|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > #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_c1, > array_tmp2_a1, > array_tmp2_a2, > 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_2D0, 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_c1, array_tmp2_a1, array_tmp2_a2, 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_2D0, > #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_c1, > array_tmp2_a1, > array_tmp2_a2, > 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_2D0, 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_c1, array_tmp2_a1, array_tmp2_a2, 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_2D0, > #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_c1, > array_tmp2_a1, > array_tmp2_a2, > 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_2D0, 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_c1, array_tmp2_a1, array_tmp2_a2, 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_2D0, > #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_c1, > array_tmp2_a1, > array_tmp2_a2, > 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_2D0, 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_c1, array_tmp2_a1, array_tmp2_a2, 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_2D0, > #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_c1, > array_tmp2_a1, > array_tmp2_a2, > 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_2D0, 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_c1, array_tmp2_a1, array_tmp2_a2, 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_2D0, > #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_c1, > array_tmp2_a1, > array_tmp2_a2, > 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_2D0, 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_c1, array_tmp2_a1, array_tmp2_a2, 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_2D0, > #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_c1, > array_tmp2_a1, > array_tmp2_a2, > 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_2D0, 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_c1, array_tmp2_a1, array_tmp2_a2, 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_2D0, > #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_c1, > array_tmp2_a1, > array_tmp2_a2, > 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_2D0, 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_c1, array_tmp2_a1, array_tmp2_a2, 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_2D0, > #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_c1, > array_tmp2_a1, > array_tmp2_a2, > 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 expt CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := expt(array_const_2D0[1] , array_tmp1[1]); > array_tmp2_c1[1] := ln(array_const_2D0[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[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; > #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 expt CONST FULL $eq_no = 1 iii = 2 > array_tmp2[2] := att(1,array_tmp2,array_tmp1,1) * array_tmp2_c1[1]; > #emit pre add CONST FULL $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; > #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 expt CONST FULL $eq_no = 1 iii = 3 > array_tmp2[3] := att(2,array_tmp2,array_tmp1,1) * array_tmp2_c1[1]; > #emit pre add CONST FULL $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; > #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 expt CONST FULL $eq_no = 1 iii = 4 > array_tmp2[4] := att(3,array_tmp2,array_tmp1,1) * array_tmp2_c1[1]; > #emit pre add CONST FULL $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; > #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 expt CONST FULL $eq_no = 1 iii = 5 > array_tmp2[5] := att(4,array_tmp2,array_tmp1,1) * array_tmp2_c1[1]; > #emit pre add CONST FULL $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; > #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 expt CONST FULL $eq_no = 1 i = 1 > array_tmp2[kkk] := att(kkk-1,array_tmp2,array_tmp1,1) * array_tmp2_c1[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_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_c1, array_tmp2_a1, array_tmp2_a2, 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] := expt(array_const_2D0[1], array_tmp1[1]); array_tmp2_c1[1] := ln(array_const_2D0[1]); array_tmp3[1] := array_const_0D0[1] + array_tmp2[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; array_tmp1[2] := array_tmp1_g[1]*array_x[2]; array_tmp1_g[2] := -array_tmp1[1]*array_x[2]; array_tmp2[2] := att(1, array_tmp2, array_tmp1, 1)*array_tmp2_c1[1]; 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; 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] := att(2, array_tmp2, array_tmp1, 1)*array_tmp2_c1[1]; 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; 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] := att(3, array_tmp2, array_tmp1, 1)*array_tmp2_c1[1]; 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; 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] := att(4, array_tmp2, array_tmp1, 1)*array_tmp2_c1[1]; 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; 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] := att(kkk - 1, array_tmp2, array_tmp1, 1)*array_tmp2_c1[1]; 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; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(0.0); > end; exact_soln_y := proc(x) return 0. end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > #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_c1, > array_tmp2_a1, > array_tmp2_a2, > 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/expt_c_sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = expt(2.0 , sin(x));"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(0.0);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2_c1:= Array(0..(max_terms + 1),[]); > array_tmp2_a1:= Array(0..(max_terms + 1),[]); > array_tmp2_a2:= 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_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2_a2[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_c1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2_a2[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_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_2D0[1] := 2.0; > array_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 ) = expt(2.0 , sin(x));"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T01:04:51-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"expt_c_sin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = expt(2.0 , sin(x));") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"expt_c_sin diffeq.mxt") > ; > logitem_str(html_log_file,"expt_c_sin maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, 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_c1, array_tmp2_a1, array_tmp2_a2, 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/expt_c_sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt(2.0 , sin(x));"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(0.0);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2_c1 := Array(0 .. max_terms + 1, []); array_tmp2_a1 := Array(0 .. max_terms + 1, []); array_tmp2_a2 := 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_c1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2_a2[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_c1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_c1[term] := 0.; term := term + 1 end do; array_tmp2_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_a1[term] := 0.; term := term + 1 end do; array_tmp2_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2_a2[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_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_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 ) = expt(2.0 , sin(x));"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T01:04:51-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "expt_c_sin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = expt(2.0 , sin(x));"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "expt_c_sin diffeq.mxt"); logitem_str(html_log_file, "expt_c_sin maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/expt_c_sinpostode.ode################# diff ( y , x , 1 ) = expt(2.0 , sin(x)); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(0.0); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 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 = 4.1269455714853000805698435866335e-169 estimated_step_error = 4.1269455714853000805698435866335e-169 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.7695466038030006895267952433587e-161 estimated_step_error = 2.7695466038030006895267952433587e-161 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 = 1.8586116837043160278490669494324e-153 estimated_step_error = 1.8586116837043160278490669494324e-153 best_h = 8.000e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.2472937507409551553632910838446e-145 estimated_step_error = 1.2472937507409551553632910838446e-145 best_h = 1.60000e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.3704542336354567594747987420092e-138 estimated_step_error = 8.3704542336354567594747987420092e-138 best_h = 3.200000e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.6173269013607545935041299714506e-130 estimated_step_error = 5.6173269013607545935041299714506e-130 best_h = 6.4000000e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.7697378984500973614110672514691e-122 estimated_step_error = 3.7697378984500973614110672514691e-122 best_h = 0.000128 opt_iter = 8 bytes used=4000144, alloc=3014104, time=0.12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.5298465701791319404568540706431e-114 estimated_step_error = 2.5298465701791319404568540706431e-114 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 = 1.6977758432309451554643385621262e-106 estimated_step_error = 1.6977758432309451554643385621262e-106 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1393910297746123342527363703039e-98 estimated_step_error = 1.1393910297746123342527363703039e-98 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 = 7.6467659599671989007440042537553e-91 estimated_step_error = 7.6467659599671989007440042537553e-91 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.1322511955953270537806687962301e-83 estimated_step_error = 5.1322511955953270537806687962301e-83 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.4449917565129474141564313896987e-75 estimated_step_error = 3.4449917565129474141564313896987e-75 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.3129630390587238467937410638897e-67 estimated_step_error = 2.3129630390587238467937410638897e-67 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.5536354806751869557178905024704e-59 estimated_step_error = 1.5536354806751869557178905024704e-59 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0445455449332762425959148345968e-51 estimated_step_error = 1.0445455449332762425959148345968e-51 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 = 7.0354697906244649135660234515283e-44 estimated_step_error = 7.0354697906244649135660234515283e-44 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.7555589349489694894096785146032e-36 estimated_step_error = 4.7555589349489694894096785146032e-36 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01307 Order of pole (three term test) = -23.04 Radius of convergence (six term test) for eq 1 = 4.306 Order of pole (six term test) = 8.008 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0 y[1] (numeric) = 0.010753524526431980387867519132301 absolute error = 0.010753524526431980387867519132301 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.003997 Order of pole (three term test) = -24.49 Radius of convergence (six term test) for eq 1 = 4.305 Order of pole (six term test) = 8.021 bytes used=8001600, alloc=4128012, time=0.25 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0 y[1] (numeric) = 0.021581391439193028270121777196319 absolute error = 0.021581391439193028270121777196319 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.304 Order of pole (six term test) = 8.037 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0 y[1] (numeric) = 0.032484027970719728754058126533753 absolute error = 0.032484027970719728754058126533753 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.303 Order of pole (six term test) = 8.056 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 0 y[1] (numeric) = 0.043461855555703909339628618490018 absolute error = 0.043461855555703909339628618490018 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.303 Order of pole (six term test) = 8.078 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0 y[1] (numeric) = 0.054515289634352069503208905226703 absolute error = 0.054515289634352069503208905226703 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.303 Order of pole (six term test) = 8.102 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0 y[1] (numeric) = 0.06564473945379868264129726827504 absolute error = 0.06564473945379868264129726827504 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.303 Order of pole (six term test) = 8.13 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0 y[1] (numeric) = 0.076850607867740779633747955571865 absolute error = 0.076850607867740779633747955571865 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.304 Order of pole (six term test) = 8.159 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0 y[1] (numeric) = 0.088133291134364037234927740847438 absolute error = 0.088133291134364037234927740847438 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.304 Order of pole (six term test) = 8.191 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0 y[1] (numeric) = 0.099493178712633421454579432318481 absolute error = 0.099493178712633421454579432318481 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.305 Order of pole (six term test) = 8.224 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0 y[1] (numeric) = 0.11093065305702427342853647511501 absolute error = 0.11093065305702427342853647511501 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.306 Order of pole (six term test) = 8.258 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0 y[1] (numeric) = 0.12244608941077257029329434886889 absolute error = 0.12244608941077257029329434886889 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.308 Order of pole (six term test) = 8.293 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0 y[1] (numeric) = 0.13403985559772594346971649734227 absolute error = 0.13403985559772594346971649734227 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.309 Order of pole (six term test) = 8.328 TOP MAIN SOLVE Loop bytes used=12002660, alloc=4390108, time=0.39 x[1] = 0.23 y[1] (analytic) = 0 y[1] (numeric) = 0.14571231181287988864450236581273 absolute error = 0.14571231181287988864450236581273 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.31 Order of pole (six term test) = 8.363 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 0 y[1] (numeric) = 0.15746381041168645264247436855312 absolute error = 0.15746381041168645264247436855312 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.311 Order of pole (six term test) = 8.397 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 0 y[1] (numeric) = 0.16929469569822552925335698609622 absolute error = 0.16929469569822552925335698609622 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.312 Order of pole (six term test) = 8.43 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 0 y[1] (numeric) = 0.18120530371233173577670905517146 absolute error = 0.18120530371233173577670905517146 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.313 Order of pole (six term test) = 8.461 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 0 y[1] (numeric) = 0.19319596201577267136146264320026 absolute error = 0.19319596201577267136146264320026 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.314 Order of pole (six term test) = 8.491 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0 y[1] (numeric) = 0.20526698947757717384817623222064 absolute error = 0.20526698947757717384817623222064 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.315 Order of pole (six term test) = 8.518 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 0 y[1] (numeric) = 0.21741869605861499040389034495976 absolute error = 0.21741869605861499040389034495976 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.315 Order of pole (six term test) = 8.542 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0 y[1] (numeric) = 0.22965138259553205533064056867426 absolute error = 0.22965138259553205533064056867426 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.315 Order of pole (six term test) = 8.564 TOP MAIN SOLVE Loop x[1] = 0.31 y[1] (analytic) = 0 y[1] (numeric) = 0.24196534058414832251949160262785 absolute error = 0.24196534058414832251949160262785 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.314 Order of pole (six term test) = 8.582 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 0 y[1] (numeric) = 0.25436085196242782653686581579058 absolute error = 0.25436085196242782653686581579058 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.314 Order of pole (six term test) = 8.597 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0 y[1] (numeric) = 0.26683818889313334163103339978252 absolute error = 0.26683818889313334163103339978252 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.312 Order of pole (six term test) = 8.608 TOP MAIN SOLVE Loop bytes used=16003472, alloc=4455632, time=0.53 x[1] = 0.34 y[1] (analytic) = 0 y[1] (numeric) = 0.27939761354628066833724408897564 absolute error = 0.27939761354628066833724408897564 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.311 Order of pole (six term test) = 8.616 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = 0 y[1] (numeric) = 0.29203937788151019908854102311535 absolute error = 0.29203937788151019908854102311535 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.309 Order of pole (six term test) = 8.621 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 0 y[1] (numeric) = 0.30476372343049599350337599265622 absolute error = 0.30476372343049599350337599265622 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.307 Order of pole (six term test) = 8.622 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 0 y[1] (numeric) = 0.31757088107951512697171109863844 absolute error = 0.31757088107951512697171109863844 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.305 Order of pole (six term test) = 8.62 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 0 y[1] (numeric) = 0.33046107085230255890717522579511 absolute error = 0.33046107085230255890717522579511 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005867 Order of pole (three term test) = -0.9475 Radius of convergence (six term test) for eq 1 = 4.302 Order of pole (six term test) = 8.615 TOP MAIN SOLVE Loop x[1] = 0.39 y[1] (analytic) = 0 y[1] (numeric) = 0.34343450169331919564540259884207 absolute error = 0.34343450169331919564540259884207 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0149 Order of pole (three term test) = -1.266 Radius of convergence (six term test) for eq 1 = 4.299 Order of pole (six term test) = 8.608 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0 y[1] (numeric) = 0.35649137125156319348666705851444 absolute error = 0.35649137125156319348666705851444 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02319 Order of pole (three term test) = -1.864 Radius of convergence (six term test) for eq 1 = 4.296 Order of pole (six term test) = 8.598 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 0 y[1] (numeric) = 0.36963186566505685581554918213996 absolute error = 0.36963186566505685581554918213996 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03057 Order of pole (three term test) = -2.727 Radius of convergence (six term test) for eq 1 = 4.293 Order of pole (six term test) = 8.587 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 0 y[1] (numeric) = 0.38285615934614372057055777201818 absolute error = 0.38285615934614372057055777201818 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03689 Order of pole (three term test) = -3.839 Radius of convergence (six term test) for eq 1 = 4.289 Order of pole (six term test) = 8.575 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 0 y[1] (numeric) = 0.39616441476773260655445538032726 absolute error = 0.39616441476773260655445538032726 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04202 Order of pole (three