|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D2, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D2[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D3[1]; > #emit pre sin 1 $eq_no = 1 > array_tmp3[1] := sin(array_x[1]); > array_tmp3_g[1] := cos(array_x[1]); > #emit pre expt LINEAR - FULL $eq_no = 1 i = 1 > array_tmp4[1] := expt(array_tmp2[1] , array_tmp3[1] ) ; > array_tmp4_a1[1] := ln(array_tmp2[1] ) ; > array_tmp4_a1[2] := array_tmp2[2] / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D2[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp3[2] := array_tmp3_g[1] * array_x[2] / 1; > array_tmp3_g[2] := -array_tmp3[1] * array_x[2] / 1; > #emit pre expt LINEAR - FULL $eq_no = 1 i = 2 > array_tmp4_a2[1] := (array_tmp4_a1[1] * array_tmp3[2] + array_tmp4_a1[2] * array_tmp3[1]) / glob_h; > array_tmp4[2] := array_tmp4[1] * array_tmp4_a2[1] * glob_h; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := array_tmp3_g[2] * array_x[2] / 2; > array_tmp3_g[3] := -array_tmp3[2] * array_x[2] / 2; > #emit pre expt LINEAR - FULL $eq_no = 1 i = 3 > array_tmp4_a1[3] := -array_tmp4_a1[2] * array_tmp2[2] * 1 / array_tmp2[1] / 2; > array_tmp4_a2[2] := ats(3,array_tmp3,array_tmp4_a1,1)*2 / glob_h; > array_tmp4[3] := ats(2,array_tmp4,array_tmp4_a2,1)*glob_h/2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := array_tmp3_g[3] * array_x[2] / 3; > array_tmp3_g[4] := -array_tmp3[3] * array_x[2] / 3; > #emit pre expt LINEAR - FULL $eq_no = 1 i = 4 > array_tmp4_a1[4] := -array_tmp4_a1[3] * array_tmp2[2] * 2 / array_tmp2[1] / 3; > array_tmp4_a2[3] := ats(4,array_tmp3,array_tmp4_a1,1)*3 / glob_h; > array_tmp4[4] := ats(3,array_tmp4,array_tmp4_a2,1)*glob_h/3; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := array_tmp3_g[4] * array_x[2] / 4; > array_tmp3_g[5] := -array_tmp3[4] * array_x[2] / 4; > #emit pre expt LINEAR - FULL $eq_no = 1 i = 5 > array_tmp4_a1[5] := -array_tmp4_a1[4] * array_tmp2[2] * 3 / array_tmp2[1] / 4; > array_tmp4_a2[4] := ats(5,array_tmp3,array_tmp4_a1,1)*4 / glob_h; > array_tmp4[5] := ats(4,array_tmp4,array_tmp4_a2,1)*glob_h/4; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sin LINEAR $eq_no = 1 > array_tmp3[kkk] := array_tmp3_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp3_g[kkk] := -array_tmp3[kkk - 1] * array_x[2] / (kkk - 1); > #emit expt LINEAR FULL $eq_no = 1 i = 1 > array_tmp4_a1[kkk] := -array_tmp4_a1[kkk-1] * array_tmp2[2] * (kkk-2) / array_tmp2[1] / (kkk - 1); > array_tmp4_a2[kkk-1] := ats(kkk,array_tmp3,array_tmp4_a1,1) * (kkk-1) / glob_h; > array_tmp4[kkk] := ats(kkk-1,array_tmp4,array_tmp4_a2,1) * glob_h/(kkk-1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := array_const_0D2[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D3[1]; array_tmp3[1] := sin(array_x[1]); array_tmp3_g[1] := cos(array_x[1]); array_tmp4[1] := expt(array_tmp2[1], array_tmp3[1]); array_tmp4_a1[1] := ln(array_tmp2[1]); array_tmp4_a1[2] := array_tmp2[2]/array_tmp2[1]; array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_0D2[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp3_g[1]*array_x[2]; array_tmp3_g[2] := -array_tmp3[1]*array_x[2]; array_tmp4_a2[1] := ( array_tmp4_a1[1]*array_tmp3[2] + array_tmp4_a1[2]*array_tmp3[1])/ glob_h; array_tmp4[2] := array_tmp4[1]*array_tmp4_a2[1]*glob_h; array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp3[3] := 1/2*array_tmp3_g[2]*array_x[2]; array_tmp3_g[3] := -1/2*array_tmp3[2]*array_x[2]; array_tmp4_a1[3] := -1/2*array_tmp4_a1[2]*array_tmp2[2]/array_tmp2[1]; array_tmp4_a2[2] := 2*ats(3, array_tmp3, array_tmp4_a1, 1)/glob_h; array_tmp4[3] := 1/2*ats(2, array_tmp4, array_tmp4_a2, 1)*glob_h; array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp3[4] := 1/3*array_tmp3_g[3]*array_x[2]; array_tmp3_g[4] := -1/3*array_tmp3[3]*array_x[2]; array_tmp4_a1[4] := -2/3*array_tmp4_a1[3]*array_tmp2[2]/array_tmp2[1]; array_tmp4_a2[3] := 3*ats(4, array_tmp3, array_tmp4_a1, 1)/glob_h; array_tmp4[4] := 1/3*ats(3, array_tmp4, array_tmp4_a2, 1)*glob_h; array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp3[5] := 1/4*array_tmp3_g[4]*array_x[2]; array_tmp3_g[5] := -1/4*array_tmp3[4]*array_x[2]; array_tmp4_a1[5] := -3/4*array_tmp4_a1[4]*array_tmp2[2]/array_tmp2[1]; array_tmp4_a2[4] := 4*ats(5, array_tmp3, array_tmp4_a1, 1)/glob_h; array_tmp4[5] := 1/4*ats(4, array_tmp4, array_tmp4_a2, 1)*glob_h; array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp3[kkk] := array_tmp3_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp3_g[kkk] := -array_tmp3[kkk - 1]*array_x[2]/(kkk - 1); array_tmp4_a1[kkk] := -array_tmp4_a1[kkk - 1]*array_tmp2[2]* (kkk - 2)/(array_tmp2[1]*(kkk - 1)); array_tmp4_a2[kkk - 1] := ats(kkk, array_tmp3, array_tmp4_a1, 1)*(kkk - 1)/glob_h; array_tmp4[kkk] := ats(kkk - 1, array_tmp4, array_tmp4_a2, 1)*glob_h/(kkk - 1); array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp5[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(0.0); > 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_0D2, > array_const_0D3, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3_g, > array_tmp3, > array_tmp4_c1, > array_tmp4_a1, > array_tmp4_a2, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/expt_lin_sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , sin(x));"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(0.0);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3_g:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4_c1:= Array(0..(max_terms + 1),[]); > array_tmp4_a1:= Array(0..(max_terms + 1),[]); > array_tmp4_a2:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3_g[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4_c1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_c1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4_a1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_a1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4_a2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4_a2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_0D2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D2[1] := 0.2; > array_const_0D3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D3[1] := 0.3; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , sin(x));"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T01:42:47-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"expt_lin_sin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , sin(x));") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"expt_lin_sin diffeq.mxt") > ; > logitem_str(html_log_file,"expt_lin_sin maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3_g, array_tmp3, array_tmp4_c1, array_tmp4_a1, array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/expt_lin_sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , sin(x));"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(0.0);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3_g := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4_c1 := Array(0 .. max_terms + 1, []); array_tmp4_a1 := Array(0 .. max_terms + 1, []); array_tmp4_a2 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_c1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_a1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4_a2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3_g[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4_c1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_c1[term] := 0.; term := term + 1 end do; array_tmp4_a1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_a1[term] := 0.; term := term + 1 end do; array_tmp4_a2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_a2[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_0D2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D2[term] := 0.; term := term + 1 end do; array_const_0D2[1] := 0.2; array_const_0D3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D3[term] := 0.; term := term + 1 end do; array_const_0D3[1] := 0.3; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , sin(x));"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T01:42:47-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "expt_lin_sin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , sin(x));"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "expt_lin_sin diffeq.mxt"); logitem_str(html_log_file, "expt_lin_sin maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/expt_lin_sinpostode.ode################# diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , sin(x)); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(0.0); 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 = 1.0008294884127150148088176447894e-167 estimated_step_error = 1.0008294884127150148088176447894e-167 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 = 7.0942333894510672736633599509993e-156 estimated_step_error = 7.0942333894510672736633599509993e-156 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 = 4.7608566268903953927523182564398e-148 estimated_step_error = 4.7608566268903953927523182564398e-148 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 = 3.1949530270890506377146090033458e-140 estimated_step_error = 3.1949530270890506377146090033458e-140 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 = 2.1440916192916019380974309587992e-132 estimated_step_error = 2.1440916192916019380974309587992e-132 best_h = 3.200000e-05 opt_iter = 6 bytes used=4000072, alloc=2948580, time=0.12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.4388687340727311318801609253558e-124 estimated_step_error = 1.4388687340727311318801609253558e-124 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 = 9.6559934225367110972574084712419e-117 estimated_step_error = 9.6559934225367110972574084712419e-117 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.4799050956027651315595944554010e-109 estimated_step_error = 6.4799050956027651315595944554010e-109 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 = 4.3484264272151058581295739979561e-101 estimated_step_error = 4.3484264272151058581295739979561e-101 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 = 2.9179591217923263957328961384620e-93 estimated_step_error = 2.9179591217923263957328961384620e-93 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 = 1.9579133956320613116579393809685e-85 estimated_step_error = 1.9579133956320613116579393809685e-85 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 = 1.3135365714766194580399836454034e-77 estimated_step_error = 1.3135365714766194580399836454034e-77 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 = 8.8096729063793952532300648663700e-70 estimated_step_error = 8.8096729063793952532300648663700e-70 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 = 5.9049416043332866942455237977617e-62 estimated_step_error = 5.9049416043332866942455237977617e-62 best_h = 0.016384 opt_iter = 15 bytes used=8001020, alloc=3996964, time=0.24 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.9532046732466681128306260585952e-54 estimated_step_error = 3.9532046732466681128306260585952e-54 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 = 2.6402473799503613584883129182483e-46 estimated_step_error = 2.6402473799503613584883129182483e-46 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 = 1.7550413712172457277811286488202e-38 estimated_step_error = 1.7550413712172457277811286488202e-38 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 = 1.1559167249811110859520527040060e-30 estimated_step_error = 1.1559167249811110859520527040060e-30 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 Radius of convergence (ratio test) for eq 1 = 0.9391 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 0 y[1] (numeric) = 0.0089130508616163470711550620085135 absolute error = 0.0089130508616163470711550620085135 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.683 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.721 Order of pole (six term test) = 0.4029 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0 y[1] (numeric) = 0.01769694305689905545082257152429 absolute error = 0.01769694305689905545082257152429 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.694 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.659 Order of pole (six term test) = 0.437 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 0 y[1] (numeric) = 0.026389519476849601120977063764858 absolute error = 0.026389519476849601120977063764858 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.704 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.593 Order of pole (six term test) = 0.4771 TOP MAIN SOLVE Loop bytes used=12002232, alloc=4193536, time=0.37 x[1] = 0.14 y[1] (analytic) = 0 y[1] (numeric) = 0.034992859903445018880788140848454 absolute error = 0.034992859903445018880788140848454 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.715 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.52 Order of pole (six term test) = 0.5243 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0 y[1] (numeric) = 0.043508997842014165853690800683198 absolute error = 0.043508997842014165853690800683198 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.725 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.438 Order of pole (six term test) = 0.58 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0 y[1] (numeric) = 0.051939921790838600501225794541086 absolute error = 0.051939921790838600501225794541086 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.736 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.344 Order of pole (six term test) = 0.6457 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0 y[1] (numeric) = 0.060287576472853039115352214767412 absolute error = 0.060287576472853039115352214767412 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.746 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.233 Order of pole (six term test) = 0.7237 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0 y[1] (numeric) = 0.068553864030719146750288990016854 absolute error = 0.068553864030719146750288990016854 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.757 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.099 Order of pole (six term test) = 0.8167 TOP MAIN SOLVE Loop x[1] = 0.19 y[1] (analytic) = 0 y[1] (numeric) = 0.076740645186497361554584344315844 absolute error = 0.076740645186497361554584344315844 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.767 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 = 0.9254 Order of pole (six term test) = 0.9286 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0 y[1] (numeric) = 0.084849740367094562651464351960624 absolute error = 0.084849740367094562651464351960624 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.777 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 = 0.6765 Order of pole (six term test) = 1.064 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (analytic) = 0 y[1] (numeric) = 0.092882930796620561069345146658184 absolute error = 0.092882930796620561069345146658184 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.788 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (analytic) = 0 y[1] (numeric) = 0.10084195955674351616515722444398 absolute error = 0.10084195955674351616515722444398 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.798 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=16003488, alloc=4324584, time=0.51 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (analytic) = 0 y[1] (numeric) = 0.10872853261609335795903141148132 absolute error = 0.10872853261609335795903141148132 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.809 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (analytic) = 0 y[1] (numeric) = 0.11654431982972303590088994824121 absolute error = 0.11654431982972303590088994824121 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.819 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.25 y[1] (analytic) = 0 y[1] (numeric) = 0.12429095590959982919301204880663 absolute error = 0.12429095590959982919301204880663 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.26 y[1] (analytic) = 0 y[1] (numeric) = 0.13197004136706296022410989659297 absolute error = 0.13197004136706296022410989659297 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.27 y[1] (analytic) = 0 y[1] (numeric) = 0.13958314342814927289663746932678 absolute error = 0.13958314342814927289663746932678 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.851 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.28 y[1] (analytic) = 0 y[1] (numeric) = 0.14713179692265569796773699247089 absolute error = 0.14713179692265569796773699247089 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.861 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.29 y[1] (analytic) = 0 y[1] (numeric) = 0.15461750514777555837447427712518 absolute error = 0.15461750514777555837447427712518 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.871 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0 y[1] (numeric) = 0.16204174070711540310471268808454 absolute error = 0.16204174070711540310471268808454 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.882 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=20004272, alloc=4390108, time=0.64 x[1] = 0.31 y[1] (analytic) = 0 y[1] (numeric) = 0.16940594632586993633027129237191 absolute error = 0.16940594632586993633027129237191 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.892 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.32 y[1] (analytic) = 0 y[1] (numeric) = 0.17671153564290467043943404877286 absolute error = 0.17671153564290467043943404877286 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.903 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.94 Order of pole (six term test) = -31.57 TOP MAIN SOLVE Loop x[1] = 0.33 y[1] (analytic) = 0 y[1] (numeric) = 0.18395989398046912166402145692739 absolute error = 0.18395989398046912166402145692739 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.913 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.303 Order of pole (six term test) = -13.94 TOP MAIN SOLVE Loop x[1] = 0.34 y[1] (analytic) = 0 y[1] (numeric) = 0.19115237909223763254597801470173 absolute error = 0.19115237909223763254597801470173 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.924 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 = 4.33 Order of pole (six term test) = -9.275 TOP MAIN SOLVE Loop x[1] = 0.35 y[1] (analytic) = 0 y[1] (numeric) = 0.19829032189035019668668412272878 absolute error = 0.19829032189035019668668412272878 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.934 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.785 Order of pole (six term