|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre sub FULL - CONST $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] - array_const_1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := array_tmp1_g[1] * array_x[2] / 1; > array_tmp1_g[2] := -array_tmp1[1] * array_x[2] / 1; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sub FULL CONST $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := array_tmp1_g[2] * array_x[2] / 2; > array_tmp1_g[3] := -array_tmp1[2] * array_x[2] / 2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre sub FULL CONST $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := array_tmp1_g[3] * array_x[2] / 3; > array_tmp1_g[4] := -array_tmp1[3] * array_x[2] / 3; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre sub FULL CONST $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := array_tmp1_g[4] * array_x[2] / 4; > array_tmp1_g[5] := -array_tmp1[4] * array_x[2] / 4; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre sub FULL CONST $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sin LINEAR $eq_no = 1 > array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp1_g[kkk] := -array_tmp1[kkk - 1] * array_x[2] / (kkk - 1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit FULL - NOT FULL sub $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_tmp2[1] - array_const_1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_tmp1_g[1]*array_x[2]; array_tmp1_g[2] := -array_tmp1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := 1/2*array_tmp1_g[2]*array_x[2]; array_tmp1_g[3] := -1/2*array_tmp1[2]*array_x[2]; array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := array_tmp2[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := 1/3*array_tmp1_g[3]*array_x[2]; array_tmp1_g[4] := -1/3*array_tmp1[3]*array_x[2]; array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := array_tmp2[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := 1/4*array_tmp1_g[4]*array_x[2]; array_tmp1_g[5] := -1/4*array_tmp1[4]*array_x[2]; array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := array_tmp2[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp1_g[kkk] := -array_tmp1[kkk - 1]*array_x[2]/(kkk - 1); array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := array_tmp2[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp3[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp3[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(2.0 - cos(x) - x); > end; exact_soln_y := proc(x) return 2.0 - cos(x) - x end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sub_sin_cpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sin(x) - 1,0;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 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(2.0 - cos(x) - x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0[1] := 0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 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 ) = sin(x) - 1,0;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T05:18:56-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sub_sin_c") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sin(x) - 1,0;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"sub_sin_c diffeq.mxt") > ; > logitem_str(html_log_file,"sub_sin_c maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sub_sin_cpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x) - 1,0;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 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(2.0 - cos(x) - x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0[term] := 0.; term := term + 1 end do; array_const_0[1] := 0; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 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 ) = sin(x) - 1,0;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T05:18:56-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sub_sin_c"); logitem_str(html_log_file, "diff ( y , x , 1 ) = sin(x) - 1,0;") ; logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "sub_sin_c diffeq.mxt"); logitem_str(html_log_file, "sub_sin_c maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/sub_sin_cpostode.ode################# diff ( y , x , 1 ) = sin(x) - 1,0; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 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(2.0 - cos(x) - x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 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 = 2.4672086055323049562331277806886e-183 estimated_step_error = 2.4672086055323049562331277806886e-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 = 1.6557156646065677204134289038210e-175 estimated_step_error = 1.6557156646065677204134289038210e-175 best_h = 4.00e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1111319694584368636820923174825e-167 estimated_step_error = 1.1111319694584368636820923174825e-167 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.4566803670241957246681619817550e-160 estimated_step_error = 7.4566803670241957246681619817550e-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 = 5.0040934120378230048946847695115e-152 estimated_step_error = 5.0040934120378230048946847695115e-152 best_h = 3.200000e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.3581901424816281269073121711214e-144 estimated_step_error = 3.3581901424816281269073121711214e-144 best_h = 6.4000000e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.2536431215809227087580736291234e-136 estimated_step_error = 2.2536431215809227087580736291234e-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 = 1.5123941176543087498746423194483e-128 estimated_step_error = 1.5123941176543087498746423194483e-128 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0149502701580566739311213784162e-120 estimated_step_error = 1.0149502701580566739311213784162e-120 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.8112127244081165253087202414269e-113 estimated_step_error = 6.8112127244081165253087202414269e-113 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.5709231343600303584753702483543e-105 estimated_step_error = 4.5709231343600303584753702483543e-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 = 3.0674887502340254951354356814932e-97 estimated_step_error = 3.0674887502340254951354356814932e-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 = 2.0585490116180929098885606683401e-89 estimated_step_error = 2.0585490116180929098885606683401e-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 = 1.3814583197402461309888420940037e-81 estimated_step_error = 1.3814583197402461309888420940037e-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 = 9.2706681184281159182706538798633e-74 estimated_step_error = 9.2706681184281159182706538798633e-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 = 6.2212490020161221570851682852212e-66 estimated_step_error = 6.2212490020161221570851682852212e-66 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.1747508750792467142506979498165e-58 estimated_step_error = 4.1747508750792467142506979498165e-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 = 2.8012747543996062244493916551861e-50 estimated_step_error = 2.8012747543996062244493916551861e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.9049958347219742339044380121961 y[1] (numeric) = 0.9049958347219742339044380121961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0.8960439020433031496421603885802 y[1] (numeric) = 0.89604390204330314964216038858012 absolute error = 8e-32 relative error = 8.9281339695043018982492888831759e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=4000928, alloc=3145152, time=0.16 x[1] = 0.12 y[1] (analytic) = 0.8871913641461337477519018321424 y[1] (numeric) = 0.88719136414613374775190183214233 absolute error = 7e-32 relative error = 7.8900677834449646703150802112003e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0.8784381062852119604054878288482 y[1] (numeric) = 0.87843810628521196040548782884815 absolute error = 5e-32 relative error = 5.6919206535156799674834546373504e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0.8697840037873628281010517729886 y[1] (numeric) = 0.86978400378736282810105177298856 absolute error = 4e-32 relative error = 4.5988429110934591878542288753573e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0.8612289220639577132650190013457 y[1] (numeric) = 0.86122892206395771326501900134562 absolute error = 8e-32 relative error = 9.2890517202183480475059375536191e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.8527727166243730509590474759817 y[1] (numeric) = 0.85277271662437305095904747598162 absolute error = 8e-32 relative error = 9.3811631681502513398392823985365e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0.8444152330904392908280700097875 y[1] (numeric) = 0.84441523309043929082807000978745 absolute error = 5e-32 relative error = 5.9212574620435414081668567452419e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0.8361563072118785854072839753885 y[1] (numeric) = 0.83615630721187858540728397538842 absolute error = 8e-32 relative error = 9.5675891349496604925193324540079e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0.8279957648827296810321224958101 y[1] (numeric) = 0.82799576488272968103212249581004 absolute error = 6e-32 relative error = 7.2464138761021190327268752107331e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0.8199334221587583688758034832518 y[1] (numeric) = 0.81993342215875836887580348325178 absolute error = 2e-32 relative error = 2.4392224367855479668575624085650e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0.8119690852758517550838614319006 y[1] (numeric) = 0.8119690852758517550838614319006 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0.8041025506693945105939770189553 y[1] (numeric) = 0.80410255066939451059397701895525 absolute error = 5e-32 relative error = 6.2181123487764461479103951291073e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 0.7963336049946251630322693519284 y[1] (numeric) = 0.79633360499462516303226935192835 absolute error = 5e-32 relative error = 6.2787755893257165696901522161668e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 0.7886620251479703950738247530366 y[1] (numeric) = 0.78866202514797039507382475303657 absolute error = 3e-32 relative error = 3.8039108063268721670251860427544e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 0.7810875782893552158554045505058 y[1] (numeric) = 0.78108757828935521585540455050576 absolute error = 4e-32 relative error = 5.1210646682671904270177260658908e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 0.7736100218654867744417823535499 y[1] (numeric) = 0.77361002186548677444178235354988 absolute error = 2e-32 relative error = 2.5852819165620305389142045360047e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 0.7662291036341094869837672905078 y[1] (numeric) = 0.76622910363410948698376729050774 absolute error = 6e-32 relative error = 7.8305561241969297442463337700022e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0.7589445616892290520754099464035 y[1] (numeric) = 0.75894456168922905207540994640347 absolute error = 3e-32 relative error = 3.9528578916524780290869744474147e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 0.7517561244873028319298752220681 y[1] (numeric) = 0.75175612448730283192987522206808 absolute error = 2e-32 relative error = 2.6604372546535602171370904575310e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0.744663510874393980357689772432 y[1] (numeric) = 0.74466351087439398035768977243189 absolute error = 1.1e-31 relative error = 1.4771772538020093147228601916431e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 0.7376664301142866021571945637978 y[1] (numeric) = 0.73766643011428660215719456379773 absolute error = 7e-32 relative error = 9.4893839738857176258646676136850e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 0.7307645819175591324246927262339 y[1] (numeric) = 0.73076458191755913242469272623385 absolute error = 5e-32 relative error = 6.8421487900792552126362806750896e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0.7239576564716130284705894216338 y[1] (numeric) = 0.72395765647161302847058942163374 absolute error = 6e-32 relative error = 8.2877775327945093773112493957858e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 0.7172453344716537714973559399734 y[1] (numeric) = 0.71724533447165377149735593997337 absolute error = 3e-32 relative error = 4.1826692427492714462626484260157e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=8002340, alloc=4324584, time=0.32 x[1] = 0.35 y[1] (analytic) = 0.7106272871526210799649676426963 y[1] (numeric) = 0.71062728715262107996496764269628 absolute error = 2e-32 relative error = 2.8144148643851062306985224707337e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 0.7041031763220651416490876318753 y[1] (numeric) = 0.7041031763220651416490876318752 absolute error = 1.0e-31 relative error = 1.4202463980116859217913254843573e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 0.6976726543939655767961870955091 y[1] (numeric) = 0.69767265439396557679618709550906 absolute error = 4e-32 relative error = 5.7333478312613615993668419081333e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 0.6913353644234897505074691922754 y[1] (numeric) = 0.69133536442348975050746919227538 absolute error = 2e-32 relative error = 2.8929519635782214877614243967053e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 0.6850909401426869585493232471189 y[1] (numeric) = 0.68509094014268695854932324711884 absolute error = 6e-32 relative error = 8.7579613864844762458398821962122e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0.6789390059971149172014732679482 y[1] (numeric) = 0.67893900599711491720147326794814 absolute error = 6e-32 relative error = 8.8373181493500704753702101804559e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 0.672879177183394894524357941723 y[1] (numeric) = 0.67287917718339489452435794172292 absolute error = 8e-32 relative error = 1.1889207262271366272577509609043e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 0.6669110596876917275639112103343 y[1] (numeric) = 0.66691105968769172756391121033427 absolute error = 3e-32 relative error = 4.4983509516319495653819418900390e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 0.6610342503251148775240895223366 y[1] (numeric) = 0.66103425032511487752408952233649 absolute error = 1.1e-31 relative error = 1.6640590097396461058646163382819e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 0.6552483367800365828344626110016 y[1] (numeric) = 0.65524833678003658283446261100157 absolute error = 3e-32 relative error = 4.5784168102468365467824666066804e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 0.6495528976473230783311593885136 y[1] (numeric) = 0.64955289764732307833115938851349 absolute error = 1.1e-31 relative error = 1.6934725470153297427241367605211e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 0.6439475024744747574636100964996 y[1] (numeric) = 0.64394750247447475746361009649953 absolute error = 7e-32 relative error = 1.0870451353722690938278465704151e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 0.6384317118046710635459807234666 y[1] (numeric) = 0.63843171180467106354598072346654 absolute error = 6e-32 relative error = 9.3980294040213765074550308448807e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 0.6330050772207158056000451688413 y[1] (numeric) = 0.63300507722071580560004516884119 absolute error = 1.1e-31 relative error = 1.7377427758236648444897403539725e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 0.6276671413898785042945318408633 y[1] (numeric) = 0.62766714138987850429453184086327 absolute error = 3e-32 relative error = 4.7796033951322224420615047706139e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0.6224174381096272838837184173962 y[1] (numeric) = 0.6224174381096272838837184173961 absolute error = 1.0e-31 relative error = 1.6066387905794319233172811479377e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 0.6172554923542487368941915264245 y[1] (numeric) = 0.61725549235424873689419152642442 absolute error = 8e-32 relative error = 1.2960597514470919768024807608486e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 0.6121808203223500996121524280115 y[1] (numeric) = 0.61218082032235009961215242801142 absolute error = 8e-32 relative error = 1.3068034368975358978783035927723e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 0.6071929294852389881933049814358 y[1] (numeric) = 