pole (three term test) = -2.004 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = -0.29589581675785895441930360603689 y[1] (numeric) = -0.2958958167578589544193036060369 absolute error = 1e-32 relative error = 3.3795678862818533916457224858548e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2026 Order of pole (three term test) = -2.112 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = -0.2953488423343940748318997413968 y[1] (numeric) = -0.29534884233439407483189974139682 absolute error = 2e-32 relative error = 6.7716534258008000505283072174429e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2112 Order of pole (three term test) = -2.224 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = -0.29476556609164395963479203632963 y[1] (numeric) = -0.29476556609164395963479203632965 absolute error = 2e-32 relative error = 6.7850530389909616280444008034619e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2198 Order of pole (three term test) = -2.341 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = -0.29414565247433725221257236581992 y[1] (numeric) = -0.29414565247433725221257236581995 absolute error = 3e-32 relative error = 1.0199028864659949735039727302842e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2282 Order of pole (three term test) = -2.463 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = -0.2934887703070099114903442902707 y[1] (numeric) = -0.29348877030700991149034429027072 absolute error = 2e-32 relative error = 6.8145707854779561967762061228483e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2365 Order of pole (three term test) = -2.589 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = -0.29279459286643878563957690504444 y[1] (numeric) = -0.29279459286643878563957690504447 absolute error = 3e-32 relative error = 1.0246090853762727568113848805458e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2447 Order of pole (three term test) = -2.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = -0.29206279795355442436531370438798 y[1] (numeric) = -0.292062797953554424365313704388 absolute error = 2e-32 relative error = 6.8478423613474112520430280600861e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2528 Order of pole (three term test) = -2.855 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = -0.29129306796482201450991136176076 y[1] (numeric) = -0.29129306796482201450991136176079 absolute error = 3e-32 relative error = 1.0298906256026301232950302568641e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2608 Order of pole (three term test) = -2.995 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = -0.29048508996307938484215056904529 y[1] (numeric) = -0.29048508996307938484215056904532 absolute error = 3e-32 relative error = 1.0327552441267466048624197896064e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2687 Order of pole (three term test) = -3.139 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = -0.28963855574782108853123866635309 y[1] (numeric) = -0.28963855574782108853123866635312 absolute error = 3e-32 relative error = 1.0357737050077003058142845217417e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2765 Order of pole (three term test) = -3.287 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = -0.28875316192491763592581491867738 y[1] (numeric) = -0.28875316192491763592581491867741 absolute error = 3e-32 relative error = 1.0389496620577501997410908168268e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2841 Order of pole (three term test) = -3.439 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = -0.28782860997575901586128907495613 y[1] (numeric) = -0.28782860997575901586128907495616 absolute error = 3e-32 relative error = 1.0422869360529033617778442476842e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2917 Order of pole (three term test) = -3.596 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = -0.28686460632581171079722014738877 y[1] (numeric) = -0.2868646063258117107972201473888 absolute error = 3e-32 relative error = 1.0457895236447173485302844577173e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2991 Order of pole (three term test) = -3.756 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = -0.28586086241257847963231662939873 y[1] (numeric) = -0.28586086241257847963231662939876 absolute error = 3e-32 relative error = 1.0494616068393956141422190713112e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3063 Order of pole (three term test) = -3.921 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = -0.2848170947529502520501675327875 y[1] (numeric) = -0.28481709475295025205016753278752 absolute error = 2e-32 relative error = 7.0220504205858703337198012415509e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3135 Order of pole (three term test) = -4.089 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = -0.2837330250099395497059669031134 y[1] (numeric) = -0.28373302500993954970596690311343 absolute error = 3e-32 relative error = 1.0573319760344802874762184515153e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3205 Order of pole (three term test) = -4.261 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = -0.28260838005878492246506033896743 y[1] (numeric) = -0.28260838005878492246506033896745 absolute error = 2e-32 relative error = 7.0769309798385425126445570561909e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3273 Order of pole (three term test) = -4.437 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = -0.28144289205241596223972513244798 y[1] (numeric) = -0.28144289205241596223972513244801 absolute error = 3e-32 relative error = 1.0659356070862431283892186371856e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3341 Order of pole (three term test) = -4.617 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = -0.28023629848626853273261871668362 y[1] (numeric) = -0.28023629848626853273261871668365 absolute error = 3e-32 relative error = 1.0705251304719894478194629762965e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3406 Order of pole (three term test) = -4.801 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = -0.27898834226243993057503499081883 y[1] (numeric) = -0.27898834226243993057503499081886 absolute error = 3e-32 relative error = 1.0753137481199652944531124717884e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.347 Order of pole (three term test) = -4.987 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = -0.27769877175317377193655671375826 y[1] (numeric) = -0.27769877175317377193655671375829 absolute error = 3e-32 relative error = 1.0803072628158693003884940508838e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3533 Order of pole (three term test) = -5.178 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = -0.27636734086366447867076753245416 y[1] (numeric) = -0.27636734086366447867076753245419 absolute error = 3e-32 relative error = 1.0855117651111815429937080574482e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3594 Order of pole (three term test) = -5.371 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = -0.2749938090941713194400944904346 y[1] (numeric) = -0.27499380909417131944009449043463 absolute error = 3e-32 relative error = 1.0909336504272550321948033058667e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3654 Order of pole (three term test) = -5.568 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = -0.27357794160143204402211939301962 y[1] (numeric) = -0.27357794160143204402211939301966 absolute error = 4e-32 relative error = 1.4621061831905610023811150531644e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3712 Order of pole (three term test) = -5.769 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = -0.27211950925936623313017780682054 y[1] (numeric) = -0.27211950925936623313017780682058 absolute error = 4e-32 relative error = 1.4699423833619609430833290202678e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3768 Order of pole (three term test) = -5.972 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=8003532, alloc=4259060, time=0.30 x[1] = 0.41 y[1] (analytic) = -0.2706182887190585715729357382516 y[1] (numeric) = -0.27061828871905857157293573825163 absolute error = 3e-32 relative error = 1.1085725263433468425554164515621e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3823 Order of pole (three term test) = -6.178 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = -0.26907406246801233942090066361435 y[1] (numeric) = -0.26907406246801233942090066361439 absolute error = 4e-32 relative error = 1.4865795548300096826453903977151e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3876 Order of pole (three term test) = -6.388 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = -0.26748661888866350403231770985318 y[1] (numeric) = -0.26748661888866350403231770985322 absolute error = 4e-32 relative error = 1.4954019070632195190138036279843e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3928 Order of pole (three term test) = -6.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = -0.26585575231614588530628435677538 y[1] (numeric) = -0.26585575231614588530628435677543 absolute error = 5e-32 relative error = 1.8807191330034431028001941529968e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3977 Order of pole (three term test) = -6.815 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = -0.26418126309529795736667898923334 y[1] (numeric) = -0.26418126309529795736667898923338 absolute error = 4e-32 relative error = 1.5141119219182029068301437893894e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4025 Order of pole (three term test) = -7.032 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = -0.26246295763690194202596211338638 y[1] (numeric) = -0.26246295763690194202596211338643 absolute error = 5e-32 relative error = 1.9050307308192151013603951249767e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4071 Order of pole (three term test) = -7.252 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = -0.26070064847314594282222863487488 y[1] (numeric) = -0.26070064847314594282222863487493 absolute error = 5e-32 relative error = 1.9179085396540685075649373970141e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4116 Order of pole (three term test) = -7.475 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = -0.25889415431229996315505352462113 y[1] (numeric) = -0.25889415431229996315505352462119 absolute error = 6e-32 relative error = 2.3175494309393691373487705535900e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4158 Order of pole (three term test) = -7.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = -0.2570433000925967480545046598988 y[1] (numeric) = -0.25704330009259674805450465989885 absolute error = 5e-32 relative error = 1.9451975593990624602006263167549e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4199 Order of pole (three term test) = -7.927 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = -0.25514791703530848639185504599842 y[1] (numeric) = -0.25514791703530848639185504599847 absolute error = 5e-32 relative error = 1.9596475872103937647829209488497e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4238 Order of pole (three term test) = -8.156 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = -0.25320784269701050886850895884244 y[1] (numeric) = -0.25320784269701050886850895884249 absolute error = 5e-32 relative error = 1.9746623748866339346502896838449e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4275 Order of pole (three term test) = -8.388 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = -0.2512229210210232168897986305738 y[1] (numeric) = -0.25122292102102321688979863057386 absolute error = 6e-32 relative error = 2.3883171072188508287160694560064e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4311 Order of pole (three term test) = -8.621 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = -0.24919300238802357843078597304384 y[1] (numeric) = -0.2491930023880235784307859730439 absolute error = 6e-32 relative error = 2.4077722658749766550378077600383e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4344 Order of pole (three term test) = -8.856 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = -0.24711794366581762922003512520681 y[1] (numeric) = -0.24711794366581762922003512520686 absolute error = 5e-32 relative error = 2.0233253505708984957927070487336e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4376 Order of pole (three term test) = -9.093 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = -0.24499760825826552099236691547182 y[1] (numeric) = -0.24499760825826552099236691547188 absolute error = 6e-32 relative error = 2.4490034995260314348978447541636e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4405 Order of pole (three term test) = -9.332 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = -0.24283186615335076318057061937052 y[1] (numeric) = -0.24283186615335076318057061937057 absolute error = 5e-32 relative error = 2.0590378351918811864487959395115e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4433 Order of pole (three term test) = -9.572 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = -0.24062059397038541021648243604545 y[1] (numeric) = -0.24062059397038541021648243604552 absolute error = 7e-32 relative error = 2.9091441777678975867115712621914e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.78 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4459 Order of pole (three term test) = -9.814 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = -0.23836367500634305358114191655352 y[1] (numeric) = -0.23836367500634305358114191655357 absolute error = 5e-32 relative error = 2.0976350527683993312597172850309e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4482 Order of pole (three term test) = -10.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = -0.23606099928131158586915387062595 y[1] (numeric) = -0.236060999281311585869153870626 absolute error = 5e-32 relative error = 2.1180966001256094251918410086433e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4504 Order of pole (three term test) = -10.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = -0.23371246358305781340101096042953 y[1] (numeric) = -0.23371246358305781340101096042958 absolute error = 5e-32 relative error = 2.1393809826590942316117834510808e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4524 Order of pole (three term test) = -10.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = -0.2313179715106961043159198497598 y[1] (numeric) = -0.23131797151069610431591984975984 absolute error = 4e-32 relative error = 1.7292214581844717019660180455095e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.09 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4542 Order of pole (three term test) = -10.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = -0.2288774335174533705934232079325 y[1] (numeric) = -0.22887743351745337059342320793254 absolute error = 4e-32 relative error = 1.7476602819801255654467759703839e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4558 Order of pole (three term test) = -11.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = -0.22639076695252279507147760126211 y[1] (numeric) = -0.22639076695252279507147760126215 absolute error = 4e-32 relative error = 1.7668565082598329132474983642033e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.78 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4572 Order of pole (three term test) = -11.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = -0.22385789610199882823814616568183 y[1] (numeric) = -0.22385789610199882823814616568188 absolute error = 5e-32 relative error = 2.2335598105155938592739817671418e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.14 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4584 Order of pole (three term test) = -11.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = -0.22127875222888609436006562967117 y[1] (numeric) = -0.22127875222888609436006562967122 absolute error = 5e-32 relative error = 2.2595933634098338561092332095638e-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 = 0.4594 Order of pole (three term test) = -11.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = -0.2186532736121749623595798875322 y[1] (numeric) = -0.21865327361217496235957988753225 absolute error = 5e-32 relative error = 2.2867254248699215634588805851300e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.87 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4602 Order of pole (three term test) = -12.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=12004496, alloc=4324584, time=0.46 x[1] = 0.67 y[1] (analytic) = -0.21598140558497665374998810803443 y[1] (numeric) = -0.21598140558497665374998810803447 absolute error = 4e-32 relative error = 1.8520112827149014848302044252260e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4608 Order of pole (three term test) = -12.