test) = -7.132 TOP MAIN SOLVE Loop x[1] = 0.36 y[1] (analytic) = 0 y[1] (numeric) = 0.20537502715210193086236306747911 absolute error = 0.20537502715210193086236306747911 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.945 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.422 Order of pole (six term test) = -5.908 TOP MAIN SOLVE Loop x[1] = 0.37 y[1] (analytic) = 0 y[1] (numeric) = 0.21240777420690704294517699179896 absolute error = 0.21240777420690704294517699179896 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.955 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.154 Order of pole (six term test) = -5.125 TOP MAIN SOLVE Loop x[1] = 0.38 y[1] (analytic) = 0 y[1] (numeric) = 0.2193898176041412387511784748081 absolute error = 0.2193898176041412387511784748081 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.966 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.941 Order of pole (six term test) = -4.588 TOP MAIN SOLVE Loop bytes used=24005248, alloc=4390108, time=0.78 x[1] = 0.39 y[1] (analytic) = 0 y[1] (numeric) = 0.2263223877624454567513857708958 absolute error = 0.2263223877624454567513857708958 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.976 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.763 Order of pole (six term test) = -4.204 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0 y[1] (numeric) = 0.2332066916010535784104421492584 absolute error = 0.2332066916010535784104421492584 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.986 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.607 Order of pole (six term test) = -3.923 TOP MAIN SOLVE Loop x[1] = 0.41 y[1] (analytic) = 0 y[1] (numeric) = 0.24004391315368729759017164120707 absolute error = 0.24004391315368729759017164120707 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.997 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.466 Order of pole (six term test) = -3.718 TOP MAIN SOLVE Loop x[1] = 0.42 y[1] (analytic) = 0 y[1] (numeric) = 0.24683521416554261064462588279101 absolute error = 0.24683521416554261064462588279101 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.007 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.335 Order of pole (six term test) = -3.571 TOP MAIN SOLVE Loop x[1] = 0.43 y[1] (analytic) = 0 y[1] (numeric) = 0.25358173467387437694615486698711 absolute error = 0.25358173467387437694615486698711 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.018 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.209 Order of pole (six term test) = -3.472 TOP MAIN SOLVE Loop x[1] = 0.44 y[1] (analytic) = 0 y[1] (numeric) = 0.26028459357266806666313489672096 absolute error = 0.26028459357266806666313489672096 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.028 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.086 Order of pole (six term test) = -3.416 TOP MAIN SOLVE Loop x[1] = 0.45 y[1] (analytic) = 0 y[1] (numeric) = 0.26694488916187112924899545697763 absolute error = 0.26694488916187112924899545697763 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.039 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.963 Order of pole (six term test) = -3.397 TOP MAIN SOLVE Loop x[1] = 0.46 y[1] (analytic) = 0 y[1] (numeric) = 0.27356369968164035434776280569276 absolute error = 0.27356369968164035434776280569276 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.049 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.838 Order of pole (six term test) = -3.415 TOP MAIN SOLVE Loop x[1] = 0.47 y[1] (analytic) = 0 y[1] (numeric) = 0.28014208383204613010006492398463 absolute error = 0.28014208383204613010006492398463 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.709 Order of pole (six term test) = -3.468 bytes used=28006568, alloc=4455632, time=0.90 TOP MAIN SOLVE Loop x[1] = 0.48 y[1] (analytic) = 0 y[1] (numeric) = 0.2866810812786596068739141545456 absolute error = 0.2866810812786596068739141545456 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.575 Order of pole (six term test) = -3.556 TOP MAIN SOLVE Loop x[1] = 0.49 y[1] (analytic) = 0 y[1] (numeric) = 0.29318171314443442320564075270416 absolute error = 0.29318171314443442320564075270416 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.081 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.433 Order of pole (six term test) = -3.68 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0 y[1] (numeric) = 0.29964498248828082234065513431963 absolute error = 0.29964498248828082234065513431963 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.091 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.28 Order of pole (six term test) = -3.838 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 0 y[1] (numeric) = 0.30607187477071666043438421854034 absolute error = 0.30607187477071666043438421854034 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.101 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.113 Order of pole (six term test) = -4.032 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 0 y[1] (numeric) = 0.31246335830696696047524661298862 absolute error = 0.31246335830696696047524661298862 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.112 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 = 0.9236 Order of pole (six term test) = -4.259 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 0 y[1] (numeric) = 0.3188203847078712795741273697958 absolute error = 0.3188203847078712795741273697958 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.122 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 = 0.6974 Order of pole (six term test) = -4.519 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 0 y[1] (numeric) = 0.32514388930894621261212246086078 absolute error = 0.32514388930894621261212246086078 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.133 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 = 0.3739 Order of pole (six term test) = -4.81 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 0 y[1] (numeric) = 0.33143479158793883441816927883249 absolute error = 0.33143479158793883441816927883249 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.143 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=32007520, alloc=4455632, time=1.04 x[1] = 0.56 y[1] (analytic) = 0 y[1] (numeric) = 0.33769399557119576856624645336748 absolute error = 0.33769399557119576856624645336748 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.154 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.57 y[1] (analytic) = 0 y[1] (numeric) = 0.34392239022916184723804745575013 absolute error = 0.34392239022916184723804745575013 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.164 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.58 y[1] (analytic) = 0 y[1] (numeric) = 0.35012084986131197784452036478501 absolute error = 0.35012084986131197784452036478501 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.175 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.59 y[1] (analytic) = 0 y[1] (numeric) = 0.35629023447080984340602252617478 absolute error = 0.35629023447080984340602252617478 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.185 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0 y[1] (numeric) = 0.36243139012917742090169472777591 absolute error = 0.36243139012917742090169472777591 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.196 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.61 y[1] (analytic) = 0 y[1] (numeric) = 0.36854514933124999140330533564397 absolute error = 0.36854514933124999140330533564397 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.206 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.62 y[1] (analytic) = 0 y[1] (numeric) = 0.37463233134068232490778949842663 absolute error = 0.37463233134068232490778949842663 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.217 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.63 y[1] (analytic) = 0 y[1] (numeric) = 0.38069374252626303905722578545102 absolute error = 0.38069374252626303905722578545102 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.227 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.64 y[1] (analytic) = 0 y[1] (numeric) = 0.38673017668928574261809067315143 absolute error = 0.38673017668928574261809067315143 relative error = -1 % Correct digits = -1 h = 0.01 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 NO COMPLEX POLE (six term test) for Equation 1 bytes used=36010872, alloc=4455632, time=1.17 TOP MAIN SOLVE Loop x[1] = 0.65 y[1] (analytic) = 0 y[1] (numeric) = 0.3927424153822174704409392348893 absolute error = 0.3927424153822174704409392348893 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.248 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.66 y[1] (analytic) = 0 y[1] (numeric) = 0.39873122821889708589368216398932 absolute error = 0.39873122821889708589368216398932 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.259 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.67 y[1] (analytic) = 0 y[1] (numeric) = 0.40469737317648875918745219163572 absolute error = 0.40469737317648875918745219163572 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.269 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.68 y[1] (analytic) = 0 y[1] (numeric) = 0.41064159688940831577639405192662 absolute error = 0.41064159688940831577639405192662 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.69 y[1] (analytic) = 0 y[1] (numeric) = 0.41656463493543317872422094015821 absolute error = 0.41656463493543317872422094015821 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0 y[1] (numeric) = 0.42246721211419979361312246237109 absolute error = 0.42246721211419979361312246237109 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.301 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.71 y[1] (analytic) = 0 y[1] (numeric) = 0.42835004271828581563665894457166 absolute error = 0.42835004271828581563665894457166 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.311 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.72 y[1] (analytic) = 0 y[1] (numeric) = 0.43421383079706794775135421094842 absolute error = 0.43421383079706794775135421094842 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.322 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=40011592, alloc=4521156, time=1.31 x[1] = 0.73 y[1] (analytic) = 0 y[1] (numeric) = 0.44005927041354013829978477532193 absolute error = 0.44005927041354013829978477532193 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.332 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.74 y[1] (analytic) = 0 y[1] (numeric) = 0.44588704589427086883683973256774 absolute error = 0.44588704589427086883683973256774 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.343 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.75 y[1] (analytic) = 0 y[1] (numeric) = 0.45169783207267248078848177315606 absolute error = 0.45169783207267248078848177315606 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.353 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.76 y[1] (analytic) = 0 y[1] (numeric) = 0.45749229452574989615419543469559 absolute error = 0.45749229452574989615419543469559 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.363 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.77 y[1] (analytic) = 0 y[1] (numeric) = 0.46327108980449067612920565809117 absolute error = 0.46327108980449067612920565809117 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.374 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.78 y[1] (analytic) = 0 y[1] (numeric) = 0.46903486565805312594946637541551 absolute error = 0.46903486565805312594946637541551 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.384 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.79 y[1] (analytic) = 0 y[1] (numeric) = 0.47478426125190408839786622174907 absolute error = 0.47478426125190408839786622174907 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.394 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8 y[1] (analytic) = 0 y[1] (numeric) = 0.48051990738005316645615727726065 absolute error = 0.48051990738005316645615727726065 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.404 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.81 y[1] (analytic) = 0 y[1] (numeric) = 0.48624242667152537199007480001697 absolute error = 0.48624242667152537199007480001697 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.414 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=44012664, alloc=4521156, time=1.44 x[1] = 0.82 y[1] (analytic) = 0 y[1] (numeric) = 0.49195243379120960679469449199405 absolute error = 0.49195243379120960679469449199405 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.424 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.83 y[1] (analytic) = 0 y[1] (numeric) = 0.4976505356352159397061504710195 absolute error = 0.4976505356352159397061504710195 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.434 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.84 y[1] (analytic) = 0 y[1] (numeric) = 0.50333733152087034392071370626457 absolute error = 0.50333733152087034392071370626457 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.444 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.85 y[1] (analytic) = 0 y[1] (numeric) = 0.50901341337147139747335805715844 absolute error = 0.50901341337147139747335805715844 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.454 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.86 y[1] (analytic) = 0 y[1] (numeric) = 0.51467936589592942253109667776973 absolute error = 0.51467936589592942253109667776973 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.464 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.87 y[1] (analytic) = 0 y[1] (numeric) = 0.52033576676340464145426056747126 absolute error = 0.52033576676340464145426056747126 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.473 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.88 y[1] (analytic) = 0 y[1] (numeric) = 0.52598318677305715535314675680255 absolute error = 0.52598318677305715535314675680255 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.482 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.89 y[1] (analytic) = 0 y[1] (numeric) = 0.53162219001901790017102445221964 absolute error = 0.53162219001901790017102445221964 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.489 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=48013608, alloc=4521156, time=1.58 x[1] = 0.9 y[1] (analytic) = 0 y[1] (numeric) = 0.5372533340506862023743292134435 absolute error = 0.5372533340506862023743292134435 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.496 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.91 y[1] (analytic) = 0 y[1] (numeric) = 0.54287717002845613750107830676704 absolute error = 0.54287717002845613750107830676704 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.502 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.92 y[1] (analytic) = 0 y[1] (numeric) = 0.54849424287497058663367314024166 absolute error = 0.54849424287497058663367314024166 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.508 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.93 y[1] (analytic) = 0 y[1] (numeric) = 0.55410509142199868499105505434248 absolute error = 0.55410509142199868499105505434248 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.514 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.94 y[1] (analytic) = 0 y[1] (numeric) = 0.55971024855302926008451911110968 absolute error = 0.55971024855302926008451911110968 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.519 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.95 y[1] (analytic) = 0 y[1] (numeric) = 0.56531024134166986119059822345939 absolute error = 0.56531024134166986119059822345939 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.96 y[1] (analytic) = 0 y[1] (numeric) = 0.57090559118593808432937823442441 absolute error = 0.57090559118593808432937823442441 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.97 y[1] (analytic) = 0 y[1] (numeric) = 0.57649681393852909468501994987527 absolute error = 0.57649681393852909468501994987527 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.535 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.98 y[1] (analytic) = 0 y[1] (numeric) = 0.58208442003314053877126703612224 absolute error = 0.58208442003314053877126703612224 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=52015728, alloc=4521156, time=1.72 x[1] = 0.99 y[1] (analytic) = 0 y[1] (numeric) = 0.58766891460693341904407240806311 absolute error = 0.58766891460693341904407240806311 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.545 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 0 y[1] (numeric) = 0.59325079761920497161893423373692 absolute error = 0.59325079761920497161893423373692 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 0 y[1] (numeric) = 0.59883056396634714088737595195358 absolute error = 0.59883056396634714088737595195358 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.555 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = 0 y[1] (numeric) = 0.60440870359316188086875103800265 absolute error = 0.60440870359316188086875103800265 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = 0 y[1] (numeric) = 0.60998570160060222989783861219663 absolute error = 0.60998570160060222989783861219663 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.566 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = 0 y[1] (numeric) = 0.61556203835000590064331097011654 absolute error = 0.61556203835000590064331097011654 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.572 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 = 0.1464 Order of pole (six term test) = -11.99 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 0 y[1] (numeric) = 0.62113818956388599947122975256732 absolute error = 0.62113818956388599947122975256732 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.579 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 = 0.2074 Order of pole (six term test) = -11.98 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 0 y[1] (numeric) = 0.62671462642334143588806143097638 absolute error = 0.62671462642334143588806143097638 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.588 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 = 0.2497 Order of pole (six term test) = -11.96 TOP MAIN SOLVE Loop bytes used=56016732, alloc=4521156, time=1.85 x[1] = 1.07 y[1] (analytic) = 0 y[1] (numeric) = 0.63229181566214760237521810170639 absolute error = 0.63229181566214760237521810170639 