0.60719292948523898819330498143573 absolute error = 7e-32 relative error = 1.1528460988395240772912730487331e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 0.6022913186361758574620312210822 y[1] (numeric) = 0.60229131863617585746203122108214 absolute error = 6e-32 relative error = 9.9619566385023728558896124778868e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 0.5974754779404942571950182023822 y[1] (numeric) = 0.59747547794049425719501820238216 absolute error = 4e-32 relative error = 6.6948354328918268263912582242656e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 0.5927448889865838739054744961337 y[1] (numeric) = 0.59274488898658387390547449613361 absolute error = 9e-32 relative error = 1.5183597812858922960406794776133e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = 0.588099024837731259866243636084 y[1] (numeric) = 0.58809902483773125986624363608392 absolute error = 8e-32 relative error = 1.3603151275769189073843417601790e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=12003892, alloc=4390108, time=0.48 x[1] = 0.58 y[1] (analytic) = 0.58353735008481306534211267195 y[1] (numeric) = 0.58353735008481306534211267194991 absolute error = 9e-32 relative error = 1.5423177280240781601294160493920e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 0.5790593208998365047520034775093 y[1] (numeric) = 0.57905932089983650475200347750925 absolute error = 5e-32 relative error = 8.6346939243291813341822545309234e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0.5746643850903217027590475010446 y[1] (numeric) = 0.57466438509032170275904750104455 absolute error = 5e-32 relative error = 8.7007305998511378027606434457198e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 0.5703519821545204820992534213452 y[1] (numeric) = 0.5703519821545204820992534213451 absolute error = 1.0e-31 relative error = 1.7533032781309397329261946605194e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 0.5661215433374660713160003456393 y[1] (numeric) = 0.56612154333746607131600034563923 absolute error = 7e-32 relative error = 1.2364835930342413053375754955958e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 0.5619724916878481274762910342229 y[1] (numeric) = 0.56197249168784812747629103422287 absolute error = 3e-32 relative error = 5.3383395884551101812714856795641e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 0.5579042421157073864138892207397 y[1] (numeric) = 0.5579042421157073864138892207396 absolute error = 1.0e-31 relative error = 1.7924222913375939187057342696076e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 0.5539162014509441710823954293201 y[1] (numeric) = 0.55391620145094417108239542932002 absolute error = 8e-32 relative error = 1.4442617816638271030487911596172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 0.5500077685026349072161829087698 y[1] (numeric) = 0.55000776850263490721618290876968 absolute error = 1.2e-31 relative error = 2.1817873650529195984031730415193e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 0.5461783341191507146970578551619 y[1] (numeric) = 0.54617833411915071469705785516181 absolute error = 9e-32 relative error = 1.6478134407353878135505839274880e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 0.5424272812490720628176059159557 y[1] (numeric) = 0.54242728124907206281760591595561 absolute error = 9e-32 relative error = 1.6592085817061577622047609656693e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 0.5387539850028933980264606845022 y[1] (numeric) = 0.53875398500289339802646068450216 absolute error = 4e-32 relative error = 7.4245390500053894791429415055099e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0.5351578127155115737441400098081 y[1] (numeric) = 0.53515781271551157374414000980806 absolute error = 4e-32 relative error = 7.4744307285791023948517216728152e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 0.5316381240094918334585420558604 y[1] (numeric) = 0.53163812400949183345854205586037 absolute error = 3e-32 relative error = 5.6429361712713405587991832667478e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 0.528194270859105020554513037748 y[1] (numeric) = 0.52819427085910502055451303774798 absolute error = 2e-32 relative error = 3.7864855988441737767727175056595e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 0.5248255976551296112098678414497 y[1] (numeric) = 0.52482559765512961120986784144959 absolute error = 1.1e-31 relative error = 2.0959343540305472972625648217509e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 0.5215314412704120902085754393012 y[1] (numeric) = 0.52153144127041209020857543930109 absolute error = 1.1e-31 relative error = 2.1091729336978825374161909507476e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 0.5183111311261791136881612469999 y[1] (numeric) = 0.51831113112617911368816124699984 absolute error = 6e-32 relative error = 1.1576058548006261498579136476086e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 0.515163989259094827660311633333 y[1] (numeric) = 0.51516398925909482766031163333292 absolute error = 8e-32 relative error = 1.5529035737737691835832167240913e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 0.5120893303890566366287094346757 y[1] (numeric) = 0.51208933038905663662870943467558 absolute error = 1.2e-31 relative error = 2.3433411492645386186692935814969e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 0.5090864619877226427837349762354 y[1] (numeric) = 0.50908646198772264278373497623536 absolute error = 4e-32 relative error = 7.8572114928808807966726908606078e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 0.506154684347763903087219138915 y[1] (numeric) = 0.50615468434776390308721913891497 absolute error = 3e-32 relative error = 5.9270418565143393797324927547233e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 0.5032932906528345790792500183577 y[1] (numeric) = 0.5032932906528345790792500183576 absolute error = 1.0e-31 relative error = 1.9869130357427862085023691031676e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=16004576, alloc=4390108, time=0.64 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 0.5005015670482529824503607593199 y[1] (numeric) = 0.50050156704825298245036075931982 absolute error = 8e-32 relative error = 1.5983965938769430410333549535385e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 0.4977787927123864483334420215631 y[1] (numeric) = 0.49777879271238644833344202156299 absolute error = 1.1e-31 relative error = 2.2098169229069051435666913427745e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 0.4951242399287328978875370821356 y[1] (numeric) = 0.49512423992873289788753708213547 absolute error = 1.3e-31 relative error = 2.6256036266516039727067954172373e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = 0.4925371741586918820773289631291 y[1] (numeric) = 0.49253717415869188207732896312907 absolute error = 3e-32 relative error = 6.0909108132281237709860143993000e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 0.4900168541150178296045839705385 y[1] (numeric) = 0.49001685411501782960458397053846 absolute error = 4e-32 relative error = 8.1629845308567921954885630375910e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 0.4875625318359481537279693357761 y[1] (numeric) = 0.48756253183594815372796933577607 absolute error = 3e-32 relative error = 6.1530568985752587412277326543068e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 0.4851734527599988052223361945172 y[1] (numeric) = 0.4851734527599988052223361945171 absolute error = 1.0e-31 relative error = 2.0611185428867042996913652822289e-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] = 0.88 y[1] (analytic) = 0.4828488558014197919845013942779 y[1] (numeric) = 0.48284885580141979198450139427784 absolute error = 6e-32 relative error = 1.2426248768967999927070343729129e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 0.4805879734263031197964469426198 y[1] (numeric) = 0.48058797342630311979644694261968 absolute error = 1.2e-31 relative error = 2.4969413850386682431795987959761e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 0.4783900317293355435152838485929 y[1] (numeric) = 0.4783900317293355435152838485928 absolute error = 1.0e-31 relative error = 2.0903445591980519652238997765662e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 0.4762542505111884534788217738253 y[1] (numeric) = 0.47625425051118845347882177382525 absolute error = 5e-32 relative error = 1.0498593964533103877956428476113e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 0.4741798433565371582025952933256 y[1] (numeric) = 0.47417984335653715820259529332555 absolute error = 5e-32 relative error = 1.0544522442385822658826662592945e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 0.472166017712701761505092915567 y[1] (numeric) = 0.47216601771270176150509291556694 absolute error = 6e-32 relative error = 1.2707394803771778728436504077003e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 0.470211974968901770039010184776 y[1] (numeric) = 0.47021197496890177003901018477591 absolute error = 9e-32 relative error = 1.9140303690894366451859536605748e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 0.4683169105361165058338190262395 y[1] (numeric) = 0.46831691053611650583381902623947 absolute error = 3e-32 relative error = 6.4059185831356832973495847815496e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 0.4664800139275433378749491996481 y[1] (numeric) = 0.46648001392754333787494919964807 absolute error = 3e-32 relative error = 6.4311436941132899334075601029712e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 0.4647004688396456869634722451501 y[1] (numeric) = 0.46470046883964568696347224515007 absolute error = 3e-32 relative error = 6.4557714079587270423953009666421e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 0.4629774532337826991233417326401 y[1] (numeric) = 0.46297745323378269912334173263999 absolute error = 1.1e-31 relative error = 2.3759256359392294032810810887588e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 0.4613101394184124246568735913464 y[1] (numeric) = 0.46131013941841242465687359134632 absolute error = 8e-32 relative error = 1.7341912341414911778129435244533e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 0.459697694131860282599063392557 y[1] (numeric) = 0.45969769413186028259906339255696 absolute error = 4e-32 relative error = 8.7013705986800856431071470386247e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 0.4581392786256445337932686442208 y[1] (numeric) = 0.45813927862564453379326864422076 absolute error = 4e-32 relative error = 8.7309693506294754999419725049129e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = 0.4566340487483504301103861919662 y[1] (numeric) = 0.45663404874835043011038619196613 absolute error = 7e-32 relative error = 1.5329562084096093554904649256233e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = 0.4551811550300446524664977001626 y[1] (numeric) = 0.45518115503004465246649770016259 absolute error = 1e-32 relative error = 2.1969275066626914213270321474112e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 bytes used=20006008, alloc=4390108, time=0.81 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = 0.4537797427672215962655265790078 y[1] (numeric) = 0.45377974276722159626552657900777 absolute error = 3e-32 relative error = 6.6111368958550666143050463547972e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 0.4524289521082730097091504271879 y[1] (numeric) = 0.45242895210827300970915042718784 absolute error = 6e-32 relative error = 1.3261750761176111318081266008646e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 0.4511279181394724380813624600436 y[1] (numeric) = 0.45112791813947243808136246004353 absolute error = 7e-32 relative error = 1.5516663275616325616235196550016e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = 0.4498757709714658756349069318241 y[1] (numeric) = 0.44987577097146587563490693182402 absolute error = 8e-32 relative error = 1.7782686946497977551400273998995e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 0.448671635826259976086475211474 y[1] (numeric) = 0.44867163582625997608647521147391 absolute error = 9e-32 relative error = 2.0059213200375091643010971452527e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = 0.4475146331246991229721029261249 y[1] (numeric) = 0.4475146331246991229721029261248 absolute error = 1.0e-31 relative error = 2.2345638018977400760840458780943e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0.4464038785744226122286299482153 y[1] (numeric) = 0.44640387857442261222862994821523 absolute error = 7e-32 relative error = 1.5680867340029145581324564906951e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 0.4453384832582931513562624880664 y[1] (numeric) = 0.44533848325829315135626248806637 absolute error = 3e-32 relative error = 6.7364490444451919223862992191953e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 0.4443175537232878323860112060389 y[1] (numeric) = 0.44431755372328783238601120603882 absolute error = 8e-32 relative error = 1.8005140541852734154029347193041e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 0.4433401920698426896287841643465 y[1] (numeric) = 0.44334019206984268962878416434641 absolute error = 9e-32 relative error = 2.0300437814990982866627060554155e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = 0.4424054960416419078248132591774 y[1] (numeric) = 0.44240549604164190782481325917737 absolute error = 3e-32 relative error = 6.7811092467025357067418170881515e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = 0.4415125591158427018474232811901 y[1] (numeric) = 0.44151255911584270184742328119003 absolute error = 7e-32 relative error = 1.5854588630543036526302881528762e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 0.440660470593726845548360376606 y[1] (numeric) = 0.44066047059372684554836037660594 absolute error = 6e-32 relative error = 1.3615925185927976907337547229455e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 0.4398483156917697846673380649495 y[1] (numeric) = 0.43984831569176978466733806494944 absolute error = 6e-32 relative error = 1.3641066217483458041890119491228e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 0.4390751756331182269704005332872 y[1] (numeric) = 0.43907517563311822697040053328718 absolute error = 2e-32 relative error = 4.5550286397224082272917241325797e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 0.4383401277394670619343204416495 y[1] (numeric) = 0.43834012773946706193432044164948 absolute error = 2e-32 relative error = 4.5626669187556677853561592709009e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 0.4376422455233264223616266443769 y[1] (numeric) = 0.43764224552332642236162664437687 absolute error = 3e-32 relative error = 6.8549141009288130490342809719642e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 0.4369805987806696612969892863352 y[1] (numeric) = 0.43698059878066966129698928633516 absolute error = 4e-32 relative error = 9.1537244700598011867621918081838e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 0.4363542536839529795244770255648 y[1] (numeric) = 0.43635425368395297952447702556475 absolute error = 5e-32 relative error = 1.1458579715419595698360326238852e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 0.4357622728754974017604527545023 y[1] (numeric) = 0.43576227287549740176045275450228 absolute error = 2e-32 relative error = 4.5896584548323769246052574685806e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 0.4352037155612237634223065843026 y[1] (numeric) = 0.43520371556122376342230658430256 absolute error = 4e-32 relative error = 9.1910980007184391568292556285828e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 0.434677637604731334552461447562 y[1] (numeric) = 0.4346776376047313345524614475619 absolute error = 1.0e-31 relative error = 2.3005554311706678480361957679571e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=24007092, alloc=4390108, time=0.98 x[1] = 1.26 y[1] (analytic) = 0.4341830916217106731136575108235 y[1] (numeric) = 0.43418309162171067311365751082345 absolute error = 5e-32 relative error = 1.1515879122156912921945894709488e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 0.433719127074681266448862983912 y[1] (numeric) = 0.43371912707468126644886298391198 absolute error = 2e-32 relative error = 4.6112792246204623287365718398905e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 0.4332847903680444872206131064074 y[1] (numeric) = 0.43328479036804448722061310640735 