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = -0.21326310057171087787068818315927 y[1] (numeric) = -0.21326310057171087787068818315932 absolute error = 5e-32 relative error = 2.3445218542711390414358294011446e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4612 Order of pole (three term test) = -12.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = -0.21049831812433910361692437878628 y[1] (numeric) = -0.21049831812433910361692437878632 absolute error = 4e-32 relative error = 1.9002527125358041154403382771179e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.12 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4614 Order of pole (three term test) = -12.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = -0.20768702495763669681805552540468 y[1] (numeric) = -0.20768702495763669681805552540472 absolute error = 4e-32 relative error = 1.9259749138473655694000881237140e-29 % Correct digits = 31 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 = 0.4614 Order of pole (three term test) = -13.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = -0.20482919498349727336929881673911 y[1] (numeric) = -0.20482919498349727336929881673916 absolute error = 5e-32 relative error = 2.4410582682819415332422202317659e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4612 Order of pole (three term test) = -13.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = -0.20192480934426274015019544471023 y[1] (numeric) = -0.20192480934426274015019544471028 absolute error = 5e-32 relative error = 2.4761692316249619195885267285066e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4608 Order of pole (three term test) = -13.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = -0.19897385644507261865388011656114 y[1] (numeric) = -0.19897385644507261865388011656119 absolute error = 5e-32 relative error = 2.5128929444960857410144762789411e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4602 Order of pole (three term test) = -13.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = -0.19597633198522637008978197167145 y[1] (numeric) = -0.19597633198522637008978197167149 absolute error = 4e-32 relative error = 2.0410627954305926409685360591369e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.29 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4594 Order of pole (three term test) = -14.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = -0.19293223898855256549367904829406 y[1] (numeric) = -0.19293223898855256549367904829411 absolute error = 5e-32 relative error = 2.5915834627807692728732978526258e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.94 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4584 Order of pole (three term test) = -14.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = -0.18984158783277887006798801397953 y[1] (numeric) = -0.18984158783277887006798801397959 absolute error = 6e-32 relative error = 3.1605298230465042685676351408717e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4572 Order of pole (three term test) = -14.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = -0.18670439627789693756658916976681 y[1] (numeric) = -0.18670439627789693756658916976686 absolute error = 5e-32 relative error = 2.6780301373074452201501922531993e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.27 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4558 Order of pole (three term test) = -14.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = -0.18352068949351643801703738581306 y[1] (numeric) = -0.18352068949351643801703738581311 absolute error = 5e-32 relative error = 2.7244884562057205532549828012176e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.94 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4542 Order of pole (three term test) = -15.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = -0.18029050008520257042324785938306 y[1] (numeric) = -0.18029050008520257042324785938312 absolute error = 6e-32 relative error = 3.3279623702660375992162042010404e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4524 Order of pole (three term test) = -15.29 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = -0.17701386811979154129811006943919 y[1] (numeric) = -0.17701386811979154129811006943924 absolute error = 5e-32 relative error = 2.8246374440088068522056754617041e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4504 Order of pole (three term test) = -15.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = -0.1736908411496786199222979586913 y[1] (numeric) = -0.17369084114967861992229795869135 absolute error = 5e-32 relative error = 2.8786779814666419430450372070066e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.99 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4482 Order of pole (three term test) = -15.78 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = -0.1703214742360735120970202290572 y[1] (numeric) = -0.17032147423607351209702022905724 absolute error = 4e-32 relative error = 2.3485001042533329193046881568146e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4459 Order of pole (three term test) = -16.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = -0.16690582997121792583869167449722 y[1] (numeric) = -0.16690582997121792583869167449727 absolute error = 5e-32 relative error = 2.9957012291675041845034509149100e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4433 Order of pole (three term test) = -16.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = -0.16344397849956033493649551112963 y[1] (numeric) = -0.16344397849956033493649551112968 absolute error = 5e-32 relative error = 3.0591521608203204765298646994933e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4405 Order of pole (three term test) = -16.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = -0.1599359975378830795434312289998 y[1] (numeric) = -0.15993599753788307954343122899984 absolute error = 4e-32 relative error = 2.5010004386614364376852209713881e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4376 Order of pole (three term test) = -16.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = -0.15638197239437707698148072760793 y[1] (numeric) = -0.15638197239437707698148072760798 absolute error = 5e-32 relative error = 3.1972994862800321661533400470990e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4344 Order of pole (three term test) = -16.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = -0.1527819959866595506956520790543 y[1] (numeric) = -0.15278199598665955069565207905434 absolute error = 4e-32 relative error = 2.6181095319302331767150452734180e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4311 Order of pole (three term test) = -17.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = -0.14913616885873032077344831017252 y[1] (numeric) = -0.14913616885873032077344831017257 absolute error = 5e-32 relative error = 3.3526407700175434045260852379676e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4275 Order of pole (three term test) = -17.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = -0.14544459919686233563923161883312 y[1] (numeric) = -0.14544459919686233563923161883318 absolute error = 6e-32 relative error = 4.1252820889408711065332284300009e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4238 Order of pole (three term test) = -17.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = -0.14170740284442226142038728953272 y[1] (numeric) = -0.14170740284442226142038728953277 absolute error = 5e-32 relative error = 3.5283971758972963002983925225355e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4199 Order of pole (three term test) = -17.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = -0.13792470331561708304741640144189 y[1] (numeric) = -0.13792470331561708304741640144194 absolute error = 5e-32 relative error = 3.6251663986242954295481957162159e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4159 Order of pole (three term test) = -18.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = -0.13409663180816280937628865753408 y[1] (numeric) = -0.13409663180816280937628865753413 absolute error = 5e-32 relative error = 3.7286544282133393947963421559049e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4116 Order of pole (three term test) = -18.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=16005856, alloc=4390108, time=0.63 x[1] = 0.93 y[1] (analytic) = -0.1302233272148715134916609998523 y[1] (numeric) = -0.13022332721487151349166099985236 absolute error = 6e-32 relative error = 4.6074694360249763002502893116156e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4072 Order of pole (three term test) = -18.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = -0.12630493613415307884691907010249 y[1] (numeric) = -0.12630493613415307884691907010255 absolute error = 6e-32 relative error = 4.7504081658591562785040198612582e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4026 Order of pole (three term test) = -18.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = -0.12234161287942816200434425672212 y[1] (numeric) = -0.12234161287942816200434425672217 absolute error = 5e-32 relative error = 4.0869168570857985761088783584216e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3978 Order of pole (three term test) = -19.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = -0.11833351948744902343888056448703 y[1] (numeric) = -0.11833351948744902343888056448709 absolute error = 6e-32 relative error = 5.0704145587729151779544392143592e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3928 Order of pole (three term test) = -19.24 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = -0.11428082572552501914472070332456 y[1] (numeric) = -0.11428082572552501914472070332462 absolute error = 6e-32 relative error = 5.2502245778399894527236610326883e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3877 Order of pole (three term test) = -19.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = -0.1101837090976496876179158430667 y[1] (numeric) = -0.11018370909764968761791584306676 absolute error = 6e-32 relative error = 5.4454511008360900345505691950404e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3824 Order of pole (three term test) = -19.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = -0.10604235484952650916302506920007 y[1] (numeric) = -0.10604235484952650916302506920014 absolute error = 7e-32 relative error = 6.6011359422685017578359635171609e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3769 Order of pole (three term test) = -19.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = -0.10185695597249055736996783939543 y[1] (numeric) = -0.10185695597249055736996783939549 absolute error = 6e-32 relative error = 5.8906138934885066166575059344933e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3713 Order of pole (three term test) = -20.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = -0.09762771320632340601115938364475 y[1] (numeric) = -0.097627713206323406011159383644807 absolute error = 5.7e-32 relative error = 5.8385061093808428503859536520212e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3655 Order of pole (three term test) = -20.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = -0.09335483504095879850105536215796 y[1] (numeric) = -0.093354835040958798501055362158026 absolute error = 6.6e-32 relative error = 7.0697998631825495911499086612909e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3595 Order of pole (three term test) = -20.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = -0.08903853771707673142269728665881 y[1] (numeric) = -0.089038537717076731422697286658877 absolute error = 6.7e-32 relative error = 7.5248315749406166650657702675256e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3534 Order of pole (three term test) = -20.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = -0.08467904522558374844095415944079 y[1] (numeric) = -0.084679045225583748440954159440853 absolute error = 6.3e-32 relative error = 7.4398571490938417697339455626387e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3472 Order of pole (three term test) = -20.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = -0.08027658930597738617205138513412 y[1] (numeric) = -0.080276589305977386172051385134179 absolute error = 5.9e-32 relative error = 7.3495897758086324639583465778279e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3408 Order of pole (three term test) = -21.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = -0.0758314094435928592457532360582 y[1] (numeric) = -0.07583140944359285924575323605826 absolute error = 6.0e-32 relative error = 7.9122886466499027606734608185916e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3342 Order of pole (three term test) = -21.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = -0.07134375286573021786224518548707 y[1] (numeric) = -0.071343752865730217862245185487121 absolute error = 5.1e-32 relative error = 7.1484885433462688643438730264906e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3275 Order of pole (three term test) = -21.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = -0.06681387453666035759231179335448 y[1] (numeric) = -0.066813874536660357592311793354544 absolute error = 6.4e-32 relative error = 9.5788487711311514905134800801987e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3207 Order of pole (three term test) = -21.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = -0.06224203715150840797873055854011 y[1] (numeric) = -0.062242037151508407978730558540176 absolute error = 6.6e-32 relative error = 1.0603766043091428518515460022972e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3137 Order of pole (three term test) = -21.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = -0.057628511129013173650751911353718 y[1] (numeric) = -0.057628511129013173650751911353774 absolute error = 5.6e-32 relative error = 9.7174122500983203599017426154748e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3066 Order of pole (three term test) = -21.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = -0.052973574603161449143905789361453 y[1] (numeric) = -0.052973574603161449143905789361512 absolute error = 5.9e-32 relative error = 1.1137628608600427609621789619586e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2993 Order of pole (three term test) = -22.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = -0.048277513413696176405909478567803 y[1] (numeric) = -0.048277513413696176405909478567863 absolute error = 6.0e-32 relative error = 1.2428146306097486698501678886122e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2919 Order of pole (three term test) = -22.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = -0.04354062109549756204784322507148 y[1] (numeric) = -0.043540621095497562047843225071545 absolute error = 6.5e-32 relative error = 1.4928588147016925347563468464415e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2844 Order of pole (three term test) = -22.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = -0.038763198866836419749655483533878 y[1] (numeric) = -0.038763198866836419749655483533943 absolute error = 6.5e-32 relative error = 1.6768481936512801485483044469664e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2768 Order of pole (three term test) = -22.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = -0.033945555616499151832059051018522 y[1] (numeric) = -0.033945555616499151832059051018584 absolute error = 6.2e-32 relative error = 1.8264541226087651991999737682343e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.269 Order of pole (three term test) = -22.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = -0.02908800788978393284453994627074 y[1] (numeric) = -0.029088007889783932844539946270807 absolute error = 6.7e-32 relative error = 2.3033547107751997828673826100967e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2612 Order of pole (three term test) = -22.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = -0.024190879873367807073038871524557 y[1] (numeric) = -0.024190879873367807073038871524625 absolute error = 6.8e-32 relative error = 2.8109767133713261146693663972663e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2532 Order of pole (three term test) = -23.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = -0.019254503379044561122357708983091 y[1] (numeric) = -0.019254503379044561122357708983152 absolute error = 6.1e-32 relative error = 3.1680900202489105368562542538333e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2451 Order of pole (three term test) = -23.15 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=20007552, alloc=4455632, time=0.79 x[1] = 1.19 y[1] (analytic) = -0.014279217826333382158931380072022 y[1] (numeric) = -0.014279217826333382158931380072078 absolute error = 5.6e-32 relative error = 3.9217834394770684108258382975221e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2369 Order of pole (three term test) = -23.