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.591 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 = 0.2811 Order of pole (six term test) = -11.93 TOP MAIN SOLVE Loop x[1] = 1.08 y[1] (analytic) = 0 y[1] (numeric) = 0.63787021965758599559345852598212 absolute error = 0.63787021965758599559345852598212 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.58 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 = 0.3043 Order of pole (six term test) = -11.91 TOP MAIN SOLVE Loop x[1] = 1.09 y[1] (analytic) = 0 y[1] (numeric) = 0.64345029651806960999467034371366 absolute error = 0.64345029651806960999467034371366 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.565 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 = 0.3207 Order of pole (six term test) = -11.87 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0 y[1] (numeric) = 0.64903250016761916270386541858298 absolute error = 0.64903250016761916270386541858298 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.547 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 = 0.3308 Order of pole (six term test) = -11.84 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 0 y[1] (numeric) = 0.65461728042724350256506754869351 absolute error = 0.65461728042724350256506754869351 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 = 0.3349 Order of pole (six term test) = -11.8 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 0 y[1] (numeric) = 0.66020508309327591498372776763479 absolute error = 0.66020508309327591498372776763479 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.333 Order of pole (six term test) = -11.76 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 0 y[1] (numeric) = 0.66579635001271645620821277809442 absolute error = 0.66579635001271645620821277809442 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.472 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 = 0.3247 Order of pole (six term test) = -11.71 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = 0 y[1] (numeric) = 0.67139151915562893459409602097286 absolute error = 0.67139151915562893459409602097286 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.439 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 = 0.3095 Order of pole (six term test) = -11.67 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = 0 y[1] (numeric) = 0.67699102468463970086251584838654 absolute error = 0.67699102468463970086251584838654 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.402 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 = 0.2865 Order of pole (six term test) = -11.62 TOP MAIN SOLVE Loop bytes used=60017672, alloc=4586680, time=1.99 x[1] = 1.16 y[1] (analytic) = 0 y[1] (numeric) = 0.68259529702158401312495018715209 absolute error = 0.68259529702158401312495018715209 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.36 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 = 0.2535 Order of pole (six term test) = -11.58 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 0 y[1] (numeric) = 0.68820476291134440427815093390914 absolute error = 0.68820476291134440427815093390914 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.314 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 = 0.2063 Order of pole (six term test) = -11.53 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 0 y[1] (numeric) = 0.69381984548292419809851246216703 absolute error = 0.69381984548292419809851246216703 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.263 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 = 0.131 Order of pole (six term test) = -11.48 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 0 y[1] (numeric) = 0.69944096430779809485329120428963 absolute error = 0.69944096430779809485329120428963 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.208 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 0 y[1] (numeric) = 0.70506853545558057640760731651835 absolute error = 0.70506853545558057640760731651835 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.147 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 0 y[1] (numeric) = 0.71070297154705176359179119761789 absolute error = 0.71070297154705176359179119761789 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.081 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 0 y[1] (numeric) = 0.71634468180457929399187726192978 absolute error = 0.71634468180457929399187726192978 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.011 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 0 y[1] (numeric) = 0.72199407209997377536094102796797 absolute error = 0.72199407209997377536094102796797 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.935 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=64018620, alloc=4586680, time=2.13 x[1] = 1.24 y[1] (analytic) = 0 y[1] (numeric) = 0.72765154499981440757798941112871 absolute error = 0.72765154499981440757798941112871 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 0 y[1] (numeric) = 0.733317499808280453593047615029 absolute error = 0.733317499808280453593047615029 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = 0 y[1] (numeric) = 0.73899233260752337621003271276751 absolute error = 0.73899233260752337621003271276751 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 0 y[1] (numeric) = 0.74467643629561364201835724191472 absolute error = 0.74467643629561364201835724191472 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 0 y[1] (numeric) = 0.75037020062209542546070828152473 absolute error = 0.75037020062209542546070828152473 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 0 y[1] (numeric) = 0.75607401222118172411228084825763 absolute error = 0.75607401222118172411228084825763 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0 y[1] (numeric) = 0.76178825464262171996166241076355 absolute error = 0.76178825464262171996166241076355 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 0 y[1] (numeric) = 0.76751330838027159006106231370625 absolute error = 0.76751330838027159006106231370625 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 0 y[1] (numeric) = 0.77324955089839938260709916706609 absolute error = 0.77324955089839938260709916706609 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=68019676, alloc=4586680, time=2.27 x[1] = 1.33 y[1] (analytic) = 0 y[1] (numeric) = 0.77899735665575403059253729174543 absolute error = 0.77899735665575403059253729174543 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 0 y[1] (numeric) = 0.78475709712742807391831018191323 absolute error = 0.78475709712742807391831018191323 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 0 y[1] (numeric) = 0.79052914082454320157078371960975 absolute error = 0.79052914082454320157078371960975 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 0 y[1] (numeric) = 0.79631385331178730745953264548259 absolute error = 0.79631385331178730745953264548259 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 0 y[1] (numeric) = 0.80211159722283137609349178377737 absolute error = 0.80211159722283137609349178377737 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 0 y[1] (numeric) = 0.80792273227365417677370105903818 absolute error = 0.80792273227365417677370105903818 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 0 y[1] (numeric) = 0.8137476152738024467308854032061 absolute error = 0.8137476152738024467308854032061 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0 y[1] (numeric) = 0.81958660013561398397257000954913 absolute error = 0.81958660013561398397257000954913 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 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 0 y[1] (numeric) = 0.82544003788143084886749738306196 absolute error = 0.82544003788143084886749738306196 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 NO COMPLEX POLE (six term test) for Equation 1 bytes used=72021032, alloc=4586680, time=2.40 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 0 y[1] (numeric) = 0.83130827664882968902690373288476 absolute error = 0.83130827664882968902690373288476 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 = 1.538 Order of pole (three term test) = -147.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 0 y[1] (numeric) = 0.83719166169389605418538268809691 absolute error = 0.83719166169389605418538268809691 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 = 0.4756 Order of pole (three term test) = -46.87 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 0 y[1] (numeric) = 0.84309053539256945588042520569382 absolute error = 0.84309053539256945588042520569382 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 = 0.2793 Order of pole (three term test) = -28.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 0 y[1] (numeric) = 0.84900523724008585011889991838466 absolute error = 0.84900523724008585011889991838466 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 = 0.1986 Order of pole (three term test) = -21.46 Radius of convergence (six term test) for eq 1 = 0.2679 Order of pole (six term test) = -11.56 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 0 y[1] (numeric) = 0.85493610384854417923685659204746 absolute error = 0.85493610384854417923685659204746 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 = 0.1556 Order of pole (three term test) = -17.92 Radius of convergence (six term test) for eq 1 = 0.4153 Order of pole (six term test) = -11.53 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = 0 y[1] (numeric) = 0.86088346894262360113745768133954 absolute error = 0.86088346894262360113745768133954 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 = 0.1293 Order of pole (three term test) = -16.04 Radius of convergence (six term test) for eq 1 = 0.5053 Order of pole (six term test) = -11.49 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = 0 y[1] (numeric) = 0.86684766335347805935592709555379 absolute error = 0.86684766335347805935592709555379 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 = 0.1117 Order of pole (three term test) = -15.08 Radius of convergence (six term test) for eq 1 = 0.5655 Order of pole (six term test) = -11.45 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 0 y[1] (numeric) = 0.87282901501083490526830874220962 absolute error = 0.87282901501083490526830874220962 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 = 0.09912 Order of pole (three term test) = -14.69 Radius of convergence (six term test) for eq 1 = 0.6065 Order of pole (six term test) = -11.41 TOP MAIN SOLVE Loop bytes used=76024956, alloc=4586680, time=2.54 x[1] = 1.5 y[1] (analytic) = 0 y[1] (numeric) = 0.87882784893332437354234864123791 absolute error = 0.87882784893332437354234864123791 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 = 0.0895 Order of pole (three term test) = -14.69 Radius of convergence (six term test) for eq 1 = 0.6344 Order of pole (six term test) = -11.37 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = 0 y[1] (numeric) = 0.88484448721706683292427376414128 absolute error = 0.88484448721706683292427376414128 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 = 0.08168 Order of pole (three term test) = -14.99 Radius of convergence (six term test) for eq 1 = 0.6534 Order of pole (six term test) = -11.33 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = 0 y[1] (numeric) = 0.89087924902254488595440234685864 absolute error = 0.89087924902254488595440234685864 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 = 0.07489 Order of pole (three term test) = -15.52 Radius of convergence (six term test) for eq 1 = 0.6666 Order of pole (six term test) = -11.3 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (analytic) = 0 y[1] (numeric) = 0.89693245055978757248555579243636 absolute error = 0.89693245055978757248555579243636 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 = 0.06862 Order of pole (three term test) = -16.22 Radius of convergence (six term test) for eq 1 = 0.6764 Order of pole (six term test) = -11.27 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = 0 y[1] (numeric) = 0.90300440507189414220673720976515 absolute error = 0.90300440507189414220673720976515 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 = 0.06251 Order of pole (three term test) = -17.07 Radius of convergence (six term test) for eq 1 = 0.6843 Order of pole (six term test) = -11.24 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 0 y[1] (numeric) = 0.9090954228169251000025473006877 absolute error = 0.9090954228169251000025473006877 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 = 0.05629 Order of pole (three term test) = -18.02 Radius of convergence (six term test) for eq 1 = 0.6918 Order of pole (six term test) = -11.22 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = 0 y[1] (numeric) = 0.91520581104818849414393800936634 absolute error = 0.91520581104818849414393800936634 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 = 0.04977 Order of pole (three term test) = -19.06 Radius of convergence (six term test) for eq 1 = 0.6998 Order of pole (six term test) = -11.19 TOP MAIN SOLVE Loop x[1] = 1.57 y[1] (analytic) = 0 y[1] (numeric) = 0.92133587399294971023047718657662 absolute error = 0.92133587399294971023047718657662 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 = 0.04282 Order of pole (three term test) = -20.14 Radius of convergence (six term test) for eq 1 = 0.7091 Order of pole (six term test) = -11.16 TOP MAIN SOLVE Loop x[1] = 1.58 y[1] (analytic) = 0 y[1] (numeric) = 0.92748591282959335269453036736189 absolute error = 0.92748591282959335269453036736189 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 = 0.03535 Order of pole (three term test) = -21.24 Radius of convergence (six term test) for eq 1 = 0.7201 Order of pole (six term test) = -11.14 TOP MAIN SOLVE Loop bytes used=80026000, alloc=4586680, time=2.67 x[1] = 1.59 y[1] (analytic) = 0 y[1] (numeric) = 0.93365622566326613972301489603156 absolute error = 0.93365622566326613972301489603156 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 = 0.02734 Order of pole (three term test) = -22.31 Radius of convergence (six term test) for eq 1 = 0.7333 Order of pole (six term test) = -11.11 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 0 y[1] (numeric) = 0.93984710750003010582443548878382 absolute error = 0.93984710750003010582443548878382 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 = 0.01878 Order of pole (three term test) = -23.32 Radius of convergence (six term test) for eq 1 = 0.749 Order of pole (six term test) = -11.07 TOP MAIN SOLVE Loop x[1] = 1.61 y[1] (analytic) = 0 y[1] (numeric) = 0.94605885021955579812133473512838 absolute error = 0.94605885021955579812133473512838 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 = 0.009728 Order of pole (three term test) = -24.24 Radius of convergence (six term test) for eq 1 = 0.7675 Order of pole (six term test) = -11.03 TOP MAIN SOLVE Loop x[1] = 1.62 y[1] (analytic) = 0 y[1] (numeric) = 0.95229174254638556691582945600128 absolute error = 0.95229174254638556691582945600128 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 = 0.0002695 Order of pole (three term test) = -25.02 Radius of convergence (six term test) for eq 1 = 0.789 Order of pole (six term test) = -10.99 TOP MAIN SOLVE Loop x[1] = 1.63 y[1] (analytic) = 0 y[1] (numeric) = 0.95854607001979748727392794704939 absolute error = 0.95854607001979748727392794704939 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 = 0.8137 Order of pole (six term test) = -10.94 TOP MAIN SOLVE Loop x[1] = 1.64 y[1] (analytic) = 0 y[1] (numeric) = 0.96482211496230090539835033265986 absolute error = 0.96482211496230090539835033265986 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 = 0.8419 Order of pole (six term test) = -10.89 TOP MAIN SOLVE Loop x[1] = 1.65 y[1] (analytic) = 0 y[1] (numeric) = 0.97112015644679508048483338828657 absolute error = 0.97112015644679508048483338828657 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 = 0.8735 Order of pole (six term test) = -10.82 TOP MAIN SOLVE Loop x[1] = 1.66 y[1] (analytic) = 0 y[1] (numeric) = 0.97744047026242288863796301396573 absolute error = 0.97744047026242288863796301396573 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 = 0.909 Order of pole (six term test) = -10.75 TOP MAIN SOLVE Loop bytes used=84027016, alloc=4586680, time=2.81 x[1] = 1.67 y[1] (analytic) = 0 y[1] (numeric) = 0.98378332887915206929304528484773 absolute error = 0.98378332887915206929304528484773 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 = 0.9485 Order of pole (six term test) = -10.67 TOP MAIN SOLVE Loop x[1] = 1.68 y[1] (analytic) = 0 y[1] (numeric) = 0.99014900141111702546278938102279 absolute error = 0.99014900141111702546278938102279 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 = 0.9923 Order of pole (six term test) = -10.57 TOP MAIN SOLVE Loop x[1] = 1.69 y[1] (analytic) = 0 y[1] (numeric) = 0.99653775357875473599262374598076 absolute error = 0.99653775357875473599262374598076 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 = 1.041 Order of pole (six term test) = -10.46 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 0 y[1] (numeric) = 1.0029498476697688998357758222879 absolute error = 1.0029498476697688998357758222879 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 = 1.094 Order of pole (six term test) = -10.33 TOP MAIN SOLVE Loop x[1] = 1.71 y[1] (analytic) = 0 y[1] (numeric) = 1.009385542498957008096723447878 absolute error = 1.009385542498957008096723447878 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 = 1.152 Order of pole (six term test) = -10.18 TOP MAIN SOLVE Loop x[1] = 1.72 y[1] (analytic) = 0 y[1] (numeric) = 1.0158450933669356281656285264113 absolute error = 1.0158450933669356281656285264113 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 = 1.216 Order of pole (six term test) = -10 TOP MAIN SOLVE Loop x[1] = 1.73 y[1] (analytic) = 0 y[1] (numeric) = 1.0223287520177997845817796566606 absolute error = 1.0223287520177997845817796566606 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 = 1.286 Order of pole (six term test) = -9.801 TOP MAIN SOLVE Loop x[1] = 1.74 y[1] (analytic) = 0 y[1] (numeric) = 1.028836766595752932204475544852 absolute error = 1.028836766595752932204475544852 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 = 1.363 Order of pole (six term test) = -9.567 TOP MAIN SOLVE Loop x[1] = 1.75 y[1] (analytic) = 0 y[1] (numeric) = 1.0353693816007446376976622809535 absolute error = 1.0353693816007446376976622809535 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 = 1.446 Order of pole (six term test) = -9.295 