absolute error = 5e-32 relative error = 1.1539754247438173551741166172085e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 0.4328791249434423586133939099388 y[1] (numeric) = 0.43287912494344235861339390993876 absolute error = 4e-32 relative error = 9.2404548279444483039185938719841e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0.4325011713754125930020158907071 y[1] (numeric) = 0.43250117137541259300201589070707 absolute error = 3e-32 relative error = 6.9363973985540701958385658059172e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 0.4321499674673303386618230213838 y[1] (numeric) = 0.43214996746733033866182302138375 absolute error = 5e-32 relative error = 1.1570057564282912649503636891646e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 0.4318245483476270404260172705726 y[1] (numeric) = 0.43182454834762704042601727057259 absolute error = 1e-32 relative error = 2.3157553312485163021517410537735e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 0.4315239465662767924842150139894 y[1] (numeric) = 0.43152394656627679248421501398937 absolute error = 3e-32 relative error = 6.9521054946581898365220113729114e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 0.4312471921915405347673605076999 y[1] (numeric) = 0.4312471921915405347673605076998 absolute error = 1.0e-31 relative error = 2.3188556774552752183297382574709e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 0.4309933129069584185799778269894 y[1] (numeric) = 0.43099331290695841857997782698932 absolute error = 8e-32 relative error = 1.8561772910214541322885183990195e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 0.4307613341085806423240247476081 y[1] (numeric) = 0.43076133410858064232402474760809 absolute error = 1e-32 relative error = 2.3214711275546685298208220906602e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 0.4305502790024270343118016103547 y[1] (numeric) = 0.43055027900242703431180161035464 absolute error = 6e-32 relative error = 1.3935654655483750570264345567853e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 0.4303591687021656367908499264018 y[1] (numeric) = 0.43035916870216563679084992640174 absolute error = 6e-32 relative error = 1.3941843084450142055690930966603e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 0.430187022327000523403836782196 y[1] (numeric) = 0.43018702232700052340383678219589 absolute error = 1.1e-31 relative error = 2.5570273925275474820938321269548e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0.4300328570997590613832519647964 y[1] (numeric) = 0.4300328570997590613832519647963 absolute error = 1.0e-31 relative error = 2.3254037069265614484426977037248e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 0.4298956884451688098364374506391 y[1] (numeric) = 0.42989568844516880983643745063903 absolute error = 7e-32 relative error = 1.6283019783979102070507062851874e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 0.4297745300883142265130178970241 y[1] (numeric) = 0.42977453008831422651301789702404 absolute error = 6e-32 relative error = 1.3960808703035663788394339656528e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 0.4296683941532633374661023754251 y[1] (numeric) = 0.42966839415326333746610237542503 absolute error = 7e-32 relative error = 1.6291633490507774882949038898853e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 0.4295762912618545070224798438708 y[1] (numeric) = 0.42957629126185450702247984387078 absolute error = 2e-32 relative error = 4.6557504235746352398558284701503e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 0.429497230632633429467133372752 y[1] (numeric) = 0.42949723063263342946713337275193 absolute error = 7e-32 relative error = 1.6298126043069615670129627529513e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4294302201799304488253518908766 y[1] (numeric) = 0.42943022017993044882535189087657 absolute error = 3e-32 relative error = 6.9860011220053532390504908983495e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4293742666130682990930253985376 y[1] (numeric) = 0.42937426661306829909302539853754 absolute error = 6e-32 relative error = 1.3973822994396902456650916352040e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=28008432, alloc=4455632, time=1.14 x[1] = 1.48 y[1] (analytic) = 0.4293283755356903442237734593522 y[1] (numeric) = 0.42932837553569034422377345935211 absolute error = 9e-32 relative error = 2.0962974992673933350480609932254e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4292915515451993851316815154363 y[1] (numeric) = 0.42929155154519938513168151543623 absolute error = 7e-32 relative error = 1.6305934684258471316023925352389e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4292627983322970899118101485657 y[1] (numeric) = 0.42926279833229708991181014856568 absolute error = 2e-32 relative error = 4.6591505431406563050295596390306e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4292411187806140934184044850838 y[1] (numeric) = 0.42924111878061409341840448508376 absolute error = 4e-32 relative error = 9.3187717229029197052670851604818e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4292255150664208032738707298473 y[1] (numeric) = 0.42922551506642080327387072984723 absolute error = 7e-32 relative error = 1.6308443357373058523925028541972e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4292149887584089413110109929239 y[1] (numeric) = 0.42921498875840894131101099292384 absolute error = 6e-32 relative error = 1.3979008555493861087745462769129e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4292085409175338423775231929236 y[1] (numeric) = 0.42920854091753384237752319292356 absolute error = 4e-32 relative error = 9.3194790379731554021075800314714e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO 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) = 0.4292051721969075263560872253044 y[1] (numeric) = 0.4292051721969075263560872253044 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = 0.4292038829417325541760793362391 y[1] (numeric) = 0.42920388294173255417607933623905 absolute error = 5e-32 relative error = 1.1649475223127897858372150083120e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 0.4292036732892666745145914663546 y[1] (numeric) = 0.4292036732892666745145914663546 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 0.4292035432688082648053890569827 y[1] (numeric) = 0.42920354326880826480538905698268 absolute error = 2e-32 relative error = 4.6597937770224998362784526554099e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008874 Order of pole (three term test) = -0.8949 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (analytic) = 0.4292024929016925680950273462434 y[1] (numeric) = 0.42920249290169256809502734624336 absolute error = 4e-32 relative error = 9.3196103614341936289442045994422e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01851 Order of pole (three term test) = -0.9018 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 0.4291995223012887262057704629465 y[1] (numeric) = 0.42919952230128872620577046294646 absolute error = 4e-32 relative error = 9.3196748648571119128955245394513e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02814 Order of pole (three term test) = -0.9135 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = 0.429193631772987609585327609601 y[1] (numeric) = 0.42919363177298760958532760960098 absolute error = 2e-32 relative error = 4.6599013870221060338671001548356e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03776 Order of pole (three term test) = -0.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = 0.4291838219141704451437442747123 y[1] (numeric) = 0.42918382191417044514374427471229 absolute error = 1e-32 relative error = 2.3300039492168537559055532820444e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04737 Order of pole (three term test) = -0.9513 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 0.4291690937141482452979716974198 y[1] (numeric) = 0.42916909371414824529797169741976 absolute error = 4e-32 relative error = 9.3203356406280138552692958625135e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05696 Order of pole (three term test) = -0.9775 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = 0.4291484486540620443644927074566 y[1] (numeric) = 0.42914844865406204436449270745656 absolute error = 4e-32 relative error = 9.3207840143549323810932896216134e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06652 Order of pole (three term test) = -1.008 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = 0.4291208888067339523596145973413 y[1] (numeric) = 0.42912088880673395235961459734123 absolute error = 7e-32 relative error = 1.6312419606197816356456569666309e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07606 Order of pole (three term test) = -1.044 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = 0.4290854169364590411852579316506 y[1] (numeric) = 0.42908541693645904118525793165057 absolute error = 3e-32 relative error = 6.9916149129912143232658759852391e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08556 Order of pole (three term test) = -1.085 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (analytic) = 0.4290410365987280840947823424486 y[1] (numeric) = 0.42904103659872808409478234244856 absolute error = 4e-32 relative error = 9.3231175080837435713130684862058e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09503 Order of pole (three term test) = -1.13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = 0.4289867522398711762480047341728 y[1] (numeric) = 0.42898675223987117624800473417277 absolute error = 3e-32 relative error = 6.9932229476460088580628546435112e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1045 Order of pole (three term test) = -1.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 0.4289215692966122720763904698331 y[1] (numeric) = 0.42892156929661227207639046983303 absolute error = 7e-32 relative error = 1.6319999974539139409110273121303e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1139 Order of pole (three term test) = -1.235 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 0.4288444942955246840876428573349 y[1] (numeric) = 0.42884449429552468408764285733482 absolute error = 8e-32 relative error = 1.8654780710527326541348011491729e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1232 Order of pole (three term test) = -1.294 NO COMPLEX POLE (six term test) for Equation 1 bytes used=32009296, alloc=4455632, time=1.30 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = 0.4287545349523775976426897830511 y[1] (numeric) = 0.42875453495237759764268978305105 absolute error = 5e-32 relative error = 1.1661684232810172885282219967766e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1325 Order of pole (three term test) = -1.358 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 0.4286507002713636671363782803312 y[1] (numeric) = 0.42865070027136366713637828033113 absolute error = 7e-32 relative error = 1.6330312759476530527313870487702e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1417 Order of pole (three term test) = -1.427 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = 0.4285320006441977709049483513426 y[1] (numeric) = 0.42853200064419777090494835134251 absolute error = 9e-32 relative error = 2.1001932146188854336964712475544e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1509 Order of pole (three term test) = -1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = 0.4283974479490770150673773153451 y[1] (numeric) = 0.42839744794907701506737731534503 absolute error = 7e-32 relative error = 1.6339966620977816548616813781038e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1601 Order of pole (three term test) = -1.578 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 0.4282460556494920903826769439426 y[1] (numeric) = 0.42824605564949209038267694394257 absolute error = 3e-32 relative error = 7.0053184621866535774580119305864e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1691 Order of pole (three term test) = -1.661 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (analytic) = 0.4280768388928801010698001765041 y[1] (numeric) = 0.42807683889288010106980017650403 absolute error = 7e-32 relative error = 1.6352204473626396055734332664361e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1781 Order of pole (three term test) = -1.748 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = 0.4278888146091090003894858417304 y[1] (numeric) = 0.42788881460910900038948584173033 absolute error = 7e-32 relative error = 1.6359390012086991137739707600837e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.187 Order of pole (three term test) = -1.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 0.4276810016087837846265532903126 y[1] (numeric) = 0.42768100160878378462655329031256 absolute error = 4e-32 relative error = 9.3527652267774882721965400966639e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1959 Order of pole (three term test) = -1.936 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = 0.4274524206813646149351702644646 y[1] (numeric) = 0.42745242068136461493517026446454 absolute error = 6e-32 relative error = 1.4036649951440030239756947461555e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2047 Order of pole (three term test) = -2.036 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0.4272020946930870553166743065306 y[1] (numeric) = 0.42720209469308705531667430653051 absolute error = 9e-32 relative error = 2.1067312430819963311993091116237e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2133 Order of pole (three term test) = -2.141 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (analytic) = 0.426929048684674634787749850842 y[1] (numeric) = 0.4269290486846746347877498508419 absolute error = 1.0e-31 relative error = 2.3423095783266545144975693171604e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2219 Order of pole (three term test) = -2.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = 0.4266323099688339625641710448309 y[1] (numeric) = 0.42663230996883396256417104483079 absolute error = 1.1e-31 relative error = 2.5783326163936257215130812668222e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2305 Order of pole (three term test) = -2.363 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = 0.4263109082275226468298375836185 y[1] (numeric) = 0.42631090822752264682983758361845 absolute error = 5e-32 relative error = 1.1728529351473910582018739731581e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2389 Order of pole (three term test) = -2.481 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = 0.4259638756089802903802829832816 y[1] (numeric) = 0.42596387560898029038028298328152 absolute error = 8e-32 relative error = 1.8780935328289941371588555916828e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2472 Order of pole (three term test) = -2.603 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = 0.4255902468245128601219498354748 y[1] (numeric) = 0.42559024682451286012194983547473 absolute error = 7e-32 relative error = 1.6447745342449935859524196283399e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2554 Order of pole (three term test) = -2.729 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = 0.4251890592450207520709354882891 y[1] (numeric) = 0.42518905924502075207093548828905 absolute error = 5e-32 relative error = 1.1759474735493334169612906451548e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2636 Order of pole (three term test) = -2.859 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = 0.4247593529972608991251480648099 y[1] (numeric) = 0.42475935299726089912514806480982 absolute error = 8e-32 relative error = 1.8834193864241027688190008022772e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2716 Order of pole (three term test) = -2.993 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = 0.4243001710598332954793137595222 y[1] (numeric) = 0.42430017105983329547931375952217 absolute error = 3e-32 relative error = 7.0704661572642889866662761460040e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2795 Order of pole (three term test) = -3.131 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 0.4238105593588823391103824155512 y[1] (numeric) = 0.42381055935888233911038241555116 absolute error = 4e-32 relative error = 9.4381791856507382981714214099092e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2873 Order of pole (three term test) = -3.273 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 0.4232895668635034222788336950803 y[1] (numeric) = 0.42328956686350342227883369508024 absolute error = 6e-32 relative error = 1.4174693802303889985221174254793e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.295 Order of pole (three term test) = -3.419 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 0.4227362456808452294663389393975 y[1] (numeric) = 0.42273624568084522946633893939746 absolute error = 4e-32 relative error = 9.4621647442549674761136802052484e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3025 Order of pole (three term test) = -3.569 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (analytic) = 0.422149651150898232599236603159 y[1] (numeric) = 0.42214965115089823259923660315898 absolute error = 2e-32 relative error = 4.7376564082131528786652670203714e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.31 Order of pole (three term test) = -3.723 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=36010256, alloc=4455632, time=1.47 x[1] = 1.93 y[1] (analytic) = 0.4215288419409599047872890647119 y[1] (numeric) = 0.42152884194095990478728906471181 absolute error = 9e-32 relative error = 2.1350852194499555374281534847491e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3173 Order of pole (three term test) = -3.