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = -0.009265370223958461990694724937489 y[1] (numeric) = -0.0092653702239584619906947249375586 absolute error = 6.96e-32 relative error = 7.5118423028610137678915052109653e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2286 Order of pole (three term test) = -23.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = -0.0042133151501998568937388290976 y[1] (numeric) = -0.0042133151501998568937388290976578 absolute error = 5.78e-32 relative error = 1.3718413633800519399581164785513e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2202 Order of pole (three term test) = -23.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 0.00087658526788393704836455628492 y[1] (numeric) = 0.0008765852678839370483645562848648 absolute error = 5.520e-32 relative error = 6.2971626403500854670620303135832e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2117 Order of pole (three term test) = -23.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 0.00600396137636108336597191703613 y[1] (numeric) = 0.0060039613763610833659719170360614 absolute error = 6.86e-32 relative error = 1.1425789691135137875250331073118e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2031 Order of pole (three term test) = -23.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 0.011168436017458419612365200814196 y[1] (numeric) = 0.011168436017458419612365200814131 absolute error = 6.5e-32 relative error = 5.8199733515411166877807903440630e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1944 Order of pole (three term test) = -23.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 0.016369624553719476873551965566288 y[1] (numeric) = 0.016369624553719476873551965566226 absolute error = 6.2e-32 relative error = 3.7875028713418152685445954509453e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1857 Order of pole (three term test) = -23.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = 0.021607134893287444330102190259666 y[1] (numeric) = 0.021607134893287444330102190259603 absolute error = 6.3e-32 relative error = 2.9157035539946493518262792978153e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1768 Order of pole (three term test) = -24.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 0.026880567516311868630706441523852 y[1] (numeric) = 0.026880567516311868630706441523786 absolute error = 6.6e-32 relative error = 2.4553053040993045415151824537890e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1679 Order of pole (three term test) = -24.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 0.032189515502477727634811658994583 y[1] (numeric) = 0.032189515502477727634811658994514 absolute error = 6.9e-32 relative error = 2.1435550962141338940428872219319e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1589 Order of pole (three term test) = -24.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 0.037533564559655367887386060002936 y[1] (numeric) = 0.037533564559655367887386060002871 absolute error = 6.5e-32 relative error = 1.7317832921701276361418446417833e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1498 Order of pole (three term test) = -24.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0.042912293053669645021398624803899 y[1] (numeric) = 0.04291229305366964502139862480384 absolute error = 5.9e-32 relative error = 1.3748973965620934025983489880817e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1407 Order of pole (three term test) = -24.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 0.0483252720391864561617960992052 y[1] (numeric) = 0.048325272039186456161796099205135 absolute error = 6.5e-32 relative error = 1.3450519212244099082070358739732e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1315 Order of pole (three term test) = -24.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 0.053772065291714703347453709797525 y[1] (numeric) = 0.053772065291714703347453709797464 absolute error = 6.1e-32 relative error = 1.1344180229841197832588830866585e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1223 Order of pole (three term test) = -24.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 0.059252229340721577013602305470776 y[1] (numeric) = 0.059252229340721577013602305470708 absolute error = 6.8e-32 relative error = 1.1476361439326713464475866319998e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1129 Order of pole (three term test) = -24.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 0.064765313503858898705434837991428 y[1] (numeric) = 0.064765313503858898705434837991365 absolute error = 6.3e-32 relative error = 9.7274291733716819907876604367640e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1036 Order of pole (three term test) = -24.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 0.070310859922298112442810069236981 y[1] (numeric) = 0.070310859922298112442810069236922 absolute error = 5.9e-32 relative error = 8.3913068429545646400731552228811e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0942 Order of pole (three term test) = -24.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 0.075888403597171364545040643517182 y[1] (numeric) = 0.07588840359717136454504064351712 absolute error = 6.2e-32 relative error = 8.1698911903729866295968456970117e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08476 Order of pole (three term test) = -24.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 0.081497472427115962272511825321987 y[1] (numeric) = 0.081497472427115962272511825321916 absolute error = 7.1e-32 relative error = 8.7119266261289316536520788492743e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07528 Order of pole (three term test) = -24.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 0.08713758724691935236715577464865 y[1] (numeric) = 0.087137587246919352367155774648581 absolute error = 6.9e-32 relative error = 7.9185116526667904059787627713018e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06577 Order of pole (three term test) = -24.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 0.092808261867261611495425304997835 y[1] (numeric) = 0.092808261867261611495425304997774 absolute error = 6.1e-32 relative error = 6.5726907036837773359658827840333e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05623 Order of pole (three term test) = -24.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0.098509003115552291734181055343105 y[1] (numeric) = 0.098509003115552291734181055343039 absolute error = 6.6e-32 relative error = 6.6998952291275524521896260884675e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04666 Order of pole (three term test) = -24.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 0.10423931087785831561062436866039 y[1] (numeric) = 0.10423931087785831561062436866033 absolute error = 6e-32 relative error = 5.7559858650931202805428285887515e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03708 Order of pole (three term test) = -24.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 0.10999867814191946683085714652921 y[1] (numeric) = 0.10999867814191946683085714652914 absolute error = 7e-32 relative error = 6.3637128356839458315585608658371e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02748 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 0.11578659104124787472659429109546 y[1] (numeric) = 0.11578659104124787472659429109539 absolute error = 7e-32 relative error = 6.0456050541347368978207940750529e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01786 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 0.12160252890030774263473904098765 y[1] (numeric) = 0.12160252890030774263473904098757 absolute error = 8e-32 relative error = 6.5788105497037522507312359744556e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008235 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 bytes used=24008772, alloc=4455632, time=0.95 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 0.12744596428077142291867951678826 y[1] (numeric) = 0.1274459642807714229186795167882 absolute error = 6e-32 relative error = 4.7078775964860096182225916620469e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 0.13331636302884779416197477964898 y[1] (numeric) = 0.1333163630288477941619747796489 absolute error = 8e-32 relative error = 6.0007637609112633999068383920777e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = 0.13921318432367874923324277927844 y[1] (numeric) = 0.13921318432367874923324277927838 absolute error = 6e-32 relative error = 4.3099366120737897075135919444880e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = 0.14513588072679945645418400828643 y[1] (numeric) = 0.14513588072679945645418400828636 absolute error = 7e-32 relative error = 4.8230664705005951030011859896990e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 0.15108389823265791001938568963964 y[1] (numeric) = 0.15108389823265791001938568963957 absolute error = 7e-32 relative error = 4.6331873097558836070264481695906e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 0.15705667632018914013543076336774 y[1] (numeric) = 0.15705667632018914013543076336767 absolute error = 7e-32 relative error = 4.4569897721057096438044016218838e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = 0.16305364800543930808642707298779 y[1] (numeric) = 0.16305364800543930808642707298773 absolute error = 6e-32 relative error = 3.6797704764016355812628796923788e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = 0.16907423989523476661188039965112 y[1] (numeric) = 0.16907423989523476661188039965106 absolute error = 6e-32 relative error = 3.5487369357495515183557362476535e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (analytic) = 0.17511787224189102161932567545367 y[1] (numeric) = 0.1751178722418910216193256754536 absolute error = 7e-32 relative error = 3.9973075908156717615373473195407e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = 0.18118395899895638736672680898556 y[1] (numeric) = 0.18118395899895638736672680898549 absolute error = 7e-32 relative error = 3.8634766778886423001133390952370e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 0.1872719078779849838567354769626 y[1] (numeric) = 0.18727190787798498385673547696254 absolute error = 6e-32 relative error = 3.2038975135070637868010051629999e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = 0.19338112040633358230479455846103 y[1] (numeric) = 0.19338112040633358230479455846096 absolute error = 7e-32 relative error = 3.6197949341132979125004336861739e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 0.19951099198597666219406514510642 y[1] (numeric) = 0.19951099198597666219406514510636 absolute error = 6e-32 relative error = 3.0073530988316329378315204721559e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 0.2056609119533339016304785055517 y[1] (numeric) = 0.20566091195333390163047850555165 absolute error = 5e-32 relative error = 2.4311863409098077953652860866190e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (analytic) = 0.21183026364010418147904376872752 y[1] (numeric) = 0.21183026364010418147904376872747 absolute error = 5e-32 relative error = 2.3603803885619055451033177742175e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 0.21801842443510004311600045213608 y[1] (numeric) = 0.21801842443510004311600045213602 absolute error = 6e-32 relative error = 2.7520609854632200559668767264851e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = 0.2242247658470763995885564027407 y[1] (numeric) = 0.22422476584707639958855640274064 absolute error = 6e-32 relative error = 2.6758863934290210456732445262080e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = 0.23044865356854716055280020566985 y[1] (numeric) = 0.2304486535685471605528002056698 absolute error = 5e-32 relative error = 2.1696807174066415081727184518192e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 0.23668944754058329257886427957142 y[1] (numeric) = 0.23668944754058329257886427957137 absolute error = 5e-32 relative error = 2.1124727156003391394030081749898e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = 0.24294650201858569828841781515634 y[1] (numeric) = 0.24294650201858569828841781515629 absolute error = 5e-32 relative error = 2.0580662649826890750683077957204e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = 0.24921916563902616034089780436544 y[1] (numeric) = 0.2492191656390261603408978043654 absolute error = 4e-32 relative error = 1.6050129971920687042953383890729e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = 0.25550678148714945952928313092579 y[1] (numeric) = 0.25550678148714945952928313092574 absolute error = 5e-32 relative error = 1.9568952224665205657301057326984e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (analytic) = 0.26180868716562964020135145441927 y[1] (numeric) = 0.26180868716562964020135145441922 absolute error = 5e-32 relative error = 1.9097914794694414566766064890004e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = 0.26812421486417326090582858477263 y[1] (numeric) = 0.26812421486417326090582858477258 absolute error = 5e-32 relative error = 1.8648073254155380857716111283772e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 0.27445269143006233359216697854263 y[1] (numeric) = 0.27445269143006233359216697854258 absolute error = 5e-32 relative error = 1.8218076033239155624040283671010e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 0.2807934384396295208853181084239 y[1] (numeric) = 0.28079343843962952088531810842385 absolute error = 5e-32 relative error = 1.7806683901821295723036080801293e-29 % Correct digits = 31 h = 0.01 bytes used=28009808, alloc=4521156, time=1.11 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = 0.28714577227065802793015728549104 y[1] (numeric) = 0.28714577227065802793015728549099 absolute error = 5e-32 relative error = 1.7412758545813090053668753699833e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 0.29350900417569849307146174395039 y[1] (numeric) = 0.29350900417569849307146174395033 absolute error = 6e-32 relative error = 2.0442303011625218032313738107172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = 0.29988244035629505022173217021171 y[1] (numeric) = 0.29988244035629505022173217021166 absolute error = 5e-32 relative error = 1.6673200318296133829095422164784e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = 0.30626538203811260518779703947673 y[1] (numeric) = 0.30626538203811260518779703947668 absolute error = 5e-32 relative error = 1.6325710619745409674605071358560e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 0.31265712554695723849507260095631 y[1] (numeric) = 0.31265712554695723849507260095626 absolute error = 5e-32 relative error = 1.5991959214916602811093416416419e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (analytic) = 0.31905696238568151838250333497186 y[1] (numeric) = 0.31905696238568151838250333497181 absolute error = 5e-32 relative error = 1.5671182859052968729986814302051e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = 0.32546417931196637965842003027136 y[1] (numeric) = 0.32546417931196637965842003027131 absolute error = 5e-32 relative error = 1.5362673737460251477478375839555e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 0.33187805841697109702457268790621 y[1] (numeric) = 0.33187805841697109702457268790615 absolute error = 6e-32 relative error = 1.8078929437575559633364728163315e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = 0.33829787720484275530907412063943 y[1] (numeric) = 0.33829787720484275530907412063938 absolute error = 5e-32 relative error = 1.4779874001315266564471022717226e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0.34472290867307649381547967807885 y[1] (numeric) = 0.3447229086730764938154796780788 absolute error = 5e-32 relative error = 1.4504403026901325820118183294164e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (analytic) = 0.35115242139371767771118065507547 y[1] (numeric) = 0.35115242139371767771118065507541 absolute error = 6e-32 relative error = 1.7086597256502197398159827196837e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = 0.35758567959539702606005263746731 y[1] (numeric) = 0.35758567959539702606005263746726 absolute error = 5e-32 relative error = 1.3982662856234698702789769863854e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = 0.3640219432461896037681196166385 y[1] (numeric) = 0.36402194324618960376811961663845 absolute error = 5e-32 relative error = 1.3735435714155502224627095658169e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = 0.37046046813728846337300776717753 y[1] (numeric) = 0.37046046813728846337300776717748 absolute error = 5e-32 relative error = 1.3496716735095892873670738158694e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = 0.37690050596748360228419822349535 y[1] (numeric) = 0.37690050596748360228419822349529 absolute error = 6e-32 relative error = 1.5919320629719820437071362455536e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = 0.38334130442843678178746420131093 y[1] (numeric) = 0.38334130442843678178746420131087 absolute error = 6e-32 relative error = 1.5651848445984762504948242263436e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = 0.3897821072907426358791998941164 y[1] (numeric) = 0.38978210729074263587919989411633 absolute error = 7e-32 relative error = 1.7958751489787152427599185064104e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = 0.39622215449076638081030758660006 y[1] (numeric) = 0.39622215449076638081030758659999 absolute error = 7e-32 relative error = 1.7666856637525878241797818842278e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 0.40266068221824832011047961217139 y[1] (numeric) = 0.40266068221824832011047961217133 absolute error = 6e-32 relative error = 1.4900883709196884443527981626383e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 0.4090969230046652248475488349816 y[1] (numeric) = 0.40909692300466522484754883498153 absolute error = 7e-32 relative error = 1.7110859569873064023929872996826e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 0.41553010581233855496842047205876 y[1] (numeric) = 0.41553010581233855496842047205868 absolute error = 8e-32 relative error = 1.9252515974409216376372983989422e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (analytic) = 0.42195945612427937478315210449821 y[1] (numeric) = 0.42195945612427937478315210449812 absolute error = 9e-32 relative error = 2.1329063419186030360114407896072e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (analytic) = 0.4283841960347597040071061729421 y[1] (numeric) = 0.42838419603475970400710617294203 absolute error = 7e-32 relative error = 1.6340472092093728935654860202402e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = 0.43480354434059993528272243563156 y[1] (numeric) = 0.43480354434059993528272243563149 absolute error = 7e-32 relative error = 1.6099224790395464389980464740548e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = 0.44121671663316183977718104381848 y[1] (numeric) = 0.4412167166331618397771810438184 absolute error = 8e-32 relative error = 1.8131679282340954161272538476086e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 0.44762292539103657430975438698765 y[1] (numeric) = 0.44762292539103657430975438698757 absolute error = 8e-32 relative error = 1.7872185596864418346701087334875e-29 % Correct digits = 31 h = 0.01 bytes used=32010868, alloc=4521156, time=1.27 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = 0.45402138007341699651755023026287 y[1] (numeric) = 0.4540213800734169965175502302628 absolute error = 7e-32 relative error = 1.5417776138357346041593569202722e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 0.46041128721414348883506884997581 y[1] (numeric) = 0.46041128721414348883506884997573 absolute error = 8e-32 relative error = 1.7375768627234137040113760235791e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = 0.46679185051641238755583638407047 y[1] (numeric) = 0.46679185051641238755583638407039 absolute error = 8e-32 relative error = 1.7138259785704464089319856108311e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0.47316227094813600997750173383288 y[1] (numeric) = 0.47316227094813600997750173383281 absolute error = 7e-32 relative error = 1.4794078965707052251149335672943e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 0.47952174683794317061922234485087 y[1] (numeric) = 0.4795217468379431706192223448508 absolute error = 7e-32 relative error = 1.4597878086154215313052917131650e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 0.48586947397180897675580152827024 y[1] (numeric) = 0.48586947397180897675580152827017 absolute error = 7e-32 relative error = 1.4407161542332566103798526917298e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = 0.49220464569030259405062057897096 y[1] (numeric) = 0.49220464569030259405062057897089 absolute error = 7e-32 relative error = 1.4221726798581319969176819249282e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = 0.49852645298644157490253243506312 y[1] (numeric) = 0.49852645298644157490253243506306 absolute error = 6e-32 relative error = 1.2035469660750744582671388021256e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = 0.50483408460414124526400361679492 y[1] (numeric) = 0.50483408460414124526400361679486 absolute error = 6e-32 relative error = 1.1885092910683354669969900040552e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = 0.51112672713724755015221357109936 y[1] (numeric) = 0.5111267271372475501522135710993 absolute error = 6e-32 relative error = 1.1738771778977784371544627165972e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = 0.51740356512914166387470180134315 y[1] (numeric) = 0.51740356512914166387470180134308 absolute error = 7e-32 relative error = 1.3529091161659913682022497268699e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 0.52366378117290457813949865744192 y[1] (numeric) = 0.52366378117290457813949865744186 absolute error = 6e-32 relative error = 1.1457733407800654135156594992620e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = 0.52990655601202978972933802366849 y[1] (numeric) = 0.52990655601202978972933802366842 absolute error = 7e-32 relative error = 1.3209876195306192752632935369085e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 0.53613106864167211930322759973159 y[1] (numeric) = 0.53613106864167211930322759973154 absolute error = 5e-32 relative error = 9.3260776934040986441898113351201e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = 0.54233649641042060415888723506791 y[1] (numeric) = 0.54233649641042060415888723506783 absolute error = 8e-32 relative error = 1.4750989566348287853815933637552e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = 0.54852201512258332045874243001117 y[1] (numeric) = 0.5485220151225833204587424300111 absolute error = 7e-32 relative error = 1.2761566185152376869996758571047e-29 % Correct digits = 31 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 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 0.55468679914097190450250402743983 y[1] (numeric) = 0.55468679914097190450250402743977 absolute error = 6e-32 relative error = 1.0816915075844663973905623669389e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = 0.56083002149017345813294086335604 y[1] (numeric) = 0.56083002149017345813294086335597 absolute error = 7e-32 relative error = 1.2481500154717822972025116132333e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = 0.56695085396029744030016196146151 y[1] (numeric) = 0.56695085396029744030016196146142 absolute error = 9e-32 relative error = 1.5874391822735051368386789932476e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 0.57304846721118506519530710466508 y[1] (numeric) = 0.57304846721118506519530710466502 absolute error = 6e-32 relative error = 1.0470318556473557572636343813927e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 0.57912203087706864720857226069039 y[1] (numeric) = 0.57912203087706864720857226069032 absolute error = 7e-32 relative error = 1.2087262488354381961404751419723e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 0.58517071367166825428037545181639 y[1] (numeric) = 0.58517071367166825428037545181631 absolute error = 8e-32 relative error = 1.3671224162610258201394094956877e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 0.59119368349371295400943694006314 y[1] (numeric) = 0.59119368349371295400943694006307 absolute error = 7e-32 relative error = 1.1840451269088096509877168895468e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 0.59719010753287386116867291544788 y[1] (numeric) = 0.5971901075328738611686729154478 absolute error = 8e-32 relative error = 1.3396069189842732753651940468227e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = 0.60315915237609612106998081823002 y[1] (numeric) = 0.60315915237609612106998081822995 absolute error = 7e-32 relative error = 1.1605560443581222049211144893632e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=36012884, alloc=4521156, time=1.44 x[1] = 2.22 y[1] (analytic) = 0.60909998411431689052295089142194 y[1] (numeric) = 0.60909998411431689052295089142188 absolute error = 6e-32 relative error = 9.8505995016967692042807471672270e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = 0.6150117684495563069608223428092 y[1] (numeric) = 0.61501176844955630696082234280912 absolute error = 8e-32 relative error = 1.3007881166514890136860490511269e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 0.62089367080236836666998790932111 y[1] (numeric) = 0.62089367080236836666998790932104 absolute error = 7e-32 relative error = 1.1274072082187665397998619031456e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 0.62674485641963856496723512816485 y[1] (numeric) = 0.62674485641963856496723512816478 absolute error = 7e-32 relative error = 1.1168819222527663999016563666901e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 0.63256449048271508463171550724418 y[1] (numeric) = 0.63256449048271508463171550724411 absolute error = 7e-32 relative error = 1.1066065366170401566848873785750e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = 0.63835173821586025392619381887266 y[1] (numeric) = 0.6383517382158602539261938188726 absolute error = 6e-32 relative error = 9.3992068021456296763212324688178e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = 0.64410576499500893214410786820847 y[1] (numeric) = 0.6441057649950089321441078682084 absolute error = 7e-32 relative error = 1.0867780387052182073474705037831e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 0.64982573645682041880484116738195 y[1] (numeric) = 0.64982573645682041880484116738189 absolute error = 6e-32 relative error = 9.2332446429638873448275997906380e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 0.65551081860801042239867047641487 y[1] (numeric) = 0.65551081860801042239867047641481 absolute error = 6e-32 relative error = 9.1531670106392951391011615918993e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = 0.66116017793494956596420605290459 y[1] (numeric) = 0.66116017793494956596420605290452 absolute error = 7e-32 relative error = 1.0587449507112810695882142239758e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 0.66677298151351484977371776637523 y[1] (numeric) = 0.66677298151351484977371776637516 absolute error = 7e-32 relative error = 1.0498325808149316415916168649112e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = 0.67234839711918043601427104620214 y[1] (numeric) = 0.67234839711918043601427104620208 absolute error = 6e-32 relative error = 8.9239448263850629283557730671416e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 0.67788559333733406659363081670191 y[1] (numeric) = 0.67788559333733406659363081670186 absolute error = 5e-32 relative error = 7.3758758839883853282663088777832e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 0.683383739673805373077787652842 y[1] (numeric) = 0.68338373967380537307778765284195 absolute error = 5e-32 relative error = 7.3165334638875281165113384740785e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = 0.68884200666559228728988640533256 y[1] (numeric) = 0.68884200666559228728988640533249 absolute error = 7e-32 relative error = 1.0161981894635303682904719356307e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = 0.69425956599177171227626993928634 y[1] (numeric) = 0.69425956599177171227626993928627 absolute error = 7e-32 relative error = 1.0082684262333899518984817716443e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = 0.69963559058458056618207316472125 y[1] (numeric) = 0.69963559058458056618207316472117 absolute error = 8e-32 relative error = 1.1434524068902211572425299542057e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 0.70496925474065326608390521385946 y[1] (numeric) = 0.70496925474065326608390521385939 absolute error = 7e-32 relative error = 9.9295110431095129934627399482736e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 0.71025973423240167500803564238939 y[1] (numeric) = 0.71025973423240167500803564238932 absolute error = 7e-32 relative error = 9.8555495442313132420878029718080e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 0.71550620641952349322635327746507 y[1] (numeric) = 0.71550620641952349322635327746501 absolute error = 6e-32 relative error = 8.3856714954643088045754215117599e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = 0.72070785036062503447619635533807 y[1] (numeric) = 0.720707850360625034476196355338 absolute error = 7e-32 relative error = 9.7126734452765663700500853683887e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 0.72586384692494428900076463136181 y[1] (numeric) = 0.72586384692494428900076463136174 absolute error = 7e-32 relative error = 9.6436818415118192231236515146561e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = 0.73097337890416013826082418751598 y[1] (numeric) = 0.73097337890416013826082418751591 absolute error = 7e-32 relative error = 9.5762721352370735205910187659408e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = 0.73603563112427355083220999432259 y[1] (numeric) = 0.73603563112427355083220999432251 absolute error = 8e-32 relative error = 1.0869039027064799701215535792567e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = 0.74104979055754655538342558495466 y[1] (numeric) = 0.74104979055754655538342558495459 absolute error = 7e-32 relative error = 9.4460589412398084282068775796188e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = 0.74601504643448475472943765471602 y[1] (numeric) = 0.74601504643448475472943765471596 absolute error = 6e-32 relative error = 8.0427332245864046923810659237528e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=40013948, alloc=4521156, time=1.60 x[1] = 2.48 y[1] (analytic) = 0.75093059035584911478736783487103 y[1] (numeric) = 0.75093059035584911478736783487095 absolute error = 8e-32 relative error = 1.0653448005372880012591857681533e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = 0.75579561640468273382279293135046 y[1] (numeric) = 0.7557956164046827338227929313504 absolute error = 6e-32 relative error = 7.9386541411049462071820408883165e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 0.76060932125833827067717317281111 y[1] (numeric) = 0.76060932125833827067717317281104 absolute error = 7e-32 relative error = 9.2031477978988305260387174412858e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = 0.76537090430049168571272527232329 y[1] (numeric) = 0.76537090430049168571272527232322 absolute error = 7e-32 relative error = 9.1458924825443003129537850860784e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 0.77007956773312792500582758186272 y[1] (numeric) = 0.77007956773312792500582758186264 absolute error = 8e-32 relative error = 1.0388536893076496215789532062561e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = 0.77473451668848415686856618655977 y[1] (numeric) = 0.77473451668848415686856618655969 absolute error = 8e-32 relative error = 1.0326117950953189994200060528489e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 0.77933495934093615008487426908811 y[1] (numeric) = 0.77933495934093615008487426908804 absolute error = 7e-32 relative error = 8.9820171879877207457997506536655e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = 0.78388010701881336531724554177741 y[1] (numeric) = 0.78388010701881336531724554177733 absolute error = 8e-32 relative error = 1.0205642327657636963853494946948e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = 0.788369174316128314976370632814 y[1] (numeric) = 0.78836917431612831497637063281393 absolute error = 7e-32 relative error = 8.8790889193151894868628202425936e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 0.79280137920420573245319857910483 y[1] (numeric) = 0.79280137920420573245319857910474 absolute error = 9e-32 relative error = 1.1352149776825534431751949508693e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = 0.79717594314319707899459986846283 y[1] (numeric) = 0.79717594314319707899459986846276 absolute error = 7e-32 relative error = 8.7809975454096045154220030403240e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = 0.80149209119346590566352832151917 y[1] (numeric) = 0.80149209119346590566352832151912 absolute error = 5e-32 relative error = 6.2383647386398091306675528672860e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 0.80574905212682957876566115139093 y[1] (numeric) = 0.80574905212682957876566115139088 absolute error = 5e-32 relative error = 6.2054059968201749387269394767610e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = 0.80994605853764286985004298276112 y[1] (numeric) = 0.80994605853764286985004298276106 absolute error = 6e-32 relative error = 7.4079007320968960019695415484034e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = 0.81408234695370890590416167164017 y[1] (numeric) = 0.81408234695370890590416167164011 absolute error = 6e-32 relative error = 7.3702617707557015496136439366283e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = 0.81815715794700297166682018102335 y[1] (numeric) = 0.81815715794700297166682018102328 absolute error = 7e-32 relative error = 8.5558134302278300017943309650365e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = 0.82216973624419465407760531177482 y[1] (numeric) = 0.82216973624419465407760531177475 absolute error = 7e-32 relative error = 8.5140570023619949877493415825268e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = 0.82611933083695381877194311950413 y[1] (numeric) = 0.82611933083695381877194311950408 absolute error = 5e-32 relative error = 6.0523943858503170553444231371954e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = 0.83000519509202591021771087398959 y[1] (numeric) = 0.83000519509202591021771087398952 absolute error = 7e-32 relative error = 8.4336821521025331937421206830591e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 0.83382658686106207057497068816867 y[1] (numeric) = 0.8338265868610620705749706881686 absolute error = 7e-32 relative error = 8.3950309456448025409951753676690e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 0.83758276859018957764621007075276 y[1] (numeric) = 0.8375827685901895776462100707527 absolute error = 6e-32 relative error = 7.1634711517515293324025917572334e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = 0.84127300742930810937191425681978 y[1] (numeric) = 0.84127300742930810937191425681973 absolute error = 5e-32 relative error = 5.9433738582420265454061526164879e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 0.84489657534109735121653353400399 y[1] (numeric) = 0.84489657534109735121653353400391 absolute error = 8e-32 relative error = 9.4686145422832145578727733078842e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = 0.84845274920972147348390956413067 y[1] (numeric) = 0.84845274920972147348390956413059 absolute error = 8e-32 relative error = 9.4289281370724291185239306149563e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = 0.85194081094921601809973564199056 y[1] (numeric) = 0.8519408109492160180997356419905 absolute error = 6e-32 relative error = 7.0427427855168902363428474626396e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 0.8553600476115427487021785032382 y[1] (numeric) = 0.85536004761154274870217850323812 absolute error = 8e-32 relative error = 9.3527866099646938133378367384998e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=44015256, alloc=4521156, time=1.76 x[1] = 2.74 y[1] (analytic) = 0.85870975149429803399069885783689 y[1] (numeric) = 0.85870975149429803399069885783681 absolute error = 8e-32 relative error = 9.3163027275265794410682386156326e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = 0.86198922024806035219747284057325 y[1] (numeric) = 0.86198922024806035219747284057319 absolute error = 6e-32 relative error = 6.9606438909680798849030505991926e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 0.86519775698336252426551880245332 y[1] (numeric) = 0.86519775698336252426551880245325 absolute error = 7e-32 relative error = 8.0906358615705562420030678682549e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = 0.8683346703772743048423381373205 y[1] (numeric) = 0.86833467037727430484233813732045 absolute error = 5e-32 relative error = 5.7581485233425017092511367909062e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 0.87139927477958098352703289221014 y[1] (numeric) = 0.87139927477958098352703289221006 absolute error = 8e-32 relative error = 9.1806365136390397741978002285340e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 0.87439089031854367394169731274994 y[1] (numeric) = 0.87439089031854367394169731274986 absolute error = 8e-32 relative error = 9.1492261511159750167342921298572e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 0.87730884300622699513340853147736 y[1] (numeric) = 0.87730884300622699513340853147731 absolute error = 5e-32 relative error = 5.6992472375711717466269199533178e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = 0.88015246484337987855015930858659 y[1] (numeric) = 0.88015246484337987855015930858651 absolute error = 8e-32 relative error = 9.0893343137129913555510329651200e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = 0.88292109392385526437116173029359 y[1] (numeric) = 0.88292109392385526437116173029352 absolute error = 7e-32 relative error = 7.9282282960199531121469777093619e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = 0.88561407453855448330746636319308 y[1] (numeric) = 0.88561407453855448330746636319299 absolute error = 9e-32 relative error = 1.0162440117823796365280366760753e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = 0.88823075727888215412093053405232 y[1] (numeric) = 0.88823075727888215412093053405224 absolute error = 8e-32 relative error = 9.0066685199105314045257474465909e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 0.89077049913969746303615885858054 y[1] (numeric) = 0.89077049913969746303615885858045 absolute error = 9e-32 relative error = 1.0103612556424088488327087478582e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = 0.89323266362174772893883838304513 y[1] (numeric) = 0.89323266362174772893883838304506 absolute error = 7e-32 relative error = 7.8367040135068897242466954851594e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 0.89561662083357019776239212933439 y[1] (numeric) = 0.89561662083357019776239212933431 absolute error = 8e-32 relative error = 8.9323934079676000881146665127543e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = 0.89792174759284805076035386859813 y[1] (numeric) = 0.89792174759284805076035386859806 absolute error = 7e-32 relative error = 7.7957795529127409450060446846518e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = 0.90014742752720665444138218344586 y[1] (numeric) = 0.90014742752720665444138218344577 absolute error = 9e-32 relative error = 9.9983621846522224439311458696499e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 0.902293051174436124804225252772 y[1] (numeric) = 0.90229305117443612480422525277191 absolute error = 9e-32 relative error = 9.9745864032594348344266578526432e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = 0.90435801608212632514784479278902 y[1] (numeric) = 0.90435801608212632514784479278895 absolute error = 7e-32 relative error = 7.7402973993922312057402011819882e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = 0.90634172690670046514371747249282 y[1] (numeric) = 0.90634172690670046514371747249275 absolute error = 7e-32 relative error = 7.7233562046080060279728361075436e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = 0.90824359551183351903924817659506 y[1] (numeric) = 0.90824359551183351903924817659497 absolute error = 9e-32 relative error = 9.9092358531062593866293510592055e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = 0.91006304106624173280922930150416 y[1] (numeric) = 0.9100630410662417328092293015041 absolute error = 6e-32 relative error = 6.5929498608913089317404687592773e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 0.91179949014082954378212603299622 y[1] (numeric) = 0.91179949014082954378212603299615 absolute error = 7e-32 relative error = 7.6771264688016372786532060843129e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 0.913452376805180291735206393855 y[1] (numeric) = 0.91345237680518029173520639385492 absolute error = 8e-32 relative error = 8.7579825759282332136626363089280e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = 0.91502114272337715767249917881028 y[1] (numeric) = 0.9150211427233771576724991788102 absolute error = 8e-32 relative error = 8.7429673768953604235715553651976e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004955 Order of pole (three term test) = -0.8935 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 0.91650523724914082546737079100655 y[1] (numeric) = 0.91650523724914082546737079100646 absolute error = 9e-32 relative error = 9.8199111518589819357569184454175e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01459 Order of pole (three term test) = -0.8988 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = 0.91790411752027042226206760723744 y[1] (numeric) = 0.91790411752027042226206760723735 absolute error = 9e-32 relative error = 9.8049456672158893666460796841696e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02423 Order of pole (three term test) = -0.9094 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=48016320, alloc=4521156, time=1.92 x[1] = 3 y[1] (analytic) = 0.91921724855237435596456447581975 y[1] (numeric) = 0.91921724855237435596456447581967 absolute error = 8e-32 relative error = 8.7030568808393971307676840426378e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03385 Order of pole (three term test) = -0.9251 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = 0.9204441033318777323629698928495 y[1] (numeric) = 0.92044410333187773236296989284942 absolute error = 8e-32 relative error = 8.6914566251672743720194965286767e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04345 Order of pole (three term test) = -0.9461 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = 0.92158416290829310028382934533761 y[1] (numeric) = 0.92158416290829310028382934533752 absolute error = 9e-32 relative error = 9.7657928187461600104315742663356e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05303 Order of pole (three term test) = -0.9722 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = 0.9226369164857413408469932282733 y[1] (numeric) = 0.9226369164857413408469932282732 absolute error = 1.0e-31 relative error = 1.0838499762278417865409868284182e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06259 Order of pole (three term test) = -1.004 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = 0.92360186151370958621011608151939 y[1] (numeric) = 0.92360186151370958621011608151928 absolute error = 1.1e-31 relative error = 1.1909893708931984742913034708715e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07212 Order of pole (three term test) = -1.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = 0.92447850377703312424396012116335 y[1] (numeric) = 0.92447850377703312424396012116327 absolute error = 8e-32 relative error = 8.6535273316960217318560412637232e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08162 Order of pole (three term test) = -1.082 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = 0.9252663574850883183289082336425 y[1] (numeric) = 0.92526635748508831832890823364241 absolute error = 9e-32 relative error = 9.7269288212989467373135067685653e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09108 Order of pole (three term test) = -1.129 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = 0.92596494536018364590666004579603 y[1] (numeric) = 0.92596494536018364590666004579596 absolute error = 7e-32 relative error = 7.5596814275481307572964867925925e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1005 Order of pole (three term test) = -1.181 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = 0.92657379872513603555199050764872 y[1] (numeric) = 0.92657379872513603555199050764862 absolute error = 1.0e-31 relative error = 1.0792448495477536354951378338254e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1099 Order of pole (three term test) = -1.238 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = 0.92709245759001976014048625171764 y[1] (numeric) = 0.92709245759001976014048625171756 absolute error = 8e-32 relative error = 8.6291285561701465111446481220628e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1192 Order of pole (three term test) = -1.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = 0.92752047073807522317192562449747 y[1] (numeric) = 0.92752047073807522317192562449739 absolute error = 8e-32 relative error = 8.6251465626780107891967710431195e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1285 Order of pole (three term test) = -1.367 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = 0.9278573958107650564578114059936 y[1] (numeric) = 0.9278573958107650564578114059935 absolute error = 1.0e-31 relative error = 1.0777518231949818993680718834501e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1377 Order of pole (three term test) = -1.439 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = 0.92810279939196503018767213679383 y[1] (numeric) = 0.92810279939196503018767213679373 absolute error = 1.0e-31 relative error = 1.0774668502833280147261783229369e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1469 Order of pole (three term test) = -1.516 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = 0.92825625709127736084408432006656 y[1] (numeric) = 0.92825625709127736084408432006647 absolute error = 9e-32 relative error = 9.6955985281497664653465416297808e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1559 Order of pole (three term test) = -1.598 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = 0.9283173536264540885326943635531 y[1] (numeric) = 0.928317353626454088532694363553 absolute error = 1.0e-31 relative error = 1.0772178243717183747205500414790e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.165 Order of pole (three term test) = -1.685 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = 0.9282856829049182830223927275049 y[1] (numeric) = 0.92828568290491828302239272750479 absolute error = 1.1e-31 relative error = 1.1849800339026341917713770608467e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1739 Order of pole (three term test) = -1.777 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (analytic) = 0.92816084810437092714356687762585 y[1] (numeric) = 0.92816084810437092714356687762576 absolute error = 9e-32 relative error = 9.6965951735425467672835178965558e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1828 Order of pole (three term test) = -1.874 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (analytic) = 0.92794246175247141716018546404701 y[1] (numeric) = 0.92794246175247141716018546404691 absolute error = 1.0e-31 relative error = 1.0776530239940134626819984913789e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1916 Order of pole (three term test) = -1.976 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = 0.92763014580557971230529331866802 y[1] (numeric) = 0.92763014580557971230529331866793 absolute error = 9e-32 relative error = 9.7021426488723592700585300265344e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2003 Order of pole (three term test) = -2.082 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = 0.92722353172654825984007444856789 y[1] (numeric) = 0.92722353172654825984007444856778 absolute error = 1.1e-31 relative error = 1.1863374497751703308344299081086e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2089 Order of pole (three term test) = -2.193 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = 0.92672226056155191775451759602275 y[1] (numeric) = 0.92672226056155191775451759602265 absolute error = 1.0e-31 relative error = 1.0790719534394750323046618907060e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2174 Order of pole (three term test) = -2.309 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = 0.92612598301594419456324680648703 y[1] (numeric) = 0.92612598301594419456324680648692 absolute error = 1.1e-31 relative error = 1.1877433741982189787569930857938e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2259 Order of pole (three term test) = -2.429 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = 0.925434359529128224553410714594 y[1] (numeric) = 0.92543435952912822455341071459391 absolute error = 9e-32 relative error = 9.7251630084053770947896655042596e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2342 Order of pole (three term test) = -2.554 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (analytic) = 0.92464706034843099730261509017142 y[1] (numeric) = 0.92464706034843099730261509017132 absolute error = 1.0e-31 relative error = 1.0814937319145037463402548618922e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2424 Order of pole (three term test) = -2.683 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (analytic) = 0.92376376560196946229349401198032 y[1] (numeric) = 0.92376376560196946229349401198024 absolute error = 8e-32 relative error = 8.6602227732831784691455759329380e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2505 Order of pole (three term test) = -2.817 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = 0.92278416537049723299721159540085 y[1] (numeric) = 0.92278416537049723299721159540076 absolute error = 9e-32 relative error = 9.7530932343063190117980445641306e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2586 Order of pole (three term test) = -2.955 NO COMPLEX POLE (six term test) for Equation 1 bytes used=52017472, alloc=4521156, time=2.09 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = 0.9217079597582207198703406058802 y[1] (numeric) = 0.92170795975822071987034060588011 absolute error = 9e-32 relative error = 9.7644811512323808330619091761630e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2664 Order of pole (three term test) = -3.098 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = 0.92053485896257362829735612228127 y[1] (numeric) = 0.92053485896257362829735612228117 absolute error = 1.0e-31 relative error = 1.0863249666905413757864246516048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2742 Order of pole (three term test) = -3.245 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (analytic) = 0.91926458334293886560339983170486 y[1] (numeric) = 0.91926458334293886560339983170478 absolute error = 8e-32 relative error = 8.7026087428580257072016872828850e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2819 Order of pole (three term test) = -3.396 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = 0.9178968634883070108478114135183 y[1] (numeric) = 0.91789686348830701084781141351821 absolute error = 9e-32 relative error = 9.8050231545590743043030532917853e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2894 Order of pole (three term test) = -3.551 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = 0.91643144028386061217679655353824 y[1] (numeric) = 0.91643144028386061217679655353816 absolute error = 8e-32 relative error = 8.7295128127883032351626031488578e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2968 Order of pole (three term test) = -3.