TOP MAIN SOLVE Loop bytes used=88028400, alloc=4586680, time=2.94 x[1] = 1.76 y[1] (analytic) = 0 y[1] (numeric) = 1.0419268378431537140916897894694 absolute error = 1.0419268378431537140916897894694 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 = 1.538 Order of pole (six term test) = -8.978 TOP MAIN SOLVE Loop x[1] = 1.77 y[1] (analytic) = 0 y[1] (numeric) = 1.0485093723975551890930472290174 absolute error = 1.0485093723975551890930472290174 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 = 1.638 Order of pole (six term test) = -8.609 TOP MAIN SOLVE Loop x[1] = 1.78 y[1] (analytic) = 0 y[1] (numeric) = 1.055117218555610129672163099696 absolute error = 1.055117218555610129672163099696 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 = 1.747 Order of pole (six term test) = -8.178 TOP MAIN SOLVE Loop x[1] = 1.79 y[1] (analytic) = 0 y[1] (numeric) = 1.0617506057781179920521358510813 absolute error = 1.0617506057781179920521358510813 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 = 1.866 Order of pole (six term test) = -7.675 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0 y[1] (numeric) = 1.068409759646271816310539920028 absolute error = 1.068409759646271816310539920028 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 = 1.996 Order of pole (six term test) = -7.087 TOP MAIN SOLVE Loop x[1] = 1.81 y[1] (analytic) = 0 y[1] (numeric) = 1.0750949018121572371369616473371 absolute error = 1.0750949018121572371369616473371 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 = 2.138 Order of pole (six term test) = -6.4 TOP MAIN SOLVE Loop x[1] = 1.82 y[1] (analytic) = 0 y[1] (numeric) = 1.081806249948536935587915278428 absolute error = 1.081806249948536935587915278428 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 = 2.292 Order of pole (six term test) = -5.598 TOP MAIN SOLVE Loop x[1] = 1.83 y[1] (analytic) = 0 y[1] (numeric) = 1.0885440176979628096588647461666 absolute error = 1.0885440176979628096588647461666 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 = 2.459 Order of pole (six term test) = -4.663 TOP MAIN SOLVE Loop x[1] = 1.84 y[1] (analytic) = 0 y[1] (numeric) = 1.0953084146212587928450510737056 absolute error = 1.0953084146212587928450510737056 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 = 2.639 Order of pole (six term test) = -3.578 TOP MAIN SOLVE Loop bytes used=92029840, alloc=4586680, time=3.08 x[1] = 1.85 y[1] (analytic) = 0 y[1] (numeric) = 1.1020996461454178982687045930063 absolute error = 1.1020996461454178982687045930063 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 = 2.833 Order of pole (six term test) = -2.324 TOP MAIN SOLVE Loop x[1] = 1.86 y[1] (analytic) = 0 y[1] (numeric) = 1.1089179135109577100762363852674 absolute error = 1.1089179135109577100762363852674 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 = 0.006749 Order of pole (three term test) = -0.9734 Radius of convergence (six term test) for eq 1 = 3.04 Order of pole (six term test) = -0.8847 TOP MAIN SOLVE Loop x[1] = 1.87 y[1] (analytic) = 0 y[1] (numeric) = 1.1157634137187791823087191626422 absolute error = 1.1157634137187791823087191626422 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 = 0.01573 Order of pole (three term test) = -1.356 Radius of convergence (six term test) for eq 1 = 3.258 Order of pole (six term test) = 0.7499 TOP MAIN SOLVE Loop x[1] = 1.88 y[1] (analytic) = 0 y[1] (numeric) = 1.1226363394765742369644661352532 absolute error = 1.1226363394765742369644661352532 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 = 0.02392 Order of pole (three term test) = -2.045 Radius of convergence (six term test) for eq 1 = 3.487 Order of pole (six term test) = 2.582 TOP MAIN SOLVE Loop x[1] = 1.89 y[1] (analytic) = 0 y[1] (numeric) = 1.1295368791448282761356515231701 absolute error = 1.1295368791448282761356515231701 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 = 0.03114 Order of pole (three term test) = -3.024 Radius of convergence (six term test) for eq 1 = 3.721 Order of pole (six term test) = 4.598 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 0 y[1] (numeric) = 1.1364652166824643365346413163976 absolute error = 1.1364652166824643365346413163976 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 = 0.03722 Order of pole (three term test) = -4.27 Radius of convergence (six term test) for eq 1 = 3.958 Order of pole (six term test) = 6.767 TOP MAIN SOLVE Loop x[1] = 1.91 y[1] (analytic) = 0 y[1] (numeric) = 1.1434215315921762170454658457335 absolute error = 1.1434215315921762170454658457335 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 = 0.042 Order of pole (three term test) = -5.752 Radius of convergence (six term test) for eq 1 = 4.19 Order of pole (six term test) = 9.033 TOP MAIN SOLVE Loop x[1] = 1.92 y[1] (analytic) = 0 y[1] (numeric) = 1.1504059988654984997510751047086 absolute error = 1.1504059988654984997510751047086 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 = 0.04537 Order of pole (three term test) = -7.435 Radius of convergence (six term test) for eq 1 = 4.411 Order of pole (six term test) = 11.32 TOP MAIN SOLVE Loop bytes used=96030672, alloc=4586680, time=3.22 x[1] = 1.93 y[1] (analytic) = 0 y[1] (numeric) = 1.1574187889276619608025743742933 absolute error = 1.1574187889276619608025743742933 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 = 0.04725 Order of pole (three term test) = -9.277 Radius of convergence (six term test) for eq 1 = 4.614 Order of pole (six term test) = 13.52 TOP MAIN SOLVE Loop x[1] = 1.94 y[1] (analytic) = 0 y[1] (numeric) = 1.164460067582283428114532420716 absolute error = 1.164460067582283428114532420716 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 = 0.04758 Order of pole (three term test) = -11.23 Radius of convergence (six term test) for eq 1 = 4.791 Order of pole (six term test) = 15.53 TOP MAIN SOLVE Loop x[1] = 1.95 y[1] (analytic) = 0 y[1] (numeric) = 1.1715299959559396867914294815427 absolute error = 1.1715299959559396867914294815427 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 = 0.04635 Order of pole (three term test) = -13.25 Radius of convergence (six term test) for eq 1 = 4.937 Order of pole (six term test) = 17.25 TOP MAIN SOLVE Loop x[1] = 1.96 y[1] (analytic) = 0 y[1] (numeric) = 1.1786287304426755590155834536347 absolute error = 1.1786287304426755590155834536347 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 = 0.04359 Order of pole (three term test) = -15.29 Radius of convergence (six term test) for eq 1 = 5.048 Order of pole (six term test) = 18.6 TOP MAIN SOLVE Loop x[1] = 1.97 y[1] (analytic) = 0 y[1] (numeric) = 1.1857564226484967914599319582201 absolute error = 1.1857564226484967914599319582201 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 = 0.03936 Order of pole (three term test) = -17.28 Radius of convergence (six term test) for eq 1 = 5.122 Order of pole (six term test) = 19.54 TOP MAIN SOLVE Loop x[1] = 1.98 y[1] (analytic) = 0 y[1] (numeric) = 1.1929132193358988687374215088309 absolute error = 1.1929132193358988687374215088309 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 = 0.03377 Order of pole (three term test) = -19.19 Radius of convergence (six term test) for eq 1 = 5.162 Order of pole (six term test) = 20.07 TOP MAIN SOLVE Loop x[1] = 1.99 y[1] (analytic) = 0 y[1] (numeric) = 1.2000992623684833345760162467687 absolute error = 1.2000992623684833345760162467687 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 = 0.02695 Order of pole (three term test) = -20.95 Radius of convergence (six term test) for eq 1 = 5.171 Order of pole (six term test) = 20.22 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0 y[1] (numeric) = 1.2073146886557136419359722654635 absolute error = 1.2073146886557136419359722654635 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 = 0.01907 Order of pole (three term test) = -22.52 Radius of convergence (six term test) for eq 1 = 5.154 Order of pole (six term test) = 20.05 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 0 y[1] (numeric) = 1.2145596300978629677954376232748 absolute error = 1.2145596300978629677954376232748 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 = 0.01034 Order of pole (three term test) = -23.87 Radius of convergence (six term test) for eq 1 = 5.117 Order of pole (six term test) = 19.62 TOP MAIN SOLVE Loop bytes used=100031748, alloc=4586680, time=3.36 x[1] = 2.02 y[1] (analytic) = 0 y[1] (numeric) = 1.2218342135312068164650019600829 absolute error = 1.2218342135312068164650019600829 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 = 0.0009821 Order of pole (three term test) = -24.94 Radius of convergence (six term test) for eq 1 = 5.064 Order of pole (six term test) = 19.01 TOP MAIN SOLVE Loop x[1] = 2.03 y[1] (analytic) = 0 y[1] (numeric) = 1.229138560673513595708942570805 absolute error = 1.229138560673513595708942570805 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 = 5.001 Order of pole (six term test) = 18.28 TOP MAIN SOLVE Loop x[1] = 2.04 y[1] (analytic) = 0 y[1] (numeric) = 1.236472788069886681324162720082 absolute error = 1.236472788069886681324162720082 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 = 4.932 Order of pole (six term test) = 17.48 TOP MAIN SOLVE Loop x[1] = 2.05 y[1] (analytic) = 0 y[1] (numeric) = 1.2438370070390117868490690170427 absolute error = 1.2438370070390117868490690170427 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 = 4.859 Order of pole (six term test) = 16.66 TOP MAIN SOLVE Loop x[1] = 2.06 y[1] (analytic) = 0 y[1] (numeric) = 1.2512313236198637244562554411994 absolute error = 1.2512313236198637244562554411994 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 = 4.786 Order of pole (six term test) = 15.84 TOP MAIN SOLVE Loop x[1] = 2.07 y[1] (analytic) = 0 y[1] (numeric) = 1.2586558385189268795599200294246 absolute error = 1.2586558385189268795599200294246 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 = 4.715 Order of pole (six term test) = 15.04 TOP MAIN SOLVE Loop x[1] = 2.08 y[1] (analytic) = 0 y[1] (numeric) = 1.2661106470579839240014354765358 absolute error = 1.2661106470579839240014354765358 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 = 4.645 Order of pole (six term test) = 14.28 TOP MAIN SOLVE Loop x[1] = 2.09 y[1] (analytic) = 0 y[1] (numeric) = 1.2735958391225274596516062659079 absolute error = 1.2735958391225274596516062659079 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 = 4.579 Order of pole (six term test) = 13.57 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 0 y[1] (numeric) = 1.28111149911084941470249403693 absolute error = 1.28111149911084941470249403693 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 = 4.517 Order of pole (six term test) = 12.91 TOP MAIN SOLVE Loop bytes used=104032808, alloc=4586680, time=3.50 x[1] = 2.11 y[1] (analytic) = 0 y[1] (numeric) = 1.288657705883863107663614480208 absolute error = 1.288657705883863107663614480208 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 = 4.459 Order of pole (six term test) = 12.3 TOP MAIN SOLVE Loop x[1] = 2.12 y[1] (analytic) = 0 y[1] (numeric) = 1.2962345327157129480091257828125 absolute error = 1.2962345327157129480091257828125 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 = 4.406 Order of pole (six term test) = 11.74 TOP MAIN SOLVE Loop x[1] = 2.13 y[1] (analytic) = 0 y[1] (numeric) = 1.3038420472452267564629247394766 absolute error = 1.3038420472452267564629247394766 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 = 4.356 Order of pole (six term test) = 11.23 TOP MAIN SOLVE Loop x[1] = 2.14 y[1] (analytic) = 0 y[1] (numeric) = 1.311480311428265661014455469918 absolute error = 1.311480311428265661014455469918 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) = 10.77 TOP MAIN SOLVE Loop x[1] = 2.15 y[1] (analytic) = 0 y[1] (numeric) = 1.3191493814910264559274161337042 absolute error = 1.3191493814910264559274161337042 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 = 4.269 Order of pole (six term test) = 10.35 TOP MAIN SOLVE Loop x[1] = 2.16 y[1] (analytic) = 0 y[1] (numeric) = 1.3268493078843511992773454649006 absolute error = 1.3268493078843511992773454649006 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 = 4.231 Order of pole (six term test) = 9.977 TOP MAIN SOLVE Loop x[1] = 2.17 y[1] (analytic) = 0 y[1] (numeric) = 1.3345801352390986690184513416989 absolute error = 1.3345801352390986690184513416989 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 = 4.196 Order of pole (six term test) = 9.636 TOP MAIN SOLVE Loop x[1] = 2.18 y[1] (analytic) = 0 y[1] (numeric) = 1.3423419023226320973686106147625 absolute error = 1.3423419023226320973686106147625 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 = 4.164 Order of pole (six term test) = 9.328 TOP MAIN SOLVE Loop x[1] = 2.19 y[1] (analytic) = 0 y[1] (numeric) = 1.3501346419964773575974188393902 absolute error = 1.3501346419964773575974188393902 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 = 4.136 Order of pole (six term test) = 9.05 TOP MAIN SOLVE Loop bytes used=108033808, alloc=4586680, time=3.64 x[1] = 2.2 y[1] (analytic) = 0 y[1] (numeric) = 1.3579583811752054853404097575992 absolute error = 1.3579583811752054853404097575992 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 = 4.109 Order of pole (six term test) = 8.801 TOP MAIN SOLVE Loop x[1] = 2.21 y[1] (analytic) = 0 y[1] (numeric) = 1.3658131407865930776317971614205 absolute error = 1.3658131407865930776317971614205 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 = 4.086 Order of pole (six term test) = 8.575 TOP MAIN SOLVE Loop x[1] = 2.22 y[1] (analytic) = 0 y[1] (numeric) = 1.3736989357331137262928341635907 absolute error = 1.3736989357331137262928341635907 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 = 4.064 Order of pole (six term test) = 8.373 TOP MAIN SOLVE Loop x[1] = 2.23 y[1] (analytic) = 0 y[1] (numeric) = 1.3816157748548132075354463202005 absolute error = 1.3816157748548132075354463202005 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 = 4.044 Order of pole (six term test) = 8.19 TOP MAIN SOLVE Loop x[1] = 2.24 y[1] (analytic) = 0 y[1] (numeric) = 1.389563660893620666103189325855 absolute error = 1.389563660893620666103189325855 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 = 4.026 Order of pole (six term test) = 8.025 TOP MAIN SOLVE Loop x[1] = 2.25 y[1] (analytic) = 0 y[1] (numeric) = 1.3975425904591474994973747932857 absolute error = 1.3975425904591474994973747932857 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 = 0.005078 Order of pole (three term test) = -0.9378 Radius of convergence (six term test) for eq 1 = 4.01 Order of pole (six term test) = 7.877 TOP MAIN SOLVE Loop x[1] = 2.26 y[1] (analytic) = 0 y[1] (numeric) = 1.4055525539960250654122927397116 absolute error = 1.4055525539960250654122927397116 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 = 0.0143 Order of pole (three term test) = -1.264 Radius of convergence (six term test) for eq 1 = 3.996 Order of pole (six term test) = 7.744 TOP MAIN SOLVE Loop x[1] = 2.27 y[1] (analytic) = 0 y[1] (numeric) = 1.4135935357528317030817586260468 absolute error = 1.4135935357528317030817586260468 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 = 0.02291 Order of pole (three term test) = -1.9 Radius of convergence (six term test) for eq 1 = 3.982 Order of pole (six term test) = 7.624 TOP MAIN SOLVE Loop bytes used=112034924, alloc=4586680, time=3.78 x[1] = 2.28 y[1] (analytic) = 0 y[1] (numeric) = 1.4216655137526588765382939616651 absolute error = 1.4216655137526588765382939616651 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 = 0.0307 Order of pole (three term test) = -2.829 Radius of convergence (six term test) for eq 1 = 3.97 Order of pole (six term test) = 7.516 TOP MAIN SOLVE Loop x[1] = 2.29 y[1] (analytic) = 0 y[1] (numeric) = 1.4297684597653655145928574674948 absolute error = 1.4297684597653655145928574674948 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 = 0.03746 Order of pole (three term test) = -4.029 Radius of convergence (six term test) for eq 1 = 3.959 Order of pole (six term test) = 7.42 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 0 y[1] (numeric) = 1.4379023392815688385135393314096 absolute error = 1.4379023392815688385135393314096 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 = 0.04304 Order of pole (three term test) = -5.47 Radius of convergence (six term test) for eq 1 = 3.949 Order of pole (six term test) = 7.335 TOP MAIN SOLVE Loop x[1] = 2.31 y[1] (analytic) = 0 y[1] (numeric) = 1.4460671114884191338433324679728 absolute error = 1.4460671114884191338433324679728 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 = 0.0473 Order of pole (three term test) = -7.117 Radius of convergence (six term test) for eq 1 = 3.94 Order of pole (six term test) = 7.259 TOP MAIN SOLVE Loop x[1] = 2.32 y[1] (analytic) = 0 y[1] (numeric) = 1.4542627292472050375495173009382 absolute error = 1.4542627292472050375495173009382 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 = 0.05011 Order of pole (three term test) = -8.927 Radius of convergence (six term test) for eq 1 = 3.933 Order of pole (six term test) = 7.192 TOP MAIN SOLVE Loop x[1] = 2.33 y[1] (analytic) = 0 y[1] (numeric) = 1.4624891390728349758131857240923 absolute error = 1.4624891390728349758131857240923 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 = 0.05141 Order of pole (three term test) = -10.85 Radius of convergence (six term test) for eq 1 = 3.926 Order of pole (six term test) = 7.134 TOP MAIN SOLVE Loop x[1] = 2.34 y[1] (analytic) = 0 y[1] (numeric) = 1.4707462811152394013941822198604 absolute error = 1.4707462811152394013941822198604 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 = 0.05115 Order of pole (three term test) = -12.85 Radius of convergence (six term test) for eq 1 = 3.919 Order of pole (six term test) = 7.084 TOP MAIN SOLVE Loop x[1] = 2.35 y[1] (analytic) = 0 y[1] (numeric) = 1.4790340891427374428667093431584 absolute error = 1.4790340891427374428667093431584 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 = 0.04934 Order of pole (three term test) = -14.85 Radius of convergence (six term test) for eq 1 = 3.914 Order of pole (six term test) = 7.043 TOP MAIN SOLVE Loop x[1] = 2.36 y[1] (analytic) = 0 y[1] (numeric) = 1.4873524905274104914125274819709 absolute error = 1.4873524905274104914125274819709 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 = 0.04601 Order of pole (three term test) = -16.82 Radius of convergence (six term test) for eq 1 = 3.91 Order