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = 0.4208728801397672061350676858407 y[1] (numeric) = 0.42087288013976720613506768584066 absolute error = 4e-32 relative error = 9.5040573739786808166200008969328e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3245 Order of pole (three term test) = -4.041 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = 0.4201808313512869284558284591307 y[1] (numeric) = 0.42018083135128692845582845913062 absolute error = 8e-32 relative error = 1.9039421608720889181869676047239e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3315 Order of pole (three term test) = -4.205 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 0.4194517647881545199315652154474 y[1] (numeric) = 0.41945176478815451993156521544738 absolute error = 2e-32 relative error = 4.7681287048824470067825467139568e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3385 Order of pole (three term test) = -4.373 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = 0.4186847533647520459146398138793 y[1] (numeric) = 0.41868475336475204591463981387924 absolute error = 6e-32 relative error = 1.4330591099344111003125323211898e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3453 Order of pole (three term test) = -4.545 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 0.4178788737899159781524738599072 y[1] (numeric) = 0.41787887378991597815247385990713 absolute error = 7e-32 relative error = 1.6751265591663227384241229565700e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3519 Order of pole (three term test) = -4.719 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = 0.4170332066592655417336357161303 y[1] (numeric) = 0.41703320665926554173363571613023 absolute error = 7e-32 relative error = 1.6785234097003953085483545770189e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3584 Order of pole (three term test) = -4.898 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0.4161468365471423869975682295008 y[1] (numeric) = 0.4161468365471423869975682295007 absolute error = 1.0e-31 relative error = 2.4029979617223809897546004014198e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3648 Order of pole (three term test) = -5.079 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 0.4152188520981523925173823401654 y[1] (numeric) = 0.41521885209815239251738234016537 absolute error = 3e-32 relative error = 7.2251054711042807175351614082125e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.371 Order of pole (three term test) = -5.263 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 0.4142483461183004450517028740902 y[1] (numeric) = 0.41424834611830044505170287409014 absolute error = 6e-32 relative error = 1.4484065069233924367079556536574e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3771 Order of pole (three term test) = -5.451 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = 0.4132344156657090830635167316961 y[1] (numeric) = 0.41323441566570908306351673169604 absolute error = 6e-32 relative error = 1.4519603819382197039308892513967e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.383 Order of pole (three term test) = -5.641 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = 0.4121761621409119320172702052914 y[1] (numeric) = 0.41217616214091193201727020529131 absolute error = 9e-32 relative error = 2.1835323889796281630828398908724e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3888 Order of pole (three term test) = -5.835 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = 0.4110726913767129021859299941674 y[1] (numeric) = 0.41107269137671290218592999416735 absolute error = 5e-32 relative error = 1.2163298863893462542924965598861e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3944 Order of pole (three term test) = -6.031 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = 0.4099231137276021631231096264879 y[1] (numeric) = 0.40992311372760216312310962648785 absolute error = 5e-32 relative error = 1.2197409300814756957188814753382e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3999 Order of pole (three term test) = -6.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = 0.4087265441587199532773271390117 y[1] (numeric) = 0.40872654415871995327732713901168 absolute error = 2e-32 relative error = 4.8932471565226848588094282943864e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4052 Order of pole (three term test) = -6.432 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 0.4074821023343593284415688497724 y[1] (numeric) = 0.4074821023343593284415688497723 absolute error = 1.0e-31 relative error = 2.4540955155361652460845067855160e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4103 Order of pole (three term test) = -6.636 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = 0.4061889127059989988370663118704 y[1] (numeric) = 0.4061889127059989988370663118704 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 = 0.4153 Order of pole (three term test) = -6.843 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 0.4048461045998574516209385237192 y[1] (numeric) = 0.40484610459985745162093852371912 absolute error = 8e-32 relative error = 1.9760595221502884236515672750757e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4201 Order of pole (three term test) = -7.053 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = 0.4034528123039596034784101570717 y[1] (numeric) = 0.40345281230395960347841015707164 absolute error = 6e-32 relative error = 1.4871627652652538596313401702366e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4247 Order of pole (three term test) = -7.265 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = 0.4020081751547072767069018829839 y[1] (numeric) = 0.40200817515470727670690188298384 absolute error = 6e-32 relative error = 1.4925069615041990440109645080858e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4292 Order of pole (three term test) = -7.479 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 0.4005113376229448418165262096097 y[1] (numeric) = 0.40051133762294484181652620960967 absolute error = 3e-32 relative error = 7.4904246601485805005942576540935e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4335 Order of pole (three term test) = -7.695 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = 0.3989614493995114201544499120086 y[1] (numeric) = 0.39896144939951142015444991200855 absolute error = 5e-32 relative error = 1.2532539190254212932639112344712e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4376 Order of pole (three term test) = -7.913 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=40011404, alloc=4455632, time=1.64 x[1] = 2.15 y[1] (analytic) = 0.397357665480271091404153882264 y[1] (numeric) = 0.39735766548027109140415388226398 absolute error = 2e-32 relative error = 5.0332488177437727217204456503726e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4415 Order of pole (three term test) = -8.133 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 0.3956991462506126030096987439834 y[1] (numeric) = 0.39569914625061260300969874398332 absolute error = 8e-32 relative error = 2.0217379986292085087287888777691e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4453 Order of pole (three term test) = -8.356 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 0.3939850575694101316244699944165 y[1] (numeric) = 0.39398505756941013162446999441646 absolute error = 4e-32 relative error = 1.0152669303442559842027348529979e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4489 Order of pole (three term test) = -8.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 0.3922145708524367005782248676625 y[1] (numeric) = 0.39221457085243670057822486766244 absolute error = 6e-32 relative error = 1.5297748849461756212907860494959e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4523 Order of pole (three term test) = -8.806 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 0.390386863155221912090205163797 y[1] (numeric) = 0.3903868631552219120902051637969 absolute error = 1.0e-31 relative error = 2.5615616056280805474685076488349e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4555 Order of pole (three term test) = -9.033 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 0.3885011172553457085241426126549 y[1] (numeric) = 0.38850111725534570852414261265488 absolute error = 2e-32 relative error = 5.1479903433211564184748924015970e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.83 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4586 Order of pole (three term test) = -9.262 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = 0.3865565217341599333776091775186 y[1] (numeric) = 0.38655652173415993337760917751859 absolute error = 1e-32 relative error = 2.5869438071147414608406587002201e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.12 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4615 Order of pole (three term test) = -9.493 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = 0.3845522710579295199177144375002 y[1] (numeric) = 0.38455227105792951991771443750011 absolute error = 9e-32 relative error = 2.3403840459036651373662607495936e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4641 Order of pole (three term test) = -9.725 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = 0.3824875656583851934119039106856 y[1] (numeric) = 0.38248756565838519341190391068559 absolute error = 1e-32 relative error = 2.6144640761816023052532468235415e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4666 Order of pole (three term test) = -9.958 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 0.3803616120126796317507622663104 y[1] (numeric) = 0.3803616120126796317507622663104 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4689 Order of pole (three term test) = -10.19 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 0.3781736227227390889133890573964 y[1] (numeric) = 0.37817362272273908891338905739636 absolute error = 4e-32 relative error = 1.0577152291059260050299501524257e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.34 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4711 Order of pole (three term test) = -10.43 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 0.3759228165940025461791265687448 y[1] (numeric) = 0.3759228165940025461791265687448 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.473 Order of pole (three term test) = -10.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = 0.3736084187135405172361343481243 y[1] (numeric) = 0.37360841871354051723613434812426 absolute error = 4e-32 relative error = 1.0706396857365649744701392088148e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4747 Order of pole (three term test) = -10.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = 0.3712296605275456953713983504607 y[1] (numeric) = 0.37122966052754569537139835046065 absolute error = 5e-32 relative error = 1.3468751373192050955855529073967e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = -11.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 0.368785779918187693742031018189 y[1] (numeric) = 0.3687857799181876937420310181889 absolute error = 1.0e-31 relative error = 2.7116012993284132483366434720788e-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 = 0.4776 Order of pole (three term test) = -11.38 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 0.366276021279824193317880571166 y[1] (numeric) = 0.36627602127982419331788057116597 absolute error = 3e-32 relative error = 8.1905443591899441646914604364461e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4788 Order of pole (three term test) = -11.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = 0.363699635594560877444164323471 y[1] (numeric) = 0.36369963559456087744416432347099 absolute error = 1e-32 relative error = 2.7495215890586253446683572123640e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4798 Order of pole (three term test) = -11.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 0.3610558805071525970936361660082 y[1] (numeric) = 0.36105588050715259709363616600818 absolute error = 2e-32 relative error = 5.5393087551730917073292082154673e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4806 Order of pole (three term test) = -12.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = 0.358344020399238276754180427816 y[1] (numeric) = 0.35834402039923827675418042781595 absolute error = 5e-32 relative error = 1.3953072230504640449327768195660e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -12.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 0.3555633264629021375231055720614 y[1] (numeric) = 0.3555633264629021375231055720613 absolute error = 1.0e-31 relative error = 2.8124385322521035022834599053856e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -12.58 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 0.3527130767735538813471291122589 y[1] (numeric) = 0.35271307677355388134712911225887 absolute error = 3e-32 relative error = 8.5054969536217019035034297392716e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = 0.3497925563621205484503630346451 y[1] (numeric) = 0.34979255636212054845036303464505 absolute error = 5e-32 relative error = 1.4294186394360494576169483813085e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = 0.3468010572865428288247166088224 y[1] (numeric) = 0.3468010572865428288247166088223 bytes used=44012204, alloc=4455632, time=1.80 absolute error = 1.0e-31 relative error = 2.8834975528167275865792623242474e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -13.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = 0.3437378787025686782111476073675 y[1] (numeric) = 0.34373787870256867821114760736748 absolute error = 2e-32 relative error = 5.8183869858886588751306068983702e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.07 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -13.55 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 0.3406023269338371592691582926181 y[1] (numeric) = 0.34060232693383715926915829261801 absolute error = 9e-32 relative error = 2.6423777197941082070923791971943e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4807 Order of pole (three term test) = -13.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 0.3373937155412454996088222273348 y[1] (numeric) = 0.33739371554124549960882222733473 absolute error = 7e-32 relative error = 2.0747274408388523471192763657496e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4799 Order of pole (three term test) = -14.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 0.334111365391592430037344395568 y[1] (numeric) = 0.3341113653915924300373443955679 absolute error = 1.0e-31 relative error = 2.9930140174308598205823227427816e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.96 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.479 Order of pole (three term test) = -14.27 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = 0.3307546047254909387435325689107 y[1] (numeric) = 0.33075460472549093874353256891069 absolute error = 1e-32 relative error = 3.0233895030122039095556589628512e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4779 Order of pole (three term test) = -14.