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = 0.91486806497647368905192722503989 y[1] (numeric) = 0.9148680649764736890519272250398 absolute error = 9e-32 relative error = 9.8374840532131151706367617592223e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3041 Order of pole (three term test) = -3.873 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = 0.9132064992391159306681830492192 y[1] (numeric) = 0.91320649923911593066818304921911 absolute error = 9e-32 relative error = 9.8553832101488590825432464617816e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3113 Order of pole (three term test) = -4.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (analytic) = 0.91144651523415119731899136172685 y[1] (numeric) = 0.91144651523415119731899136172678 absolute error = 7e-32 relative error = 7.6800995812702136312589831715663e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3183 Order of pole (three term test) = -4.211 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = 0.90958789567552004834407236211712 y[1] (numeric) = 0.90958789567552004834407236211705 absolute error = 7e-32 relative error = 7.6957928236295818995433967223259e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3252 Order of pole (three term test) = -4.386 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = 0.9076304338897961385965257208083 y[1] (numeric) = 0.9076304338897961385965257208082 absolute error = 1.0e-31 relative error = 1.1017700185683937857297704407218e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3319 Order of pole (three term test) = -4.564 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = 0.90557393387610644507600588277941 y[1] (numeric) = 0.90557393387610644507600588277934 absolute error = 7e-32 relative error = 7.7299044706797902865602956634592e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3385 Order of pole (three term test) = -4.746 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = 0.9034182103649054064823442831939 y[1] (numeric) = 0.90341821036490540648234428319381 absolute error = 9e-32 relative error = 9.9621635879630460918988286697725e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3449 Order of pole (three term test) = -4.932 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = 0.90116308887559318093572798607285 y[1] (numeric) = 0.90116308887559318093572798607279 absolute error = 6e-32 relative error = 6.6580623131006959756921054794083e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3512 Order of pole (three term test) = -5.121 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (analytic) = 0.89880840577296835097249840671811 y[1] (numeric) = 0.89880840577296835097249840671801 absolute error = 1.0e-31 relative error = 1.1125841654095431521307057951279e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3573 Order of pole (three term test) = -5.314 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = 0.89635400832250553014657702309764 y[1] (numeric) = 0.89635400832250553014657702309755 absolute error = 9e-32 relative error = 1.0040675800449844731375392274446e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3633 Order of pole (three term test) = -5.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = 0.89379975474444845213206867390098 y[1] (numeric) = 0.8937997547444484521320686739009 absolute error = 8e-32 relative error = 8.9505506770779178383167297484809e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3691 Order of pole (three term test) = -5.709 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (analytic) = 0.89114551426670925111917507173854 y[1] (numeric) = 0.89114551426670925111917507173846 absolute error = 8e-32 relative error = 8.9772095263060429546178368547458e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3748 Order of pole (three term test) = -5.911 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = 0.88839116717656477150943740333013 y[1] (numeric) = 0.88839116717656477150943740333004 absolute error = 9e-32 relative error = 1.0130672537642734259822034266169e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3803 Order of pole (three term test) = -6.116 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = 0.88553660487114087543361267070477 y[1] (numeric) = 0.88553660487114087543361267070467 absolute error = 1.0e-31 relative error = 1.1292587957394661283684375881122e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3856 Order of pole (three term test) = -6.324 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (analytic) = 0.88258172990667584842210001530429 y[1] (numeric) = 0.88258172990667584842210001530421 absolute error = 8e-32 relative error = 9.0643163447830714017959239816489e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3907 Order of pole (three term test) = -6.535 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = 0.8795264560465541366395293775808 y[1] (numeric) = 0.87952645604655413663952937758071 absolute error = 9e-32 relative error = 1.0232779171253970557378335950611e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3957 Order of pole (three term test) = -6.749 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (analytic) = 0.87637070830810178343749817577408 y[1] (numeric) = 0.87637070830810178343749817577399 absolute error = 9e-32 relative error = 1.0269626671314885740488014821159e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4005 Order of pole (three term test) = -6.965 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = 0.87311442300813506856792046770421 y[1] (numeric) = 0.87311442300813506856792046770413 absolute error = 8e-32 relative error = 9.1626020475502574581597653689522e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4052 Order of pole (three term test) = -7.185 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = 0.86975754780725399021930261927372 y[1] (numeric) = 0.86975754780725399021930261927366 absolute error = 6e-32 relative error = 6.8984741956268178023126223220768e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4096 Order of pole (three term test) = -7.406 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (analytic) = 0.86630004175287236807458386666302 y[1] (numeric) = 0.86630004175287236807458386666296 absolute error = 6e-32 relative error = 6.9260068230628201503455420144125e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4139 Order of pole (three term test) = -7.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (analytic) = 0.86274187532097648482692365368564 y[1] (numeric) = 0.86274187532097648482692365368555 absolute error = 9e-32 relative error = 1.0431857149221624558360784543961e-29 % Correct digits = 31 h = 0.01 bytes used=56018768, alloc=4586680, time=2.25 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.418 Order of pole (three term test) = -7.856 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = 0.85908303045660432401376651403474 y[1] (numeric) = 0.85908303045660432401376651403466 absolute error = 8e-32 relative error = 9.3122547138988232968776220604891e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4219 Order of pole (three term test) = -8.085 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = 0.85532350061303760362429939797077 y[1] (numeric) = 0.85532350061303760362429939797072 absolute error = 5e-32 relative error = 5.8457414024241596299535111018670e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.29 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4257 Order of pole (three term test) = -8.315 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = 0.85146329078969894768551081712189 y[1] (numeric) = 0.85146329078969894768551081712183 absolute error = 6e-32 relative error = 7.0466925173429782679073420516100e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4292 Order of pole (three term test) = -8.548 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = 0.84750241756874668192178804625017 y[1] (numeric) = 0.84750241756874668192178804625012 absolute error = 5e-32 relative error = 5.8996881853666405770256916657530e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.91 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4326 Order of pole (three term test) = -8.782 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (analytic) = 0.84344090915035988459651857592372 y[1] (numeric) = 0.84344090915035988459651857592365 absolute error = 7e-32 relative error = 8.2993365914056140569399249151583e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.22 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4357 Order of pole (three term test) = -9.019 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = 0.839278805386706469765516132928 y[1] (numeric) = 0.83927880538670646976551613292792 absolute error = 8e-32 relative error = 9.5319933598393641049807976550032e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4387 Order of pole (three term test) = -9.257 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = 0.83501615781458722738514307855304 y[1] (numeric) = 0.83501615781458722738514307855298 absolute error = 6e-32 relative error = 7.1854896984308195477835895693558e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.88 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4415 Order of pole (three term test) = -9.496 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = 0.8306530296867488930064769500473 y[1] (numeric) = 0.83065302968674889300647695004722 absolute error = 8e-32 relative error = 9.6309767304609893763293275259111e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.21 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4441 Order of pole (three term test) = -9.737 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = 0.82618949600185946913435209027272 y[1] (numeric) = 0.82618949600185946913435209027265 absolute error = 7e-32 relative error = 8.4726325302787986562870064883829e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4465 Order of pole (three term test) = -9.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = 0.82162564353313917072003794951773 y[1] (numeric) = 0.82162564353313917072003794951768 absolute error = 5e-32 relative error = 6.0854965267382525308002062900183e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4487 Order of pole (three term test) = -10.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = 0.81696157085564051867199326643866 y[1] (numeric) = 0.81696157085564051867199326643859 absolute error = 7e-32 relative error = 8.5683344844098184907332384119188e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.26 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4508 Order of pole (three term test) = -10.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = 0.81219738837217125769372059364597 y[1] (numeric) = 0.81219738837217125769372059364591 absolute error = 6e-32 relative error = 7.3873667730271430238060381726399e-30 % Correct digits = 32 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 = 0.4526 Order of pole (three term test) = -10.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = 0.80733321833785392817426215919527 y[1] (numeric) = 0.8073332183378539281742621591952 absolute error = 7e-32 relative error = 8.6705214662313452130424749486713e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.99 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4542 Order of pole (three term test) = -10.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = 0.80236919488331607624821433110504 y[1] (numeric) = 0.80236919488331607624821433110499 absolute error = 5e-32 relative error = 6.2315453183956310271700707051073e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4556 Order of pole (three term test) = -11.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = 0.79730546403650524149104920032299 y[1] (numeric) = 0.79730546403650524149104920032291 absolute error = 8e-32 relative error = 1.0033795528627800638220174630416e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4568 Order of pole (three term test) = -11.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = 0.79214218374312301800464188503733 y[1] (numeric) = 0.79214218374312301800464188503727 absolute error = 6e-32 relative error = 7.5743977825396159470420393066476e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4579 Order of pole (three term test) = -11.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (analytic) = 0.78687952388567264185970551879465 y[1] (numeric) = 0.78687952388567264185970551879458 absolute error = 7e-32 relative error = 8.8958980218896184152430831824258e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.04 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4587 Order of pole (three term test) = -11.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = 0.78151766630111471597869945382537 y[1] (numeric) = 0.7815176663011147159786994538253 absolute error = 7e-32 relative error = 8.9569312401223905200753403068558e-30 % Correct digits = 32 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 = 0.4593 Order of pole (three term test) = -12.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = 0.77605680479712584254694138546834 y[1] (numeric) = 0.77605680479712584254694138546827 absolute error = 7e-32 relative error = 9.0199582771906966729668773614687e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.28 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4597 Order of pole (three term test) = -12.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = 0.77049714516695509291323870920928 y[1] (numeric) = 0.77049714516695509291323870920921 absolute error = 7e-32 relative error = 9.0850433955640494109459658478394e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.92 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.46 Order of pole (three term test) = -12.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = 0.76483890520287340566635470001596 y[1] (numeric) = 0.7648389052028734056663547000159 absolute error = 6e-32 relative error = 7.8447892218669248968515066851508e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.46 Order of pole (three term test) = -12.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = 0.75908231470821116513191771359289 y[1] (numeric) = 0.75908231470821116513191771359281 absolute error = 8e-32 relative error = 1.0539041478097371605239444712928e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.21 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4598 Order of pole (three term test) = -13.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (analytic) = 0.75322761550797937490772564536437 y[1] (numeric) = 0.75322761550797937490772564536429 absolute error = 8e-32 relative error = 1.0620959501869526691901821314860e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.86 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4594 Order of pole (three term test) = -13.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = 0.74727506145807000422543690773517 y[1] (numeric) = 0.74727506145807000422543690773512 absolute error = 5e-32 relative error = 6.6909766669371885942059857707212e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.52 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4589 Order of pole (three term test) = -13.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = 0.74122491845303124887490327716559 y[1] (numeric) = 0.74122491845303124887490327716552 absolute error = 7e-32 relative error = 9.4438271376646449946588044424926e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.18 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4581 Order of pole (three term test) = -13.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=60020012, alloc=4586680, time=2.41 x[1] = 3.77 y[1] (analytic) = 0.73507746443241361313530777519592 y[1] (numeric) = 0.73507746443241361313530777519587 absolute error = 5e-32 relative error = 6.8020041994631477201001547489913e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.86 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4571 Order of pole (three term test) = -14.