of pole (six term test) = 7.009 TOP MAIN SOLVE Loop bytes used=116035720, alloc=4652204, time=3.92 x[1] = 2.37 y[1] (analytic) = 0 y[1] (numeric) = 1.4957014062325241146572763177802 absolute error = 1.4957014062325241146572763177802 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 = 0.04125 Order of pole (three term test) = -18.69 Radius of convergence (six term test) for eq 1 = 3.906 Order of pole (six term test) = 6.982 TOP MAIN SOLVE Loop x[1] = 2.38 y[1] (analytic) = 0 y[1] (numeric) = 1.5040807508020385016933980959159 absolute error = 1.5040807508020385016933980959159 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 = 0.03517 Order of pole (three term test) = -20.42 Radius of convergence (six term test) for eq 1 = 3.903 Order of pole (six term test) = 6.963 TOP MAIN SOLVE Loop x[1] = 2.39 y[1] (analytic) = 0 y[1] (numeric) = 1.5124904323522464094805332256123 absolute error = 1.5124904323522464094805332256123 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 = 0.02793 Order of pole (three term test) = -21.95 Radius of convergence (six term test) for eq 1 = 3.901 Order of pole (six term test) = 6.95 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 0 y[1] (numeric) = 1.5209303525655762988590803542118 absolute error = 1.5209303525655762988590803542118 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 = 0.01974 Order of pole (three term test) = -23.24 Radius of convergence (six term test) for eq 1 = 3.9 Order of pole (six term test) = 6.944 TOP MAIN SOLVE Loop x[1] = 2.41 y[1] (analytic) = 0 y[1] (numeric) = 1.5294004066865970191409017438932 absolute error = 1.5294004066865970191409017438932 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 = 0.0108 Order of pole (three term test) = -24.26 Radius of convergence (six term test) for eq 1 = 3.899 Order of pole (six term test) = 6.945 TOP MAIN SOLVE Loop x[1] = 2.42 y[1] (analytic) = 0 y[1] (numeric) = 1.5379004835202590244169800722717 absolute error = 1.5379004835202590244169800722717 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 = 0.00136 Order of pole (three term test) = -24.96 Radius of convergence (six term test) for eq 1 = 3.899 Order of pole (six term test) = 6.951 TOP MAIN SOLVE Loop x[1] = 2.43 y[1] (analytic) = 0 y[1] (numeric) = 1.5464304654324056831871468309762 absolute error = 1.5464304654324056831871468309762 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 = 3.899 Order of pole (six term test) = 6.964 TOP MAIN SOLVE Loop x[1] = 2.44 y[1] (analytic) = 0 y[1] (numeric) = 1.5549902283525867765913444008162 absolute error = 1.5549902283525867765913444008162 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 = 3.9 Order of pole (six term test) = 6.981 TOP MAIN SOLVE Loop x[1] = 2.45 y[1] (analytic) = 0 y[1] (numeric) = 1.5635796417792047704019376744535 absolute error = 1.5635796417792047704019376744535 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 = 3.902 Order of pole (six term test) = 7.004 TOP MAIN SOLVE Loop bytes used=120036860, alloc=4652204, time=4.05 x[1] = 2.46 y[1] (analytic) = 0 y[1] (numeric) = 1.5721985687870228930955959680842 absolute error = 1.5721985687870228930955959680842 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 = 3.904 Order of pole (six term test) = 7.03 TOP MAIN SOLVE Loop x[1] = 2.47 y[1] (analytic) = 0 y[1] (numeric) = 1.5808468660370624579102775554215 absolute error = 1.5808468660370624579102775554215 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 = 3.907 Order of pole (six term test) = 7.061 TOP MAIN SOLVE Loop x[1] = 2.48 y[1] (analytic) = 0 y[1] (numeric) = 1.5895243837889152320318511759073 absolute error = 1.5895243837889152320318511759073 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 = 3.909 Order of pole (six term test) = 7.094 TOP MAIN SOLVE Loop x[1] = 2.49 y[1] (analytic) = 0 y[1] (numeric) = 1.598230965915494982243754581872 absolute error = 1.598230965915494982243754581872 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 = 3.912 Order of pole (six term test) = 7.13 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 0 y[1] (numeric) = 1.6069664499202506148823937477615 absolute error = 1.6069664499202506148823937477615 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 = 3.916 Order of pole (six term test) = 7.168 TOP MAIN SOLVE Loop x[1] = 2.51 y[1] (analytic) = 0 y[1] (numeric) = 1.6157306669568615802126642494287 absolute error = 1.6157306669568615802126642494287 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 = 3.919 Order of pole (six term test) = 7.207 TOP MAIN SOLVE Loop x[1] = 2.52 y[1] (analytic) = 0 y[1] (numeric) = 1.6245234418514344288838395792618 absolute error = 1.6245234418514344288838395792618 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 = 3.923 Order of pole (six term test) = 7.246 TOP MAIN SOLVE Loop x[1] = 2.53 y[1] (analytic) = 0 y[1] (numeric) = 1.6333445931272175925261694734761 absolute error = 1.6333445931272175925261694734761 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 = 3.926 Order of pole (six term test) = 7.285 TOP MAIN SOLVE Loop x[1] = 2.54 y[1] (analytic) = 0 y[1] (numeric) = 1.6421939330318496134493703203516 absolute error = 1.6421939330318496134493703203516 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 = 3.929 Order of pole (six term test) = 7.323 TOP MAIN SOLVE Loop bytes used=124038648, alloc=4652204, time=4.20 x[1] = 2.55 y[1] (analytic) = 0 y[1] (numeric) = 1.6510712675671541715168033274756 absolute error = 1.6510712675671541715168033274756 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 = 3.933 Order of pole (six term test) = 7.359 TOP MAIN SOLVE Loop x[1] = 2.56 y[1] (analytic) = 0 y[1] (numeric) = 1.6599763965214933513670161605053 absolute error = 1.6599763965214933513670161605053 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 = 3.936 Order of pole (six term test) = 7.393 TOP MAIN SOLVE Loop x[1] = 2.57 y[1] (analytic) = 0 y[1] (numeric) = 1.6689091135046886620712092327471 absolute error = 1.6689091135046886620712092327471 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 = 3.938 Order of pole (six term test) = 7.425 TOP MAIN SOLVE Loop x[1] = 2.58 y[1] (analytic) = 0 y[1] (numeric) = 1.6778692059855173659427169344792 absolute error = 1.6778692059855173659427169344792 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 = 3.941 Order of pole (six term test) = 7.453 TOP MAIN SOLVE Loop x[1] = 2.59 y[1] (analytic) = 0 y[1] (numeric) = 1.6868564553317896954998222342324 absolute error = 1.6868564553317896954998222342324 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 = 3.943 Order of pole (six term test) = 7.477 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 0 y[1] (numeric) = 1.6958706368530105395260104421455 absolute error = 1.6958706368530105395260104421455 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 = 3.944 Order of pole (six term test) = 7.497 TOP MAIN SOLVE Loop x[1] = 2.61 y[1] (analytic) = 0 y[1] (numeric) = 1.7049115198456271628220407348329 absolute error = 1.7049115198456271628220407348329 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 = 3.945 Order of pole (six term test) = 7.513 TOP MAIN SOLVE Loop x[1] = 2.62 y[1] (analytic) = 0 y[1] (numeric) = 1.7139788676408624916991038945711 absolute error = 1.7139788676408624916991038945711 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 = 3.946 Order of pole (six term test) = 7.524 TOP MAIN SOLVE Loop x[1] = 2.63 y[1] (analytic) = 0 y[1] (numeric) = 1.7230724376551314506632006224266 absolute error = 1.7230724376551314506632006224266 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 = 0.002866 Order of pole (three term test) = -0.9072 Radius of convergence (six term test) for eq 1 = 3.947 Order of pole (six term test) = 7.531 bytes used=128040372, alloc=4652204, time=4.34 TOP MAIN SOLVE Loop x[1] = 2.64 y[1] (analytic) = 0 y[1] (numeric) = 1.732191981443035777270213059022 absolute error = 1.732191981443035777270213059022 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 = 0.01233 Order of pole (three term test) = -1.164 Radius of convergence (six term test) for eq 1 = 3.947 Order of pole (six term test) = 7.534 TOP MAIN SOLVE Loop x[1] = 2.65 y[1] (analytic) = 0 y[1] (numeric) = 1.7413372447529306740093895158048 absolute error = 1.7413372447529306740093895158048 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 = 0.02136 Order of pole (three term test) = -1.737 Radius of convergence (six term test) for eq 1 = 3.946 Order of pole (six term test) = 7.533 TOP MAIN SOLVE Loop x[1] = 2.66 y[1] (analytic) = 0 y[1] (numeric) = 1.7505079675850545805551980708208 absolute error = 1.7505079675850545805551980708208 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 = 0.02975 Order of pole (three term test) = -2.612 Radius of convergence (six term test) for eq 1 = 3.945 Order of pole (six term test) = 7.527 TOP MAIN SOLVE Loop x[1] = 2.67 y[1] (analytic) = 0 y[1] (numeric) = 1.7597038842522112691000572621774 absolute error = 1.7597038842522112691000572621774 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.133 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.03727 Order of pole (three term test) = -3.765 Radius of convergence (six term test) for eq 1 = 3.944 Order of pole (six term test) = 7.519 TOP MAIN SOLVE Loop x[1] = 2.68 y[1] (analytic) = 0 y[1] (numeric) = 1.7689247234429913820574179928555 absolute error = 1.7689247234429913820574179928555 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.466 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.04373 Order of pole (three term test) = -5.169 Radius of convergence (six term test) for eq 1 = 3.943 Order of pole (six term test) = 7.507 TOP MAIN SOLVE Loop x[1] = 2.69 y[1] (analytic) = 0 y[1] (numeric) = 1.7781702082875184475443501700997 absolute error = 1.7781702082875184475443501700997 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.332 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.04896 Order of pole (three term test) = -6.787 Radius of convergence (six term test) for eq 1 = 3.941 Order of pole (six term test) = 7.492 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 0 y[1] (numeric) = 1.787440056425702326074045465559 absolute error = 1.787440056425702326074045465559 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 = 0.05283 Order of pole (three term test) = -8.576 Radius of convergence (six term test) for eq 1 = 3.939 Order of pole (six term test) = 7.476 TOP MAIN SOLVE Loop x[1] = 2.71 y[1] (analytic) = 0 y[1] (numeric) = 1.7967339800779809641872061786121 absolute error = 1.7967339800779809641872061786121 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 = 0.05523 Order of pole (three term test) = -10.49 Radius of convergence (six term test) for eq 1 = 3.937 Order of pole (six term test) = 7.458 TOP MAIN SOLVE Loop bytes used=132041176, alloc=4652204, time=4.48 x[1] = 2.72 y[1] (analytic) = 0 y[1] (numeric) = 1.8060516861185292597159609600447 absolute error = 1.8060516861185292597159609600447 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 = 0.05608 Order of pole (three term test) = -12.48 Radius of convergence (six term test) for eq 1 = 3.935 Order of pole (six term test) = 7.439 TOP MAIN SOLVE Loop x[1] = 2.73 y[1] (analytic) = 0 y[1] (numeric) = 1.8153928761509117814028102224579 absolute error = 1.8153928761509117814028102224579 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 = 0.05537 Order of pole (three term test) = -14.48 Radius of convergence (six term test) for eq 1 = 3.933 Order of pole (six term test) = 7.42 TOP MAIN SOLVE Loop x[1] = 2.74 y[1] (analytic) = 0 y[1] (numeric) = 1.8247572465861540350936371555688 absolute error = 1.8247572465861540350936371555688 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 = 0.05309 Order of pole (three term test) = -16.45 Radius of convergence (six term test) for eq 1 = 3.93 Order of pole (six term test) = 7.402 TOP MAIN SOLVE Loop x[1] = 2.75 y[1] (analytic) = 0 y[1] (numeric) = 1.8341444887232049320930000098996 absolute error = 1.8341444887232049320930000098996 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 = 0.0493 Order of pole (three term test) = -18.32 Radius of convergence (six term test) for eq 1 = 3.929 Order of pole (six term test) = 7.384 TOP MAIN SOLVE Loop x[1] = 2.76 y[1] (analytic) = 0 y[1] (numeric) = 1.8435542888317610949142849536628 absolute error = 1.8435542888317610949142849536628 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 = 0.04411 Order of pole (three term test) = -20.05 Radius of convergence (six term test) for eq 1 = 3.927 Order of pole (six term test) = 7.368 TOP MAIN SOLVE Loop x[1] = 2.77 y[1] (analytic) = 0 y[1] (numeric) = 1.8529863282374216339729895267233 absolute error = 1.8529863282374216339729895267233 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 = 0.03765 Order of pole (three term test) = -21.59 Radius of convergence (six term test) for eq 1 = 3.925 Order of pole (six term test) = 7.355 TOP MAIN SOLVE Loop x[1] = 2.78 y[1] (analytic) = 0 y[1] (numeric) = 1.8624402834091400481442048946366 absolute error = 1.8624402834091400481442048946366 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 = 0.03008 Order of pole (three term test) = -22.88 Radius of convergence (six term test) for eq 1 = 3.924 Order of pole (six term test) = 7.343 TOP MAIN SOLVE Loop x[1] = 2.79 y[1] (analytic) = 0 y[1] (numeric) = 1.8719158260489379449067149260755 absolute error = 1.8719158260489379449067149260755 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 = 0.02164 Order of pole (three term test) = -23.9 Radius of convergence (six term test) for eq 1 = 3.923 Order of pole (six term test) = 7.335 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 0 y[1] (numeric) = 1.8814126231838433443791699661568 absolute error = 1.8814126231838433443791699661568 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 = 0.01254 Order of pole (three term test) = -24.61 Radius of convergence (six term test) for eq 1 = 3.923 Order of pole (six term test) = 7.33 TOP MAIN SOLVE Loop bytes used=136042336, alloc=4652204, time=4.61 x[1] = 2.81 y[1] (analytic) = 0 y[1] (numeric) = 1.8909303372600144282493983849743 absolute error = 1.8909303372600144282493983849743 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 = 0.003042 Order of pole (three term test) = -24.99 Radius of convergence (six term test) for eq 1 = 3.922 Order of pole (six term test) = 7.329 TOP MAIN SOLVE Loop x[1] = 2.82 y[1] (analytic) = 0 y[1] (numeric) = 1.9004686262390077217107654159021 absolute error = 1.9004686262390077217107654159021 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 = 3.923 Order of pole (six term test) = 7.331 TOP MAIN SOLVE Loop x[1] = 2.83 y[1] (analytic) = 0 y[1] (numeric) = 1.9100271436961478563241458820429 absolute error = 1.9100271436961478563241458820429 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 = 3.923 Order of pole (six term test) = 7.336 TOP MAIN SOLVE Loop x[1] = 2.84 y[1] (analytic) = 0 y[1] (numeric) = 1.9196055389209542564611390392089 absolute error = 1.9196055389209542564611390392089 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 = 3.924 Order of pole (six term test) = 7.345 TOP MAIN SOLVE Loop x[1] = 2.85 y[1] (analytic) = 0 y[1] (numeric) = 1.9292034570195783238564156328044 absolute error = 1.9292034570195783238564156328044 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 = 3.925 Order of pole (six term test) = 7.357 TOP MAIN SOLVE Loop x[1] = 2.86 y[1] (analytic) = 0 y[1] (numeric) = 1.9388205390192029659657789662691 absolute error = 1.9388205390192029659657789662691 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 = 3.927 Order of pole (six term test) = 7.372 TOP MAIN SOLVE Loop x[1] = 2.87 y[1] (analytic) = 0 y[1] (numeric) = 1.9484564219743546264076019971462 absolute error = 1.9484564219743546264076019971462 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 = 3.929 Order of pole (six term test) = 7.39 TOP MAIN SOLVE Loop x[1] = 2.88 y[1] (analytic) = 0 y[1] (numeric) = 1.9581107390750763318258254671118 absolute error = 1.9581107390750763318258254671118 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 = 3.931 Order of pole (six term test) = 7.41 TOP MAIN SOLVE Loop x[1] = 2.89 y[1] (analytic) = 0 y[1] (numeric) = 1.9677831197569086710672634524606 absolute error = 1.9677831197569086710672634524606 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.934 Order of pole (six term test) = 7.432 TOP MAIN SOLVE Loop bytes used=140043100, alloc=4652204, time=4.75 x[1] = 2.9 y[1] (analytic) = 0 y[1] (numeric) = 1.9774731898126240715732324815317 absolute error = 1.9774731898126240715732324815317 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.738 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.936 Order of pole (six term test) = 7.454 TOP MAIN SOLVE Loop x[1] = 2.91 y[1] (analytic) = 0 y[1] (numeric) = 1.9871805715056582362448707865095 absolute error = 1.9871805715056582362448707865095 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.963 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.939 Order of pole (six term test) = 7.478 TOP MAIN SOLVE Loop x[1] = 2.92 y[1] (analytic) = 0 y[1] (numeric) = 1.9969048836851811535897502379871 absolute error = 1.9969048836851811535897502379871 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.608 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.941 Order of pole (six term test) = 7.501 TOP MAIN SOLVE Loop x[1] = 2.93 y[1] (analytic) = 0 y[1] (numeric) = 2.0066457419027486964655825718129 absolute error = 2.0066457419027486964655825718129 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.291 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.944 Order of pole (six term test) = 7.524 TOP MAIN SOLVE Loop x[1] = 2.94 y[1] (analytic) = 0 y[1] (numeric) = 2.016402758530474481907290502422 absolute error = 2.016402758530474481907290502422 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 = 3.946 Order of pole (six term test) = 7.546 TOP MAIN SOLVE Loop x[1] = 2.95 y[1] (analytic) = 0 y[1] (numeric) = 2.0261755428806603779870695479384 absolute error = 2.0261755428806603779870695479384 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 = 3.949 Order of pole (six term test) = 7.566 TOP MAIN SOLVE Loop x[1] = 2.96 y[1] (analytic) = 0 y[1] (numeric) = 2.0359637013268228149694437528335 absolute error = 2.0359637013268228149694437528335 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 = 3.951 Order of pole (six term test) = 7.584 TOP MAIN SOLVE Loop x[1] = 2.97 y[1] (analytic) = 0 y[1] (numeric) = 2.0457668374260508886637195982653 absolute error = 2.0457668374260508886637195982653 