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 0.3273227692245436502013552441779 y[1] (numeric) = 0.32732276922454365020135524417785 absolute error = 5e-32 relative error = 1.5275442071584077546426840772550e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4765 Order of pole (three term test) = -14.75 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = 0.3238152020777741113106750925374 y[1] (numeric) = 0.32381520207777411131067509253735 absolute error = 5e-32 relative error = 1.5440905701515203357354170475968e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.475 Order of pole (three term test) = -14.99 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = 0.3202312540473073417019030673365 y[1] (numeric) = 0.32023125404730734170190306733644 absolute error = 6e-32 relative error = 1.8736459743287979931653780762234e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4733 Order of pole (three term test) = -15.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = 0.3165702835332930802042763146862 y[1] (numeric) = 0.31657028353329308020427631468615 absolute error = 5e-32 relative error = 1.5794280954593009793384037105888e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.23 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4714 Order of pole (three term test) = -15.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = 0.3128316566380652352072155840616 y[1] (numeric) = 0.3128316566380652352072155840615 absolute error = 1.0e-31 relative error = 3.1966074365580058947981961922107e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4693 Order of pole (three term test) = -15.7 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = 0.3090147472295311230231920335903 y[1] (numeric) = 0.30901474722953112302319203359028 absolute error = 2e-32 relative error = 6.4721830201664536190227813557779e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.467 Order of pole (three term test) = -15.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = 0.3051189370037841553810913325716 y[1] (numeric) = 0.30511893700378415538109133257152 absolute error = 8e-32 relative error = 2.6219283793259879363519724314459e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4646 Order of pole (three term test) = -16.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 0.3011436155469337148335027904674 y[1] (numeric) = 0.3011436155469337148335027904673 absolute error = 1.0e-31 relative error = 3.3206747491020555880615396829046e-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 = 0.4619 Order of pole (three term test) = -16.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = 0.2970881803961460351419175078784 y[1] (numeric) = 0.29708818039614603514191750787836 absolute error = 4e-32 relative error = 1.3464015951985311107070934416683e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4591 Order of pole (three term test) = -16.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 0.2929520370998899826026642604518 y[1] (numeric) = 0.2929520370998899826026642604518 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 = 0.4561 Order of pole (three term test) = -16.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = 0.288734599277381713785655172555 y[1] (numeric) = 0.28873459927738171378565517255494 absolute error = 6e-32 relative error = 2.0780329115444584100321255398755e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4529 Order of pole (three term test) = -17.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 0.2844352886772222652697043558066 y[1] (numeric) = 0.28443528867722226526970435580651 absolute error = 9e-32 relative error = 3.1641643488945628010684280014190e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4495 Order of pole (three term test) = -17.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = 0.2800535352352222116643104758323 y[1] (numeric) = 0.28005353523522221166431047583223 absolute error = 7e-32 relative error = 2.4995220982018915917527454920209e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.446 Order of pole (three term test) = -17.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = 0.2755887771314076095002881233824 y[1] (numeric) = 0.27558877713140760950028812338239 absolute error = 1e-32 relative error = 3.6285947868014053171012101593521e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4422 Order of pole (three term test) = -17.76 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 0.2710404608462015264423637215671 y[1] (numeric) = 0.27104046084620152644236372156707 absolute error = 3e-32 relative error = 1.1068458157995503001067707443303e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4383 Order of pole (three term test) = -17.98 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = 0.2664080412157755377176324945692 y[1] (numeric) = 0.26640804121577553771763249456918 absolute error = 2e-32 relative error = 7.5072809021560742850849606753346e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4342 Order of pole (three term test) = -18.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = 0.2616909814865656546563597454083 y[1] (numeric) = 0.26169098148656565465635974540826 absolute error = 4e-32 relative error = 1.5285203858679198340220367664097e-29 % Correct digits = 31 h = 0.01 bytes used=48013260, alloc=4455632, time=1.97 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.43 Order of pole (three term test) = -18.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 0.2568887533689472337977021516452 y[1] (numeric) = 0.25688875336894723379770215164515 absolute error = 5e-32 relative error = 1.9463678087996829545529466354954e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4255 Order of pole (three term test) = -18.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = 0.2520008370900634991141674487226 y[1] (numeric) = 0.2520008370900634991141674487226 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 = 0.4209 Order of pole (three term test) = -18.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = 0.2470267214458023945466136767484 y[1] (numeric) = 0.2470267214458023945466136767483 absolute error = 1.0e-31 relative error = 4.0481450514631866185265307877401e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4161 Order of pole (three term test) = -19.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = 0.2419659038519165692078483901949 y[1] (numeric) = 0.24196590385191656920784839019488 absolute error = 2e-32 relative error = 8.2656273803932411077974685536160e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4112 Order of pole (three term test) = -19.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = 0.236817890394281383298907316266 y[1] (numeric) = 0.23681789039428138329890731626594 absolute error = 6e-32 relative error = 2.5335923692295869030190351571857e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4061 Order of pole (three term test) = -19.46 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = 0.2315821958782859089793023660538 y[1] (numeric) = 0.23158219587828590897930236605376 absolute error = 4e-32 relative error = 1.7272484980245652429339827633388e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4008 Order of pole (three term test) = -19.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = 0.2262583438773519871323110038826 y[1] (numeric) = 0.22625834387735198713231100388254 absolute error = 6e-32 relative error = 2.6518359045589160864067034308684e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3954 Order of pole (three term test) = -19.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 0.2208458667805764881600628584297 y[1] (numeric) = 0.22084586678057648816006285842969 absolute error = 1e-32 relative error = 4.5280448965502239304752531772373e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3898 Order of pole (three term test) = -20.06 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 0.2153443058394920126220458186207 y[1] (numeric) = 0.21534430583949201262204581862061 absolute error = 9e-32 relative error = 4.1793536006975714277245536016126e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3841 Order of pole (three term test) = -20.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = 0.2097532112139413556859348843289 y[1] (numeric) = 0.20975321121394135568593488432882 absolute error = 8e-32 relative error = 3.8140059709695046908079693628289e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3782 Order of pole (three term test) = -20.44 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 0.2040721420170611479825272819433 y[1] (numeric) = 0.20407214201706114798252728194328 absolute error = 2e-32 relative error = 9.8004557615355111721041793984088e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3722 Order of pole (three term test) = -20.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = 0.1983006663593701745381845937161 y[1] (numeric) = 0.19830066635937017453818459371603 absolute error = 7e-32 relative error = 3.5299931808167791755740883881645e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.366 Order of pole (three term test) = -20.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = 0.1924383613919579629896287999871 y[1] (numeric) = 0.19243836139195796298962879998702 absolute error = 8e-32 relative error = 4.1571752857038833500804850301628e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3596 Order of pole (three term test) = -21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 0.1864848133487693222582611248928 y[1] (numeric) = 0.18648481334876932225826112489274 absolute error = 6e-32 relative error = 3.2174201707131108185218789412739e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3532 Order of pole (three term test) = -21.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = 0.1804396175879806032653732517793 y[1] (numeric) = 0.18043961758798060326537325177923 absolute error = 7e-32 relative error = 3.8794141184581418520344985212835e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3465 Order of pole (three term test) = -21.35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = 0.1743023786324635440966594895267 y[1] (numeric) = 0.17430237863246354409665948952667 absolute error = 3e-32 relative error = 1.7211469077687358161090552180450e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3398 Order of pole (three term test) = -21.52 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 0.1680727102093326532652331971401 y[1] (numeric) = 0.16807271020933265326523319714006 absolute error = 4e-32 relative error = 2.3799223532589231126639893781862e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3329 Order of pole (three term test) = -21.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = 0.1617502352885721763677772078291 y[1] (numeric) = 0.16175023528857217636777720782903 absolute error = 7e-32 relative error = 4.3276598562664083715101906476794e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3258 Order of pole (three term test) = -21.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 0.1553345861207387834693516691176 y[1] (numeric) = 0.15533458612073878346935166911755 absolute error = 5e-32 relative error = 3.2188581595817880613638656793052e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3187 Order of pole (three term test) = -22.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 0.1488254042737362069795396196241 y[1] (numeric) = 0.14882540427373620697953961962405 absolute error = 5e-32 relative error = 3.3596414700835919596640443618781e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3114 Order of pole (three term test) = -22.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 0.1422223406686581525867881173662 y[1] (numeric) = 0.14222234066865815258678811736611 absolute error = 9e-32 relative error = 6.3281197297741771942522801781255e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.304 Order of pole (three term test) = -22.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = 0.1355250556146958989897204783588 y[1] (numeric) = 0.13552505561469589898972047835879 absolute error = 1e-32 relative error = 7.3787093867206886589777604273651e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2965 Order of pole (three term test) = -22.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=52014652, alloc=4455632, time=2.14 x[1] = 2.82 y[1] (analytic) = 0.12873321884310709569453606376 y[1] (numeric) = 0.12873321884310709569453606375999 absolute error = 1e-32 relative error = 7.7680027656167326519698481109811e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2888 Order of pole (three term test) = -22.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = 0.1218465095402423620270251127245 y[1] (numeric) = 0.12184650954024236202702511272448 absolute error = 2e-32 relative error = 1.6414093498012416244944179857052e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.281 Order of pole (three term test) = -22.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = 0.1148646163796263847268194935862 y[1] (numeric) = 0.11486461637962638472681949358619 absolute error = 1e-32 relative error = 8.7059011862714119626435241173836e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2732 Order of pole (three term test) = -22.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 0.1077872375530903060408541071749 y[1] (numeric) = 0.10778723755309030604085410717488 absolute error = 2e-32 relative error = 1.8555072431603097036381293193752e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2652 Order of pole (three term test) = -23.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = 0.1006140808009522891031731663928 y[1] (numeric) = 0.10061408080095228910317316639272 absolute error = 8e-32 relative error = 7.9511733708790011053946961438090e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2571 Order of pole (three term test) = -23.17 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 0.0933448634412432425696937587379 y[1] (numeric) = 0.09334486344124324256969375873789 absolute error = 1.0e-32 relative error = 1.0712962268453677961268388894773e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2489 Order of pole (three term test) = -23.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = 0.0859793123979747819598179047655 y[1] (numeric) = 0.085979312397974781959817904765478 absolute error = 2.2e-32 relative error = 2.5587550523977211626610187598430e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2406 Order of pole (three term test) = -23.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = 0.0785171642284466009323155072093 y[1] (numeric) = 0.078517164228446600932315507209236 absolute error = 6.4e-32 relative error = 8.1510839863996179153029399388928e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2322 Order of pole (three term test) = -23.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 0.0709581651495905217811066693455 y[1] (numeric) = 0.070958165149590521781106669345485 absolute error = 1.5e-32 relative error = 2.1139216280998439101148941391699e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2237 Order of pole (three term test) = -23.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = 0.0633020710633485907678471066028 y[1] (numeric) = 0.063302071063348590767847106602705 absolute error = 9.5e-32 relative error = 1.5007407878476864679833374769290e-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 = 0.2151 Order of pole (three term test) = -23.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = 0.0555486475810826805029317351583 y[1] (numeric) = 0.055548647581082680502931735158218 absolute error = 8.2e-32 relative error = 1.4761835538895358439877848266890e-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 = 0.2065 Order of pole (three term test) = -23.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = 0.0476976700470131584350196046763 y[1] (numeric) = 0.047697670047013158435019604676278 absolute error = 2.2e-32 relative error = 4.6123846255625742480749714097407e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1977 Order of pole (three term test) = -23.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = 0.0397489235606842776017633813283 y[1] (numeric) = 0.039748923560684277601763381328274 absolute error = 2.6e-32 relative error = 6.5410576365183988586856498704531e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1889 Order of pole (three term test) = -24.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 0.031702202998454043121389404702 y[1] (numeric) = 0.031702202998454043121389404701921 absolute error = 7.9e-32 relative error = 2.4919403867249361939277520267643e-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 = 0.18 Order of pole (three term test) = -24.