term test) = -5.176 Radius of convergence (six term test) for eq 1 = 4.286 Order of pole (six term test) = 8.561 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 0 y[1] (numeric) = 0.40955678225062748513237940328886 absolute error = 0.40955678225062748513237940328886 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04583 Order of pole (three term test) = -6.708 Radius of convergence (six term test) for eq 1 = 4.282 Order of pole (six term test) = 8.548 TOP MAIN SOLVE Loop x[1] = 0.45 bytes used=20005304, alloc=4521156, time=0.66 y[1] (analytic) = 0 y[1] (numeric) = 0.42303339975208406371516852862314 absolute error = 0.42303339975208406371516852862314 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04825 Order of pole (three term test) = -8.404 Radius of convergence (six term test) for eq 1 = 4.278 Order of pole (six term test) = 8.534 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 0 y[1] (numeric) = 0.43659439265573590502563106513004 absolute error = 0.43659439265573590502563106513004 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04922 Order of pole (three term test) = -10.23 Radius of convergence (six term test) for eq 1 = 4.275 Order of pole (six term test) = 8.522 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 0 y[1] (numeric) = 0.4502398735630347574585695116376 absolute error = 0.4502398735630347574585695116376 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0487 Order of pole (three term test) = -12.13 Radius of convergence (six term test) for eq 1 = 4.272 Order of pole (six term test) = 8.51 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 0 y[1] (numeric) = 0.46396994208635153284695561371331 absolute error = 0.46396994208635153284695561371331 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04672 Order of pole (three term test) = -14.08 Radius of convergence (six term test) for eq 1 = 4.269 Order of pole (six term test) = 8.5 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 0 y[1] (numeric) = 0.47778468464388603463193822038849 absolute error = 0.47778468464388603463193822038849 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04329 Order of pole (three term test) = -16.02 Radius of convergence (six term test) for eq 1 = 4.266 Order of pole (six term test) = 8.493 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0 y[1] (numeric) = 0.49168417425653510782461071394079 absolute error = 0.49168417425653510782461071394079 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03851 Order of pole (three term test) = -17.92 Radius of convergence (six term test) for eq 1 = 4.263 Order of pole (six term test) = 8.487 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 0 y[1] (numeric) = 0.50566847034687034829667404371002 absolute error = 0.50566847034687034829667404371002 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03246 Order of pole (three term test) = -19.72 Radius of convergence (six term test) for eq 1 = 4.261 Order of pole (six term test) = 8.485 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 0 y[1] (numeric) = 0.51973761854037786893891343912268 absolute error = 0.51973761854037786893891343912268 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02529 Order of pole (three term test) = -21.38 Radius of convergence (six term test) for eq 1 = 4.259 Order of pole (six term test) = 8.486 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 0 y[1] (numeric) = 0.5338916504691138702209197672488 absolute error = 0.5338916504691138702209197672488 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01715 Order of pole (three term test) = -22.87 Radius of convergence (six term test) for eq 1 = 4.257 Order of pole (six term test) = 8.49 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 0 y[1] (numeric) = 0.54813058357793089886648908719111 absolute error = 0.54813058357793089886648908719111 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008247 Order of pole (three term test) = -24.13 Radius of convergence (six term test) for eq 1 = 4.256 Order of pole (six term test) = 8.497 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 0 y[1] (numeric) = 0.5624544209334306969811254737423 absolute error = 0.5624544209334306969811254737423 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.256 Order of pole (six term test) = 8.508 TOP MAIN SOLVE Loop x[1] = 0.56 y[1] (analytic) = 0 y[1] (numeric) = 0.57686315103580044135350883700701 absolute error = 0.57686315103580044135350883700701 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.255 Order of pole (six term test) = 8.522 TOP MAIN SOLVE Loop bytes used=24006560, alloc=4521156, time=0.81 x[1] = 0.57 y[1] (analytic) = 0 y[1] (numeric) = 0.59135674763368994519936558552384 absolute error = 0.59135674763368994519936558552384 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.255 Order of pole (six term test) = 8.54 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 0 y[1] (numeric) = 0.60593516954228803880416089690187 absolute error = 0.60593516954228803880416089690187 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.255 Order of pole (six term test) = 8.561 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 0 y[1] (numeric) = 0.62059836046475685792062459794025 absolute error = 0.62059836046475685792062459794025 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.256 Order of pole (six term test) = 8.585 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0 y[1] (numeric) = 0.63534624881718314605587365661195 absolute error = 0.63534624881718314605587365661195 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.257 Order of pole (six term test) = 8.612 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 0 y[1] (numeric) = 0.65017874755720591571309239551369 absolute error = 0.65017874755720591571309239551369 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.258 Order of pole (six term test) = 8.64 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 0 y[1] (numeric) = 0.66509575401647991111881160024312 absolute error = 0.66509575401647991111881160024312 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.26 Order of pole (six term test) = 8.671 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 0 y[1] (numeric) = 0.68009714973713426797275225021232 absolute error = 0.68009714973713426797275225021232 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.261 Order of pole (six term test) = 8.703 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 0 y[1] (numeric) = 0.69518280031238557143380622332963 absolute error = 0.69518280031238557143380622332963 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.263 Order of pole (six term test) = 8.736 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 0 y[1] (numeric) = 0.71035255523146416916802447540884 absolute error = 0.71035255523146416916802447540884 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.265 Order of pole (six term test) = 8.769 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 0 y[1] (numeric) = 0.72560624772901209923888448843834 absolute error = 0.72560624772901209923888448843834 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.266 Order of pole (six term test) = 8.803 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 0 y[1] (numeric) = 0.74094369463911034047157447247121 absolute error = 0.74094369463911034047157447247121 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.268 Order of pole (six term test) = 8.835 TOP MAIN SOLVE Loop bytes used=28007232, alloc=4521156, time=0.96 x[1] = 0.68 y[1] (analytic) = 0 y[1] (numeric) = 0.75636469625409228338212094310892 absolute error = 0.75636469625409228338212094310892 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.27 Order of pole (six term test) = 8.866 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 0 y[1] (numeric) = 0.77186903618829935070198788609364 absolute error = 0.77186903618829935070198788609364 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.271 Order of pole (six term test) = 8.896 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0 y[1] (numeric) = 0.78745648124693356599170804524214 absolute error = 0.78745648124693356599170804524214 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.272 Order of pole (six term test) = 8.923 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 0 y[1] (numeric) = 0.80312678130016057504156701608922 absolute error = 0.80312678130016057504156701608922 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.273 Order of pole (six term test) = 8.947 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 0 y[1] (numeric) = 0.81887966916261516610420738961155 absolute error = 0.81887966916261516610420738961155 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.274 Order of pole (six term test) = 8.969 TOP MAIN SOLVE Loop x[1] = 0.73 y[1] (analytic) = 0 y[1] (numeric) = 0.83471486047845971008287209561067 absolute error = 0.83471486047845971008287209561067 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.274 Order of pole (six term test) = 8.987 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 0 y[1] (numeric) = 0.8506320536121441493943405012952 absolute error = 0.8506320536121441493943405012952 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.274 Order of pole (six term test) = 9.002 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 0 y[1] (numeric) = 0.8666309295450142033226430932477 absolute error = 0.8666309295450142033226430932477 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.273 Order of pole (six term test) = 9.013 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 0 y[1] (numeric) = 0.88271115177791232746996945216955 absolute error = 0.88271115177791232746996945216955 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.273 Order of pole (six term test) = 9.02 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 0 y[1] (numeric) = 0.89887236623991366479818544905182 absolute error = 0.89887236623991366479818544905182 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.272 Order of pole (six term test) = 9.023 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 0 y[1] (numeric) = 0.91511420120333675535832736894442 absolute error = 0.91511420120333675535832736894442 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.27 Order of pole (six term test) = 9.023 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 0 y[1] (numeric) = 0.93143626720516613096836479708012 absolute error = 0.93143626720516613096836479708012 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.006221 Order of pole (three term test) = -0.956 Radius of convergence (six term test) for eq 1 = 4.268 Order of pole (six term test) = 9.019 TOP MAIN SOLVE Loop bytes used=32008340, alloc=4586680, time=1.11 x[1] = 0.8 y[1] (analytic) = 0 y[1] (numeric) = 0.94783815697502110988972658229438 absolute error = 0.94783815697502110988972658229438 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01538 Order of pole (three term test) = -1.296 Radius of convergence (six term test) for eq 1 = 4.266 Order of pole (six term test) = 9.012 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 0 y[1] (numeric) = 0.96431944536980212526937973138404 absolute error = 0.96431944536980212526937973138404 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02389 Order of pole (three term test) = -1.924 Radius of convergence (six term test) for eq 1 = 4.264 Order of pole (six term test) = 9.002 TOP MAIN SOLVE Loop x[1] = 0.82 y[1] (analytic) = 0 y[1] (numeric) = 0.98087968931514277028985615427915 absolute error = 0.98087968931514277028985615427915 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03158 Order of pole (three term test) = -2.825 Radius of convergence (six term test) for eq 1 = 4.261 Order of pole (six term test) = 8.989 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 0 y[1] (numeric) = 0.99751842775379242337570174301392 absolute error = 0.99751842775379242337570174301392 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03827 Order of pole (three term test) = -3.978 Radius of convergence (six term test) for eq 1 = 4.258 Order of pole (six term test) = 8.975 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = 0 y[1] (numeric) = 1.0142351816010508294536758232552 absolute error = 1.0142351816010508294536758232552 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04381 Order of pole (three term test) = -5.358 Radius of convergence (six term test) for eq 1 = 4.255 Order of pole (six term test) = 8.958 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 0 y[1] (numeric) = 1.0310294537073723594119020347971 absolute error = 1.0310294537073723594119020347971 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04805 Order of pole (three term test) = -6.933 Radius of convergence (six term test) for eq 1 = 4.252 Order of pole (six term test) = 8.941 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 0 y[1] (numeric) = 1.0479007288282538510526791957778 absolute error = 1.0479007288282538510526791957778 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05091 Order of pole (three term test) = -8.665 Radius of convergence (six term test) for eq 1 = 4.249 Order of pole (six term test) = 8.923 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 0 y[1] (numeric) = 1.0648484736015159527358102884836 absolute error = 1.0648484736015159527358102884836 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0523 Order of pole (three term test) = -10.51 Radius of convergence (six term test) for eq 1 = 4.245 Order of pole (six term test) = 8.905 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 0 y[1] (numeric) = 1.0818721365320837475651100554116 absolute error = 1.0818721365320837475651100554116 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0522 Order of pole (three term test) = -12.43 Radius of convergence (six term test) for eq 1 = 4.242 Order of pole (six term test) = 8.888 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 0 y[1] (numeric) = 1.0989711479843681336324072381265 absolute error = 1.0989711479843681336324072381265 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05059 Order of pole (three term test) = -14.38 Radius of convergence (six term test) for eq 1 = 4.239 Order of pole (six term test) = 8.872 TOP MAIN SOLVE Loop x[1] = 0.9 y[1] (analytic) = 0 y[1] (numeric) = 1.1161449201823449770050086992444 absolute error = 1.1161449201823449770050086992444 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04751 Order of pole (three term test) = -16.3 Radius of convergence (six term test) for eq 1 = 4.237 Order of pole (six term test) = 8.858 TOP MAIN SOLVE Loop bytes used=36009176, alloc=4586680, time=1.25 x[1] = 0.91 y[1] (analytic) = 0 y[1] (numeric) = 1.1333928472174244415806322687843 absolute error = 1.1333928472174244415806322687843 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04302 Order of pole (three term test) = -18.15 Radius of convergence (six term test) for eq 1 = 4.234 Order of pole (six term test) = 8.846 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 0 y[1] (numeric) = 1.1507143050641981366467413724879 absolute error = 1.1507143050641981366467413724879 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03724 Order of pole (three term test) = -19.88 Radius of convergence (six term test) for eq 1 = 4.232 Order of pole (six term test) = 8.837 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 0 y[1] (numeric) = 1.1681086516041468122290252985616 absolute error = 1.1681086516041468122290252985616 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0303 Order of pole (three term test) = -21.44 Radius of convergence (six term test) for eq 1 = 4.23 Order of pole (six term test) = 8.83 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 0 y[1] (numeric) = 1.1855752266573862776068882356767 absolute error = 1.1855752266573862776068882356767 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02236 Order of pole (three term test) = -22.8 Radius of convergence (six term test) for eq 1 = 4.229 Order of pole (six term test) = 8.827 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 0 y[1] (numeric) = 1.2031133520225240234715397792378 absolute error = 1.2031133520225240234715397792378 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01364 Order of pole (three term test) = -23.91 Radius of convergence (six term test) for eq 1 = 4.227 Order of pole (six term test) = 8.827 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 0 y[1] (numeric) = 1.2207223315246936971107718350892 absolute error = 1.2207223315246936971107718350892 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004342 Order of pole (three term test) = -24.75 Radius of convergence (six term test) for eq 1 = 4.227 Order of pole (six term test) = 8.831 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 0 y[1] (numeric) = 1.238401451071829116974253909617 absolute error = 1.238401451071829116974253909617 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.226 Order of pole (six term test) = 8.839 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 0 y[1] (numeric) = 1.2561499787192339224960153069654 absolute error = 1.2561499787192339224960153069654 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.226 Order of pole (six term test) = 8.851 TOP MAIN SOLVE Loop x[1] = 0.99 y[1] (analytic) = 0 y[1] (numeric) = 1.273967164742497241856400110027 absolute error = 1.273967164742497241856400110027 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.227 Order of pole (six term test) = 8.866 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 0 y[1] (numeric) = 1.2918522417187999294177519312924 absolute error = 1.2918522417187999294177519312924 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.228 Order of pole (six term test) = 8.884 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 0 y[1] (numeric) = 1.3098044246166499810594005607028 absolute error = 1.3098044246166499810594005607028 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.229 Order of pole (six term test) = 8.905 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = 0 y[1] (numeric) = 1.3278229108940796849856375155048 absolute error = 1.3278229108940796849856375155048 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 bytes used=40010416, alloc=4586680, time=1.40 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.23 Order of pole (six term test) = 8.93 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = 0 y[1] (numeric) = 1.3459068806053309134217661965042 absolute error = 1.3459068806053309134217661965042 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.232 Order of pole (six term test) = 8.956 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = 0 y[1] (numeric) = 1.3640554965160487127975889122219 absolute error = 1.3640554965160487127975889122219 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.234 Order of pole (six term test) = 8.984 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 0 y[1] (numeric) = 1.3822679042269970126011565584637 absolute error = 1.3822679042269970126011565584637 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.236 Order of pole (six term test) = 9.013 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 0 y[1] (numeric) = 1.4005432323063038523244162236316 absolute error = 1.4005432323063038523244162236316 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.238 Order of pole (six term test) = 9.043 TOP MAIN SOLVE Loop x[1] = 1.07 y[1] (analytic) = 0 y[1] (numeric) = 1.4188805924302370282652280982682 absolute error = 1.4188805924302370282652280982682 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.24 Order of pole (six term test) = 9.074 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 0 y[1] (numeric) = 1.4372790795325044940305054779499 absolute error = 1.4372790795325044940305054779499 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.242 Order of pole (six term test) = 9.103 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = 0 y[1] (numeric) = 1.4557377719620672172128916154865 absolute error = 1.4557377719620672172128916154865 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.244 Order of pole (six term test) = 9.132 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0 y[1] (numeric) = 1.4742557316494455068662062436629 absolute error = 1.4742557316494455068662062436629 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.246 Order of pole (six term test) = 9.159 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 0 y[1] (numeric) = 1.4928320042814930892194215202288 absolute error = 1.4928320042814930892194215202288 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.247 Order of pole (six term test) = 9.184 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 