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 = 3.953 Order of pole (six term test) = 7.599 TOP MAIN SOLVE Loop x[1] = 2.98 y[1] (analytic) = 0 y[1] (numeric) = 2.0555845520426311352440226917361 absolute error = 2.0555845520426311352440226917361 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 = 3.954 Order of pole (six term test) = 7.611 bytes used=144045156, alloc=4652204, time=4.88 TOP MAIN SOLVE Loop x[1] = 2.99 y[1] (analytic) = 0 y[1] (numeric) = 2.065416443472872810219606170714 absolute error = 2.065416443472872810219606170714 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 = 3.955 Order of pole (six term test) = 7.619 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 0 y[1] (numeric) = 2.0752621075710665209284705275146 absolute error = 2.0752621075710665209284705275146 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 = 3.956 Order of pole (six term test) = 7.624 TOP MAIN SOLVE Loop x[1] = 3.01 y[1] (analytic) = 0 y[1] (numeric) = 2.0851211378765081430423772402391 absolute error = 2.0851211378765081430423772402391 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 = 0.004571 Order of pole (three term test) = -0.9291 Radius of convergence (six term test) for eq 1 = 3.957 Order of pole (six term test) = 7.625 TOP MAIN SOLVE Loop x[1] = 3.02 y[1] (analytic) = 0 y[1] (numeric) = 2.0949931257415190981697490827824 absolute error = 2.0949931257415190981697490827824 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 = 0.01413 Order of pole (three term test) = -1.242 Radius of convergence (six term test) for eq 1 = 3.957 Order of pole (six term test) = 7.622 TOP MAIN SOLVE Loop x[1] = 3.03 y[1] (analytic) = 0 y[1] (numeric) = 2.1048776604603932826935077849557 absolute error = 2.1048776604603932826935077849557 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 = 0.02337 Order of pole (three term test) = -1.869 Radius of convergence (six term test) for eq 1 = 3.957 Order of pole (six term test) = 7.616 TOP MAIN SOLVE Loop x[1] = 3.04 y[1] (analytic) = 0 y[1] (numeric) = 2.1147743293992002183609305116416 absolute error = 2.1147743293992002183609305116416 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 = 0.03207 Order of pole (three term test) = -2.795 Radius of convergence (six term test) for eq 1 = 3.956 Order of pole (six term test) = 7.606 TOP MAIN SOLVE Loop x[1] = 3.05 y[1] (analytic) = 0 y[1] (numeric) = 2.1246827181263733436365975458893 absolute error = 2.1246827181263733436365975458893 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 = 0.04 Order of pole (three term test) = -3.994 Radius of convergence (six term test) for eq 1 = 3.955 Order of pole (six term test) = 7.592 TOP MAIN SOLVE Loop x[1] = 3.06 y[1] (analytic) = 0 y[1] (numeric) = 2.134602410544011782127893802732 absolute error = 2.134602410544011782127893802732 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 = 0.04697 Order of pole (three term test) = -5.438 Radius of convergence (six term test) for eq 1 = 3.954 Order of pole (six term test) = 7.575 TOP MAIN SOLVE Loop bytes used=148046060, alloc=4652204, time=5.02 x[1] = 3.07 y[1] (analytic) = 0 y[1] (numeric) = 2.1445329890198234110906761079973 absolute error = 2.1445329890198234110906761079973 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 = 0.05278 Order of pole (three term test) = -7.088 Radius of convergence (six term test) for eq 1 = 3.952 Order of pole (six term test) = 7.556 TOP MAIN SOLVE Loop x[1] = 3.08 y[1] (analytic) = 0 y[1] (numeric) = 2.1544740345196366096200549692893 absolute error = 2.1544740345196366096200549692893 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 = 0.05728 Order of pole (three term test) = -8.902 Radius of convergence (six term test) for eq 1 = 3.951 Order of pole (six term test) = 7.534 TOP MAIN SOLVE Loop x[1] = 3.09 y[1] (analytic) = 0 y[1] (numeric) = 2.1644251267404076930305902856233 absolute error = 2.1644251267404076930305902856233 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 = 0.06036 Order of pole (three term test) = -10.83 Radius of convergence (six term test) for eq 1 = 3.949 Order of pole (six term test) = 7.511 TOP MAIN SOLVE Loop x[1] = 3.1 y[1] (analytic) = 0 y[1] (numeric) = 2.1743858442436507374373011310674 absolute error = 2.1743858442436507374373011310674 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 = 0.06192 Order of pole (three term test) = -12.83 Radius of convergence (six term test) for eq 1 = 3.947 Order of pole (six term test) = 7.487 TOP MAIN SOLVE Loop x[1] = 3.11 y[1] (analytic) = 0 y[1] (numeric) = 2.1843557645892162668720804776772 absolute error = 2.1843557645892162668720804776772 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 = 0.06192 Order of pole (three term test) = -14.83 Radius of convergence (six term test) for eq 1 = 3.945 Order of pole (six term test) = 7.462 TOP MAIN SOLVE Loop x[1] = 3.12 y[1] (analytic) = 0 y[1] (numeric) = 2.1943344644693451145202080275453 absolute error = 2.1943344644693451145202080275453 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 = 0.06035 Order of pole (three term test) = -16.79 Radius of convergence (six term test) for eq 1 = 3.943 Order of pole (six term test) = 7.437 TOP MAIN SOLVE Loop x[1] = 3.13 y[1] (analytic) = 0 y[1] (numeric) = 2.2043215198429236798520313612191 absolute error = 2.2043215198429236798520313612191 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.166 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.05724 Order of pole (three term test) = -18.65 Radius of convergence (six term test) for eq 1 = 3.941 Order of pole (six term test) = 7.412 TOP MAIN SOLVE Loop x[1] = 3.14 y[1] (analytic) = 0 y[1] (numeric) = 2.2143165060698667844716843367042 absolute error = 2.2143165060698667844716843367042 relative error = -1 % Correct digits = -1 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.486 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.05267 Order of pole (three term test) = -20.36 Radius of convergence (six term test) for eq 1 = 3.939 Order of pole (six term test) = 7.389 TOP MAIN SOLVE Loop x[1] = 3.15 y[1] (analytic) = 0 y[1] (numeric) = 2.224318998045554381227285875657 absolute error = 2.224318998045554381227285875657 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 = 0.04676 Order of pole (three term test) = -21.86 Radius of convergence (six term test) for eq 1 = 3.938 Order of pole (six term test) = 7.367 TOP MAIN SOLVE Loop bytes used=152047168, alloc=4652204, time=5.16 x[1] = 3.16 y[1] (analytic) = 0 y[1] (numeric) = 2.2343285703352484932485748701939 absolute error = 2.2343285703352484932485748701939 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 = 0.03967 Order of pole (three term test) = -23.13 Radius of convergence (six term test) for eq 1 = 3.937 Order of pole (six term test) = 7.348 TOP MAIN SOLVE Loop x[1] = 3.17 y[1] (analytic) = 0 y[1] (numeric) = 2.2443447973084169517261395549006 absolute error = 2.2443447973084169517261395549006 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 = 0.03159 Order of pole (three term test) = -24.11 Radius of convergence (six term test) for eq 1 = 3.936 Order of pole (six term test) = 7.332 TOP MAIN SOLVE Loop x[1] = 3.18 y[1] (analytic) = 0 y[1] (numeric) = 2.2543672532728907629545870403173 absolute error = 2.2543672532728907629545870403173 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 = 0.02275 Order of pole (three term test) = -24.78 Radius of convergence (six term test) for eq 1 = 3.935 Order of pole (six term test) = 7.318 TOP MAIN SOLVE Loop x[1] = 3.19 y[1] (analytic) = 0 y[1] (numeric) = 2.264395512608782265870135036991 absolute error = 2.264395512608782265870135036991 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 = 0.01339 Order of pole (three term test) = -25.12 Radius of convergence (six term test) for eq 1 = 3.935 Order of pole (six term test) = 7.308 TOP MAIN SOLVE Loop x[1] = 3.2 y[1] (analytic) = 0 y[1] (numeric) = 2.274429149902091640369122044976 absolute error = 2.274429149902091640369122044976 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 = 0.003772 Order of pole (three term test) = -25.13 Radius of convergence (six term test) for eq 1 = 3.935 Order of pole (six term test) = 7.301 TOP MAIN SOLVE Loop x[1] = 3.21 y[1] (analytic) = 0 y[1] (numeric) = 2.284467740077929793355178389324 absolute error = 2.284467740077929793355178389324 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 = 3.935 Order of pole (six term test) = 7.298 TOP MAIN SOLVE Loop x[1] = 3.22 y[1] (analytic) = 0 y[1] (numeric) = 2.2945108585332861828976788823632 absolute error = 2.2945108585332861828976788823632 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 = 3.936 Order of pole (six term test) = 7.298 TOP MAIN SOLVE Loop x[1] = 3.23 y[1] (analytic) = 0 y[1] (numeric) = 2.3045580812692707401738337719129 absolute error = 2.3045580812692707401738337719129 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 = 3.937 Order of pole (six term test) = 7.302 TOP MAIN SOLVE Loop bytes used=156048160, alloc=4652204, time=5.30 x[1] = 3.24 y[1] (analytic) = 0 y[1] (numeric) = 2.3146089850227597130073482625657 absolute error = 2.3146089850227597130073482625657 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 = 3.939 Order of pole (six term test) = 7.309 TOP MAIN SOLVE Loop x[1] = 3.25 y[1] (analytic) = 0 y[1] (numeric) = 2.32466314739737598272080500834 absolute error = 2.32466314739737598272080500834 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 = 3.941 Order of pole (six term test) = 7.32 TOP MAIN SOLVE Loop x[1] = 3.26 y[1] (analytic) = 0 y[1] (numeric) = 2.334720146993735196518662811795 absolute error = 2.334720146993735196518662811795 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 = 3.943 Order of pole (six term test) = 7.333 TOP MAIN SOLVE Loop x[1] = 3.27 y[1] (analytic) = 0 y[1] (numeric) = 2.3447795635388899094662891350898 absolute error = 2.3447795635388899094662891350898 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 = 3.946 Order of pole (six term test) = 7.349 TOP MAIN SOLVE Loop x[1] = 3.28 y[1] (analytic) = 0 y[1] (numeric) = 2.3548409780149048420049164255718 absolute error = 2.3548409780149048420049164255718 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 = 3.949 Order of pole (six term test) = 7.366 TOP MAIN SOLVE Loop x[1] = 3.29 y[1] (analytic) = 0 y[1] (numeric) = 2.3649039727864973294464958303659 absolute error = 2.3649039727864973294464958303659 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 = 3.951 Order of pole (six term test) = 7.385 TOP MAIN SOLVE Loop x[1] = 3.3 y[1] (analytic) = 0 y[1] (numeric) = 2.3749681317276780675590067846964 absolute error = 2.3749681317276780675590067846964 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 = 3.954 Order of pole (six term test) = 7.405 TOP MAIN SOLVE Loop x[1] = 3.31 y[1] (analytic) = 0 y[1] (numeric) = 2.3850330403473283416468214507927 absolute error = 2.3850330403473283416468214507927 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 = 3.958 Order of pole (six term test) = 7.425 TOP MAIN SOLVE Loop x[1] = 3.32 y[1] (analytic) = 0 y[1] (numeric) = 2.3950982859136510638521782551634 absolute error = 2.3950982859136510638521782551634 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 = 3.961 Order of pole (six term test) = 7.445 TOP MAIN SOLVE Loop bytes used=160049240, alloc=4652204, time=5.44 x[1] = 3.33 y[1] (analytic) = 0 y[1] (numeric) = 2.4051634575774341330906905731181 absolute error = 2.4051634575774341330906905731181 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 = 3.964 Order of pole (six term test) = 7.464 TOP MAIN SOLVE Loop x[1] = 3.34 y[1] (analytic) = 0 y[1] (numeric) = 2.4152281464940658723652763262666 absolute error = 2.4152281464940658723652763262666 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 = 3.967 Order of pole (six term test) = 7.482 TOP MAIN SOLVE Loop x[1] = 3.35 y[1] (analytic) = 0 y[1] (numeric) = 2.4252919459442435874024920757836 absolute error = 2.4252919459442435874024920757836 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 = 3.969 Order of pole (six term test) = 7.498 TOP MAIN SOLVE Loop x[1] = 3.36 y[1] (analytic) = 0 y[1] (numeric) = 2.4353544514533176267942038256635 absolute error = 2.4353544514533176267942038256635 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 = 3.972 Order of pole (six term test) = 7.511 TOP MAIN SOLVE Loop x[1] = 3.37 y[1] (analytic) = 0 y[1] (numeric) = 2.4454152609092147052280521152468 absolute error = 2.4454152609092147052280521152468 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 = 3.974 Order of pole (six term test) = 7.521 TOP MAIN SOLVE Loop x[1] = 3.38 y[1] (analytic) = 0 y[1] (numeric) = 2.4554739746788856760289201196201 absolute error = 2.4554739746788856760289201196201 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 = 3.976 Order of pole (six term test) = 7.528 TOP MAIN SOLVE Loop x[1] = 3.39 y[1] (analytic) = 0 y[1] (numeric) = 2.4655301957232244051451239456812 absolute error = 2.4655301957232244051451239456812 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 = 0.004045 Order of pole (three term test) = -0.9207 Radius of convergence (six term test) for eq 1 = 3.977 Order of pole (six term test) = 7.532 TOP MAIN SOLVE Loop x[1] = 3.4 y[1] (analytic) = 0 y[1] (numeric) = 2.4755835297104059038932372490682 absolute error = 2.4755835297104059038932372490682 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 = 0.01376 Order of pole (three term test) = -1.212 Radius of convergence (six term test) for eq 1 = 3.978 Order of pole (six term test) = 7.532 TOP MAIN SOLVE Loop x[1] = 3.41 y[1] (analytic) = 0 y[1] (numeric) = 2.4856335851275934201851913452249 absolute error = 2.4856335851275934201851913452249 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 = 0.02334 Order of pole (three term test) = -1.813 Radius of convergence (six term test) for eq 1 = 3.979 Order of pole (six term test) = 7.529 TOP MAIN SOLVE Loop bytes used=164050144, alloc=4652204, time=5.59 x[1] = 3.42 y[1] (analytic) = 0 y[1] (numeric) = 2.4956799733909657655299102504859 absolute error = 2.4956799733909657655299102504859 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 = 0.03255 Order of pole (three term test) = -2.71 Radius of convergence (six term test) for eq 1 = 3.98 Order of pole (six term test) = 7.521 TOP MAIN SOLVE Loop x[1] = 3.43 y[1] (analytic) = 0 y[1] (numeric) = 2.5057223089540177657306893309397 absolute error = 2.5057223089540177657306893309397 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 = 0.04116 Order of pole (three term test) = -3.88 Radius of convergence (six term test) for eq 1 = 3.98 Order of pole (six term test) = 7.511 TOP MAIN SOLVE Loop x[1] = 3.44 y[1] (analytic) = 0 y[1] (numeric) = 2.5157602094140883647659385757219 absolute error = 2.5157602094140883647659385757219 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) = -5.295 Radius of convergence (six term test) for eq 1 = 3.98 Order of pole (six term test) = 7.496 TOP MAIN SOLVE Loop x[1] = 3.45 y[1] (analytic) = 0 y[1] (numeric) = 2.5257932956170725817012159174452 absolute error = 2.5257932956170725817012159174452 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 = 0.05578 Order of pole (three term test) = -6.919 Radius of convergence (six term test) for eq 1 = 3.979 Order of pole (six term test) = 7.479 TOP MAIN SOLVE Loop x[1] = 3.46 y[1] (analytic) = 0 y[1] (numeric) = 2.5358211917602752174740020233627 absolute error = 2.5358211917602752174740020233627 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 = 0.06141 Order of pole (three term test) = -8.713 Radius of convergence (six term test) for eq 1 = 3.978 Order of pole (six term test) = 7.458 TOP MAIN SOLVE Loop x[1] = 3.47 y[1] (analytic) = 0 y[1] (numeric) = 2.545843525493365929845239073634 absolute error = 2.545843525493365929845239073634 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 = 0.06572 Order of pole (three term test) = -10.63 Radius of convergence (six term test) for eq 1 = 3.977 Order of pole (six term test) = 7.435 TOP MAIN SOLVE Loop x[1] = 3.48 y[1] (analytic) = 0 y[1] (numeric) = 2.5558599280173970385391654351451 absolute error = 2.5558599280173970385391654351451 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 = 0.0686 Order of pole (three term test) = -12.62 Radius of convergence (six term test) for eq 1 = 3.976 Order of pole (six term test) = 7.41 TOP MAIN SOLVE Loop x[1] = 3.49 y[1] (analytic) = 0 y[1] (numeric) = 2.5658700341818471864049395798494 absolute error = 2.5658700341818471864049395798494 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 = 0.06996 Order of pole (three term test) = -14.64 Radius of convergence (six term test) for eq 1 = 3.975 Order of pole (six term test) = 7.384 TOP MAIN SOLVE Loop x[1] = 3.5 y[1] (analytic) = 0 y[1] (numeric) = 2.5758734825796557641366132155711 absolute error = 2.5758734825796557641366132155711 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 = 0.06976 Order of pole (three term test) = -16.62 Radius of convergence (six term test) for eq 1 = 3.973 Order of pole (six term test) = 7.357 TOP MAIN SOLVE Loop bytes used=168051096, alloc=4652204, time=5.73 x[1] = 3.51 y[1] (analytic) = 0 y[1] (numeric) = 2.5858699156402148034894578425802 absolute error = 2.5858699156402148034894578425802 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 = 0.06801 Order of pole (three term test) = -18.52 Radius of convergence (six term test) for eq 1 = 3.972 Order of pole (six term test) = 7.329 TOP MAIN SOLVE Loop x[1] = 3.52 y[1] (analytic) = 0 y[1] (numeric) = 2.5958589797202868548417969001357 absolute error = 2.5958589797202868548417969001357 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 = 0.06473 Order of pole (three term test) = -20.29 Radius of convergence (six term test) for eq 1 = 3.97 Order of pole (six term test) = 7.301 TOP MAIN SOLVE Loop x[1] = 3.53 y[1] (analytic) = 0 y[1] (numeric) = 2.6058403251928191871911092048687 absolute error = 2.6058403251928191871911092048687 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 = 0.06001 Order of pole (three term test) = -21.87 Radius of convergence (six term test) for eq 1 = 3.969 Order of pole (six term test) = 7.274 TOP MAIN SOLVE Loop x[1] = 3.54 y[1] (analytic) = 0 y[1] (numeric) = 2.6158136065336264800707699181866 absolute error = 2.6158136065336264800707699181866 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 = 0.05397 Order of pole (three term test) = -23.23 Radius of convergence (six term test) for eq 1 = 3.968 Order of pole (six term test) = 7.249 TOP MAIN SOLVE Loop x[1] = 3.55 y[1] (analytic) = 0 y[1] (numeric) = 