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 0.0235573130340064054563873229762 y[1] (numeric) = 0.023557313034006405456387322976111 absolute error = 8.9e-32 relative error = 3.7780200089680482554478297640419e-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 = 0.1711 Order of pole (three term test) = -24.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = 0.0153140681578837292470763748061 y[1] (numeric) = 0.015314068157883729247076374806096 absolute error = 4e-33 relative error = 2.6119774045414495130814691184547e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.162 Order of pole (three term test) = -24.33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 0.0069722926960375844844419643954 y[1] (numeric) = 0.0069722926960375844844419643953548 absolute error = 4.52e-32 relative error = 6.4828029990318047301241079468969e-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 = 0.1529 Order of pole (three term test) = -24.41 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = -0.0014681791726039950414158127892 y[1] (numeric) = -0.0014681791726039950414158127892073 absolute error = 7.3e-33 relative error = 4.9721451824252203494790109983734e-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 = 0.1438 Order of pole (three term test) = -24.49 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = -0.0100075033995545427284272052687 y[1] (numeric) = -0.010007503399554542728427205268786 absolute error = 8.6e-32 relative error = 8.5935519146391756598368313718463e-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 = 0.1345 Order of pole (three term test) = -24.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = -0.0186458260511741377683744258176 y[1] (numeric) = -0.01864582605117413776837442581763 absolute error = 3.0e-32 relative error = 1.6089391758597299445795199207813e-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 = 0.1253 Order of pole (three term test) = -24.62 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = -0.027383283294062890860533466737 y[1] (numeric) = -0.027383283294062890860533466737011 absolute error = 1.1e-32 relative error = 4.0170493369525801287718168196055e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1159 Order of pole (three term test) = -24.68 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = -0.0362200013814443976723926912916 y[1] (numeric) = -0.03622000138144439767239269129162 absolute error = 2.0e-32 relative error = 5.5218109434545888227098046895603e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1066 Order of pole (three term test) = -24.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=56015980, alloc=4455632, time=2.31 x[1] = 3.04 y[1] (analytic) = -0.0451560966405405216907550451568 y[1] (numeric) = -0.045156096640540521690755045156862 absolute error = 6.2e-32 relative error = 1.3730150436505456018789735445771e-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 = 0.09716 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = -0.0541916754609387689744177984351 y[1] (numeric) = -0.05419167546093876897441779843513 absolute error = 3.0e-32 relative error = 5.5359056063184333140653685140977e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08771 Order of pole (three term test) = -24.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = -0.0633268342839534180612607282068 y[1] (numeric) = -0.063326834283953418061260728206895 absolute error = 9.5e-32 relative error = 1.5001539406505962533069871661187e-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 = 0.07822 Order of pole (three term test) = -24.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = -0.0725616595929814689078863372732 y[1] (numeric) = -0.072561659592981468907886337273277 absolute error = 7.7e-32 relative error = 1.0611664676898849464489079296756e-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 = 0.06871 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = -0.0818962279048543752588814626402 y[1] (numeric) = -0.081896227904854375258881462640253 absolute error = 5.3e-32 relative error = 6.4716045361178888076065378290814e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05916 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = -0.0913306057621864252652564819142 y[1] (numeric) = -0.091330605762186425265256481914289 absolute error = 8.9e-32 relative error = 9.7448165658448566809894210437354e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04959 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = -0.1008648497267205355076239454585 y[1] (numeric) = -0.10086484972672053550762394545858 absolute error = 8e-32 relative error = 7.9314052632556354668104199415439e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04001 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = -0.1104990063736721238391691632832 y[1] (numeric) = -0.11049900637367212383916916328321 absolute error = 1e-32 relative error = 9.0498551327993069194674628190650e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0304 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = -0.1202331122870716266564150260244 y[1] (numeric) = -0.12023311228707162665641502602445 absolute error = 5e-32 relative error = 4.1585881833133232517686014487989e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02079 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = -0.1300671940561061263421727608608 y[1] (numeric) = -0.13006719405610612634217276086083 absolute error = 3e-32 relative error = 2.3065001300065811544886011726131e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01116 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = -0.140001268272460454714885693655 y[1] (numeric) = -0.14000126827246045471488569365499 absolute error = 1e-32 relative error = 7.1427924356647364439923500669696e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001534 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = -0.1500353415286580383718053432053 y[1] (numeric) = -0.15003534152865803837180534320532 absolute error = 2e-32 relative error = 1.3330192604107098518837596529979e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (analytic) = -0.160169410417401651840082905726 y[1] (numeric) = -0.16016941041740165184008290572609 absolute error = 9e-32 relative error = 5.6190504644713310385352692548079e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (analytic) = -0.1704034615319141444599116498647 y[1] (numeric) = -0.17040346153191414445991164986476 absolute error = 6e-32 relative error = 3.5210552333036294255854658983897e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = -0.1807374714672791069273158461397 y[1] (numeric) = -0.18073747146727910692731584613973 absolute error = 3e-32 relative error = 1.6598660895525048928839412956076e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = -0.1911714068227813434310491703005 y[1] (numeric) = -0.19117140682278134343104917030056 absolute error = 6e-32 relative error = 3.1385446703136346642812699908770e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = -0.2017052242052469153383392777164 y[1] (numeric) = -0.20170522420524691533833927771646 absolute error = 6e-32 relative error = 2.9746378774476597165638255273052e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = -0.2123388702333824224278933347958 y[1] (numeric) = -0.2123388702333824224278933347958 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = -0.2230722815431130877456572625241 y[1] (numeric) = -0.22307228154311308774565726252418 absolute error = 8e-32 relative error = 3.5862815158654497839341107263930e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (analytic) = -0.233905384793919112279291505415 y[1] (numeric) = -0.2339053847939191122792915054151 absolute error = 1.0e-31 relative error = 4.2752329147148270839391901792863e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (analytic) = -0.2448380966761696658211761562575 y[1] (numeric) = -0.24483809667616966582117615625757 absolute error = 7e-32 relative error = 2.8590321910803013220019796335742e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = -0.2558703239194537806269707748284 y[1] (numeric) = -0.25587032391945378062697077482844 absolute error = 4e-32 relative error = 1.5632918811089528725491325053395e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = -0.2670019633019073147873054328283 y[1] (numeric) = -0.26700196330190731478730543282838 absolute error = 8e-32 relative error = 2.9962326497779922547890534379932e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO 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=60017300, alloc=4521156, time=2.48 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = -0.2782329016605350526240382595053 y[1] (numeric) = -0.2782329016605350526240382595053 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (analytic) = -0.2895630159025269099096415838683 y[1] (numeric) = -0.28956301590252690990964158386833 absolute error = 3e-32 relative error = 1.0360439128075195958404259653322e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = -0.3009921730175671122986248744605 y[1] (numeric) = -0.30099217301756711229862487446056 absolute error = 6e-32 relative error = 1.9934073168240876144259430920296e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = -0.3125202300911351160634089488972 y[1] (numeric) = -0.31252023009113511606340894889719 absolute error = 1e-32 relative error = 3.1997928572764281741801027489061e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = -0.3241470343187969410536619294145 y[1] (numeric) = -0.32414703431879694105366192941451 absolute error = 1e-32 relative error = 3.0850197414316157011063128906887e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = -0.3358724230214854867577104152688 y[1] (numeric) = -0.33587242302148548675771041526884 absolute error = 4e-32 relative error = 1.1909283781074587481175572804932e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (analytic) = -0.3476962236617683034471532851407 y[1] (numeric) = -0.34769622366176830344715328514077 absolute error = 7e-32 relative error = 2.0132516615450662043204279664245e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = -0.3596182538611011916411200989301 y[1] (numeric) = -0.35961825386110119164112009893012 absolute error = 2e-32 relative error = 5.5614529533099818341221628225524e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = -0.3716383214180659045446056247285 y[1] (numeric) = -0.3716383214180659045446056247285 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = -0.3837562243275901297058346922217 y[1] (numeric) = -0.38375622432759012970583469222171 absolute error = 1e-32 relative error = 2.6058209264284369879591321136608e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = -0.3959717508011478279105082340292 y[1] (numeric) = -0.39597175080114782791050823402918 absolute error = 2e-32 relative error = 5.0508653608584708052526746157886e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = -0.4082846792879379092958746500094 y[1] (numeric) = -0.40828467928793790929587465000946 absolute error = 6e-32 relative error = 1.4695628575787364855047803969858e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (analytic) = -0.4206947784970391288346639253275 y[1] (numeric) = -0.42069477849703912883466392532756 absolute error = 6e-32 relative error = 1.4262121392225048269732118717962e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = -0.4332018074205389857177984602343 y[1] (numeric) = -0.43320180742053898571779846023434 absolute error = 4e-32 relative error = 9.2335718168343722388859369484583e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = -0.445805515357634313765216359047 y[1] (numeric) = -0.44580551535763431376521635904707 absolute error = 7e-32 relative error = 1.5701914307597690108885413230013e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (analytic) = -0.4585056419397011528258498543986 y[1] (numeric) = -0.45850564193970115282584985439862 absolute error = 2e-32 relative error = 4.3619964882853575869875520376383e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = -0.4713019171563313942005103587744 y[1] (numeric) = -0.47130191715633139420051035877447 absolute error = 7e-32 relative error = 1.4852475123028391706475012931769e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = -0.4841940613823335964448349870275 y[1] (numeric) = -0.48419406138233359644483498702754 absolute error = 4e-32 relative error = 8.2611504746265044094873626465198e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (analytic) = -0.4971817854056952714932148600522 y[1] (numeric) = -0.49718178540569527149321486005228 absolute error = 8e-32 relative error = 1.6090694057651531835115002756588e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = -0.510264790456503844898394624218 y[1] (numeric) = -0.510264790456503844898394624218 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (analytic) = -0.5234427682368233981148199464733 y[1] (numeric) = -0.52344276823682339811481994647335 absolute error = 5e-32 relative error = 9.5521426666034845559608632497757e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = -0.5367154009515242051764018526177 y[1] (numeric) = -0.53671540095152420517640185261775 absolute error = 5e-32 relative error = 9.3159242144638902039118890239370e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=64019308, alloc=4521156, time=2.65 x[1] = 3.49 y[1] (analytic) = -0.5500823613400619808407213272332 y[1] (numeric) = -0.55008236134006198084072132723326 absolute error = 6e-32 relative error = 1.0907457540327835349187017981835e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (analytic) = -0.5635433127092036623013423733282 y[1] (numeric) = -0.56354331270920366230134237332827 absolute error = 7e-32 relative error = 1.2421405492947618786524677576335e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (analytic) = -0.5770979089666964519173336942424 y[1] (numeric) = -0.57709790896669645191733369424245 absolute error = 5e-32 relative error = 8.6640410965144275184819031114097e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = -0.5907457946558767540837834877278 y[1] (numeric) = -0.59074579465587675408378348772779 absolute error = 1e-32 relative error = 1.6927754865906805059069236622072e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = -0.604486604991215545378460985316 y[1] (numeric) = -0.60448660499121554537846098531601 absolute error = 1e-32 relative error = 1.6542963760372028284164795514243e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = -0.6183199658947966234772311138702 y[1] (numeric) = -0.61831996589479662347723111387026 absolute error = 6e-32 relative error = 9.7037138228540778820247810258349e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = -0.6322454940337240870437291772895 y[1] (numeric) = -0.63224549403372408704372917728955 absolute error = 5e-32 relative error = 7.9083204976282505718708645078196e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (analytic) = -0.6462627968584553058764793868963 y[1] (numeric) = -0.64626279685845530587647938689636 absolute error = 6e-32 relative error = 9.2841488465165696497262932724068e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = -0.6603714726420555480483865639633 y[1] (numeric) = -0.66037147264205554804838656396328 absolute error = 2e-32 relative error = 3.0285984220340026746680535994075e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = -0.674571110520370338608599145451 y[1] (numeric) = -0.674571110520370338608599145451 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = -0.6888612905331115326443501606522 y[1] (numeric) = -0.68886129053311153264435016065218 absolute error = 2e-32 relative error = 2.9033421205192047187600121574191e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = -0.7032415836658529941297082747341 y[1] (numeric) = -0.70324158366585299412970827473408 absolute error = 2e-32 relative error = 2.8439728913276337572401084972268e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = -0.7177115518929316810283503064616 y[1] (numeric) = -0.7177115518929316810283503064616 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = -0.732270748221249846577595727932 y[1] (numeric) = -0.73227074822124984657759572793202 absolute error = 2e-32 relative error = 2.7312302244192823224438584799313e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = -0.746918716734973976570076455602 y[1] (numeric) = -0.74691871673497397657007645560201 absolute error = 1e-32 relative error = 