0 y[1] (numeric) = 1.5114656194846064298309863376566 absolute error = 1.5114656194846064298309863376566 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.249 Order of pole (six term test) = 9.206 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 0 y[1] (numeric) = 1.5301555910163299865201236753258 absolute error = 1.5301555910163299865201236753258 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.25 Order of pole (six term test) = 9.225 TOP MAIN SOLVE Loop bytes used=44012428, alloc=4586680, time=1.54 x[1] = 1.14 y[1] (analytic) = 0 y[1] (numeric) = 1.548900916965311236473617753948 absolute error = 1.548900916965311236473617753948 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.251 Order of pole (six term test) = 9.241 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = 0 y[1] (numeric) = 1.5677005799595524605884251141578 absolute error = 1.5677005799595524605884251141578 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.251 Order of pole (six term test) = 9.253 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 0 y[1] (numeric) = 1.5865535473828993961525537226633 absolute error = 1.5865535473828993961525537226633 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.251 Order of pole (six term test) = 9.261 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 0 y[1] (numeric) = 1.6054587715996999932656562190749 absolute error = 1.6054587715996999932656562190749 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.251 Order of pole (six term test) = 9.265 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 0 y[1] (numeric) = 1.62441519018755963891790670856 absolute error = 1.62441519018755963891790670856 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.25 Order of pole (six term test) = 9.265 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 0 y[1] (numeric) = 1.6434217261781123534149467579449 absolute error = 1.6434217261781123534149467579449 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009329 Order of pole (three term test) = -1.038 Radius of convergence (six term test) for eq 1 = 4.249 Order of pole (six term test) = 9.262 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 0 y[1] (numeric) = 1.6624772883057206249525585638698 absolute error = 1.6624772883057206249525585638698 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0185 Order of pole (three term test) = -1.481 Radius of convergence (six term test) for eq 1 = 4.248 Order of pole (six term test) = 9.254 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 0 y[1] (numeric) = 1.6815807712640097377500140528912 absolute error = 1.6815807712640097377500140528912 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02709 Order of pole (three term test) = -2.214 Radius of convergence (six term test) for eq 1 = 4.246 Order of pole (six term test) = 9.244 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 0 y[1] (numeric) = 1.7007310559701356754241098224122 absolute error = 1.7007310559701356754241098224122 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.386 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.0349 Order of pole (three term test) = -3.217 Radius of convergence (six term test) for eq 1 = 4.244 Order of pole (six term test) = 9.23 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 0 y[1] (numeric) = 1.7199270098366789524278671287943 absolute error = 1.7199270098366789524278671287943 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04173 Order of pole (three term test) = -4.468 Radius of convergence (six term test) for eq 1 = 4.241 Order of pole (six term test) = 9.213 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 0 y[1] (numeric) = 1.7391674870510500505997048836808 absolute error = 1.7391674870510500505997048836808 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04743 Order of pole (three term test) = -5.937 Radius of convergence (six term test) for eq 1 = 4.239 Order of pole (six term test) = 9.194 TOP MAIN SOLVE Loop bytes used=48013404, alloc=4586680, time=1.69 x[1] = 1.25 y[1] (analytic) = 0 y[1] (numeric) = 1.7584513288622855233782308965566 absolute error = 1.7584513288622855233782308965566 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05186 Order of pole (three term test) = -7.587 Radius of convergence (six term test) for eq 1 = 4.236 Order of pole (six term test) = 9.174 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = 0 y[1] (numeric) = 1.7777773638751072852257561880793 absolute error = 1.7777773638751072852257561880793 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05489 Order of pole (three term test) = -9.379 Radius of convergence (six term test) for eq 1 = 4.233 Order of pole (six term test) = 9.152 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 0 y[1] (numeric) = 1.7971444083511111364314739345896 absolute error = 1.7971444083511111364314739345896 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05646 Order of pole (three term test) = -11.27 Radius of convergence (six term test) for eq 1 = 4.231 Order of pole (six term test) = 9.13 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 0 y[1] (numeric) = 1.8165512665169441918509671946061 absolute error = 1.8165512665169441918509671946061 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05652 Order of pole (three term test) = -13.2 Radius of convergence (six term test) for eq 1 = 4.228 Order of pole (six term test) = 9.108 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 0 y[1] (numeric) = 1.8359967308793245943436574087664 absolute error = 1.8359967308793245943436574087664 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05505 Order of pole (three term test) = -15.14 Radius of convergence (six term test) for eq 1 = 4.225 Order of pole (six term test) = 9.086 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0 y[1] (numeric) = 1.8554795825467507076852175548876 absolute error = 1.8554795825467507076852175548876 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0521 Order of pole (three term test) = -17.03 Radius of convergence (six term test) for eq 1 = 4.222 Order of pole (six term test) = 9.066 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 0 y[1] (numeric) = 1.8749985915577409074655767328839 absolute error = 1.8749985915577409074655767328839 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04772 Order of pole (three term test) = -18.81 Radius of convergence (six term test) for eq 1 = 4.22 Order of pole (six term test) = 9.048 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 0 y[1] (numeric) = 1.8945525172154391297457890979968 absolute error = 1.8945525172154391297457890979968 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04202 Order of pole (three term test) = -20.45 Radius of convergence (six term test) for eq 1 = 4.218 Order of pole (six term test) = 9.032 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 0 y[1] (numeric) = 1.9141401084284155037394210106595 absolute error = 1.9141401084284155037394210106595 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03515 Order of pole (three term test) = -21.89 Radius of convergence (six term test) for eq 1 = 4.216 Order of pole (six term test) = 9.018 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 0 y[1] (numeric) = 1.9337601040574856940835763149549 absolute error = 1.9337601040574856940835763149549 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02729 Order of pole (three term test) = -23.1 Radius of convergence (six term test) for eq 1 = 4.215 Order of pole (six term test) = 9.008 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 0 y[1] (numeric) = 1.9534112332683670178121931702435 absolute error = 1.9534112332683670178121931702435 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01863 Order of pole (three term test) = -24.04 Radius of convergence (six term test) for eq 1 = 4.214 Order of pole (six term test) = 9.001 TOP MAIN SOLVE Loop bytes used=52014216, alloc=4652204, time=1.83 x[1] = 1.36 y[1] (analytic) = 0 y[1] (numeric) = 1.9730922158899839882314970169621 absolute error = 1.9730922158899839882314970169621 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009397 Order of pole (three term test) = -24.7 Radius of convergence (six term test) for eq 1 = 4.213 Order of pole (six term test) = 8.998 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 0 y[1] (numeric) = 1.9928017627782306796542073563531 absolute error = 1.9928017627782306796542073563531 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.213 Order of pole (six term test) = 8.999 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 0 y[1] (numeric) = 2.0125385761849922103305544330424 absolute error = 2.0125385761849922103305544330424 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.213 Order of pole (six term test) = 9.004 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 0 y[1] (numeric) = 2.0323013501322227126889793219947 absolute error = 2.0323013501322227126889793219947 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.213 Order of pole (six term test) = 9.012 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0 y[1] (numeric) = 2.052088770790872406737556211638 absolute error = 2.052088770790872406737556211638 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.214 Order of pole (six term test) = 9.024 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 0 y[1] (numeric) = 2.0718995168644518205383981739576 absolute error = 2.0718995168644518205383981739576 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.215 Order of pole (six term test) = 9.039 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 0 y[1] (numeric) = 2.091732259977016817189689177016 absolute error = 2.091732259977016817189689177016 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.217 Order of pole (six term test) = 9.057 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 0 y[1] (numeric) = 2.1115856650653538966390440250404 absolute error = 2.1115856650653538966390440250404 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.219 Order of pole (six term test) = 9.078 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 0 y[1] (numeric) = 2.1314583907751412485699711771888 absolute error = 2.1314583907751412485699711771888 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.525 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.221 Order of pole (six term test) = 9.102 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 0 y[1] (numeric) = 2.1513490898608572449592593883021 absolute error = 2.1513490898608572449592593883021 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.894 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.223 Order of pole (six term test) = 9.126 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 0 y[1] (numeric) = 2.1712564095892044828429357833329 absolute error = 2.1712564095892044828429357833329 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.551 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.225 Order of pole (six term test) = 9.152 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = 0 y[1] (numeric) = 2.1911789921458141242253832503445 absolute error = 2.1911789921458141242253832503445 relative error = -1 % Correct digits = -1 h = 0.01 bytes used=56015508, alloc=4652204, time=1.98 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.238 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.228 Order of pole (six term test) = 9.179 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = 0 y[1] (numeric) = 2.2111154750449921355122611436301 absolute error = 2.2111154750449921355122611436301 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.23 Order of pole (six term test) = 9.205 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 0 y[1] (numeric) = 2.2310644915422661076453504875123 absolute error = 2.2310644915422661076453504875123 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.233 Order of pole (six term test) = 9.231 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 0 y[1] (numeric) = 2.2510246710494886442710940199701 absolute error = 2.2510246710494886442710940199701 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.235 Order of pole (six term test) = 9.255 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = 0 y[1] (numeric) = 2.270994639552250842484288670445 absolute error = 2.270994639552250842484288670445 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.237 Order of pole (six term test) = 9.277 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = 0 y[1] (numeric) = 2.2909730200293571623423088298669 absolute error = 2.2909730200293571623423088298669 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.239 Order of pole (six term test) = 9.297 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (analytic) = 0 y[1] (numeric) = 2.3109584328741109905136917533595 absolute error = 2.3109584328741109905136917533595 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.241 Order of pole (six term test) = 9.314 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = 0 y[1] (numeric) = 2.3309494963171584528546524322253 absolute error = 2.3309494963171584528546524322253 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.242 Order of pole (six term test) = 9.328 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 0 y[1] (numeric) = 2.3509448268506365228162539219462 absolute error = 2.3509448268506365228162539219462 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.243 Order of pole (six term test) = 9.338 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = 0 y[1] (numeric) = 2.3709430396533702094586055570582 absolute error = 2.3709430396533702094586055570582 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.244 Order of pole (six term test) = 9.344 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 0 y[1] (numeric) = 2.3909427490168625922347334237184 absolute error = 2.3909427490168625922347334237184 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.244 Order of pole (six term test) = 9.347 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 0 y[1] (numeric) = 2.4109425687718207010136417172499 absolute error = 2.4109425687718207010136417172499 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008845 Order of pole (three term test) = -1.022 Radius of convergence (six term test) for eq 1 = 4.244 Order of pole (six term test) = 9.345 bytes used=60017272, alloc=4652204, time=2.12 TOP MAIN SOLVE Loop x[1] = 1.59 y[1] (analytic) = 0 y[1] (numeric) = 2.4309411127149597201047698101734 absolute error = 2.4309411127149597201047698101734 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01825 Order of pole (three term test) = -1.451 Radius of convergence (six term test) for eq 1 = 4.243 Order of pole (six term test) = 9.339 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 0 y[1] (numeric) = 2.4509369950358277250450173992913 absolute error = 2.4509369950358277250450173992913 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02722 Order of pole (three term test) = -2.172 Radius of convergence (six term test) for eq 1 = 4.242 Order of pole (six term test) = 9.33 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = 0 y[1] (numeric) = 2.4709288307433931409891530952379 absolute error = 2.4709288307433931409891530952379 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03554 Order of pole (three term test) = -3.166 Radius of convergence (six term test) for eq 1 = 4.241 Order of pole (six term test) = 9.317 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = 0 y[1] (numeric) = 2.4909152360921373417323651125771 absolute error = 2.4909152360921373417323651125771 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04302 Order of pole (three term test) = -4.41 Radius of convergence (six term test) for eq 1 = 4.239 Order of pole (six term test) = 9.3 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 0 y[1] (numeric) = 2.510894829007395288370760692677 absolute error = 2.510894829007395288370760692677 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04947 Order of pole (three term test) = -5.875 Radius of convergence (six term test) for eq 1 = 4.237 Order of pole (six term test) = 9.28 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = 0 y[1] (numeric) = 2.5308662295096878357063491215847 absolute error = 2.5308662295096878357063491215847 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05472 Order of pole (three term test) = -7.523 Radius of convergence (six term test) for eq 1 = 4.235 Order of pole (six term test) = 9.258 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = 0 y[1] (numeric) = 2.5508280601377903117170316035095 absolute error = 2.5508280601377903117170316035095 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05866 Order of pole (three term test) = -9.315 Radius of convergence (six term test) for eq 1 = 4.233 Order of pole (six term test) = 9.235 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = 0 y[1] (numeric) = 2.5707789463702831993858257624895 absolute error = 2.5707789463702831993858257624895 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06117 Order of pole (three term test) = -11.2 Radius of convergence (six term test) for eq 1 = 4.231 Order of pole (six term test) = 9.209 TOP MAIN SOLVE Loop x[1] = 1.67 y[1] (analytic) = 0 y[1] (numeric) = 2.5907175170453322192228109755599 absolute error = 2.5907175170453322192228109755599 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.19 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.06219 Order of pole (three term test) = -13.14 Radius of convergence (six term test) for eq 1 = 4.228 Order of pole (six term test) = 9.183 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = 0 y[1] (numeric) = 2.6106424047784468228864467917689 absolute error = 2.6106424047784468228864467917689 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.499 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.06168 Order of pole (three term test) = -15.09 Radius of convergence (six term test) for eq 1 = 4.226 Order of pole (six term test) = 9.157 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 0 y[1] (numeric) = 2.6305522463779680610526148054239 absolute error = 2.6305522463779680610526148054239 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.843 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.05965 Order of pole (three term test) = -16.98 Radius of convergence (six term test) for eq 1 = 4.223 Order of pole (six term test) = 9.131 TOP MAIN SOLVE Loop bytes used=64018088, alloc=4652204, time=2.27 x[1] = 1.7 y[1] (analytic) = 0 y[1] (numeric) = 2.6504456832580389793952265089867 absolute error = 2.6504456832580389793952265089867 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.581 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.05614 Order of pole (three term test) = -18.77 Radius of convergence (six term test) for eq 1 = 4.221 Order of pole (six term test) = 9.106 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = 0 y[1] (numeric) = 2.6703213618488131222123938271554 absolute error = 2.6703213618488131222123938271554 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05124 Order of pole (three term test) = -20.41 Radius of convergence (six term test) for eq 1 = 4.219 Order of pole (six term test) = 9.082 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 0 y[1] (numeric) = 2.690177934003659380519007632865 absolute error = 2.690177934003659380519007632865 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04508 Order of pole (three term test) = -21.86 Radius of convergence (six term test) for eq 1 = 4.217 Order of pole (six term test) = 9.061 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = 0 y[1] (numeric) = 2.710014057403124306679444748079 absolute error = 2.710014057403124306679444748079 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0378 Order of pole (three term test) = -23.07 Radius of convergence (six term test) for eq 1 = 4.215 Order of pole (six term test) = 9.042 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = 0 y[1] (numeric) = 2.7298283959554161269163555708078 absolute error = 2.7298283959554161269163555708078 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0296 Order of pole (three term test) = -24.03 Radius of convergence (six term test) for eq 1 = 4.214 Order of pole (six term test) = 9.026 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 0 y[1] (numeric) = 2.74961962019317801204764476536 absolute error = 2.74961962019317801204764476536 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02069 Order of pole (three term test) = -24.69 Radius of convergence (six term test) for eq 1 = 4.213 Order of pole (six term test) = 9.014 TOP MAIN SOLVE Loop x[1] = 1.76 y[1] (analytic) = 