2.625778482405916015272922966399 absolute error = 2.625778482405916015272922966399 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 = 0.04677 Order of pole (three term test) = -24.33 Radius of convergence (six term test) for eq 1 = 3.967 Order of pole (six term test) = 7.225 TOP MAIN SOLVE Loop x[1] = 3.56 y[1] (analytic) = 0 y[1] (numeric) = 2.6357346157426312195243814420235 absolute error = 2.6357346157426312195243814420235 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 = 0.03859 Order of pole (three term test) = -25.13 Radius of convergence (six term test) for eq 1 = 3.966 Order of pole (six term test) = 7.203 TOP MAIN SOLVE Loop x[1] = 3.57 y[1] (analytic) = 0 y[1] (numeric) = 2.6456816738265912552671983728082 absolute error = 2.6456816738265912552671983728082 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 = 0.02964 Order of pole (three term test) = -25.61 Radius of convergence (six term test) for eq 1 = 3.965 Order of pole (six term test) = 7.184 TOP MAIN SOLVE Loop x[1] = 3.58 y[1] (analytic) = 0 y[1] (numeric) = 2.6556193283684062033480599885809 absolute error = 2.6556193283684062033480599885809 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 = 0.02018 Order of pole (three term test) = -25.77 Radius of convergence (six term test) for eq 1 = 3.965 Order of pole (six term test) = 7.167 TOP MAIN SOLVE Loop x[1] = 3.59 y[1] (analytic) = 0 y[1] (numeric) = 2.6655472555821492266516456429385 absolute error = 2.6655472555821492266516456429385 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 = 0.01045 Order of pole (three term test) = -25.59 Radius of convergence (six term test) for eq 1 = 3.965 Order of pole (six term test) = 7.154 bytes used=172054636, alloc=4652204, time=5.87 TOP MAIN SOLVE Loop x[1] = 3.6 y[1] (analytic) = 0 y[1] (numeric) = 2.6754651362587689454824434760971 absolute error = 2.6754651362587689454824434760971 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 = 0.0007207 Order of pole (three term test) = -25.09 Radius of convergence (six term test) for eq 1 = 3.966 Order of pole (six term test) = 7.144 TOP MAIN SOLVE Loop x[1] = 3.61 y[1] (analytic) = 0 y[1] (numeric) = 2.6853726558372270917989905577791 absolute error = 2.6853726558372270917989905577791 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 = 3.967 Order of pole (six term test) = 7.137 TOP MAIN SOLVE Loop x[1] = 3.62 y[1] (analytic) = 0 y[1] (numeric) = 2.6952695044733483382604729876585 absolute error = 2.6952695044733483382604729876585 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 = 3.968 Order of pole (six term test) = 7.134 TOP MAIN SOLVE Loop x[1] = 3.63 y[1] (analytic) = 0 y[1] (numeric) = 2.7051553771063710175215539976197 absolute error = 2.7051553771063710175215539976197 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 = 3.97 Order of pole (six term test) = 7.134 TOP MAIN SOLVE Loop x[1] = 3.64 y[1] (analytic) = 0 y[1] (numeric) = 2.7150299735231892554102503945334 absolute error = 2.7150299735231892554102503945334 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 = 3.972 Order of pole (six term test) = 7.137 TOP MAIN SOLVE Loop x[1] = 3.65 y[1] (analytic) = 0 y[1] (numeric) = 2.7248929984202788366906172365478 absolute error = 2.7248929984202788366906172365478 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 = 3.974 Order of pole (six term test) = 7.143 TOP MAIN SOLVE Loop x[1] = 3.66 y[1] (analytic) = 0 y[1] (numeric) = 2.7347441614633009022360338546192 absolute error = 2.7347441614633009022360338546192 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 = 3.977 Order of pole (six term test) = 7.152 TOP MAIN SOLVE Loop x[1] = 3.67 y[1] (analytic) = 0 y[1] (numeric) = 2.7445831773443793398553658799213 absolute error = 2.7445831773443793398553658799213 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 = 3.979 Order of pole (six term test) = 7.162 TOP MAIN SOLVE Loop bytes used=176055284, alloc=4652204, time=6.01 x[1] = 3.68 y[1] (analytic) = 0 y[1] (numeric) = 2.7544097658370494760068019811118 absolute error = 2.7544097658370494760068019811118 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 = 3.983 Order of pole (six term test) = 7.175 TOP MAIN SOLVE Loop x[1] = 3.69 y[1] (analytic) = 0 y[1] (numeric) = 2.764223651848877400536435317336 absolute error = 2.764223651848877400536435317336 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 = 3.986 Order of pole (six term test) = 7.189 TOP MAIN SOLVE Loop x[1] = 3.7 y[1] (analytic) = 0 y[1] (numeric) = 2.7740245654717509597762429332512 absolute error = 2.7740245654717509597762429332512 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 = 3.989 Order of pole (six term test) = 7.204 TOP MAIN SOLVE Loop x[1] = 3.71 y[1] (analytic) = 0 y[1] (numeric) = 2.7838122420298451332680621505595 absolute error = 2.7838122420298451332680621505595 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 = 3.992 Order of pole (six term test) = 7.219 TOP MAIN SOLVE Loop x[1] = 3.72 y[1] (analytic) = 0 y[1] (numeric) = 2.7935864221252661645405100895995 absolute error = 2.7935864221252661645405100895995 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 = 3.996 Order of pole (six term test) = 7.234 TOP MAIN SOLVE Loop x[1] = 3.73 y[1] (analytic) = 0 y[1] (numeric) = 2.803346851681380445304944356203 absolute error = 2.803346851681380445304944356203 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 = 3.999 Order of pole (six term test) = 7.248 TOP MAIN SOLVE Loop x[1] = 3.74 y[1] (analytic) = 0 y[1] (numeric) = 2.8130932819838357537625397406676 absolute error = 2.8130932819838357537625397406676 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 = 4.002 Order of pole (six term test) = 7.261 TOP MAIN SOLVE Loop x[1] = 3.75 y[1] (analytic) = 0 y[1] (numeric) = 2.8228254697192840200941201578551 absolute error = 2.8228254697192840200941201578551 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 = 4.005 Order of pole (six term test) = 7.273 TOP MAIN SOLVE Loop x[1] = 3.76 y[1] (analytic) = 0 y[1] (numeric) = 2.8325431770118163343640429209726 absolute error = 2.8325431770118163343640429209726 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 = 4.008 Order of pole (six term test) = 7.282 TOP MAIN SOLVE Loop bytes used=180056776, alloc=4652204, time=6.16 x[1] = 3.77 y[1] (analytic) = 0 y[1] (numeric) = 2.8422461714571224227963086780989 absolute error = 2.8422461714571224227963086780989 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 = 4.011 Order of pole (six term test) = 7.288 TOP MAIN SOLVE Loop x[1] = 3.78 y[1] (analytic) = 0 y[1] (numeric) = 2.8519342261543882965236603161984 absolute error = 2.8519342261543882965236603161984 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 = 0.004636 Order of pole (three term test) = -0.928 Radius of convergence (six term test) for eq 1 = 4.013 Order of pole (six term test) = 7.291 TOP MAIN SOLVE Loop x[1] = 3.79 y[1] (analytic) = 0 y[1] (numeric) = 2.8616071197359472213792319299586 absolute error = 2.8616071197359472213792319299586 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 = 0.01451 Order of pole (three term test) = -1.229 Radius of convergence (six term test) for eq 1 = 4.015 Order of pole (six term test) = 7.292 TOP MAIN SOLVE Loop x[1] = 3.8 y[1] (analytic) = 0 y[1] (numeric) = 2.8712646363947005670683135712574 absolute error = 2.8712646363947005670683135712574 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 = 0.02439 Order of pole (three term test) = -1.83 Radius of convergence (six term test) for eq 1 = 4.017 Order of pole (six term test) = 7.289 TOP MAIN SOLVE Loop x[1] = 3.81 y[1] (analytic) = 0 y[1] (numeric) = 2.8809065659093264681608985734976 absolute error = 2.8809065659093264681608985734976 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 = 0.03408 Order of pole (three term test) = -2.719 Radius of convergence (six term test) for eq 1 = 4.018 Order of pole (six term test) = 7.282 TOP MAIN SOLVE Loop x[1] = 3.82 y[1] (analytic) = 0 y[1] (numeric) = 2.8905327036672955668829249439814 absolute error = 2.8905327036672955668829249439814 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 = 0.04334 Order of pole (three term test) = -3.875 Radius of convergence (six term test) for eq 1 = 4.019 Order of pole (six term test) = 7.272 TOP MAIN SOLVE Loop x[1] = 3.83 y[1] (analytic) = 0 y[1] (numeric) = 2.9001428506857144078178653979022 absolute error = 2.9001428506857144078178653979022 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 = 0.05196 Order of pole (three term test) = -5.272 Radius of convergence (six term test) for eq 1 = 4.02 Order of pole (six term test) = 7.258 TOP MAIN SOLVE Loop x[1] = 3.84 y[1] (analytic) = 0 y[1] (numeric) = 2.9097368136300183165862598640307 absolute error = 2.9097368136300183165862598640307 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 = 0.05975 Order of pole (three term test) = -6.877 Radius of convergence (six term test) for eq 1 = 4.02 Order of pole (six term test) = 7.242 TOP MAIN SOLVE Loop x[1] = 3.85 y[1] (analytic) = 0 y[1] (numeric) = 2.9193144048305368176378837429936 absolute error = 2.9193144048305368176378837429936 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 = 0.06652 Order of pole (three term test) = -8.653 Radius of convergence (six term test) for eq 1 = 4.02 Order of pole (six term test) = 7.222 TOP MAIN SOLVE Loop bytes used=184058004, alloc=4652204, time=6.30 x[1] = 3.86 y[1] (analytic) = 0 y[1] (numeric) = 2.9288754422969558298215486295326 absolute error = 2.9288754422969558298215486295326 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 = 0.07211 Order of pole (three term test) = -10.56 Radius of convergence (six term test) for eq 1 = 4.019 Order of pole (six term test) = 7.199 TOP MAIN SOLVE Loop x[1] = 3.87 y[1] (analytic) = 0 y[1] (numeric) = 2.9384197497307020218058698550895 absolute error = 2.9384197497307020218058698550895 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 = 0.07639 Order of pole (three term test) = -12.55 Radius of convergence (six term test) for eq 1 = 4.019 Order of pole (six term test) = 7.174 TOP MAIN SOLVE Loop x[1] = 3.88 y[1] (analytic) = 0 y[1] (numeric) = 2.9479471565352758121879265334511 absolute error = 2.9479471565352758121879265334511 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 = 0.07924 Order of pole (three term test) = -14.58 Radius of convergence (six term test) for eq 1 = 4.018 Order of pole (six term test) = 7.146 TOP MAIN SOLVE Loop x[1] = 3.89 y[1] (analytic) = 0 y[1] (numeric) = 2.9574574978245605607846955086887 absolute error = 2.9574574978245605607846955086887 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 = 0.0806 Order of pole (three term test) = -16.59 Radius of convergence (six term test) for eq 1 = 4.017 Order of pole (six term test) = 7.117 TOP MAIN SOLVE Loop x[1] = 3.9 y[1] (analytic) = 0 y[1] (numeric) = 2.9669506144291365177548671769841 absolute error = 2.9669506144291365177548671769841 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 = 0.08042 Order of pole (three term test) = -18.54 Radius of convergence (six term test) for eq 1 = 4.016 Order of pole (six term test) = 7.087 TOP MAIN SOLVE Loop x[1] = 3.91 y[1] (analytic) = 0 y[1] (numeric) = 2.9764263529006290755071612457407 absolute error = 2.9764263529006290755071612457407 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) = -20.38 Radius of convergence (six term test) for eq 1 = 4.015 Order of pole (six term test) = 7.056 TOP MAIN SOLVE Loop x[1] = 3.92 y[1] (analytic) = 0 y[1] (numeric) = 2.9858845655141218045363928802629 absolute error = 2.9858845655141218045363928802629 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 = 0.07548 Order of pole (three term test) = -22.07 Radius of convergence (six term test) for eq 1 = 4.014 Order of pole (six term test) = 7.025 TOP MAIN SOLVE Loop x[1] = 3.93 y[1] (analytic) = 0 y[1] (numeric) = 2.9953251102686656481700923096042 absolute error = 2.9953251102686656481700923096042 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 = 0.07082 Order of pole (three term test) = -23.56 Radius of convergence (six term test) for eq 1 = 4.013 Order of pole (six term test) = 6.995 TOP MAIN SOLVE Loop x[1] = 3.94 y[1] (analytic) = 0 y[1] (numeric) = 3.004747850885916502544260879202 absolute error = 3.004747850885916502544260879202 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 = 0.06484 Order of pole (three term test) = -24.81 Radius of convergence (six term test) for eq 1 = 4.012 Order of pole (six term test) = 6.965 TOP MAIN SOLVE Loop bytes used=188058968, alloc=4652204, time=6.44 x[1] = 3.95 y[1] (analytic) = 0 y[1] (numeric) = 3.0141526568069342168516406523108 absolute error = 3.0141526568069342168516406523108 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 = 0.05769 Order of pole (three term test) = -25.79 Radius of convergence (six term test) for eq 1 = 4.011 Order of pole (six term test) = 6.936 TOP MAIN SOLVE Loop x[1] = 3.96 y[1] (analytic) = 0 y[1] (numeric) = 3.0235394031871768149703451491951 absolute error = 3.0235394031871768149703451491951 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 = 0.04953 Order of pole (three term test) = -26.47 Radius of convergence (six term test) for eq 1 = 4.01 Order of pole (six term test) = 6.909 TOP MAIN SOLVE Loop x[1] = 3.97 y[1] (analytic) = 0 y[1] (numeric) = 3.0329079708897244629902072559608 absolute error = 3.0329079708897244629902072559608 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 = 0.04057 Order of pole (three term test) = -26.85 Radius of convergence (six term test) for eq 1 = 4.01 Order of pole (six term test) = 6.885 TOP MAIN SOLVE Loop x[1] = 3.98 y[1] (analytic) = 0 y[1] (numeric) = 3.0422582464767683879675646396235 absolute error = 3.0422582464767683879675646396235 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 = 0.03102 Order of pole (three term test) = -26.9 Radius of convergence (six term test) for eq 1 = 4.01 Order of pole (six term test) = 6.862 TOP MAIN SOLVE Loop x[1] = 3.99 y[1] (analytic) = 0 y[1] (numeric) = 3.051590122199400591567391195229 absolute error = 3.051590122199400591567391195229 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 = 0.02114 Order of pole (three term test) = -26.64 Radius of convergence (six term test) for eq 1 = 4.01 Order of pole (six term test) = 6.843 TOP MAIN SOLVE Loop x[1] = 4 y[1] (analytic) = 0 y[1] (numeric) = 3.0609034959857407982564480794867 absolute error = 3.0609034959857407982564480794867 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 = 0.01115 Order of pole (three term test) = -26.06 Radius of convergence (six term test) for eq 1 = 4.011 Order of pole (six term test) = 6.826 TOP MAIN SOLVE Loop x[1] = 4.01 y[1] (analytic) = 0 y[1] (numeric) = 3.0701982714274376316035876378726 absolute error = 3.0701982714274376316035876378726 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 = 0.001311 Order of pole (three term test) = -25.18 Radius of convergence (six term test) for eq 1 = 4.012 Order of pole (six term test) = 6.812 TOP MAIN SOLVE Loop x[1] = 4.02 y[1] (analytic) = 0 y[1] (numeric) = 3.0794743577645815242825101730191 absolute error = 3.0794743577645815242825101730191 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 = 4.013 Order of pole (six term test) = 6.802 TOP MAIN SOLVE Loop x[1] = 4.03 y[1] (analytic) = 0 y[1] (numeric) = 3.0887316698690673378635363514423 absolute error = 3.0887316698690673378635363514423 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 = 4.015 Order of pole (six term test) = 6.795 TOP MAIN SOLVE Loop bytes used=192059884, alloc=4652204, time=6.58 x[1] = 4.04 y[1] (analytic) = 0 y[1] (numeric) = 3.09797012822644509777452413963 absolute error = 3.09797012822644509777452413963 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 = 4.017 Order of pole (six term test) = 6.79 TOP MAIN SOLVE Loop x[1] = 4.05 y[1] (analytic) = 0 y[1] (numeric) = 3.1071896589162976373003556387345 absolute error = 3.1071896589162976373003556387345 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 = 4.019 Order of pole (six term test) = 6.788 TOP MAIN SOLVE Loop x[1] = 4.06 y[1] (analytic) = 0 y[1] (numeric) = 3.1163901935911842926104616149444 absolute error = 3.1163901935911842926104616149444 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 = 4.022 Order of pole (six term test) = 6.789 TOP MAIN SOLVE Loop x[1] = 4.07 y[1] (analytic) = 0 y[1] (numeric) = 3.125571669454190099029582220695 absolute error = 3.125571669454190099029582220695 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 = 4.024 Order of pole (six term test) = 6.792 TOP MAIN SOLVE Loop x[1] = 4.08 y[1] (analytic) = 0 y[1] (numeric) = 3.1347340292351202076115628045639 absolute error = 3.1347340292351202076115628045639 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 = 4.027 Order of pole (six term test) = 6.797 TOP MAIN SOLVE Loop x[1] = 4.09 y[1] (analytic) = 0 y[1] (numeric) = 3.1438772211653794710891647160874 absolute error = 3.1438772211653794710891647160874 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 = 4.031 Order of pole (six term test) = 6.803 TOP MAIN SOLVE Loop x[1] = 4.1 y[1] (analytic) = 0 y[1] (numeric) = 3.1530011989515773400391452419972 absolute error = 3.1530011989515773400391452419972 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 = 4.034 Order of pole (six term test) = 6.809 TOP MAIN SOLVE Loop x[1] = 4.11 y[1] (analytic) = 0 y[1] (numeric) = 3.1621059217478983642388005655753 absolute error = 3.1621059217478983642388005655753 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 = 4.037 Order of pole (six term test) = 6.815 TOP MAIN SOLVE Loop x[1] = 4.12 y[1] (analytic) = 0 y[1] (numeric) = 3.171191354127278711346650354769 absolute error = 3.171191354127278711346650354769 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 = 4.04 Order of pole (six term test) = 6.821 bytes used=196061472, alloc=4652204, time=6.72 TOP MAIN SOLVE Loop x[1] = 4.13 y[1] (analytic) = 0 y[1] (numeric) = 3.180257466051429195894399399935 absolute error = 3.180257466051429195894399399935 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 = 4.043 Order of pole (six term test) = 6.826 TOP MAIN SOLVE Loop x[1] = 4.14 y[1] (analytic) = 0 y[1] (numeric) = 3.1893042328397453568359527713959 absolute error = 3.1893042328397453568359527713959 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 = 4.046 Order of pole (six term test) = 6.828 TOP MAIN SOLVE Loop x[1] = 4.15 y[1] (analytic) = 0 y[1] (numeric) = 3.1983316351371451322943208293686 absolute error = 3.1983316351371451322943208293686 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 = 4.049 Order of pole (six term