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = 0.72883298938568288460613159157497 y[1] (numeric) = 0.72883298938568288460613159157493 absolute error = 4e-32 relative error = 5.4882257777210538019140266942360e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4559 Order of pole (three term test) = -14.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = 0.72249179535569624000198998840034 y[1] (numeric) = 0.7224917953556962400019899884003 absolute error = 4e-32 relative error = 5.5363950507295727798401701481937e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.21 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4546 Order of pole (three term test) = -14.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = 0.71605419644073788684964504758801 y[1] (numeric) = 0.71605419644073788684964504758794 absolute error = 7e-32 relative error = 9.7757963500453199975502311071455e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.453 Order of pole (three term test) = -14.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = 0.70952051879511081358401691547202 y[1] (numeric) = 0.70952051879511081358401691547197 absolute error = 5e-32 relative error = 7.0470125493916218480893182071288e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4512 Order of pole (three term test) = -15.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = 0.70289110062828138876366783530422 y[1] (numeric) = 0.70289110062828138876366783530416 absolute error = 6e-32 relative error = 8.5361729500300706670325628551091e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4493 Order of pole (three term test) = -15.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = 0.69616629220257371899581896608258 y[1] (numeric) = 0.69616629220257371899581896608253 absolute error = 5e-32 relative error = 7.1821920365904137292038333847295e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4471 Order of pole (three term test) = -15.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = 0.68934645582941084465717639641198 y[1] (numeric) = 0.68934645582941084465717639641193 absolute error = 5e-32 relative error = 7.2532468365041181140593908867522e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4448 Order of pole (three term test) = -15.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = 0.6824319658641000226002930853971 y[1] (numeric) = 0.68243196586410002260029308539704 absolute error = 6e-32 relative error = 8.7920852189313244780638898397283e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4422 Order of pole (three term test) = -16.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = 0.67542320869915951572638867217997 y[1] (numeric) = 0.67542320869915951572638867217992 absolute error = 5e-32 relative error = 7.4027660518651968976200454882906e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4395 Order of pole (three term test) = -16.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = 0.66832058275618448056491012459681 y[1] (numeric) = 0.66832058275618448056491012459676 absolute error = 5e-32 relative error = 7.4814394902814044490459074450743e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4365 Order of pole (three term test) = -16.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = 0.66112449847624971580797614702272 y[1] (numeric) = 0.66112449847624971580797614702267 absolute error = 5e-32 relative error = 7.5628720634675139947415990595761e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4334 Order of pole (three term test) = -16.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = 0.65383537830884720708445462860523 y[1] (numeric) = 0.65383537830884720708445462860518 absolute error = 5e-32 relative error = 7.6471848509215852139685180421565e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4301 Order of pole (three term test) = -17.13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = 0.64645365669935657610393929830775 y[1] (numeric) = 0.64645365669935657610393929830772 absolute error = 3e-32 relative error = 4.6407038910063697065293673298775e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4266 Order of pole (three term test) = -17.37 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = 0.6389797800750467156354021405968 y[1] (numeric) = 0.63897978007504671563540214059675 absolute error = 5e-32 relative error = 7.8249737408165895653512674072230e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4229 Order of pole (three term test) = -17.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = 0.63141420682960706558880611380905 y[1] (numeric) = 0.631414206829607065588806113809 absolute error = 5e-32 relative error = 7.9187321823268636294131270641332e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4191 Order of pole (three term test) = -17.83 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = 0.62375740730620715972039578715595 y[1] (numeric) = 0.62375740730620715972039578715592 absolute error = 3e-32 relative error = 4.8095621228066276780527034943859e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.415 Order of pole (three term test) = -18.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = 0.61600986377908324716359481967777 y[1] (numeric) = 0.61600986377908324716359481967773 absolute error = 4e-32 relative error = 6.4934025170650536838315169182556e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4108 Order of pole (three term test) = -18.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = 0.60817207043365096807720984259931 y[1] (numeric) = 0.60817207043365096807720984259924 absolute error = 7e-32 relative error = 1.1509900471109632703506055679755e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4064 Order of pole (three term test) = -18.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = 0.6002445333451432381806816194103 y[1] (numeric) = 0.60024453334514323818068161941027 absolute error = 3e-32 relative error = 4.9979630522932007242856826129475e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4018 Order of pole (three term test) = -18.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = 0.59222777045577267279208024296509 y[1] (numeric) = 0.59222777045577267279208024296505 absolute error = 4e-32 relative error = 6.7541581120413169831847270278538e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.397 Order of pole (three term test) = -18.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = 0.58412231155041805717799035320031 y[1] (numeric) = 0.58412231155041805717799035320026 absolute error = 5e-32 relative error = 8.5598510810666559151964507762295e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3921 Order of pole (three term test) = -19.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = 0.57592869823083454654489088558312 y[1] (numeric) = 0.57592869823083454654489088558306 absolute error = 6e-32 relative error = 1.0417956282489635176344360408362e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.387 Order of pole (three term test) = -19.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4 y[1] (analytic) = 0.56764748388838745582855718250515 y[1] (numeric) = 0.56764748388838745582855718250512 absolute error = 3e-32 relative error = 5.2849701357786146070971518083003e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3817 Order of pole (three term test) = -19.59 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = 0.55927923367530967655079878512338 y[1] (numeric) = 0.55927923367530967655079878512332 absolute error = 6e-32 relative error = 1.0728093658280379135085821245677e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3763 Order of pole (three term test) = -19.8 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = 0.55082452447448293539083546565604 y[1] (numeric) = 0.55082452447448293539083546565601 absolute error = 3e-32 relative error = 5.4463805925528932135741751945876e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3707 Order of pole (three term test) = -20 NO COMPLEX POLE (six term test) for Equation 1 bytes used=64021764, alloc=4586680, time=2.57 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = 0.54228394486774328674109524092231 y[1] (numeric) = 0.54228394486774328674109524092227 absolute error = 4e-32 relative error = 7.3762095261285178343879996937894e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3649 Order of pole (three term test) = -20.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = 0.53365809510271140936342836359004 y[1] (numeric) = 0.53365809510271140936342836358999 absolute error = 5e-32 relative error = 9.3692947710980876797514248716761e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.359 Order of pole (three term test) = -20.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = 0.52494758705814845531085908673153 y[1] (numeric) = 0.52494758705814845531085908673152 absolute error = 1e-32 relative error = 1.9049520840815484667985647822839e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3529 Order of pole (three term test) = -20.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (analytic) = 0.51615304420783837751118452419248 y[1] (numeric) = 0.51615304420783837751118452419244 absolute error = 4e-32 relative error = 7.7496394623400254670407421322348e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3467 Order of pole (three term test) = -20.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (analytic) = 0.50727510158299784080107547511097 y[1] (numeric) = 0.50727510158299784080107547511095 absolute error = 2e-32 relative error = 3.9426338760936996258529120573544e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3403 Order of pole (three term test) = -20.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = 0.49831440573321499973189444168865 y[1] (numeric) = 0.49831440573321499973189444168862 absolute error = 3e-32 relative error = 6.0202955513313507341708461577264e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3338 Order of pole (three term test) = -21.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = 0.48927161468591860512023895058378 y[1] (numeric) = 0.48927161468591860512023895058373 absolute error = 5e-32 relative error = 1.0219272587905356800773778753260e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3271 Order of pole (three term test) = -21.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = 0.48014739790437908006622471634729 y[1] (numeric) = 0.48014739790437908006622471634724 absolute error = 5e-32 relative error = 1.0413468909386332812777814437450e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3203 Order of pole (three term test) = -21.53 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = 0.47094243624424338498968992438793 y[1] (numeric) = 0.47094243624424338498968992438791 absolute error = 2e-32 relative error = 4.2468035285797568915482502830143e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3133 Order of pole (three term test) = -21.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = 0.46165742190860567011774388638701 y[1] (numeric) = 0.46165742190860567011774388638697 absolute error = 4e-32 relative error = 8.6644334308826082021160123789610e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3062 Order of pole (three term test) = -21.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = 0.45229305840161589277528604808012 y[1] (numeric) = 0.4522930584016158927752860480801 absolute error = 2e-32 relative error = 4.4219117734592556035397134733919e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.299 Order of pole (three term test) = -22.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = 0.44285006048062875576214334698957 y[1] (numeric) = 0.44285006048062875576214334698955 absolute error = 2e-32 relative error = 4.5162012574400098508853783065026e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2916 Order of pole (three term test) = -22.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = 0.43332915410689550202514922813642 y[1] (numeric) = 0.4333291541068955020251492281364 absolute error = 2e-32 relative error = 4.6154291282848496878898993108683e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2841 Order of pole (three term test) = -22.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = 0.42373107639480127972962813799347 y[1] (numeric) = 0.42373107639480127972962813799346 absolute error = 1e-32 relative error = 2.3599873969788186022187536459784e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2765 Order of pole (three term test) = -22.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = 0.41405657555965097068114729520476 y[1] (numeric) = 0.41405657555965097068114729520472 absolute error = 4e-32 relative error = 9.6605155819430788589342105553740e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2688 Order of pole (three term test) = -22.67 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (analytic) = 0.40430641086400655382382805298088 y[1] (numeric) = 0.40430641086400655382382805298087 absolute error = 1e-32 relative error = 2.4733716140265763173015694324885e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2609 Order of pole (three term test) = -22.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = 0.3944813525625792542247325590139 y[1] (numeric) = 0.39448135256257925422473255901387 absolute error = 3e-32 relative error = 7.6049222111812994749534331676334e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.253 Order of pole (three term test) = -22.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 0.38458218184567990652360574518817 y[1] (numeric) = 0.38458218184567990652360574518814 absolute error = 3e-32 relative error = 7.8006734103032382552159394687660e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2449 Order of pole (three term test) = -23.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = 0.37460969078123114026229619032355 y[1] (numeric) = 0.37460969078123114026229619032352 absolute error = 3e-32 relative error = 8.0083352722233082216272055074414e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2367 Order of pole (three term test) = -23.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = 0.36456468225534517278723299840531 y[1] (numeric) = 0.36456468225534517278723299840528 absolute error = 3e-32 relative error = 8.2289924011310742203721162897984e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2284 Order of pole (three term test) = -23.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = 0.35444796991147117352012555015853 y[1] (numeric) = 0.3544479699114711735201255501585 absolute error = 3e-32 relative error = 8.4638656577700137319609700959745e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.22 Order of pole (three term test) = -23.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = 0.34426037808811634129530244150598 y[1] (numeric) = 0.34426037808811634129530244150594 absolute error = 4e-32 relative error = 1.1619112319037093293807033639318e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2116 Order of pole (three term test) = -23.61 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = 0.3340027417551450141455388129389 y[1] (numeric) = 0.33400274175514501414553881293887 absolute error = 3e-32 relative error = 8.9819621965836383061483725463792e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.203 Order of pole (three term test) = -23.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = 0.32367590644866030836056384030922 y[1] (numeric) = 0.32367590644866030836056384030919 absolute error = 3e-32 relative error = 9.2685304659086310338964592615140e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1943 Order of pole (three term test) = -23.83 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = 0.31328072820447296082242366576454 y[1] (numeric) = 0.31328072820447296082242366576451 absolute error = 3e-32 relative error = 9.5760758001109836162387476586488e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1856 Order of pole (three term test) = -23.94 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = 0.30281807349016222551823826712258 y[1] (numeric) = 0.30281807349016222551823826712254 absolute error = 4e-32 relative error = 1.3209251197914214437923967111389e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1767 Order of pole (three term test) = -24.04 NO COMPLEX POLE (six term test) for Equation 1 bytes used=68022652, alloc=4586680, time=2.73 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (analytic) = 0.29228881913573385172238244886678 y[1] (numeric) = 0.29228881913573385172238244886673 absolute error = 5e-32 relative error = 1.7106367649588699559329251964321e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1678 Order of pole (three term test) = -24.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = 0.28169385226288034760550250769287 y[1] (numeric) = 0.28169385226288034760550250769284 absolute error = 3e-32 relative error = 1.0649859682419910196462603179435e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1589 Order of pole (three term test) = -24.