0 y[1] (numeric) = 2.7693864076663217110274356857922 absolute error = 2.7693864076663217110274356857922 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0113 Order of pole (three term test) = -25.04 Radius of convergence (six term test) for eq 1 = 4.213 Order of pole (six term test) = 9.005 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = 0 y[1] (numeric) = 2.7891274433306964064688982146171 absolute error = 2.7891274433306964064688982146171 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.00169 Order of pole (three term test) = -25.07 Radius of convergence (six term test) for eq 1 = 4.212 Order of pole (six term test) = 9 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 0 y[1] (numeric) = 2.8088414199323716112042949716875 absolute error = 2.8088414199323716112042949716875 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.213 Order of pole (six term test) = 8.998 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = 0 y[1] (numeric) = 2.8285270383873170847227718201363 absolute error = 2.8285270383873170847227718201363 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.213 Order of pole (six term test) = 9.001 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0 y[1] (numeric) = 2.8481830081562671023966308505539 absolute error = 2.8481830081562671023966308505539 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.214 Order of pole (six term test) = 9.007 TOP MAIN SOLVE Loop bytes used=68019936, alloc=4652204, time=2.41 x[1] = 1.81 y[1] (analytic) = 0 y[1] (numeric) = 2.8678080476145609528945900142945 absolute error = 2.8678080476145609528945900142945 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.216 Order of pole (six term test) = 9.016 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = 0 y[1] (numeric) = 2.8874008844167562639840686474904 absolute error = 2.8874008844167562639840686474904 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.218 Order of pole (six term test) = 9.029 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = 0 y[1] (numeric) = 2.9069602558558166577186777601509 absolute error = 2.9069602558558166577186777601509 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.22 Order of pole (six term test) = 9.045 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = 0 y[1] (numeric) = 2.9264849092166803062545673911845 absolute error = 2.9264849092166803062545673911845 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.222 Order of pole (six term test) = 9.063 TOP MAIN SOLVE Loop x[1] = 1.85 y[1] (analytic) = 0 y[1] (numeric) = 2.9459736021240211925023179694805 absolute error = 2.9459736021240211925023179694805 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.225 Order of pole (six term test) = 9.083 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = 0 y[1] (numeric) = 2.965425102884020268573293159845 absolute error = 2.965425102884020268573293159845 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.227 Order of pole (six term test) = 9.104 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = 0 y[1] (numeric) = 2.9848381908199692424180270496733 absolute error = 2.9848381908199692424180270496733 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.23 Order of pole (six term test) = 9.126 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = 0 y[1] (numeric) = 3.0042116566015354019125596093301 absolute error = 3.0042116566015354019125596093301 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.233 Order of pole (six term test) = 9.149 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 0 y[1] (numeric) = 3.0235443025675216985086146451902 absolute error = 3.0235443025675216985086146451902 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.236 Order of pole (six term test) = 9.17 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 0 y[1] (numeric) = 3.042834943041962251868635931739 absolute error = 3.042834943041962251868635931739 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.238 Order of pole (six term test) = 9.191 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 0 y[1] (numeric) = 3.0620824046433994949750329806326 absolute error = 3.0620824046433994949750329806326 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.241 Order of pole (six term test) = 9.21 TOP MAIN SOLVE Loop bytes used=72020940, alloc=4652204, time=2.56 x[1] = 1.92 y[1] (analytic) = 0 y[1] (numeric) = 3.0812855265871953482403434056237 absolute error = 3.0812855265871953482403434056237 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.438 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.243 Order of pole (six term test) = 9.227 TOP MAIN SOLVE Loop x[1] = 1.93 y[1] (analytic) = 0 y[1] (numeric) = 3.1004431609807350832582029106268 absolute error = 3.1004431609807350832582029106268 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.245 Order of pole (six term test) = 9.242 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = 0 y[1] (numeric) = 3.1195541731113889040451913397363 absolute error = 3.1195541731113889040451913397363 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.247 Order of pole (six term test) = 9.253 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = 0 y[1] (numeric) = 3.1386174417271027278797201416651 absolute error = 3.1386174417271027278797201416651 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.249 Order of pole (six term test) = 9.261 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 0 y[1] (numeric) = 3.1576318593094961810362605453492 absolute error = 3.1576318593094961810362605453492 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.25 Order of pole (six term test) = 9.265 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = 0 y[1] (numeric) = 3.1765963323393524286861179574136 absolute error = 3.1765963323393524286861179574136 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008346 Order of pole (three term test) = -1.005 Radius of convergence (six term test) for eq 1 = 4.251 Order of pole (six term test) = 9.266 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 0 y[1] (numeric) = 3.1955097815543911248023842971488 absolute error = 3.1955097815543911248023842971488 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01797 Order of pole (three term test) = -1.415 Radius of convergence (six term test) for eq 1 = 4.251 Order of pole (six term test) = 9.262 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = 0 y[1] (numeric) = 3.2143711421992224888607419968909 absolute error = 3.2143711421992224888607419968909 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02733 Order of pole (three term test) = -2.114 Radius of convergence (six term test) for eq 1 = 4.251 Order of pole (six term test) = 9.254 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0 y[1] (numeric) = 3.2331793642673872832581443923473 absolute error = 3.2331793642673872832581443923473 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0362 Order of pole (three term test) = -3.088 Radius of convergence (six term test) for eq 1 = 4.251 Order of pole (six term test) = 9.243 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 0 y[1] (numeric) = 3.2519334127353942704744839472688 absolute error = 3.2519334127353942704744839472688 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04437 Order of pole (three term test) = -4.312 Radius of convergence (six term test) for eq 1 = 4.25 Order of pole (six term test) = 9.228 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 0 y[1] (numeric) = 3.2706322677886735638953394518561 absolute error = 3.2706322677886735638953394518561 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05165 Order of pole (three term test) = -5.758 Radius of convergence (six term test) for eq 1 = 4.249 Order of pole (six term test) = 9.209 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = 0 y[1] (numeric) = 3.289274925039371142747485883857 absolute error = 3.289274925039371142747485883857 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05786 Order of pole (three term test) = -7.392 Radius of convergence (six term test) for eq 1 = 4.248 Order of pole (six term test) = 9.187 bytes used=76023424, alloc=4652204, time=2.71 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = 0 y[1] (numeric) = 3.3078603957359166716699808788201 absolute error = 3.3078603957359166716699808788201 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06286 Order of pole (three term test) = -9.174 Radius of convergence (six term test) for eq 1 = 4.246 Order of pole (six term test) = 9.163 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = 0 y[1] (numeric) = 3.326387706964303641007867910474 absolute error = 3.326387706964303641007867910474 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0665 Order of pole (three term test) = -11.06 Radius of convergence (six term test) for eq 1 = 4.244 Order of pole (six term test) = 9.136 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = 0 y[1] (numeric) = 3.3448559018410277169992407880058 absolute error = 3.3448559018410277169992407880058 relative error = -1 % Correct digits = -1 h = 0.01 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) = -13 Radius of convergence (six term test) for eq 1 = 4.242 Order of pole (six term test) = 9.108 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = 0 y[1] (numeric) = 3.3632640396976360537387345247056 absolute error = 3.3632640396976360537387345247056 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06942 Order of pole (three term test) = -14.96 Radius of convergence (six term test) for eq 1 = 4.24 Order of pole (six term test) = 9.078 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 0 y[1] (numeric) = 3.3816111962568471633449858048185 absolute error = 3.3816111962568471633449858048185 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06861 Order of pole (three term test) = -16.87 Radius of convergence (six term test) for eq 1 = 4.238 Order of pole (six term test) = 9.048 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = 0 y[1] (numeric) = 3.3998964638002077594455345478231 absolute error = 3.3998964638002077594455345478231 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06629 Order of pole (three term test) = -18.7 Radius of convergence (six term test) for eq 1 = 4.236 Order of pole (six term test) = 9.018 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 0 y[1] (numeric) = 3.4181189513272597743460832720984 absolute error = 3.4181189513272597743460832720984 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0625 Order of pole (three term test) = -20.38 Radius of convergence (six term test) for eq 1 = 4.234 Order of pole (six term test) = 8.989 TOP MAIN SOLVE Loop x[1] = 2.11 y[1] (analytic) = 0 y[1] (numeric) = 3.4362777847061974946255168187968 absolute error = 3.4362777847061974946255168187968 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05735 Order of pole (three term test) = -21.89 Radius of convergence (six term test) for eq 1 = 4.232 Order of pole (six term test) = 8.96 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = 0 y[1] (numeric) = 3.4543721068160014560849153001552 absolute error = 3.4543721068160014560849153001552 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05096 Order of pole (three term test) = -23.18 Radius of convergence (six term test) for eq 1 = 4.23 Order of pole (six term test) = 8.934 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 0 y[1] (numeric) = 3.4724010776800423798169988452522 absolute error = 3.4724010776800423798169988452522 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04348 Order of pole (three term test) = -24.21 Radius of convergence (six term test) for eq 1 = 4.229 Order of pole (six term test) = 8.909 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = 0 y[1] (numeric) = 3.4903638745911550096483373257227 absolute error = 3.4903638745911550096483373257227 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0351 Order of pole (three term test) = -24.96 Radius of convergence (six term test) for eq 1 = 4.228 Order of pole (six term test) = 8.887 TOP MAIN SOLVE Loop bytes used=80024536, alloc=4652204, time=2.86 x[1] = 2.15 y[1] (analytic) = 0 y[1] (numeric) = 3.5082596922281882205029868295712 absolute error = 3.5082596922281882205029868295712 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02605 Order of pole (three term test) = -25.41 Radius of convergence (six term test) for eq 1 = 4.227 Order of pole (six term test) = 8.868 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 0 y[1] (numeric) = 3.526087742764044200680883169927 absolute error = 3.526087742764044200680883169927 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01654 Order of pole (three term test) = -25.54 Radius of convergence (six term test) for eq 1 = 4.226 Order of pole (six term test) = 8.853 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 0 y[1] (numeric) = 3.543847255965225862158695296624 absolute error = 3.543847255965225862158695296624 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.006835 Order of pole (three term test) = -25.36 Radius of convergence (six term test) for eq 1 = 4.226 Order of pole (six term test) = 8.841 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 0 y[1] (numeric) = 3.5615374792829178955175946116942 absolute error = 3.5615374792829178955175946116942 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.227 Order of pole (six term test) = 8.832 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 0 y[1] (numeric) = 3.5791576779356330538929199054448 absolute error = 3.5791576779356330538929199054448 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.227 Order of pole (six term test) = 8.828 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 0 y[1] (numeric) = 3.5967071349834613175420549575306 absolute error = 3.5967071349834613175420549575306 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.228 Order of pole (six term test) = 8.827 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = 0 y[1] (numeric) = 3.6141851513939655515681530401912 absolute error = 3.6141851513939655515681530401912 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.23 Order of pole (six term test) = 8.829 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = 0 y[1] (numeric) = 3.6315910460997731185659237654345 absolute error = 3.6315910460997731185659237654345 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.232 Order of pole (six term test) = 8.835 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = 0 y[1] (numeric) = 3.6489241560479186402424589712806 absolute error = 3.6489241560479186402424589712806 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.234 Order of pole (six term test) = 8.844 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 0 y[1] (numeric) = 3.666183836240998712410592958902 absolute error = 3.666183836240998712410592958902 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.236 Order of pole (six term test) = 8.856 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 0 y[1] (numeric) = 3.6833694597702048613873489899345 absolute error = 3.6833694597702048613873489899345 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.239 Order of pole (six term test) = 8.87 TOP MAIN SOLVE Loop bytes used=84025504, alloc=4717728, time=3.00 x[1] = 2.26 y[1] (analytic) = 0 y[1] (numeric) = 3.7004804178403063822256555250844 absolute error = 3.7004804178403063822256555250844 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.242 Order of pole (six term test) = 8.886 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = 0 y[1] (numeric) = 3.7175161197866599160745792860097 absolute error = 3.7175161197866599160745792860097 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.245 Order of pole (six term test) = 8.903 TOP MAIN SOLVE Loop x[1] = 2.28 y[1] (analytic) = 0 y[1] (numeric) = 3.7344759930843277012565699567366 absolute error = 3.7344759930843277012565699567366 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.248 Order of pole (six term test) = 8.92 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 0 y[1] (numeric) = 3.7513594833493913665708784594637 absolute error = 3.7513594833493913665708784594637 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.251 Order of pole (six term test) = 8.938 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 0 y[1] (numeric) = 3.7681660543325529223302197327656 absolute error = 3.7681660543325529223302197327656 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.254 Order of pole (six term test) = 8.956 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = 0 y[1] (numeric) = 3.7848951879051192414129355736507 absolute error = 3.7848951879051192414129355736507 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.257 Order of pole (six term test) = 8.972 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 0 y[1] (numeric) = 3.8015463840374708061167673745169 absolute error = 3.8015463840374708061167673745169 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.26 Order of pole (six term test) = 8.987 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = 0 y[1] (numeric) = 3.8181191607701198240363065633185 absolute error = 3.8181191607701198240363065633185 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.263 Order of pole (six term test) = 9 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 0 y[1] (numeric) = 3.8346130541774669850099440586425 absolute error = 3.8346130541774669850099440586425 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.266 Order of pole (six term test) = 9.011 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 0 y[1] (numeric) = 3.8510276183243701391014020044439 absolute error = 3.8510276183243701391014020044439 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.268 Order of pole (six term test) = 9.018 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = 0 y[1] (numeric) = 3.8673624252156420205547532755951 absolute error = 3.8673624252156420205547532755951 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001818 Order of pole (three term test) = -0.8981 Radius of convergence (six term test) for eq 1 = 4.27 Order of pole (six term test) = 9.022 TOP MAIN SOLVE Loop x[1] = 2.37 y[1] (analytic) = 0 y[1] (numeric) = 3.8836170647385978228994892991921 absolute error = 3.8836170647385978228994892991921 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0116 bytes used=88026140, alloc=4717728, time=3.15 Order of pole (three term test) = -1.102 Radius of convergence (six term test) for eq 1 = 4.271 Order of pole (six term test) = 9.023 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = 0 y[1] (numeric) = 3.8997911445987769443416341732773 absolute error = 3.8997911445987769443416341732773 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02143 Order of pole (three term test) = -1.597 Radius of convergence (six term test) for eq 1 = 4.273 Order of pole (six term test) = 9.021 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 0 y[1] (numeric) = 3.9158842902489665689627913237748 absolute error = 3.9158842902489665689627913237748 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03107 Order of pole (three term test) = -2.373 Radius of convergence (six term test) for eq 1 = 4.273 Order of pole (six term test) = 9.014 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 0 y[1] (numeric) = 3.9318961448116579270103747300083 absolute error = 3.9318961448116579270103747300083 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04032 Order of pole (three term test) = -3.413 Radius of convergence (six term test) for eq 1 = 4.274 Order of pole (six term test) = 9.004 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 0 y[1] (numeric) = 3.947826368995069085889754498755 absolute error = 3.947826368995069085889754498755 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04897 Order of pole (three term test) = -4.693 Radius of convergence (six term test) for eq 1 = 4.274 Order of pole (six term test) = 8.99 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = 0 y[1] (numeric) = 3.9636746410028709617917511448182 absolute error = 3.9636746410028709617917511448182 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05683 Order of pole (three term test) = -6.185 Radius of convergence (six term test) for eq 1 = 4.274 Order of pole (six term test) = 8.972 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 0 y[1] (numeric) = 3.9794406564377559098709494099605 absolute error = 3.9794406564377559098709494099605 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06371 Order of pole (three term test) = -7.854 Radius of convergence (six term test) for eq 1 = 4.273 Order of pole (six term test) = 8.951 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = 0 y[1] (numeric) = 3.9951241281989907484269272046857 absolute error = 3.9951241281989907484269272046857 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06946 Order of pole (three term test) = -9.663 Radius of convergence (six term test) for eq 1 = 4.272 Order of pole (six term test) = 8.927 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = 0 y[1] (numeric) = 4.01072478637409839975394326193 absolute error = 4.01072478637409839975394326193 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07394 Order of pole (three term test) = -11.57 Radius of convergence (six term test) for eq 1 = 4.271 Order of pole (six term test) = 8.9 TOP MAIN SOLVE Loop x[1] = 2.46 y[1] (analytic) = 0 y[1] (numeric) = 4.0262423781248144875596205848591 absolute error = 4.0262423781248144875596205848591 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07705 Order of pole (three term test) = -13.53 Radius of convergence (six term test) for eq 1 = 4.27 Order of pole (six term test) = 8.871 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = 0 y[1] (numeric) = 4.0416766675674672186721169569259 absolute error = 4.0416766675674672186721169569259 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0787 Order of pole (three term test) = -15.5 Radius of convergence (six term test) for eq 1 = 4.268 Order of pole (six term test) = 8.84 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = 0 y[1] (numeric) = 4.0570274356479306959332155430709 absolute error = 4.0570274356479306959332155430709 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07886 Order of pole (three term test) = -17.43 Radius of convergence (six term test) for eq 1 = 4.267 Order of pole (six term test) = 8.808 TOP MAIN SOLVE Loop bytes used=92026932, alloc=4717728, time=3.30 x[1] = 2.49 y[1] (analytic) = 0 y[1] (numeric) = 4.0722944800113034606939844922503 absolute error = 4.0722944800113034606939844922503 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0775 Order of pole (three term test) = -19.27 Radius of convergence (six term test) for eq 1 = 4.265 Order of pole (six term test) = 8.775 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 0 y[1] (numeric) = 4.0874776148664655483740844429411 absolute error = 4.0874776148664655483740844429411 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07466 Order of pole (three term test) = -20.98 Radius of convergence (six term test) for eq 1 = 4.263 Order of pole (six term test) = 8.741 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = 0 y[1] (numeric) = 4.1025766708456686604951966596309 absolute error = 4.1025766708456686604951966596309 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07039 Order of pole (three term test) = -22.52 Radius of convergence (six term test) for eq 1 = 4.261 Order of pole (six term test) = 8.708 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 0 y[1] (numeric) = 4.1175914948593152130228973235316 absolute error = 4.1175914948593152130228973235316 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0648 Order of pole (three term test) = -23.85 Radius of convergence (six term test) for eq 1 = 4.26 Order of pole (six term test) = 8.676 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = 0 y[1] (numeric) = 4.1325219499460830155025878437862 absolute error = 4.1325219499460830155025878437862 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05802 Order of pole (three term test) = -24.94 Radius of convergence (six term test) for eq 1 = 4.258 Order of pole (six term test) = 8.645 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 0 y[1] (numeric) = 4.1473679151185531702838024087438 absolute error = 4.1473679151185531702838024087438 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0502 Order of pole (three term test) = -25.75 Radius of convergence (six term test) for eq 1 = 4.257 Order of pole (six term test) = 8.616 TOP MAIN SOLVE Loop x[1] = 2.55 y[1] (analytic) = 0 y[1] (numeric) = 4.1621292852044994581937466078011 absolute error = 4.1621292852044994581937466078011 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04153 Order of pole (three term test) = -26.27 Radius of convergence (six term test) for eq 1 = 4.256 Order of pole (six term test) = 8.589 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = 0 y[1] (numeric) = 4.1768059706839979986092912540658 absolute error = 4.1768059706839979986092912540658 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03222 Order of pole (three term test) = -26.48 Radius of convergence (six term test) for eq 1 = 4.255 Order of pole (six term test) = 8.565 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 0 y[1] (numeric) = 4.1913978975225163404075800069219 absolute error = 4.1913978975225163404075800069219 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0225 Order of pole (three term test) = -26.39 Radius of convergence (six term test) for eq 1 = 4.255 Order of pole (six term test) = 8.543 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = 0 y[1] (numeric) = 4.2059050070001413583193137532942 absolute error = 4.2059050070001413583193137532942 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0126 Order of pole (three term test) = -25.99 Radius of convergence (six term test) for eq 1 = 4.255 Order of pole (six term test) = 8.525 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = 0 y[1] (numeric) = 4.220327255537105399478601155013 absolute error = 4.220327255537105399478601155013 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.002765 Order of pole (three term test) = -25.29 Radius of convergence (six term test) for eq 1 = 4.255 Order of pole (six term test) = 8.51 TOP MAIN SOLVE Loop bytes used=96028044, alloc=4717728, time=3.45 x[1] = 2.6 y[1] (analytic) = 0 y[1] (numeric) = 4.2346646145157700503072937884093 absolute error = 4.2346646145157700503072937884093 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.256 Order of pole (six term test) = 8.499 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = 0 y[1] (numeric) = 4.2489170700992266772662773447477 absolute error = 4.2489170700992266772662773447477 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.257 Order of pole (six term test) = 8.491 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = 0 y[1] (numeric) = 4.2630846230466725395482894777961 absolute error = 4.2630846230466725395482894777961 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.259 Order of pole (six term test) = 8.486 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = 0 y[1] (numeric) = 4.277167288525720780686825054511 absolute error = 4.277167288525720780686825054511 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.261 Order of pole (six term test) = 8.485 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = 0 y[1] (numeric) = 4.2911650959218019826298391637347 absolute error = 4.2911650959218019826298391637347 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.263 Order of pole (six term test) = 8.487 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = 0 y[1] (numeric) = 4.3050780886448142134900527625854 absolute error = 4.3050780886448142134900527625854 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.265 Order of pole (six term test) = 8.492 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = 0 y[1] (numeric) = 4.3189063239331776224416095881369 absolute error = 4.3189063239331776224416095881369 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.268 Order of pole (six term test) = 8.499 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 0 y[1] (numeric) = 4.3326498726554486356752729893681 absolute error = 4.3326498726554486356752729893681 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.271 Order of pole (six term test) = 8.509 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 0 y[1] (numeric) = 4.346308819109647689617337579421 absolute error = 4.346308819109647689617337579421 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.274 Order of pole (six term test) = 8.52 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = 0 y[1] (numeric) = 4.3598832608204532054961256149766 absolute error = 4.3598832608204532054961256149766 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.278 Order of pole (six term test) = 8.532 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 0 y[1] (numeric) = 4.3733733083344131666013892192323 absolute error = 4.3733733083344131666013892192323 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.281 Order of pole (six term test) = 8.546 TOP MAIN SOLVE Loop bytes used=100029300, alloc=4717728, time=3.60 x[1] = 2.71 y[1] (analytic) = 0 y[1] (numeric) = 4.3867790850133242100779266512838 absolute error = 4.3867790850133242100779266512838 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.285 Order of pole (six term test) = 8.559 TOP MAIN SOLVE Loop x[1] = 2.72 y[1] (analytic) = 0 y[1] (numeric) = 4.4001007268259265927246900442672 absolute error = 4.4001007268259265927246900442672 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.288 Order of pole (six term test) = 8.573 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 0 y[1] (numeric) = 4.4133383821380617389747590415184 absolute error = 4.4133383821380617389747590415184 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.292 Order of pole (six term test) = 8.585 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = 0 y[1] (numeric) = 4.4264922115014373329837668009027 absolute error = 4.4264922115014373329837668009027 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.295 Order of pole (six term test) = 8.597 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = 0 y[1] (numeric) = 4.4395623874411430795557826970704 absolute error = 4.4395623874411430795557826970704 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.299 Order of pole (six term test) = 8.606 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 0 y[1] (numeric) = 4.452549094242058334507865564658 absolute error = 4.452549094242058334507865564658 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.302 Order of pole (six term test) = 8.614 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = 0 y[1] (numeric) = 4.4654525277342907980531137099835 absolute error = 4.4654525277342907980531137099835 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.002161 Order of pole (three term test) = -0.9 Radius of convergence (six term test) for eq 1 = 4.304 Order of pole (six term test) = 8.619 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 0 y[1] (numeric) = 4.4782728950777833789103676131999 absolute error = 4.4782728950777833789103676131999 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01206 Order of pole (three term test) = -1.107 Radius of convergence (six term test) for eq 1 = 4.307 Order of pole (six term test) = 8.622 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 0 y[1] (numeric) = 4.491010414546224176171619364781 absolute error = 4.491010414546224176171619364781 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02214 Order of pole (three term test) = -1.595 Radius of convergence (six term test) for eq 1 = 4.309 Order of pole (six term test) = 8.621 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 0 y[1] (numeric) = 4.5036653153103922945160338426311 absolute error = 4.5036653153103922945160338426311 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03221 Order of pole (three term test) = -2.356 Radius of convergence (six term test) for eq 1 = 4.311 Order of pole (six term test) = 8.617 TOP MAIN SOLVE Loop x[1] = 2.81 y[1] (analytic) = 0 y[1] (numeric) = 4.5162378372210699101823748860054 absolute error = 4.5162378372210699101823748860054 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04206 Order of pole (three term test) = -3.373 Radius of convergence (six term test) for eq 1 = 4.312 Order of pole (six term test) = 8.61 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = 0 y[1] (numeric) = 4.5287282305916486442136829901382 absolute error = 4.5287282305916486442136829901382 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0515 Order of pole (three term test) = -4.626 Radius of convergence (six term test) for eq 1 = 4.313 Order of pole (six term test) = 8.599 TOP MAIN SOLVE Loop bytes used=104030164, alloc=4717728, time=3.74 x[1] = 2.83 y[1] (analytic) = 0 y[1] (numeric) = 4.5411367559805558798619659215018 absolute error = 4.5411367559805558798619659215018 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06032 Order of pole (three term test) = -6.089 Radius of convergence (six term test) for eq 1 = 4.314 Order of pole (six term test) = 8.584 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = 0 y[1] (numeric) = 4.5534636839736241866524187404207 absolute error = 4.5534636839736241866524187404207 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06834 Order of pole (three term test) = -7.733 Radius of convergence (six term test) for eq 1 = 4.315 Order of pole (six term test) = 8.567 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 0 y[1] (numeric) = 4.5657092949665244883904510407341 absolute error = 4.5657092949665244883904510407341 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07541 Order of pole (three term test) = -9.522 Radius of convergence (six term test) for eq 1 = 4.315 Order of pole (six term test) = 8.546 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = 0 y[1] (numeric) = 4.5778738789473810402480220207351 absolute error = 4.5778738789473810402480220207351 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08136 Order of pole (three term test) = -11.42 Radius of convergence (six term test) for eq 1 = 4.315 Order of pole (six term test) = 8.522 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 0 y[1] (numeric) = 4.5899577352796836648445145118974 absolute error = 4.5899577352796836648445145118974 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08607 Order of pole (three term test) = -13.39 Radius of convergence (six term test) for eq 1 = 4.314 Order of pole (six term test) = 8.495 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = 0 y[1] (numeric) = 4.6019611724856100427517592804864 absolute error = 4.6019611724856100427517592804864 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08944 Order of pole (three term test) = -15.38 Radius of convergence (six term test) for eq 1 = 4.313 Order of pole (six term test) = 8.466 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = 0 y[1] (numeric) = 4.6138845080298681628627987621198 absolute error = 4.6138845080298681628627987621198 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09139 Order of pole (three term test) = -17.36 Radius of convergence (six term test) for eq 1 = 4.313 Order of pole (six term test) = 8.435 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 0 y[1] (numeric) = 4.6257280681041663162752266465558 absolute error = 4.6257280681041663162752266465558 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09186 Order of pole (three term test) = -19.28 Radius of convergence (six term test) for eq 1 = 4.312 Order of pole (six term test) = 8.402 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = 0 y[1] (numeric) = 4.6374921874124152673999786709449 absolute error = 4.6374921874124152673999786709449 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09085 Order of pole (three term test) = -21.09 Radius of convergence (six term test) for eq 1 = 4.31 Order of pole (six term test) = 8.368 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = 0 y[1] (numeric) = 4.6491772089567644615009900936377 absolute error = 4.6491772089567644615009900936377 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08836 Order of pole (three term test) = -22.77 Radius of convergence (six term test) for eq 1 = 4.309 Order of pole (six term test) = 8.333 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = 0 y[1] (numeric) = 4.6607834838245713323206204848449 absolute error = 4.6607834838245713323206204848449 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08446 Order of pole (three term test) = -24.26 Radius of convergence (six term test) for eq 1 = 4.308 Order of pole (six term test) = 8.298 TOP MAIN SOLVE Loop bytes used=108031200, alloc=4717728, time=3.89 x[1] = 2.94 y[1] (analytic) = 0 y[1] (numeric) = 4.67231137097639996030211263142 absolute error = 4.67231137097639996030211263142 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07921 Order of pole (three term test) = -25.54 Radius of convergence (six term test) for eq 1 = 4.307 Order of pole (six term test) = 8.263 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 0 y[1] (numeric) = 4.683761237035142504563995308223 absolute error = 4.683761237035142504563995308223 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07273 Order of pole (three term test) = -26.58 Radius of convergence (six term test) for eq 1 = 4.306 Order of pole (six term test) = 8.229 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 0 y[1] (numeric) = 4.6951334560763539935182921077343 absolute error = 4.6951334560763539935182921077343 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06515 Order of pole (three term test) = -27.35 Radius of convergence (six term test) for eq 1 = 4.305 Order of pole (six term test) = 8.196 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = 0 y[1] (numeric) = 4.7064284094198882130837150663789 absolute error = 4.7064284094198882130837150663789 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05665 Order of pole (three term test) = -27.84 Radius of convergence (six term test) for eq 1 = 4.304 Order of pole (six term test) = 8.164 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 0 y[1] (numeric) = 4.7176464854229195809763704201137 absolute error = 4.7176464854229195809763704201137 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0474 Order of pole (three term test) = -28.04 Radius of convergence (six term test) for eq 1 = 4.303 Order of pole (six term test) = 8.134 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = 0 y[1] (numeric) = 4.7287880792744330436319614014343 absolute error = 4.7287880792744330436319614014343 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03762 Order of pole (three term test) = -27.94 Radius of convergence (six term test) for eq 1 = 4.303 Order of pole (six term test) = 8.107 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 0 y[1] (numeric) = 4.7398535927912611819095230686327 absolute error = 4.7398535927912611819095230686327 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02752 Order of pole (three term test) = -27.54 Radius of convergence (six term test) for eq 1 = 4.303 Order of pole (six term test) = 8.081 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = 0 y[1] (numeric) = 4.7508434342157448657464535450269 absolute error = 4.7508434342157448657464535450269 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01732 Order of pole (three term test) = -26.85 Radius of convergence (six term test) for eq 1 = 4.303 Order of pole (six term test) = 8.059 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = 0 y[1] (numeric) = 4.7617580180150909591900976309034 absolute error = 4.7617580180150909591900976309034 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007242 Order of pole (three term test) = -25.9 Radius of convergence (six term test) for eq 1 = 4.303 Order of pole (six term test) = 8.04 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = 0 y[1] (numeric) = 4.7725977646824977484460569677604 absolute error = 4.7725977646824977484460569677604 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.304 Order of pole (six term test) = 8.023 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = 0 y[1] (numeric) = 4.7833631005401159493917662248865 absolute error = 4.7833631005401159493917662248865 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.306 Order of pole (six term test) = 8.01 TOP MAIN SOLVE Loop bytes used=112032196, alloc=4717728, time=4.03 x[1] = 3.05 y[1] (analytic) = 0 y[1] (numeric) = 4.7940544575439103499490231100648 absolute error = 4.7940544575439103499490231100648 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.307 Order of pole (six term test) = 7.999 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = 0 y[1] (numeric) = 4.804672273090484359242883245206 absolute error = 4.804672273090484359242883245206 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.309 Order of pole (six term test) = 7.992 TOP MAIN SOLVE Loop x[1] = 3.07 y[1] (analytic) = 0 y[1] (numeric) = 4.8152169898259269719561936523615 absolute error = 4.8152169898259269719561936523615 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.312 Order of pole (six term test) = 7.988 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = 0 y[1] (numeric) = 