1.3388337681124488270074274874001e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = -0.7616549926411259927765627558659 y[1] (numeric) = -0.76165499264112599277656275586593 absolute error = 3e-32 relative error = 3.9387912230407052420243521864590e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = -0.7764791023160621634275955254717 y[1] (numeric) = -0.77647910231606216342759552547175 absolute error = 5e-32 relative error = 6.4393233315437941262487144896753e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = -0.7913905633528350729016090798401 y[1] (numeric) = -0.7913905633528350729016090798401 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = -0.8063888846094339144620438135202 y[1] (numeric) = -0.80638888460943391446204381352022 absolute error = 2e-32 relative error = 2.4801929170547523593322339543679e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (analytic) = -0.8214735662578982820543751314638 y[1] (numeric) = -0.82147356625789828205437513146387 absolute error = 7e-32 relative error = 8.5212723665442674703799462699580e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = -0.8366440998343005498248069716278 y[1] (numeric) = -0.83664409983430054982480697162787 absolute error = 7e-32 relative error = 8.3667595353703772664612408071827e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = -0.8518999682895918411643298936456 y[1] (numeric) = -0.85189996828959184116432989364563 absolute error = 3e-32 relative error = 3.5215402179475028276446033219075e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = -0.8672406460413065027236108273902 y[1] (numeric) = -0.86724064604130650272361082739029 absolute error = 9e-32 relative error = 1.0377742372987591446913405581965e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO 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=68020160, alloc=4521156, time=2.81 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = -0.8826655990261199129943999105103 y[1] (numeric) = -0.88266559902611991299439991051037 absolute error = 7e-32 relative error = 7.9305231876300363489514814703110e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = -0.8981742847532543697203943020784 y[1] (numeric) = -0.89817428475325436972039430207841 absolute error = 1e-32 relative error = 1.1133696621861302776334866835528e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (analytic) = -0.9137661523587277155933226437975 y[1] (numeric) = -0.9137661523587277155933226437975 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = -0.9294406426604392774168875977093 y[1] (numeric) = -0.92944064266043927741688759770932 absolute error = 2e-32 relative error = 2.1518318741422604068984305519930e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = -0.9451971882140876101905548624369 y[1] (numeric) = -0.94519718821408761019055486243694 absolute error = 4e-32 relative error = 4.2319211799157385009878450724463e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = -0.9610352133699144543853782538038 y[1] (numeric) = -0.96103521336991445438537825380382 absolute error = 2e-32 relative error = 2.0810891964997905080398700880350e-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 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = -0.9769541343302692320634197407623 y[1] (numeric) = -0.97695413433026923206341974076232 absolute error = 2e-32 relative error = 2.0471790125245324563386030179976e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = -0.9929533592079883254391227481598 y[1] (numeric) = -0.99295335920798832543912274815988 absolute error = 8e-32 relative error = 8.0567731865886011232866094824093e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = -1.0090322880855833000034318256493 y[1] (numeric) = -1.0090322880855833000034318256493 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = -1.025190313075232153437669625635 y[1] (numeric) = -1.0251903130752321534376696256351 absolute error = 1e-31 relative error = 9.7542864699953168828023519408051e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = -1.0414268183795675912422723433438 y[1] (numeric) = -1.0414268183795675912422723433439 absolute error = 1e-31 relative error = 9.6022109508949786990876429426039e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = -1.0577411803532562503034774729765 y[1] (numeric) = -1.0577411803532562503034774729766 absolute error = 1e-31 relative error = 9.4541086096886925047009608042986e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = -1.0741327675653627125269230597523 y[1] (numeric) = -1.0741327675653627125269230597524 absolute error = 1e-31 relative error = 9.3098360854087656908545545604140e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = -1.0906009408624920721887649260472 y[1] (numeric) = -1.0906009408624920721887649260473 absolute error = 1e-31 relative error = 9.1692567146435696046221277276597e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = -1.1071450534327047428001953906352 y[1] (numeric) = -1.1071450534327047428001953906353 absolute error = 1e-31 relative error = 9.0322401468488581598243078491540e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = -1.1237644508701971120579391906727 y[1] (numeric) = -1.1237644508701971120579391906729 absolute error = 2e-31 relative error = 1.7797323971685365271592158677858e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = -1.1404584712407415768691319229587 y[1] (numeric) = -1.1404584712407415768691319229589 absolute error = 2e-31 relative error = 1.7536806910856959605178648649884e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = -1.1572264451478794145016116973683 y[1] (numeric) = -1.1572264451478794145016116973685 absolute error = 2e-31 relative error = 1.7282702174546524575336963248517e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = -1.1740676957998598706276695153856 y[1] (numeric) = -1.1740676957998598706276695153858 absolute error = 2e-31 relative error = 1.7034792858664382881175823645110e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = -1.1909815390773187704082363861256 y[1] (numeric) = -1.1909815390773187704082363861258 absolute error = 2e-31 relative error = 1.6792871546518233495808830678029e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = -1.2079672836016898848127974157074 y[1] (numeric) = -1.2079672836016898848127974157076 absolute error = 2e-31 relative error = 1.6556739798753288865036814873082e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = -1.225024230804342211095410160473 y[1] (numeric) = -1.2250242308043422110954101604732 absolute error = 2e-31 relative error = 1.6326207675800944785592861931395e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=72020992, alloc=4521156, time=2.98 x[1] = 3.94 y[1] (analytic) = -1.2421516749964362537563938505644 y[1] (numeric) = -1.2421516749964362537563938505646 absolute error = 2e-31 relative error = 1.6101093290444888874566606488806e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = -1.2593489034394923204198066883598 y[1] (numeric) = -1.25934890343949232041980668836 absolute error = 2e-31 relative error = 1.5881222388312450629464340598253e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = -1.2766151964166637758559301912485 y[1] (numeric) = -1.2766151964166637758559301912487 absolute error = 2e-31 relative error = 1.5666427954279471834201023552181e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = -1.2939498273047081268827525106807 y[1] (numeric) = -1.2939498273047081268827525106809 absolute error = 2e-31 relative error = 1.5456549842940906895988613746045e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = -1.3113520626466487410979362833252 y[1] (numeric) = -1.3113520626466487410979362833254 absolute error = 2e-31 relative error = 1.5251434431448416882091394929425e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = -1.3288211622251199333299490479899 y[1] (numeric) = -1.3288211622251199333299490479901 absolute error = 2e-31 relative error = 1.5050934293151883650820579084305e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4 y[1] (analytic) = -1.3463563791363880853608318169022 y[1] (numeric) = -1.3463563791363880853608318169025 absolute error = 3e-31 relative error = 2.2282361835908047739775467002530e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = -1.363956959865041396870317585315 y[1] (numeric) = -1.3639569598650413968703175853152 absolute error = 2e-31 relative error = 1.4663219286610720907428927363392e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = -1.3816221443593407986884466192346 y[1] (numeric) = -1.3816221443593407986884466192349 absolute error = 3e-31 relative error = 2.1713606808112519067417288967605e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = -1.3993511661072244933281454781476 y[1] (numeric) = -1.3993511661072244933281454781478 absolute error = 2e-31 relative error = 1.4292338109551774431242919625047e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = -1.4171432522129585224070534208273 y[1] (numeric) = -1.4171432522129585224070534208276 absolute error = 3e-31 relative error = 2.1169348937133284765504263120032e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = -1.4349976234744256959657292715176 y[1] (numeric) = -1.4349976234744256959657292715179 absolute error = 3e-31 relative error = 2.0905957967626317344344898148424e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (analytic) = -1.4529134944610451548537141522107 y[1] (numeric) = -1.4529134944610451548537141522109 absolute error = 2e-31 relative error = 1.3765444450923042037280428687759e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (analytic) = -1.4708900735923147742921442269604 y[1] (numeric) = -1.4708900735923147742921442269606 absolute error = 2e-31 relative error = 1.3597209172235790946251143982340e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = -1.4889265632169685544380089817521 y[1] (numeric) = -1.4889265632169685544380089817523 absolute error = 2e-31 relative error = 1.3432495929677070833239964427856e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = -1.5070221596927410822769628863557 y[1] (numeric) = -1.5070221596927410822769628863559 absolute error = 2e-31 relative error = 1.3271204986181288854395237643258e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = -1.5251760534667310884649713203402 y[1] (numeric) = -1.5251760534667310884649713203404 absolute error = 2e-31 relative error = 1.3113240241701882470277558700875e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = -1.5433874291563560628300760061255 y[1] (numeric) = -1.5433874291563560628300760061257 absolute error = 2e-31 relative error = 1.2958509070488132465921910612713e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = -1.5616554656308898331401917272407 y[1] (numeric) = -1.5616554656308898331401917272409 absolute error = 2e-31 relative error = 1.2806922166996830514740936757006e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = -1.5799793360935749534470053079295 y[1] (numeric) = -1.5799793360935749534470053079297 absolute error = 2e-31 relative error = 1.2658393399909308324580269845786e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = -1.5983582081643016908355692264027 y[1] (numeric) = -1.5983582081643016908355692264029 absolute error = 2e-31 relative error = 1.2512839673761114307392261657974e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = -1.6167912439628453427498138283373 y[1] (numeric) = -1.6167912439628453427498138283375 absolute error = 2e-31 relative error = 1.2370180797725553384839043260372e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=76023148, alloc=4521156, time=3.14 x[1] = 4.16 y[1] (analytic) = -1.6352776001926535612316097892908 y[1] (numeric) = -1.635277600192653561231609789291 absolute error = 2e-31 relative error = 1.2230339361123629142237624707952e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = -1.6538164282251753054107794572422 y[1] (numeric) = -1.6538164282251753054107794572424 absolute error = 2e-31 relative error = 1.2093240615261865599905848161302e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (analytic) = -1.6724068741847229894210819669533 y[1] (numeric) = -1.6724068741847229894210819669535 absolute error = 2e-31 relative error = 1.1958812361226238556293150752240e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = -1.6910480790338593395980987485076 y[1] (numeric) = -1.6910480790338593395980987485078 absolute error = 2e-31 relative error = 1.1826984843285195620845289907576e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = -1.7097391786593004223444551186229 y[1] (numeric) = -1.7097391786593004223444551186231 absolute error = 2e-31 relative error = 1.1697690647577655037859388244154e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = -1.7284793039583262524311770505132 y[1] (numeric) = -1.7284793039583262524311770505134 absolute error = 2e-31 relative error = 1.1570864605783096660516585994530e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = -1.7472675809256903407463615868448 y[1] (numeric) = -1.747267580925690340746361586845 absolute error = 2e-31 relative error = 1.1446443703490530985403967318545e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = -1.7661031307410194906088104104552 y[1] (numeric) = -1.7661031307410194906088104104554 absolute error = 2e-31 relative error = 1.1324366993001378882884881209487e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = -1.7849850698566951027398281302941 y[1] (numeric) = -1.7849850698566951027398281302943 absolute error = 2e-31 relative error = 1.1204575510318229464154561063283e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = -1.8039125100862072008359222794552 y[1] (numeric) = -1.8039125100862072008359222794554 absolute error = 2e-31 relative error = 1.1087012196087170387737703297844e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = -1.822884558692972342413475864514 y[1] (numeric) = -1.8228845586929723424134758645143 absolute error = 3e-31 relative error = 1.6457432730413998213644863078827e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = -1.8419003184796065332083226779057 y[1] (numeric) = -1.841900318479606533208322677906 absolute error = 3e-31 relative error = 1.6287526365576313422009405757544e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = -1.860958887877644217913179263164 y[1] (numeric) = -1.8609588878776442179131792631643 absolute error = 3e-31 relative error = 1.6120721524489939989438827237340e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (analytic) = -1.8800593610376943754286253662208 y[1] (numeric) = -1.8800593610376943754286253662211 absolute error = 3e-31 relative error = 1.5956942967716492756571919276248e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = -1.899200827920024703093237603664 y[1] (numeric) = -1.8992008279200247030932376036643 absolute error = 3e-31 relative error = 1.5796117798061163867012665094386e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = -1.9183823743855648315499399031558 y[1] (numeric) = -1.9183823743855648315499399031561 absolute error = 3e-31 relative error = 1.5638175371376962801049287815783e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = -1.9376030822873194700029198405699 y[1] (numeric) = -1.9376030822873194700029198405703 absolute error = 4e-31 relative error = 2.0644062948527328351412177081287e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = -1.9568620295621823406267625493371 y[1] (numeric) = -1.9568620295621823406267625493375 absolute error = 4e-31 relative error = 2.0440889237832154309629725619021e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (analytic) = -1.9761582903231417208108726455763 y[1] (numeric) = -1.9761582903231417208108726455767 absolute error = 4e-31 relative error = 2.0241293521815599893024024052150e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = -1.9954909349518683727617974225641 y[1] (numeric) = -1.9954909349518683727617974225645 absolute error = 4e-31 relative error = 2.0045192538529275621681784663522e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = -2.0148590301916766017476474330366 y[1] (numeric) = -2.0148590301916766017476474330369 absolute error = 3e-31 relative error = 1.4889379132963984287109719208574e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = -2.0342616392408491469562573075772 y[1] (numeric) = -2.0342616392408491469562573075775 absolute error = 3e-31 relative error = 1.4747365541039979071044369736920e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = -2.0536978218463165725557714761559 y[1] (numeric) = -2.0536978218463165725557714761562 absolute error = 3e-31 relative error = 1.4607796571079470251515678914219e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO 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=80024836, alloc=4521156, time=3.31 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = -2.0731666343976817910966146332443 y[1] (numeric) = -2.0731666343976817910966146332445 absolute error = 2e-31 relative error = 9.6470778895255617865808878131191e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = -2.0926671300215803168808602577823 y[1] (numeric) = -2.0926671300215803168808602577825 absolute error = 2e-31 relative error = 9.5571817003661509178567446659480e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = -2.1121983586763668133522935335094 y[1] (numeric) = -2.1121983586763668133522935335096 absolute error = 2e-31 relative error = 9.4688076609117469715139970379767e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = -2.1317593672471184659313348565068 y[1] (numeric) = -2.131759367247118465931334856507 absolute error = 2e-31 relative error = 9.3819219501436129212950670300211e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = -2.1513491996409456800367096510664 y[1] (numeric) = -2.1513491996409456800367096510666 absolute error = 2e-31 relative error = 9.2964917101035691969558466848461e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = -2.1709668968826005733034876438366 y[1] (numeric) = -2.1709668968826005733034876438369 absolute error = 3e-31 relative error = 1.3818727518636278261207968033714e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = -2.1906114972103737012279432702555 y[1] (numeric) = -2.1906114972103737012279432702558 absolute error = 3e-31 relative error = 1.3694806239355262967392023395378e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = -2.2102820361722694266465863988873 y[1] (numeric) = -2.2102820361722694266465863988876 absolute error = 3e-31 relative error = 1.3572928481088102818317358718794e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = -2.2299775467224503155925613446698 y[1] (numeric) = -2.2299775467224503155925613446701 absolute error = 3e-31 relative error = 1.3453050253395170104888613075830e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.2496970593179409151701985931512 y[1] (numeric) = -2.2496970593179409151701985931514 absolute error = 2e-31 relative error = 8.8900858527430194627094674203568e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = -2.2694396020155812431505179934839 y[1] (numeric) = -2.2694396020155812431505179934842 absolute error = 3e-31 relative error = 1.3219122453558924737057014831949e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.2892042005692202940195181752062 y[1] (numeric) = -2.2892042005692202940195181752065 absolute error = 3e-31 relative error = 1.3104990805337668557773312676805e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.3089898785271398422096416782592 y[1] (numeric) = -2.3089898785271398422096416782596 absolute error = 4e-31 relative error = 1.7323592611638137343188889410608e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.3287956573296988002152788818011 y[1] (numeric) = -2.3287956573296988002152788818015 absolute error = 4e-31 relative error = 1.7176260130038969599014767355197e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.3486205564071883672378692086186 y[1] (numeric) = -2.348620556407188367237869208619 absolute error = 4e-31 relative error = 1.7031273907093003994720156209098e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.3684635932778881829272807804022 y[1] (numeric) = -2.3684635932778881829272807804026 absolute error = 4e-31 relative error = 1.6888585542765766149274677582496e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = -2.3883237836463136806858075749921 y[1] (numeric) = -2.3883237836463136806858075749925 absolute error = 4e-31 relative error = 1.6748147916079870513808001972386e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = -2.4082001415016448158813262073901 y[1] (numeric) = -2.4082001415016448158813262073905 absolute error = 4e-31 relative error = 1.6609915143953860509223686552978e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.4280916792163263261788146856254 y[1] (numeric) = -2.4280916792163263261788146856258 absolute error = 4e-31 relative error = 1.6473842541608691112740115257729e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = -2.4479974076448296640463665993177 y[1] (numeric) = -2.4479974076448296640463665993181 absolute error = 4e-31 relative error = 1.6339886584472822696571858398737e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.4679163362225667253247514756035 y[1] (numeric) = -2.4679163362225667253247514756039 absolute error = 4e-31 relative error = 1.6208004871520343723555666689326e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.4878474730649454825700921787708 y[1] (numeric) = -2.4878474730649454825700921787712 absolute error = 4e-31 relative error = 1.6078156089979796118272318109625e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for 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=84026192, alloc=4521156, time=3.48 x[1] = 4.61 y[1] (analytic) = -2.5077898250665576176888711718273 y[1] (numeric) = -2.5077898250665576176888711718277 absolute error = 4e-31 relative error = 1.5950299981354452633134118949241e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.5277423980004882351846582243842 y[1] (numeric) = -2.5277423980004882351846582243846 absolute error = 4e-31 relative error = 1.5824397308697701391507807778120e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.5477041966177377251279927125974 y[1] (numeric) = -2.5477041966177377251279927125978 absolute error = 4e-31 relative error = 1.5700409825089939346738727475548e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.5676742247467458337459747992399 y[1] (numeric) = -2.5676742247467458337459747992403 absolute error = 4e-31 relative error = 1.5578300243265973291359888939524e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.5876514853930079893074429838229 y[1] (numeric) = -2.5876514853930079893074429838233 absolute error = 4e-31 relative error = 1.5458032206344383290833656193031e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.607634980838773921754162833204 y[1] (numeric) = -2.6076349808387739217541628332044 absolute error = 4e-31 relative error = 1.5339570259612627414332812330753e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.6276237127428186062991456798947 y[1] (numeric) = -2.6276237127428186062991456798951 absolute error = 4e-31 relative error = 1.5222879823323866254476539237295e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.6476166822402755539808796320554 y[1] (numeric) = -2.6476166822402755539808796320558 absolute error = 4e-31 relative error = 1.5107927166463568320489674655736e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 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) = -2.667612890042522465927611603558 y[1] (numeric) = -2.6676128900425224659276116035584 absolute error = 4e-31 relative error = 1.4994679381445929831635730780069e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = -2.6876113365371092628494917036729 y[1] (numeric) = -2.6876113365371092628494917036733 absolute error = 4e-31 relative error = 1.4883104359702011164775201917405e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = -2.7076110218877184970389038522753 y[1] (numeric) = -2.7076110218877184970389038522757 absolute error = 4e-31 relative error = 1.4773170768123263245212853633167e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = -2.7276109461341481509210826531746 y[1] (numeric) = -2.727610946134148150921082653175 absolute error = 4e-31 relative error = 1.4664848026325796154701934540513e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007339 Order of pole (three term test) = -0.8943 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = -2.7476101092923068239584801849428 y[1] (numeric) = -2.7476101092923068239584801849432 absolute error = 4e-31 relative error = 1.4558106284702334449399374630207e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01698 Order of pole (three term test) = -0.9004 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = -2.767607511454211308473521317219 y[1] (numeric) = -2.7676075114542113084735213172194 absolute error = 4e-31 relative error = 1.4452916403230314086696500369671e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02661 Order of pole (three term test) = -0.9113 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = -2.7876021528879765547154963123733 y[1] (numeric) = -2.7876021528879765547154963123737 absolute error = 4e-31 relative error = 1.4349249931006009096922849153355e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03623 Order of pole (three term test) = -0.927 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = -2.8075930341377880262584087164105 y[1] (numeric) = -2.8075930341377880262584087164109 absolute error = 4e-31 relative error = 1.4247079086475936559374946784274e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04584 Order of pole (three term test) = -0.9476 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = -2.8275791561238464485775487727873 y[1] (numeric) = -2.8275791561238464485775487727876 absolute error = 3e-31 relative error = 1.0609782553753560103884704694123e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05543 Order of pole (three term test) = -0.973 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = -2.8475595202422749564132217146596 y[1] (numeric) = -2.8475595202422749564132217146599 absolute error = 3e-31 relative error = 1.0535337290315024430881900614407e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.065 Order of pole (three term test) = -1.003 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = -2.8675331284649786492901502413476 y[1] (numeric) = -2.8675331284649786492901502413479 absolute error = 3e-31 relative error = 1.0461954110381742278103216421208e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07454 Order of pole (three term test) = -1.038 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = -2.8874989834394465693202152576495 y[1] (numeric) = -2.8874989834394465693202152576498 absolute error = 3e-31 relative error = 1.0389614047332227147087011194988e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08405 Order of pole (three term test) = -1.078 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = -2.9074560885884861211739226395384 y[1] (numeric) = -2.9074560885884861211739226395387 absolute error = 3e-31 relative error = 1.0318298569580262048543543563270e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09353 Order of pole (three term test) = -1.122 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = -2.9274034482098799608617106191698 y[1] (numeric) = -2.9274034482098799608617106191701 absolute error = 3e-31 relative error = 1.0247989568484361623412040022147e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.103 Order of pole (three term test) = -1.172 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = -2.9473400675759553877192667889538 y[1] (numeric) = -2.9473400675759553877192667889542 absolute error = 4e-31 relative error = 1.3571559128871771076824201589613e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1124 Order of pole (three term test) = -1.226 NO COMPLEX POLE (six term test) for Equation 1 bytes used=88027848, alloc=4521156, time=3.64 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = -2.9672649530330562827406304097327 y[1] (numeric) = -2.9672649530330562827406304097331 absolute error = 4e-31 relative error = 1.3480427475515155716498906254833e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1217 Order of pole (three term test) = -1.284 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = -2.9871771121009076461481397184653 y[1] (numeric) = -2.9871771121009076461481397184657 absolute error = 4e-31 relative error = 1.3390568586630490105113625117771e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.131 Order of pole (three term test) = -1.348 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = -3.0070755535718627978282707459854 y[1] (numeric) = -3.0070755535718627978282707459858 absolute error = 4e-31 relative error = 1.3301960422140781408026580213539e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1403 Order of pole (three term test) = -1.416 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = -3.026959287610023315996029785628 y[1] (numeric) = -3.0269592876100233159960297856284 absolute error = 4e-31 relative error = 1.3214581432835372395559478025543e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1495 Order of pole (three term test) = -1.488 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = -3.0468273258502218021766327470316 y[1] (numeric) = -3.046827325850221802176632747032 absolute error = 4e-31 relative error = 1.3128410547137895031480888312155e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1586 Order of pole (three term test) = -1.566 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = -3.0666786814968575743104585897138 y[1] (numeric) = -3.0666786814968575743104585897142 absolute error = 4e-31 relative error = 1.3043427158294864874183555020239e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1677 Order of pole (three term test) = -1.648 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = -3.0865123694225754044943291441219 y[1] (numeric) = -3.0865123694225754044943291441223 absolute error = 4e-31 relative error = 1.2959611111969461572007166018071e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1767 Order of pole (three term test) = -1.734 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = -3.1063274062667774335675731995194 y[1] (numeric) = -3.1063274062667774335675731995198 absolute error = 4e-31 relative error = 1.2876942694225684681686692865292e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1856 Order of pole (three term test) = -1.825 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = -3.1261228105339584114335092408118 y[1] (numeric) = -3.1261228105339584114335092408122 absolute error = 4e-31 relative error = 1.2795402619888687976219358412126e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1945 Order of pole (three term test) = -1.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (analytic) = -3.1458976026918544296742604464858 y[1] (numeric) = -3.1458976026918544296742604464862 absolute error = 4e-31 relative error = 1.2714972021267680881083449224025e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2033 Order of pole (three term test) = -2.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = -3.1656508052693953316674308040397 y[1] (numeric) = -3.1656508052693953316674308040402 absolute error = 5e-31 relative error = 1.5794540546535430180187357710469e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.212 Order of pole (three term test) = -2.124 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = -3.1853814429544510050452574116347 y[1] (numeric) = -3.1853814429544510050452574116352 absolute error = 5e-31 relative error = 1.5696707253252799601835466321994e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2206 Order of pole (three term test) = -2.232 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = -3.2050885426913617819484480229353 y[1] (numeric) = -3.2050885426913617819484480229358 absolute error = 5e-31 relative error = 1.5600193047401503810314612721986e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2291 Order of pole (three term test) = -2.345 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = -3.2247711337782431941159535140125 y[1] (numeric) = -3.224771133778243194115953514013 absolute error = 5e-31 relative error = 1.5504976299331490486930039227712e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2375 Order of pole (three term test) = -2.462 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = -3.2444282479640553524162533206808 y[1] (numeric) = -3.2444282479640553524162533206812 absolute error = 4e-31 relative error = 1.2328828669612531188160711284781e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2459 Order of pole (three term test) = -2.583 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = -3.264058919545427243963091597697 y[1] (numeric) = -3.2640589195454272439630915976974 absolute error = 4e-31 relative error = 1.2254680747481924744708744190963e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2541 Order of pole (three term test) = -2.709 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin(x) - 1,0; Iterations = 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=90956636, alloc=4521156, time=3.76