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = 0.27103407021284890894582734713482 y[1] (numeric) = 0.27103407021284890894582734713478 absolute error = 4e-32 relative error = 1.4758292183926225993461158961186e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1498 Order of pole (three term test) = -24.32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = 0.26031038047292256816773948577981 y[1] (numeric) = 0.26031038047292256816773948577978 absolute error = 3e-32 relative error = 1.1524703680850942393767670842510e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1407 Order of pole (three term test) = -24.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = 0.2495237006015202940923510301183 y[1] (numeric) = 0.24952370060152029409235103011827 absolute error = 3e-32 relative error = 1.2022906011605222429991746021675e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1315 Order of pole (three term test) = -24.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (analytic) = 0.23867495815192194753371816776908 y[1] (numeric) = 0.23867495815192194753371816776905 absolute error = 3e-32 relative error = 1.2569395730617172335619042228254e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1223 Order of pole (three term test) = -24.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = 0.22776509059462417219118585593169 y[1] (numeric) = 0.22776509059462417219118585593166 absolute error = 3e-32 relative error = 1.3171465355678204751812334906579e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.113 Order of pole (three term test) = -24.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = 0.21679504523833347415207026470415 y[1] (numeric) = 0.21679504523833347415207026470412 absolute error = 3e-32 relative error = 1.3837954629922248443878893795488e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1036 Order of pole (three term test) = -24.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = 0.20576577914960291670837815082275 y[1] (numeric) = 0.20576577914960291670837815082272 absolute error = 3e-32 relative error = 1.4579683815251110227383821568882e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09424 Order of pole (three term test) = -24.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = 0.194678259071119030085479961853 y[1] (numeric) = 0.19467825907111903008547996185298 absolute error = 2e-32 relative error = 1.0273360823867695172311779199151e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08481 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = 0.18353346133864570805858216931543 y[1] (numeric) = 0.18353346133864570805858216931541 absolute error = 2e-32 relative error = 1.0897195450968537724322644946199e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07534 Order of pole (three term test) = -24.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 0.17233237179663203527350642914081 y[1] (numeric) = 0.1723323717966320352735064291408 absolute error = 1e-32 relative error = 5.8027403068536159070636400185577e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06583 Order of pole (three term test) = -24.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = 0.1610759857124911603707407304847 y[1] (numeric) = 0.16107598571249116037074073048468 absolute error = 2e-32 relative error = 1.2416500145278350486245092372055e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0563 Order of pole (three term test) = -24.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = 0.1497653076895575007150849835282 y[1] (numeric) = 0.14976530768955750071508498352817 absolute error = 3e-32 relative error = 2.0031341345210465371836236602329e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04674 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = 0.1384013515787297346366194469752 y[1] (numeric) = 0.13840135157872973463661944697519 absolute error = 1e-32 relative error = 7.2253629649790601294376862026474e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03716 Order of pole (three term test) = -24.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = 0.12698514038880720657137507250654 y[1] (numeric) = 0.12698514038880720657137507250652 absolute error = 2e-32 relative error = 1.5749874307153855693549953809121e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02756 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = 0.11551770619552753933122590465757 y[1] (numeric) = 0.11551770619552753933122590465755 absolute error = 2e-32 relative error = 1.7313363170618716248581415958194e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01794 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = 0.104000090049313415911452826877 y[1] (numeric) = 0.10400009004931341591145282687699 absolute error = 1e-32 relative error = 9.6153762898266044757716889917776e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008319 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = 0.092433341881736660740497394609888 y[1] (numeric) = 0.092433341881736660740497394609879 absolute error = 9e-33 relative error = 9.7367463047208671900980519667260e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (analytic) = 0.080818520410707917069043398884685 y[1] (numeric) = 0.080818520410707917069043398884678 absolute error = 7e-33 relative error = 8.6613810354693730593069445937883e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = 0.06915669304440038326420070507445 y[1] (numeric) = 0.069156693044400383264200705074432 absolute error = 1.8e-32 relative error = 2.6027849522017391804427153217602e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 0.057448935783916236098751186852869 y[1] (numeric) = 0.057448935783916236098751186852856 absolute error = 1.3e-32 relative error = 2.2628791678399657017248419523518e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (analytic) = 0.045696333124704533684744863322871 y[1] (numeric) = 0.045696333124704533684744863322854 absolute error = 1.7e-32 relative error = 3.7202109748297051576324846087264e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (analytic) = 0.033899977956739554474866976963034 y[1] (numeric) = 0.033899977956739554474866976963019 absolute error = 1.5e-32 relative error = 4.4247816382482025511062343693181e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = 0.02206097146346869172366416331858 y[1] (numeric) = 0.022060971463468691723664163318565 absolute error = 1.5e-32 relative error = 6.7993379279959955490901328340380e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = 0.01018042301953918494372203111763 y[1] (numeric) = 0.010180423019539184943722031117618 absolute error = 1.2e-32 relative error = 1.1787329442959805306854968221116e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=72026144, alloc=4586680, time=2.90 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = -0.001740549912686868810896696545408 y[1] (numeric) = -0.001740549912686868810896696545429 absolute error = 2.10e-32 relative error = 1.2065152425064626989282491192014e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = -0.01370082188781962057026258116442 y[1] (numeric) = -0.013700821887819620570262581164439 absolute error = 1.9e-32 relative error = 1.3867781185369239540758579171475e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (analytic) = -0.025699259583320929173969853962253 y[1] (numeric) = -0.02569925958332092917396985396228 absolute error = 2.7e-32 relative error = 1.0506139257616302719706294241445e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = -0.03773472190656625364715255198978 y[1] (numeric) = -0.037734721906566253647152551989806 absolute error = 2.6e-32 relative error = 6.8902058068369429533605554727127e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = -0.04980606010307889906358283302262 y[1] (numeric) = -0.049806060103078899063582833022638 absolute error = 1.8e-32 relative error = 3.6140180457452566745624488580375e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = -0.061912117865926379963133390082163 y[1] (numeric) = -0.061912117865926379963133390082173 absolute error = 1.0e-32 relative error = 1.6151926867782932345076385546614e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (analytic) = -0.074051731446268509586556443453603 y[1] (numeric) = -0.074051731446268509586556443453621 absolute error = 1.8e-32 relative error = 2.4307331710482274959069268011313e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (analytic) = -0.086223729765046668370587033536524 y[1] (numeric) = -0.086223729765046668370587033536547 absolute error = 2.3e-32 relative error = 2.6674791339545750291082113991145e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (analytic) = -0.098426934525803551330264936440523 y[1] (numeric) = -0.098426934525803551330264936440543 absolute error = 2.0e-32 relative error = 2.0319641261159881939684829233447e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = -0.11066016032862254116243883984314 y[1] (numeric) = -0.11066016032862254116243883984316 absolute error = 2e-32 relative error = 1.8073351728939206553771840026707e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = -0.12292221478517570215392218028141 y[1] (numeric) = -0.12292221478517570215392218028142 absolute error = 1e-32 relative error = 8.1352260187277313323090379612120e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (analytic) = -0.13521189863486923928886603007388 y[1] (numeric) = -0.1352118986348692392888660300739 absolute error = 2e-32 relative error = 1.4791597634472002322870799664040e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (analytic) = -0.14752800586207511734165213884477 y[1] (numeric) = -0.14752800586207511734165213884478 absolute error = 1e-32 relative error = 6.7783740053729624686004448743084e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = -0.15986932381443738623293561517245 y[1] (numeric) = -0.15986932381443738623293561517246 absolute error = 1e-32 relative error = 6.2551087109163876979599766189231e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = -0.17223463332224161153622184659338 y[1] (numeric) = -0.17223463332224161153622184659339 absolute error = 1e-32 relative error = 5.8060332043036576947469987935469e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = -0.18462270881883566276927702086938 y[1] (numeric) = -0.18462270881883566276927702086939 absolute error = 1e-32 relative error = 5.4164517810280202152819150322417e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = -0.19703231846208996700736552704464 y[1] (numeric) = -0.19703231846208996700736552704466 absolute error = 2e-32 relative error = 1.0150619023370068611721799402904e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = -0.20946222425688519143228639814157 y[1] (numeric) = -0.20946222425688519143228639814159 absolute error = 2e-32 relative error = 9.5482610628023940442671926720635e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = -0.22191118217861517570083469275032 y[1] (numeric) = -0.22191118217861517570083469275034 absolute error = 2e-32 relative error = 9.0126147784216219795011621236619e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = -0.23437794229769279349691401350386 y[1] (numeric) = -0.23437794229769279349691401350388 absolute error = 2e-32 relative error = 8.5332262088883776116394850841267e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = -0.24686124890504628234122454158609 y[1] (numeric) = -0.2468612489050462823412245415861 absolute error = 1e-32 relative error = 4.0508585467970474326175198703968e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = -0.25935984063859344168927572985987 y[1] (numeric) = -0.25935984063859344168927572985988 absolute error = 1e-32 relative error = 3.8556470328552373079422397468947e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = -0.27187245061068096157032802873513 y[1] (numeric) = -0.27187245061068096157032802873514 absolute error = 1e-32 relative error = 3.6781954102145917692159906034694e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = -0.28439780653647600752453059794193 y[1] (numeric) = -0.28439780653647600752453059794195 absolute error = 2e-32 relative error = 7.0324030426144865983769889435662e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = -0.29693463086329705240063957936783 y[1] (numeric) = -0.29693463086329705240063957936784 absolute error = 1e-32 relative error = 3.3677446012027496171244789494515e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = -0.30948164090087081169979051793909 y[1] (numeric) = -0.3094816409008708116997905179391 absolute error = 1e-32 relative error = 3.2312094413390653087170197909956e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=76027716, alloc=4586680, time=3.05 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = -0.32203754895250200660924176617827 y[1] (numeric) = -0.32203754895250200660924176617828 absolute error = 1e-32 relative error = 3.1052279563445941421795295988548e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = -0.33460106244714254768105040289026 y[1] (numeric) = -0.33460106244714254768105040289028 absolute error = 2e-32 relative error = 5.9772673325445376403357593752965e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = -0.34717088407234660229139778506942 y[1] (numeric) = -0.34717088407234660229139778506944 absolute error = 2e-32 relative error = 5.7608517642372968942667064321634e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = -0.35974571190809788058371791054913 y[1] (numeric) = -0.35974571190809788058371791054916 absolute error = 3e-32 relative error = 8.3392237925170664461429473683671e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = -0.37232423956149534756972590570914 y[1] (numeric) = -0.37232423956149534756972590570916 absolute error = 2e-32 relative error = 5.3716620823707283049926015767761e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = -0.38490515630228344345357972770201 y[1] (numeric) = -0.38490515630228344345357972770203 absolute error = 2e-32 relative error = 5.1960852362011733153369402072849e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = -0.39748714719921277007227302914862 y[1] (numeric) = -0.39748714719921277007227302914863 absolute error = 1e-32 relative error = 2.5158046166932275506959450917567e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = -0.41006889325721707862634035367603 y[1] (numeric) = -0.41006889325721707862634035367605 absolute error = 2e-32 relative error = 4.8772292482704688867217439654627e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = -0.42264907155539227262529648910407 y[1] (numeric) = -0.42264907155539227262529648910408 absolute error = 1e-32 relative error = 2.3660290943498269849301941142033e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = -0.43522635538576302020801675445973 y[1] (numeric) = -0.43522635538576302020801675445974 absolute error = 1e-32 relative error = 2.2976549733842512319165986487778e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = -0.44779941439282245173542686223781 y[1] (numeric) = -0.44779941439282245173542686223782 absolute error = 1e-32 relative error = 2.2331427149272048927852950420984e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = -0.46036691471383030180718618647054 y[1] (numeric) = -0.46036691471383030180718618647056 absolute error = 2e-32 relative error = 4.3443608480058225572411147875372e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (analytic) = -0.47292751911985473964113499873053 y[1] (numeric) = -0.47292751911985473964113499873054 absolute error = 1e-32 relative error = 2.1144889218141870928045875615280e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = -0.48547988715754301808959258096779 y[1] (numeric) = -0.4854798871575430180895925809678 absolute error = 1e-32 relative error = 2.0598175670158918937425615017215e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = -0.49802267529160595946543507368428 y[1] (numeric) = -0.4980226752916059594654350736843 absolute error = 2e-32 relative error = 4.0158814030484556759682829750776e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = -0.51055453704800118582838145025179 y[1] (numeric) = -0.5105545370480011858283814502518 absolute error = 1e-32 relative error = 1.9586546146116849723938652537800e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = -0.5230741231577998924530391899478 y[1] (numeric) = -0.52307412315779989245303918994783 absolute error = 3e-32 relative error = 5.7353248176166542281749337386588e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = -0.53558008170172185587980631918807 y[1] (numeric) = -0.53558008170172185587980631918809 absolute error = 2e-32 relative error = 3.7342688205381222026774619421742e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = -0.54807105825532326225232209669286 y[1] (numeric) = -0.54807105825532326225232209669288 absolute error = 2e-32 relative error = 3.6491618557028130657379472405511e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = (0.2 * x + 0.3) * sin(x); Iterations = 490 Total Elapsed Time = 3 Seconds Elapsed Time(since restart) = 3 Seconds Time to Timeout = 2 Minutes 56 Seconds Percent Done = 100.2 % > quit bytes used=78988444, alloc=4586680, time=3.17