4.8256890554567389149858665863179 absolute error = 4.8256890554567389149858665863179 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.314 Order of pole (six term test) = 7.986 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = 0 y[1] (numeric) = 4.8360889225628920265925313122485 absolute error = 4.8360889225628920265925313122485 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.317 Order of pole (six term test) = 7.987 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = 0 y[1] (numeric) = 4.8464170484130732277899219278242 absolute error = 4.8464170484130732277899219278242 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.32 Order of pole (six term test) = 7.991 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = 0 y[1] (numeric) = 4.8566738947821617837314495698172 absolute error = 4.8566738947821617837314495698172 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.324 Order of pole (six term test) = 7.996 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = 0 y[1] (numeric) = 4.8668599277709859212128863287956 absolute error = 4.8668599277709859212128863287956 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.327 Order of pole (six term test) = 8.002 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = 0 y[1] (numeric) = 4.876975617628402268923080368511 absolute error = 4.876975617628402268923080368511 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.331 Order of pole (six term test) = 8.01 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = 0 y[1] (numeric) = 4.8870214385757390214477689634728 absolute error = 4.8870214385757390214477689634728 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.335 Order of pole (six term test) = 8.018 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = 0 y[1] (numeric) = 4.8969978686336411978815644404764 absolute error = 4.8969978686336411978815644404764 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.339 Order of pole (six term test) = 8.026 TOP MAIN SOLVE Loop x[1] = 3.16 y[1] (analytic) = 0 y[1] (numeric) = 4.9069053894513538727555033275414 absolute error = 4.9069053894513538727555033275414 relative error = -1 % Correct digits = -1 h = 0.01 bytes used=116033464, alloc=4717728, time=4.18 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.342 Order of pole (six term test) = 8.034 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (analytic) = 0 y[1] (numeric) = 4.9167444861384768022771564698026 absolute error = 4.9167444861384768022771564698026 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.346 Order of pole (six term test) = 8.042 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = 0 y[1] (numeric) = 4.9265156470992214539526382784095 absolute error = 4.9265156470992214539526382784095 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.35 Order of pole (six term test) = 8.048 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = 0 y[1] (numeric) = 4.9362193638691990737718514362393 absolute error = 4.9362193638691990737718514362393 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.353 Order of pole (six term test) = 8.053 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = 0 y[1] (numeric) = 4.9458561309547660934595021555217 absolute error = 4.9458561309547660934595021555217 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001555 Order of pole (three term test) = -0.8964 Radius of convergence (six term test) for eq 1 = 4.357 Order of pole (six term test) = 8.056 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = 0 y[1] (numeric) = 4.9554264456749508919082154177065 absolute error = 4.9554264456749508919082154177065 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01152 Order of pole (three term test) = -1.076 Radius of convergence (six term test) for eq 1 = 4.36 Order of pole (six term test) = 8.057 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = 0 y[1] (numeric) = 4.964930808005983680815044709468 absolute error = 4.964930808005983680815044709468 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02185 Order of pole (three term test) = -1.524 Radius of convergence (six term test) for eq 1 = 4.362 Order of pole (six term test) = 8.055 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (analytic) = 0 y[1] (numeric) = 4.9743697204284490856539784772207 absolute error = 4.9743697204284490856539784772207 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03235 Order of pole (three term test) = -2.233 Radius of convergence (six term test) for eq 1 = 4.365 Order of pole (six term test) = 8.05 TOP MAIN SOLVE Loop x[1] = 3.24 y[1] (analytic) = 0 y[1] (numeric) = 4.9837436877770788402679634276144 absolute error = 4.9837436877770788402679634276144 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04284 Order of pole (three term test) = -3.19 Radius of convergence (six term test) for eq 1 = 4.367 Order of pole (six term test) = 8.042 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = 0 y[1] (numeric) = 4.9930532170931999073074320012598 absolute error = 4.9930532170931999073074320012598 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05312 Order of pole (three term test) = -4.379 Radius of convergence (six term test) for eq 1 = 4.369 Order of pole (six term test) = 8.031 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = 0 y[1] (numeric) = 5.0022988174798512781525954710347 absolute error = 5.0022988174798512781525954710347 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06303 Order of pole (three term test) = -5.777 Radius of convergence (six term test) for eq 1 = 4.37 Order of pole (six term test) = 8.017 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = 0 y[1] (numeric) = 5.0114809999595806954311339230173 absolute error = 5.0114809999595806954311339230173 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07238 Order of pole (three term test) = -7.36 Radius of convergence (six term test) for eq 1 = 4.372 Order of pole (six term test) = 7.999 TOP MAIN SOLVE Loop bytes used=120034732, alloc=4717728, time=4.33 x[1] = 3.28 y[1] (analytic) = 0 y[1] (numeric) = 5.0206002773349305793034724434412 absolute error = 5.0206002773349305793034724434412 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08099 Order of pole (three term test) = -9.099 Radius of convergence (six term test) for eq 1 = 4.372 Order of pole (six term test) = 7.978 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = 0 y[1] (numeric) = 5.0296571640516205257833029252666 absolute error = 5.0296571640516205257833029252666 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08872 Order of pole (three term test) = -10.96 Radius of convergence (six term test) for eq 1 = 4.373 Order of pole (six term test) = 7.954 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = 0 y[1] (numeric) = 5.0386521760644318818686247260693 absolute error = 5.0386521760644318818686247260693 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09541 Order of pole (three term test) = -12.92 Radius of convergence (six term test) for eq 1 = 4.373 Order of pole (six term test) = 7.927 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = 0 y[1] (numeric) = 5.0475858307057980884859955144659 absolute error = 5.0475858307057980884859955144659 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.101 Order of pole (three term test) = -14.93 Radius of convergence (six term test) for eq 1 = 4.373 Order of pole (six term test) = 7.897 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = 0 y[1] (numeric) = 5.0564586465571027184379554572087 absolute error = 5.0564586465571027184379554572087 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1052 Order of pole (three term test) = -16.95 Radius of convergence (six term test) for eq 1 = 4.372 Order of pole (six term test) = 7.865 TOP MAIN SOLVE Loop x[1] = 3.33 y[1] (analytic) = 0 y[1] (numeric) = 5.0652711433226854228651458354878 absolute error = 5.0652711433226854228651458354878 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1082 Order of pole (three term test) = -18.96 Radius of convergence (six term test) for eq 1 = 4.372 Order of pole (six term test) = 7.83 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = 0 y[1] (numeric) = 5.074023841706554336301326051094 absolute error = 5.074023841706554336301326051094 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1097 Order of pole (three term test) = -20.9 Radius of convergence (six term test) for eq 1 = 4.371 Order of pole (six term test) = 7.793 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = 0 y[1] (numeric) = 5.0827172632918018772605939998933 absolute error = 5.0827172632918018772605939998933 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1097 Order of pole (three term test) = -22.75 Radius of convergence (six term test) for eq 1 = 4.37 Order of pole (six term test) = 7.754 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = 0 y[1] (numeric) = 5.0913519304227193184414495627402 absolute error = 5.0913519304227193184414495627402 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1083 Order of pole (three term test) = -24.46 Radius of convergence (six term test) for eq 1 = 4.368 Order of pole (six term test) = 7.715 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = 0 y[1] (numeric) = 5.0999283660896039879943311053647 absolute error = 5.0999283660896039879943311053647 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1055 Order of pole (three term test) = -26.01 Radius of convergence (six term test) for eq 1 = 4.367 Order of pole (six term test) = 7.674 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = 0 y[1] (numeric) = 5.1084470938162515007550229182182 absolute error = 5.1084470938162515007550229182182 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1013 Order of pole (three term test) = -27.36 Radius of convergence (six term test) for eq 1 = 4.366 Order of pole (six term test) = 7.633 TOP MAIN SOLVE Loop bytes used=124035976, alloc=4717728, time=4.47 x[1] = 3.39 y[1] (analytic) = 0 y[1] (numeric) = 5.1169086375501240057198030141213 absolute error = 5.1169086375501240057198030141213 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09583 Order of pole (three term test) = -28.49 Radius of convergence (six term test) for eq 1 = 4.365 Order of pole (six term test) = 7.593 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = 0 y[1] (numeric) = 5.1253135215551840731022095236697 absolute error = 5.1253135215551840731022095236697 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08912 Order of pole (three term test) = -29.37 Radius of convergence (six term test) for eq 1 = 4.363 Order of pole (six term test) = 7.553 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = 0 y[1] (numeric) = 5.1336622703073825307896970263359 absolute error = 5.1336622703073825307896970263359 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08133 Order of pole (three term test) = -29.99 Radius of convergence (six term test) for eq 1 = 4.362 Order of pole (six term test) = 7.513 TOP MAIN SOLVE Loop x[1] = 3.42 y[1] (analytic) = 0 y[1] (numeric) = 5.141955408392787295588191970534 absolute error = 5.141955408392787295588191970534 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07261 Order of pole (three term test) = -30.33 Radius of convergence (six term test) for eq 1 = 4.361 Order of pole (six term test) = 7.476 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = 0 y[1] (numeric) = 5.1501934604083390289358054889729 absolute error = 5.1501934604083390289358054889729 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06313 Order of pole (three term test) = -30.39 Radius of convergence (six term test) for eq 1 = 4.361 Order of pole (six term test) = 7.44 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = 0 y[1] (numeric) = 5.158376950865218279373176768998 absolute error = 5.158376950865218279373176768998 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05308 Order of pole (three term test) = -30.17 Radius of convergence (six term test) for eq 1 = 4.36 Order of pole (six term test) = 7.406 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (analytic) = 0 y[1] (numeric) = 5.1665064040948076545259100596898 absolute error = 5.1665064040948076545259100596898 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04264 Order of pole (three term test) = -29.68 Radius of convergence (six term test) for eq 1 = 4.36 Order of pole (six term test) = 7.375 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = 0 y[1] (numeric) = 5.1745823441572314931945477010159 absolute error = 5.1745823441572314931945477010159 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03201 Order of pole (three term test) = -28.91 Radius of convergence (six term test) for eq 1 = 4.36 Order of pole (six term test) = 7.346 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (analytic) = 0 y[1] (numeric) = 5.1826052947524544828331392504052 absolute error = 5.1826052947524544828331392504052 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02141 Order of pole (three term test) = -27.9 Radius of convergence (six term test) for eq 1 = 4.361 Order of pole (six term test) = 7.32 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = 0 y[1] (numeric) = 5.1905757791339196886678134063176 absolute error = 5.1905757791339196886678134063176 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01103 Order of pole (three term test) = -26.65 Radius of convergence (six term test) for eq 1 = 4.362 Order of pole (six term test) = 7.298 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = 0 y[1] (numeric) = 5.198494320024705527368348480212 absolute error = 5.198494320024705527368348480212 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001062 Order of pole (three term test) = -25.21 Radius of convergence (six term test) for eq 1 = 4.363 Order of pole (six term test) = 7.278 TOP MAIN SOLVE Loop bytes used=128037060, alloc=4717728, time=4.62 x[1] = 3.5 y[1] (analytic) = 0 y[1] (numeric) = 5.2063614395361803299144586508849 absolute error = 5.2063614395361803299144586508849 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.365 Order of pole (six term test) = 7.262 TOP MAIN SOLVE Loop x[1] = 3.51 y[1] (analytic) = 0 y[1] (numeric) = 5.2141776590891322944415571473196 absolute error = 5.2141776590891322944415571473196 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.367 Order of pole (six term test) = 7.25 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = 0 y[1] (numeric) = 5.2219434993373518297285051657412 absolute error = 5.2219434993373518297285051657412 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.369 Order of pole (six term test) = 7.24 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = 0 y[1] (numeric) = 5.2296594800936425328977365958464 absolute error = 5.2296594800936425328977365958464 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.372 Order of pole (six term test) = 7.233 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = 0 y[1] (numeric) = 5.2373261202582363301084632583029 absolute error = 5.2373261202582363301084632583029 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.375 Order of pole (six term test) = 7.228 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = 0 y[1] (numeric) = 5.2449439377495876357873667900937 absolute error = 5.2449439377495876357873667900937 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.379 Order of pole (six term test) = 7.226 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (analytic) = 0 y[1] (numeric) = 5.2525134494375207534896234977202 absolute error = 5.2525134494375207534896234977202 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.382 Order of pole (six term test) = 7.225 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = 0 y[1] (numeric) = 5.260035171078704149029742270359 absolute error = 5.260035171078704149029742270359 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.386 Order of pole (six term test) = 7.225 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = 0 y[1] (numeric) = 5.2675096172544246732637435406996 absolute error = 5.2675096172544246732637435406996 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.389 Order of pole (six term test) = 7.225 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = 0 y[1] (numeric) = 5.2749373013106342970242756269634 absolute error = 5.2749373013106342970242756269634 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.393 Order of pole (six term test) = 7.224 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = 0 y[1] (numeric) = 5.2823187353002414433779221364196 absolute error = 5.2823187353002414433779221364196 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.396 Order of pole (six term test) = 7.221 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = 0 y[1] (numeric) = 5.2896544299276185617472631643286 absolute error = 5.2896544299276185617472631643286 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.399 Order of pole (six term test) = 7.216 bytes used=132038668, alloc=4717728, time=4.77 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = 0 y[1] (numeric) = 5.2969448944952971836672573542893 absolute error = 5.2969448944952971836672573542893 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.402 Order of pole (six term test) = 7.207 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = 0 y[1] (numeric) = 5.3041906368528213301656768251916 absolute error = 5.3041906368528213301656768251916 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.404 Order of pole (six term test) = 7.192 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = 0 y[1] (numeric) = 5.3113921633477298051029341860115 absolute error = 5.3113921633477298051029341860115 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.405 Order of pole (six term test) = 7.17 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = 0 y[1] (numeric) = 5.3185499787786376064041362607174 absolute error = 5.3185499787786376064041362607174 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.405 Order of pole (six term test) = 7.141 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = 0 y[1] (numeric) = 5.3256645863503864170874938153675 absolute error = 5.3256645863503864170874938153675 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.404 Order of pole (six term test) = 7.101 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = 0 y[1] (numeric) = 5.332736487631233899456940579996 absolute error = 5.332736487631233899456940579996 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.009532 Order of pole (three term test) = -1.009 Radius of convergence (six term test) for eq 1 = 4.402 Order of pole (six term test) = 7.05 TOP MAIN SOLVE Loop x[1] = 3.68 y[1] (analytic) = 0 y[1] (numeric) = 5.3397661825120513078995238189577 absolute error = 5.3397661825120513078995238189577 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02 Order of pole (three term test) = -1.378 Radius of convergence (six term test) for eq 1 = 4.398 Order of pole (six term test) = 6.986 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = 0 y[1] (numeric) = 5.3467541691674987575254632134679 absolute error = 5.3467541691674987575254632134679 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03084 Order of pole (three term test) = -1.993 Radius of convergence (six term test) for eq 1 = 4.393 Order of pole (six term test) = 6.907 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = 0 y[1] (numeric) = 5.353700944019147336526572718641 absolute error = 5.353700944019147336526572718641 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0419 Order of pole (three term test) = -2.845 Radius of convergence (six term test) for eq 1 = 4.385 Order of pole (six term test) = 6.812 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = 0 y[1] (numeric) = 5.3606070017005171287241018132256 absolute error = 5.3606070017005171287241018132256 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05302 Order of pole (three term test) = -3.922 Radius of convergence (six term test) for eq 1 = 4.375 Order of pole (six term test) = 6.7 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = 0 y[1] (numeric) = 5.3674728350240001184493599985401 absolute error = 5.3674728350240001184493599985401 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06402 Order of pole (three term test) = -5.207 Radius of convergence (six term test) for eq 1 = 4.363 Order of pole (six term test) = 6.568 TOP MAIN SOLVE Loop bytes used=136040100, alloc=4717728, time=4.92 x[1] = 3.73 y[1] (analytic) = 0 y[1] (numeric) = 5.3742989349496368817723771180817 absolute error = 5.3742989349496368817723771180817 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07475 Order of pole (three term test) = -6.682 Radius of convergence (six term test) for eq 1 = 4.349 Order of pole (six term test) = 6.415 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (analytic) = 0 y[1] (numeric) = 5.3810857905557159252921379310358 absolute error = 5.3810857905557159252921379310358 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08504 Order of pole (three term test) = -8.325 Radius of convergence (six term test) for eq 1 = 4.332 Order of pole (six term test) = 6.241 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = 0 y[1] (numeric) = 5.3878338890111645153584896018065 absolute error = 5.3878338890111645153584896018065 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09475 Order of pole (three term test) = -10.11 Radius of convergence (six term test) for eq 1 = 4.312 Order of pole (six term test) = 6.045 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = 0 y[1] (numeric) = 5.3945437155496998458484301123851 absolute error = 5.3945437155496998458484301123851 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1037 Order of pole (three term test) = -12.01 Radius of convergence (six term test) for eq 1 = 4.289 Order of pole (six term test) = 5.826 TOP MAIN SOLVE Loop x[1] = 3.77 y[1] (analytic) = 0 y[1] (numeric) = 5.4012157534457094206126082177004 absolute error = 5.4012157534457094206126082177004 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1118 Order of pole (three term test) = -14 Radius of convergence (six term test) for eq 1 = 4.263 Order of pole (six term test) = 5.584 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = 0 y[1] (numeric) = 5.4078504839918295765934032247303 absolute error = 5.4078504839918295765934032247303 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1189 Order of pole (three term test) = -16.04 Radius of convergence (six term test) for eq 1 = 4.233 Order of pole (six term test) = 5.319 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = 0 y[1] (numeric) = 5.4144483864781911445539502545882 absolute error = 5.4144483864781911445539502545882 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1248 Order of pole (three term test) = -18.11 Radius of convergence (six term test) for eq 1 = 4.201 Order of pole (six term test) = 5.031 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = 0 y[1] (numeric) = 5.4210099381733013355167843600201 absolute error = 5.4210099381733013355167843600201 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1296 Order of pole (three term test) = -20.17 Radius of convergence (six term test) for eq 1 = 4.166 Order of pole (six term test) = 4.722 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = 0 y[1] (numeric) = 5.4275356143065310515696731131368 absolute error = 5.4275356143065310515696731131368 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.133 Order of pole (three term test) = -22.19 Radius of convergence (six term test) for eq 1 = 4.128 Order of pole (six term test) = 4.393 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = 0 y[1] (numeric) = 5.4340258880521769488429788546885 absolute error = 5.4340258880521769488429788546885 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1351 Order of pole (three term test) = -24.14 Radius of convergence (six term test) for eq 1 = 4.087 Order of pole (six term test) = 4.046 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = 0 y[1] (numeric) = 5.440481230515067727396375419537 absolute error = 5.440481230515067727396375419537 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1358 Order of pole (three term test) = -25.98 Radius of convergence (six term test) for eq 1 = 4.043 Order of pole (six term test) = 3.682 TOP MAIN SOLVE Loop bytes used=140041228, alloc=4717728, time=5.06 x[1] = 3.84 y[1] (analytic) = 0 y[1] (numeric) = 5.4469021107176842866828288988075 absolute error = 5.4469021107176842866828288988075 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1351 Order of pole (three term test) = -27.68 Radius of convergence (six term test) for eq 1 = 3.997 Order of pole (six term test) = 3.304 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = 0 y[1] (numeric) = 5.4532889955887635654058438411236 absolute error = 5.4532889955887635654058438411236 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.133 Order of pole (three term test) = -29.23 Radius of convergence (six term test) for eq 1 = 3.949 Order of pole (six term test) = 2.915 TOP MAIN SOLVE Loop x[1] = 3.86 y[1] (analytic) = 0 y[1] (numeric) = 5.4596423499533560801854256680652 absolute error = 5.4596423499533560801854256680652 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1296 Order of pole (three term test) = -30.59 Radius of convergence (six term test) for eq 1 = 3.899 Order of pole (six term test) = 2.517 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = 0 y[1] (numeric) = 5.4659626365243073877447034395202 absolute error = 5.4659626365243073877447034395202 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1248 Order of pole (three term test) = -31.73 Radius of convergence (six term test) for eq 1 = 3.847 Order of pole (six term test) = 2.114 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = 0 y[1] (numeric) = 5.472250315895133919581073480798 absolute error = 5.472250315895133919581073480798 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1187 Order of pole (three term test) = -32.65 Radius of convergence (six term test) for eq 1 = 3.794 Order of pole (six term test) = 1.707 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = 0 y[1] (numeric) = 5.4785058465342638755644579160099 absolute error = 5.4785058465342638755644579160099 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1115 Order of pole (three term test) = -33.32 Radius of convergence (six term test) for eq 1 = 3.74 Order of pole (six term test) = 1.301 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = 0 y[1] (numeric) = 5.4847296847806141128955216496837 absolute error = 5.4847296847806141128955216496837 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1033 Order of pole (three term test) = -33.74 Radius of convergence (six term test) for eq 1 = 3.685 Order of pole (six term test) = 0.8976 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = 0 y[1] (numeric) = 5.4909222848404742286567178748727 absolute error = 5.4909222848404742286567178748727 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09414 Order of pole (three term test) = -33.9 Radius of convergence (six term test) for eq 1 = 3.631 Order of pole (six term test) = 0.5 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = 0 y[1] (numeric) = 5.4970840987856693071108857806957 absolute error = 5.4970840987856693071108857806957 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08424 Order of pole (three term test) = -33.8 Radius of convergence (six term test) for eq 1 = 3.577 Order of pole (six term test) = 0.1105 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = 0 y[1] (numeric) = 5.5032155765529730862718405572087 absolute error = 5.5032155765529730862718405572087 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07374 Order of pole (three term test) = -33.43 Radius of convergence (six term test) for eq 1 = 3.523 Order of pole (six term test) = -0.2683 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = 0 y[1] (numeric) = 5.5093171659447435914291645569801 absolute error = 5.5093171659447435914291645569801 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06281 Order of pole (three term test) = -32.82 Radius of convergence (six term test) for eq 1 = 3.471 Order of pole (six term test) = -0.6344 TOP MAIN SOLVE Loop x[1] = 3.95 y[1] (analytic) = 0 y[1] (numeric) = 5.5153893126307535856097130183107 absolute error = 5.5153893126307535856097130183107 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05163 Order of pole (three term test) = -31.95 Radius of convergence (six term test) for eq 1 = 3.42 Order of pole (six term test) = -0.9859 bytes used=144044340, alloc=4717728, time=5.21 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = 0 y[1] (numeric) = 5.5214324601511884977700789549944 absolute error = 5.5214324601511884977700789549944 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04037 Order of pole (three term test) = -30.87 Radius of convergence (six term test) for eq 1 = 3.37 Order of pole (six term test) = -1.321 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = 0 y[1] (numeric) = 5.5274470499207848082208057669435 absolute error = 5.5274470499207848082208057669435 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02922 Order of pole (three term test) = -29.57 Radius of convergence (six term test) for eq 1 = 3.323 Order of pole (six term test) = -1.639 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = 0 y[1] (numeric) = 5.5334335212340821967824373097826 absolute error = 5.5334335212340821967824373097826 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01834 Order of pole (three term test) = -28.09 Radius of convergence (six term test) for eq 1 = 3.278 Order of pole (six term test) = -1.938 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = 0 y[1] (numeric) = 5.5393923112717630918780960178755 absolute error = 5.5393923112717630918780960178755 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007903 Order of pole (three term test) = -26.45 Radius of convergence (six term test) for eq 1 = 3.235 Order of pole (six term test) = -2.217 TOP MAIN SOLVE Loop x[1] = 4 y[1] (analytic) = 0 y[1] (numeric) = 5.5453238551080535976043375858278 absolute error = 5.5453238551080535976043375858278 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.196 Order of pole (six term test) = -2.475 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = 0 y[1] (numeric) = 5.5512285857191601202333134382003 absolute error = 5.5512285857191601202333134382003 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.16 Order of pole (six term test) = -2.712 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = 0 y[1] (numeric) = 5.5571069339927163650411327813208 absolute error = 5.5571069339927163650411327813208 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.127 Order of pole (six term test) = -2.928 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = 0 y[1] (numeric) = 5.5629593287382157283006480602054 absolute error = 5.5629593287382157283006480602054 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.097 Order of pole (six term test) = -3.121 TOP MAIN SOLVE Loop x[1] = 4.04 y[1] (analytic) = 0 y[1] (numeric) = 5.5687861966984044672070621273803 absolute error = 5.5687861966984044672070621273803 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.071 Order of pole (six term test) = -3.291 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = 0 y[1] (numeric) = 5.5745879625616113919215398831288 absolute error = 5.5745879625616113919215398831288 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.05 Order of pole (six term test) = -3.438 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (analytic) = 0 y[1] (numeric) = 5.5803650489749901883354681156423 absolute error = 5.5803650489749901883354681156423 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.032 Order of pole (six term test) = -3.562 TOP MAIN SOLVE Loop bytes used=148045308, alloc=4717728, time=5.35 x[1] = 4.07 y[1] (analytic) = 0 y[1] (numeric) = 5.5861178765586508471043971260529 absolute error = 5.5861178765586508471043971260529 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.019 Order of pole (six term test) = -3.663 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = 0 y[1] (numeric) = 5.5918468639206570435183266540284 absolute error = 5.5918468639206570435183266540284 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.01 Order of pole (six term test) = -3.739 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = 0 y[1] (numeric) = 5.5975524276728666834200927170343 absolute error = 5.5975524276728666834200927170343 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.005 Order of pole (six term test) = -3.791 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = 0 y[1] (numeric) = 5.603234982447593202226158308886 absolute error = 5.603234982447593202226158308886 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.005 Order of pole (six term test) = -3.818 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = 0 y[1] (numeric) = 5.6088949409150655767276904251628 absolute error = 5.6088949409150655767276904251628 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.01 Order of pole (six term test) = -3.82 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = 0 y[1] (numeric) = 5.6145327138016653823514150254472 absolute error = 5.6145327138016653823514150254472 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.019 Order of pole (six term test) = -3.797 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = 0 y[1] (numeric) = 5.6201487099089196015496033042181 absolute error = 5.6201487099089196015496033042181 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.033 Order of pole (six term test) = -3.749 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = 0 y[1] (numeric) = 5.6257433361332282615899079816467 absolute error = 5.6257433361332282615899079816467 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.051 Order of pole (six term test) = -3.677 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = 0 y[1] (numeric) = 5.6313169974863063518647086280806 absolute error = 5.6313169974863063518647086280806 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.074 Order of pole (six term test) = -3.583 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = 0 y[1] (numeric) = 5.6368700971163198415848164169347 absolute error = 5.6368700971163198415848164169347 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.099 Order of pole (six term test) = -3.468 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = 0 y[1] (numeric) = 5.6424030363296959880248888755019 absolute error = 5.6424030363296959880248888755019 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.002571 Order of pole (three term test) = -0.9011 Radius of convergence (six term test) for eq 1 = 3.127 Order of pole (six term test) = -3.337 TOP MAIN SOLVE Loop bytes used=152046448, alloc=4717728, time=5.50 x[1] = 4.18 y[1] (analytic) = 0 y[1] (numeric) = 5.6479162146135884930209236390656 absolute error = 5.6479162146135884930209236390656 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01275 Order of pole (three term test) = -1.081 Radius of convergence (six term test) for eq 1 = 3.156 Order of pole (six term test) = -3.196 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = 0 y[1] (numeric) = 5.6534100296589784308688622529742 absolute error = 5.6534100296589784308688622529742 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0235 Order of pole (three term test) = -1.494 Radius of convergence (six term test) for eq 1 = 3.184 Order of pole (six term test) = -3.055 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 0 y[1] (numeric) = 5.6588848773843922338344406916113 absolute error = 5.6588848773843922338344406916113 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0347 Order of pole (three term test) = -2.134 Radius of convergence (six term test) for eq 1 = 3.209 Order of pole (six term test) = -2.929 TOP MAIN SOLVE Loop x[1] = 4.21 y[1] (analytic) = 0 y[1] (numeric) = 5.6643411519602183818662011451366 absolute error = 5.6643411519602183818662011451366 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04618 Order of pole (three term test) = -2.994 Radius of convergence (six term test) for eq 1 = 3.226 Order of pole (six term test) = -2.834 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = 0 y[1] (numeric) = 5.6697792458336048005254370928773 absolute error = 5.6697792458336048005254370928773 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05779 Order of pole (three term test) = -4.06 Radius of convergence (six term test) for eq 1 = 3.233 Order of pole (six term test) = -2.795 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = 0 y[1] (numeric) = 5.6751995497539193253391132013599 absolute error = 5.6751995497539193253391132013599 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06937 Order of pole (three term test) = -5.318 Radius of convergence (six term test) for eq 1 = 3.223 Order of pole (six term test) = -2.836 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = 0 y[1] (numeric) = 5.6806024527987559414854843358549 absolute error = 5.6806024527987559414854843358549 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08074 Order of pole (three term test) = -6.751 Radius of convergence (six term test) for eq 1 = 3.193 Order of pole (six term test) = -2.985 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = 0 y[1] (numeric) = 5.6859883424004698546886450908449 absolute error = 5.6859883424004698546886450908449 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09174 Order of pole (three term test) = -8.337 Radius of convergence (six term test) for eq 1 = 3.137 Order of pole (six term test) = -3.262 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = 0 y[1] (numeric) = 5.691357604373224792189133249644 absolute error = 5.691357604373224792189133249644 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1022 Order of pole (three term test) = -10.05 Radius of convergence (six term test) for eq 1 = 3.054 Order of pole (six term test) = -3.676 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = 0 y[1] (numeric) = 5.6967106229405362714444355398554 absolute error = 5.6967106229405362714444355398554 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.112 Order of pole (three term test) = -11.87 Radius of convergence (six term test) for eq 1 = 2.941 Order of pole (six term test) = -4.221 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = 0 y[1] (numeric) = 5.7020477807632949085768749299668 absolute error = 5.7020477807632949085768749299668 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1209 Order of pole (three term test) = -13.77 Radius of convergence (six term test) for eq 1 = 2.802 Order of pole (six term test) = -4.871 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (analytic) = 0 y[1] (numeric) = 5.7073694589682541683173304493251 absolute error = 5.7073694589682541683173304493251 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1288 Order of pole (three term test) = -15.72 Radius of convergence (six term test) for eq 1 = 2.641 Order of pole (six term test) = -5.59 TOP MAIN SOLVE Loop bytes used=156047724, alloc=4717728, time=5.65 x[1] = 4.3 y[1] (analytic) = 0 y[1] (numeric) = 5.712676037176967282091087219387 absolute error = 5.712676037176967282091087219387 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1357 Order of pole (three term test) = -17.68 Radius of convergence (six term test) for eq 1 = 2.465 Order of pole (six term test) = -6.333 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = 0 y[1] (numeric) = 5.7179678935351583807652071399033 absolute error = 5.7179678935351583807652071399033 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1413 Order of pole (three term test) = -19.63 Radius of convergence (six term test) for eq 1 = 2.28 Order of pole (six term test) = -7.061 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = 0 y[1] (numeric) = 5.7232454047425132032420963363907 absolute error = 5.7232454047425132032420963363907 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1455 Order of pole (three term test) = -21.54 Radius of convergence (six term test) for eq 1 = 2.095 Order of pole (six term test) = -7.741 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = 0 y[1] (numeric) = 5.7285089460828750513666868896316 absolute error = 5.7285089460828750513666868896316 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1484 Order of pole (three term test) = -23.38 Radius of convergence (six term test) for eq 1 = 1.914 Order of pole (six term test) = -8.356 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (analytic) = 0 y[1] (numeric) = 5.7337588914548319653481683696915 absolute error = 5.7337588914548319653481683696915 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1499 Order of pole (three term test) = -25.11 Radius of convergence (six term test) for eq 1 = 1.741 Order of pole (six term test) = -8.895 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = 0 y[1] (numeric) = 5.7389956134026813919226222705118 absolute error = 5.7389956134026813919226222705118 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1499 Order of pole (three term test) = -26.72 Radius of convergence (six term test) for eq 1 = 1.579 Order of pole (six term test) = -9.359 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = 0 y[1] (numeric) = 5.7442194831477589096489013797976 absolute error = 5.7442194831477589096489013797976 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1485 Order of pole (three term test) = -28.18 Radius of convergence (six term test) for eq 1 = 1.429 Order of pole (six term test) = -9.752 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = 0 y[1] (numeric) = 5.7494308706201178618926265172058 absolute error = 5.7494308706201178618926265172058 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1457 Order of pole (three term test) = -29.48 Radius of convergence (six term test) for eq 1 = 1.292 Order of pole (six term test) = -10.08 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = 0 y[1] (numeric) = 5.7546301444905470280752659662938 absolute error = 5.7546301444905470280752659662938 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1415 Order of pole (three term test) = -30.58 Radius of convergence (six term test) for eq 1 = 1.167 Order of pole (six term test) = -10.36 TOP MAIN SOLVE Loop x[1] = 4.39 y[1] (analytic) = 0 y[1] (numeric) = 5.7598176722029137375167463700452 absolute error = 5.7598176722029137375167463700452 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1361 Order of pole (three term test) = -31.49 Radius of convergence (six term test) for eq 1 = 1.055 Order of pole (six term test) = -10.58 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 0 y[1] (numeric) = 5.7649938200068200975573127470773 absolute error = 5.7649938200068200975573127470773 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1295 Order of pole (three term test) = -32.2 Radius of convergence (six term test) for eq 1 = 0.9552 Order of pole (six term test) = -10.77 TOP MAIN SOLVE Loop bytes used=160048504, alloc=4717728, time=5.80 x[1] = 4.41 y[1] (analytic) = 0 y[1] (numeric) = 5.7701589529905602684901351450593 absolute error = 5.7701589529905602684901351450593 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1219 Order of pole (three term test) = -32.69 Radius of convergence (six term test) for eq 1 = 0.8659 Order of pole (six term test) = -10.93 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = 0 y[1] (numeric) = 5.7753134351143669720592744996905 absolute error = 5.7753134351143669720592744996905 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1133 Order of pole (three term test) = -32.98 Radius of convergence (six term test) for eq 1 = 0.787 Order of pole (six term test) = -11.05 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = 0 y[1] (numeric) = 5.7804576292439356677727659634558 absolute error = 5.7804576292439356677727659634558 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1039 Order of pole (three term test) = -33.05 Radius of convergence (six term test) for eq 1 = 0.7178 Order of pole (six term test) = -11.16 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = 0 y[1] (numeric) = 5.7855918971842150719480982451971 absolute error = 5.7855918971842150719480982451971 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09393 Order of pole (three term test) = -32.93 Radius of convergence (six term test) for eq 1 = 0.6579 Order of pole (six term test) = -11.25 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = 0 y[1] (numeric) = 5.7907165997134529281530369618555 absolute error = 5.7907165997134529281530369618555 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08344 Order of pole (three term test) = -32.62 Radius of convergence (six term test) for eq 1 = 0.6067 Order of pole (six term test) = -11.32 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = 0 y[1] (numeric) = 5.7958320966174861644395512235286 absolute error = 5.7958320966174861644395512235286 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07259 Order of pole (three term test) = -32.12 Radius of convergence (six term test) for eq 1 = 0.5638 Order of pole (six term test) = -11.39 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = 0 y[1] (numeric) = 5.8009387467242647924085588255036 absolute error = 5.8009387467242647924085588255036 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06152 Order of pole (three term test) = -31.46 Radius of convergence (six term test) for eq 1 = 0.5289 Order of pole (six term test) = -11.44 TOP MAIN SOLVE Loop x[1] = 4.48 y[1] (analytic) = 0 y[1] (numeric) = 5.8060369079385991156091183941127 absolute error = 5.8060369079385991156091183941127 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05038 Order of pole (three term test) = -30.64 Radius of convergence (six term test) for eq 1 = 0.5015 Order of pole (six term test) = -11.48 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = 0 y[1] (numeric) = 5.811126937277120019992991007065 absolute error = 5.811126937277120019992991007065 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03929 Order of pole (three term test) = -29.68 Radius of convergence (six term test) for eq 1 = 0.4814 Order of pole (six term test) = -11.52 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 0 y[1] (numeric) = 5.8162091909034423170440156485194 absolute error = 5.8162091909034423170440156485194 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02836 Order of pole (three term test) = -28.59 Radius of convergence (six term test) for eq 1 = 0.4679 Order of pole (six term test) = -11.55 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (analytic) = 0 y[1] (numeric) = 5.8212840241635213007155764700966 absolute error = 5.8212840241635213007155764700966 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01772 Order of pole (three term test) = -27.39 Radius of convergence (six term test) for eq 1 = 0.4605 Order of pole (six term test) = -11.58 TOP MAIN SOLVE Loop bytes used=164049288, alloc=4717728, time=5.95 x[1] = 4.52 y[1] (analytic) = 0 y[1] (numeric) = 5.8263517916211928623767286104343 absolute error = 5.8263517916211928623767286104343 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007464 Order of pole (three term test) = -26.08 Radius of convergence (six term test) for eq 1 = 0.4586 Order of pole (six term test) = -11.6 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = 0 y[1] (numeric) = 5.8314128470938876835303238494022 absolute error = 5.8314128470938876835303238494022 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4616 Order of pole (six term test) = -11.62 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = 0 y[1] (numeric) = 5.8364675436885101940704896057751 absolute error = 5.8364675436885101940704896057751 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.335 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4686 Order of pole (six term test) = -11.64 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = 0 y[1] (numeric) = 5.8415162338374731442413787688803 absolute error = 5.8415162338374731442413787688803 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.253 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4792 Order of pole (six term test) = -11.66 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = 0 y[1] (numeric) = 5.8465592693348787911969469324778 absolute error = 5.8465592693348787911969469324778 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.168 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4926 Order of pole (six term test) = -11.68 TOP MAIN SOLVE Loop x[1] = 4.57 y[1] (analytic) = 0 y[1] (numeric) = 5.8515970013728378460986143132187 absolute error = 5.8515970013728378460986143132187 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5084 Order of pole (six term test) = -11.7 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = 0 y[1] (numeric) = 5.8566297805779174649831423462292 absolute error = 5.8566297805779174649831423462292 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5261 Order of pole (six term test) = -11.72 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = 0 y[1] (numeric) = 5.8616579570477096961490012830637 absolute error = 5.8616579570477096961490012830637 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5452 Order of pole (six term test) = -11.73 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 0 y[1] (numeric) = 5.8666818803875119185108923085783 absolute error = 5.8666818803875119185108923085783 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5653 Order of pole (six term test) = -11.75 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (analytic) = 0 y[1] (numeric) = 5.8717018997471109192266298969245 absolute error = 5.8717018997471109192266298969245 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.586 Order of pole (six term test) = -11.77 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (analytic) = 0 y[1] (numeric) = 5.8767183638576623648786367499439 absolute error = 5.8767183638576623648786367499439 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.607 Order of pole (six term test) = -11.79 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (analytic) = 0 y[1] (numeric) = 5.8817316210686575185667347855463 absolute error = 5.8817316210686575185667347855463 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6278 Order of pole (six term test) = -11.81 bytes used=168050300, alloc=4717728, time=6.09 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = 0 y[1] (numeric) = 5.8867420193849691454150445851635 absolute error = 5.8867420193849691454150445851635 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.648 Order of pole (six term test) = -11.83 TOP MAIN SOLVE Loop x[1] = 4.65 y[1] (analytic) = 0 y[1] (numeric) = 5.8917499065039686311912887636374 absolute error = 5.8917499065039686311912887636374 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.667 Order of pole (six term test) = -11.85 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (analytic) = 0 y[1] (numeric) = 5.896755629852706412961548141454 absolute error = 5.896755629852706412961548141454 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6844 Order of pole (six term test) = -11.87 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (analytic) = 0 y[1] (numeric) = 5.9017595366251478869396438237346 absolute error = 5.9017595366251478869396438237346 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6998 Order of pole (six term test) = -11.88 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = 0 y[1] (numeric) = 5.9067619738194570169220295091438 absolute error = 5.9067619738194570169220295091438 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7125 Order of pole (six term test) = -11.9 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = 0 y[1] (numeric) = 5.9117632882753199169126473693587 absolute error = 5.9117632882753199169126473693587 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7223 Order of pole (six term test) = -11.91 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = 0 y[1] (numeric) = 5.9167638267113007237258993159971 absolute error = 5.9167638267113007237258993159971 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7286 Order of pole (six term test) = -11.92 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = 0 y[1] (numeric) = 5.9217639357622221094999395429633 absolute error = 5.9217639357622221094999395429633 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.7314 Order of pole (six term test) = -11.92 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = 0 y[1] (numeric) = 5.9267639620165628101490455334 absolute error = 5.9267639620165628101490455334 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007313 Order of pole (three term test) = -0.9715 Radius of convergence (six term test) for eq 1 = 0.7304 Order of pole (six term test) = -11.92 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = 0 y[1] (numeric) = 5.9317642520538645638268988290313 absolute error = 5.9317642520538645638268988290313 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01666 Order of pole (three term test) = -1.311 Radius of convergence (six term test) for eq 1 = 0.7257 Order of pole (six term test) = -11.91 TOP MAIN SOLVE Loop x[1] = 4.74 y[1] (analytic) = 0 y[1] (numeric) = 5.9367651524821408634580891695895 absolute error = 5.9367651524821408634580891695895 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02539 Order of pole (three term test) = -1.906 Radius of convergence (six term test) for eq 1 = 0.7176 Order of pole (six term test) = -11.9 TOP MAIN SOLVE Loop bytes used=172051104, alloc=4717728, time=6.24 x[1] = 4.75 y[1] (analytic) = 0 y[1] (numeric) = 5.9417670099752799293207746491089 absolute error = 5.9417670099752799293207746491089 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03323 Order of pole (three term test) = -2.737 Radius of convergence (six term test) for eq 1 = 0.7062 Order of pole (six term test) = -11.89 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = 0 y[1] (numeric) = 5.9467701713104343015287487323348 absolute error = 5.9467701713104343015287487323348 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03992 Order of pole (three term test) = -3.776 Radius of convergence (six term test) for eq 1 = 0.6921 Order of pole (six term test) = -11.88 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = 0 y[1] (numeric) = 5.9517749834053894380675768761054 absolute error = 5.9517749834053894380675768761054 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04529 Order of pole (three term test) = -4.993 Radius of convergence (six term test) for eq 1 = 0.6756 Order of pole (six term test) = -11.86 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = 0 y[1] (numeric) = 5.9567817933559036817902034476319 absolute error = 5.9567817933559036817902034476319 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04923 Order of pole (three term test) = -6.356 Radius of convergence (six term test) for eq 1 = 0.6572 Order of pole (six term test) = -11.84 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = 0 y[1] (numeric) = 5.9617909484730119294775768812496 absolute error = 5.9617909484730119294775768812496 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05169 Order of pole (three term test) = -7.834 Radius of convergence (six term test) for eq 1 = 0.6375 Order of pole (six term test) = -11.82 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = 0 y[1] (numeric) = 5.9668027963202852977263523116341 absolute error = 5.9668027963202852977263523116341 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05268 Order of pole (three term test) = -9.398 Radius of convergence (six term test) for eq 1 = 0.617 Order of pole (six term test) = -11.8 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = 0 y[1] (numeric) = 5.9718176847510390340474605036791 absolute error = 5.9718176847510390340474605036791 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05222 Order of pole (three term test) = -11.02 Radius of convergence (six term test) for eq 1 = 0.5961 Order of pole (six term test) = -11.78 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = 0 y[1] (numeric) = 5.976835961945480867157068934715 absolute error = 5.976835961945480867157068934715 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0504 Order of pole (three term test) = -12.68 Radius of convergence (six term test) for eq 1 = 0.5751 Order of pole (six term test) = -11.76 TOP MAIN SOLVE Loop x[1] = 4.83 y[1] (analytic) = 0 y[1] (numeric) = 5.9818579764477919280279723142335 absolute error = 5.9818579764477919280279723142335 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04728 Order of pole (three term test) = -14.36 Radius of convergence (six term test) for eq 1 = 0.5547 Order of pole (six term test) = -11.74 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = 0 y[1] (numeric) = 5.9868840772031323028595306014183 absolute error = 5.9868840772031323028595306014183 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04296 Order of pole (three term test) = -16.04 Radius of convergence (six term test) for eq 1 = 0.535 Order of pole (six term test) = -11.72 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = 0 y[1] (numeric) = 5.9919146135945632007348032732354 absolute error = 5.9919146135945632007348032732354 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03755 Order of pole (three term test) = -17.71 Radius of convergence (six term test) for eq 1 = 0.5166 Order of pole (six term test) = -11.71 TOP MAIN SOLVE Loop bytes used=176052072, alloc=4717728, time=6.39 x[1] = 4.86 y[1] (analytic) = 0 y[1] (numeric) = 5.9969499354798776323835403526736 absolute error = 5.9969499354798776323835403526736 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.126 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.03112 Order of pole (three term test) = -19.35 Radius of convergence (six term test) for eq 1 = 0.4999 Order of pole (six term test) = -11.69 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = 0 y[1] (numeric) = 6.0019903932283314021804375232896 absolute error = 6.0019903932283314021804375232896 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.213 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.02379 Order of pole (three term test) = -20.95 Radius of convergence (six term test) for eq 1 = 0.4853 Order of pole (six term test) = -11.67 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = 0 y[1] (numeric) = 6.0070363377572661133031009337819 absolute error = 6.0070363377572661133031009337819 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.296 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.01564 Order of pole (three term test) = -22.51 Radius of convergence (six term test) for eq 1 = 0.4733 Order of pole (six term test) = -11.65 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = 0 y[1] (numeric) = 6.0120881205686157758794426478479 absolute error = 6.0120881205686157758794426478479 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.006771 Order of pole (three term test) = -24 Radius of convergence (six term test) for eq 1 = 0.4645 Order of pole (six term test) = -11.63 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = 0 y[1] (numeric) = 6.0171460937852884899981689574685 absolute error = 6.0171460937852884899981689574685 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4595 Order of pole (six term test) = -11.61 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = 0 y[1] (numeric) = 6.0222106101874145496696441882093 absolute error = 6.0222106101874145496696441882093 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.459 Order of pole (six term test) = -11.59 TOP MAIN SOLVE Loop x[1] = 4.92 y[1] (analytic) = 0 y[1] (numeric) = 6.0272820232484521802414181037681 absolute error = 6.0272820232484521802414181037681 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4636 Order of pole (six term test) = -11.56 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (analytic) = 0 y[1] (numeric) = 6.0323606871711419804296095106965 absolute error = 6.0323606871711419804296095106965 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.4741 Order of pole (six term test) = -11.53 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = 0 y[1] (numeric) = 6.0374469569233009910635864834291 absolute error = 6.0374469569233009910635864834291 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.491 Order of pole (six term test) = -11.5 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = 0 y[1] (numeric) = 6.0425411882734471558994787154446 absolute error = 6.0425411882734471558994787154446 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5149 Order of pole (six term test) = -11.46 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = 0 y[1] (numeric) = 6.0476437378262447754836995506024 absolute error = 6.0476437378262447754836995506024 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5461 Order of pole (six term test) = -11.41 TOP MAIN SOLVE Loop bytes used=180053640, alloc=4783252, time=6.54 x[1] = 4.97 y[1] (analytic) = 0 y[1] (numeric) = 6.0527549630577613830898826146057 absolute error = 6.0527549630577613830898826146057 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5852 Order of pole (six term test) = -11.35 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = 0 y[1] (numeric) = 6.057875222350526292263977263246 absolute error = 6.057875222350526292263977263246 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6323 Order of pole (six term test) = -11.29 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = 0 y[1] (numeric) = 6.0630048750283808785488693647078 absolute error = 6.0630048750283808785488693647078 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6881 Order of pole (six term test) = -11.21 Finished! diff ( y , x , 1 ) = expt(2.0 , sin(x)); Iterations = 490 Total Elapsed Time = 6 Seconds Elapsed Time(since restart) = 6 Seconds Time to Timeout = 2 Minutes 53 Seconds Percent Done = 100.2 % > quit bytes used=180947408, alloc=4783252, time=6.57