test) = 6.828 TOP MAIN SOLVE Loop x[1] = 4.16 y[1] (analytic) = 0 y[1] (numeric) = 3.2073396588808746564352271166614 absolute error = 3.2073396588808746564352271166614 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 = 4.051 Order of pole (six term test) = 6.824 TOP MAIN SOLVE Loop x[1] = 4.17 y[1] (analytic) = 0 y[1] (numeric) = 3.2163282952663226463561349602988 absolute error = 3.2163282952663226463561349602988 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 = 4.053 Order of pole (six term test) = 6.816 TOP MAIN SOLVE Loop x[1] = 4.18 y[1] (analytic) = 0 y[1] (numeric) = 3.2252975407118837573110157453127 absolute error = 3.2252975407118837573110157453127 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 = 4.054 Order of pole (six term test) = 6.803 TOP MAIN SOLVE Loop x[1] = 4.19 y[1] (analytic) = 0 y[1] (numeric) = 3.2342473968229111633133112391792 absolute error = 3.2342473968229111633133112391792 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 = 0.009017 Order of pole (three term test) = -1.017 Radius of convergence (six term test) for eq 1 = 4.055 Order of pole (six term test) = 6.785 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 0 y[1] (numeric) = 3.2431778703547984680083382599344 absolute error = 3.2431778703547984680083382599344 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 = 0.01915 Order of pole (three term test) = -1.432 Radius of convergence (six term test) for eq 1 = 4.055 Order of pole (six term test) = 6.76 TOP MAIN SOLVE Loop bytes used=200062544, alloc=4652204, time=6.87 x[1] = 4.21 y[1] (analytic) = 0 y[1] (numeric) = 3.2520889731752308685336221521127 absolute error = 3.2520889731752308685336221521127 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 = 0.02938 Order of pole (three term test) = -2.131 Radius of convergence (six term test) for eq 1 = 4.054 Order of pole (six term test) = 6.73 TOP MAIN SOLVE Loop x[1] = 4.22 y[1] (analytic) = 0 y[1] (numeric) = 3.260980722225645283757059824455 absolute error = 3.260980722225645283757059824455 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 = 0.0395 Order of pole (three term test) = -3.099 Radius of convergence (six term test) for eq 1 = 4.053 Order of pole (six term test) = 6.692 TOP MAIN SOLVE Loop x[1] = 4.23 y[1] (analytic) = 0 y[1] (numeric) = 3.2698531394819389186764458917599 absolute error = 3.2698531394819389186764458917599 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 = 0.04931 Order of pole (three term test) = -4.317 Radius of convergence (six term test) for eq 1 = 4.051 Order of pole (six term test) = 6.647 TOP MAIN SOLVE Loop x[1] = 4.24 y[1] (analytic) = 0 y[1] (numeric) = 3.278706251914465469768474301575 absolute error = 3.278706251914465469768474301575 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 = 0.0586 Order of pole (three term test) = -5.76 Radius of convergence (six term test) for eq 1 = 4.048 Order of pole (six term test) = 6.595 TOP MAIN SOLVE Loop x[1] = 4.25 y[1] (analytic) = 0 y[1] (numeric) = 3.2875400914473578825886705957889 absolute error = 3.2875400914473578825886705957889 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 = 0.0672 Order of pole (three term test) = -7.399 Radius of convergence (six term test) for eq 1 = 4.044 Order of pole (six term test) = 6.536 TOP MAIN SOLVE Loop x[1] = 4.26 y[1] (analytic) = 0 y[1] (numeric) = 3.2963546949172162538511606635093 absolute error = 3.2963546949172162538511606635093 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 = 0.0749 Order of pole (three term test) = -9.198 Radius of convergence (six term test) for eq 1 = 4.039 Order of pole (six term test) = 6.468 TOP MAIN SOLVE Loop x[1] = 4.27 y[1] (analytic) = 0 y[1] (numeric) = 3.3051501040311991264700790444814 absolute error = 3.3051501040311991264700790444814 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 = 0.08156 Order of pole (three term test) = -11.12 Radius of convergence (six term test) for eq 1 = 4.034 Order of pole (six term test) = 6.394 TOP MAIN SOLVE Loop x[1] = 4.28 y[1] (analytic) = 0 y[1] (numeric) = 3.3139263653245560585385995816658 absolute error = 3.3139263653245560585385995816658 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 = 0.08702 Order of pole (three term test) = -13.13 Radius of convergence (six term test) for eq 1 = 4.027 Order of pole (six term test) = 6.312 TOP MAIN SOLVE Loop x[1] = 4.29 y[1] (analytic) = 0 y[1] (numeric) = 3.3226835301176389568759061722493 absolute error = 3.3226835301176389568759061722493 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 = 0.09117 Order of pole (three term test) = -15.17 Radius of convergence (six term test) for eq 1 = 4.02 Order of pole (six term test) = 6.223 TOP MAIN SOLVE Loop bytes used=204063240, alloc=4652204, time=7.00 x[1] = 4.3 y[1] (analytic) = 0 y[1] (numeric) = 3.3314216544724292535073978170495 absolute error = 3.3314216544724292535073978170495 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 = 0.09392 Order of pole (three term test) = -17.22 Radius of convergence (six term test) for eq 1 = 4.013 Order of pole (six term test) = 6.128 TOP MAIN SOLVE Loop x[1] = 4.31 y[1] (analytic) = 0 y[1] (numeric) = 3.340140799148617570179756289686 absolute error = 3.340140799148617570179756289686 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 = 0.09519 Order of pole (three term test) = -19.21 Radius of convergence (six term test) for eq 1 = 4.004 Order of pole (six term test) = 6.027 TOP MAIN SOLVE Loop x[1] = 4.32 y[1] (analytic) = 0 y[1] (numeric) = 3.3488410295592720626697994817339 absolute error = 3.3488410295592720626697994817339 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 = 0.09496 Order of pole (three term test) = -21.11 Radius of convergence (six term test) for eq 1 = 3.995 Order of pole (six term test) = 5.92 TOP MAIN SOLVE Loop x[1] = 4.33 y[1] (analytic) = 0 y[1] (numeric) = 3.3575224157261311641414872584263 absolute error = 3.3575224157261311641414872584263 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 = 0.09322 Order of pole (three term test) = -22.88 Radius of convergence (six term test) for eq 1 = 3.985 Order of pole (six term test) = 5.81 TOP MAIN SOLVE Loop x[1] = 4.34 y[1] (analytic) = 0 y[1] (numeric) = 3.3661850322345559560525550147305 absolute error = 3.3661850322345559560525550147305 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 = 0.09001 Order of pole (three term test) = -24.47 Radius of convergence (six term test) for eq 1 = 3.975 Order of pole (six term test) = 5.695 TOP MAIN SOLVE Loop x[1] = 4.35 y[1] (analytic) = 0 y[1] (numeric) = 3.3748289581881768870196511561954 absolute error = 3.3748289581881768870196511561954 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 = 0.08538 Order of pole (three term test) = -25.85 Radius of convergence (six term test) for eq 1 = 3.965 Order of pole (six term test) = 5.579 TOP MAIN SOLVE Loop x[1] = 4.36 y[1] (analytic) = 0 y[1] (numeric) = 3.383454277163269035521119255283 absolute error = 3.383454277163269035521119255283 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 = 0.07944 Order of pole (three term test) = -26.99 Radius of convergence (six term test) for eq 1 = 3.954 Order of pole (six term test) = 5.46 TOP MAIN SOLVE Loop x[1] = 4.37 y[1] (analytic) = 0 y[1] (numeric) = 3.3920610771628895722450826949183 absolute error = 3.3920610771628895722450826949183 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 = 0.07232 Order of pole (three term test) = -27.86 Radius of convergence (six term test) for eq 1 = 3.944 Order of pole (six term test) = 5.341 TOP MAIN SOLVE Loop x[1] = 4.38 y[1] (analytic) = 0 y[1] (numeric) = 3.4006494505708105231643879661541 absolute error = 3.4006494505708105231643879661541 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 = 0.06416 Order of pole (three term test) = -28.44 Radius of convergence (six term test) for eq 1 = 3.933 Order of pole (six term test) = 5.222 TOP MAIN SOLVE Loop bytes used=208064336, alloc=4652204, time=7.15 x[1] = 4.39 y[1] (analytic) = 0 y[1] (numeric) = 3.4092194941052793659170788336914 absolute error = 3.4092194941052793659170788336914 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 = 0.05515 Order of pole (three term test) = -28.73 Radius of convergence (six term test) for eq 1 = 3.922 Order of pole (six term test) = 5.106 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 0 y[1] (numeric) = 3.4177713087726394106589660725607 absolute error = 3.4177713087726394106589660725607 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 = 0.04549 Order of pole (three term test) = -28.7 Radius of convergence (six term test) for eq 1 = 3.912 Order of pole (six term test) = 4.992 TOP MAIN SOLVE Loop x[1] = 4.41 y[1] (analytic) = 0 y[1] (numeric) = 3.4263049998208413230898692741847 absolute error = 3.4263049998208413230898692741847 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 = 0.0354 Order of pole (three term test) = -28.38 Radius of convergence (six term test) for eq 1 = 3.902 Order of pole (six term test) = 4.882 TOP MAIN SOLVE Loop x[1] = 4.42 y[1] (analytic) = 0 y[1] (numeric) = 3.4348206766928765426814742388649 absolute error = 3.4348206766928765426814742388649 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 = 0.02509 Order of pole (three term test) = -27.75 Radius of convergence (six term test) for eq 1 = 3.893 Order of pole (six term test) = 4.778 TOP MAIN SOLVE Loop x[1] = 4.43 y[1] (analytic) = 0 y[1] (numeric) = 3.4433184529801627340837568610336 absolute error = 3.4433184529801627340837568610336 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 = 0.01478 Order of pole (three term test) = -26.85 Radius of convergence (six term test) for eq 1 = 3.885 Order of pole (six term test) = 4.681 TOP MAIN SOLVE Loop x[1] = 4.44 y[1] (analytic) = 0 y[1] (numeric) = 3.4517984463759107850761098913641 absolute error = 3.4517984463759107850761098913641 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 = 0.004719 Order of pole (three term test) = -25.69 Radius of convergence (six term test) for eq 1 = 3.877 Order of pole (six term test) = 4.592 TOP MAIN SOLVE Loop x[1] = 4.45 y[1] (analytic) = 0 y[1] (numeric) = 3.4602607786285022310617131791805 absolute error = 3.4602607786285022310617131791805 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 = 3.871 Order of pole (six term test) = 4.512 TOP MAIN SOLVE Loop x[1] = 4.46 y[1] (analytic) = 0 y[1] (numeric) = 3.4687055754949053447671516909957 absolute error = 3.4687055754949053447671516909957 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 = 3.866 Order of pole (six term test) = 4.443 TOP MAIN SOLVE Loop x[1] = 4.47 y[1] (analytic) = 0 y[1] (numeric) = 3.4771329666941574812757931711742 absolute error = 3.4771329666941574812757931711742 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 = 3.862 Order of pole (six term test) = 4.385 TOP MAIN SOLVE Loop bytes used=212065276, alloc=4652204, time=7.29 x[1] = 4.48 y[1] (analytic) = 0 y[1] (numeric) = 3.4855430858609406135485064740989 absolute error = 3.4855430858609406135485064740989 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 = 3.86 Order of pole (six term test) = 4.34 TOP MAIN SOLVE Loop x[1] = 4.49 y[1] (analytic) = 0 y[1] (numeric) = 3.4939360704992763329074185721172 absolute error = 3.4939360704992763329074185721172 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 = 3.86 Order of pole (six term test) = 4.31 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 0 y[1] (numeric) = 3.5023120619363659232985079367339 absolute error = 3.5023120619363659232985079367339 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 = 3.861 Order of pole (six term test) = 4.294 TOP MAIN SOLVE Loop x[1] = 4.51 y[1] (analytic) = 0 y[1] (numeric) = 3.5106712052766004482098225453267 absolute error = 3.5106712052766004482098225453267 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 = 3.864 Order of pole (six term test) = 4.295 TOP MAIN SOLVE Loop x[1] = 4.52 y[1] (analytic) = 0 y[1] (numeric) = 3.5190136493557651155884417761066 absolute error = 3.5190136493557651155884417761066 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 = 3.87 Order of pole (six term test) = 4.314 TOP MAIN SOLVE Loop x[1] = 4.53 y[1] (analytic) = 0 y[1] (numeric) = 3.5273395466954615096365750876427 absolute error = 3.5273395466954615096365750876427 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 = 3.877 Order of pole (six term test) = 4.351 TOP MAIN SOLVE Loop x[1] = 4.54 y[1] (analytic) = 0 y[1] (numeric) = 3.5356490534577705996218145939834 absolute error = 3.5356490534577705996218145939834 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 = 3.887 Order of pole (six term test) = 4.407 TOP MAIN SOLVE Loop x[1] = 4.55 y[1] (analytic) = 0 y[1] (numeric) = 3.5439423294001787554354416346164 absolute error = 3.5439423294001787554354416346164 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 = 3.9 Order of pole (six term test) = 4.483 TOP MAIN SOLVE Loop x[1] = 4.56 y[1] (analytic) = 0 y[1] (numeric) = 3.5522195378307883181829723822163 absolute error = 3.5522195378307883181829723822163 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 = 3.914 Order of pole (six term test) = 4.58 TOP MAIN SOLVE Loop bytes used=216066400, alloc=4652204, time=7.43 x[1] = 4.57 y[1] (analytic) = 0 y[1] (numeric) = 3.560480845563833592179966708075 absolute error = 3.560480845563833592179966708075 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 = 3.932 Order of pole (six term test) = 4.698 TOP MAIN SOLVE Loop x[1] = 4.58 y[1] (analytic) = 0 y[1] (numeric) = 3.5687264228755224429204917651392 absolute error = 3.5687264228755224429204917651392 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 = 3.952 Order of pole (six term test) = 4.837 TOP MAIN SOLVE Loop x[1] = 4.59 y[1] (analytic) = 0 y[1] (numeric) = 3.5769564434602230044321722030096 absolute error = 3.5769564434602230044321722030096 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 = 3.974 Order of pole (six term test) = 4.997 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 0 y[1] (numeric) = 3.5851710843870143194566750835597 absolute error = 3.5851710843870143194566750835597 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 = 3.998 Order of pole (six term test) = 5.176 TOP MAIN SOLVE Loop x[1] = 4.61 y[1] (analytic) = 0 y[1] (numeric) = 3.5933705260566190576034503971137 absolute error = 3.5933705260566190576034503971137 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 = 4.024 Order of pole (six term test) = 5.374 TOP MAIN SOLVE Loop x[1] = 4.62 y[1] (analytic) = 0 y[1] (numeric) = 3.601554952158735780502692235033 absolute error = 3.601554952158735780502692235033 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 = 0.008323 Order of pole (three term test) = -0.9912 Radius of convergence (six term test) for eq 1 = 4.052 Order of pole (six term test) = 5.588 TOP MAIN SOLVE Loop x[1] = 4.63 y[1] (analytic) = 0 y[1] (numeric) = 3.6097245496297875494953375288379 absolute error = 3.6097245496297875494953375288379 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) = -1.361 Radius of convergence (six term test) for eq 1 = 4.082 Order of pole (six term test) = 5.814 TOP MAIN SOLVE Loop x[1] = 4.64 y[1] (analytic) = 0 y[1] (numeric) = 3.6178795086111030009874566880882 absolute error = 3.6178795086111030009874566880882 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) = -2 Radius of convergence (six term test) for eq 1 = 4.112 Order of pole (six term test) = 6.049 TOP MAIN SOLVE Loop bytes used=220067444, alloc=4652204, time=7.57 x[1] = 4.65 y[1] (analytic) = 0 y[1] (numeric) = 3.6260200224075453476870831313138 absolute error = 3.6260200224075453476870831313138 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) = -2.897 Radius of convergence (six term test) for eq 1 = 4.142 Order of pole (six term test) = 6.285 TOP MAIN SOLVE Loop x[1] = 4.66 y[1] (analytic) = 0 y[1] (numeric) = 3.634146287446604100936417737462 absolute error = 3.634146287446604100936417737462 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 = 0.05052 Order of pole (three term test) = -4.035 Radius of convergence (six term test) for eq 1 = 4.171 Order of pole (six term test) = 6.516 TOP MAIN SOLVE Loop x[1] = 4.67 y[1] (analytic) = 0 y[1] (numeric) = 3.6422585032379636506341500499501 absolute error = 3.6422585032379636506341500499501 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 = 0.06086 Order of pole (three term test) = -5.394 Radius of convergence (six term test) for eq 1 = 4.198 Order of pole (six term test) = 6.731 TOP MAIN SOLVE Loop x[1] = 4.68 y[1] (analytic) = 0 y[1] (numeric) = 3.6503568723335621851738950747163 absolute error = 3.6503568723335621851738950747163 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 = 0.07073 Order of pole (three term test) = -6.951 Radius of convergence (six term test) for eq 1 = 4.222 Order of pole (six term test) = 6.917 TOP MAIN SOLVE Loop x[1] = 4.69 y[1] (analytic) = 0 y[1] (numeric) = 3.6584416002881537847479617090693 absolute error = 3.6584416002881537847479617090693 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 = 0.07997 Order of pole (three term test) = -8.677 Radius of convergence (six term test) for eq 1 = 4.241 Order of pole (six term test) = 7.062 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (analytic) = 0 y[1] (numeric) = 3.6665128956203858776035148153796 absolute error = 3.6665128956203858776035148153796 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 = 0.0884 Order of pole (three term test) = -10.54 Radius of convergence (six term test) for eq 1 = 4.253 Order of pole (six term test) = 7.149 TOP MAIN SOLVE Loop x[1] = 4.71 y[1] (analytic) = 0 y[1] (numeric) = 3.6745709697744036106937043427891 absolute error = 3.6745709697744036106937043427891 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 = 0.09587 Order of pole (three term test) = -12.51 Radius of convergence (six term test) for eq 1 = 4.257 Order of pole (six term test) = 7.162 TOP MAIN SOLVE Loop x[1] = 4.72 y[1] (analytic) = 0 y[1] (numeric) = 3.6826160370819920539231469491415 absolute error = 3.6826160370819920539231469491415 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) = -14.55 Radius of convergence (six term test) for eq 1 = 4.25 Order of pole (six term test) = 7.084 TOP MAIN SOLVE Loop x[1] = 4.73 y[1] (analytic) = 0 y[1] (numeric) = 3.6906483147252665311097437159894 absolute error = 3.6906483147252665311097437159894 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 = 0.1074 Order of pole (three term test) = -16.61 Radius of convergence (six term test) for eq 1 = 4.231 Order of pole (six term test) = 6.901 TOP MAIN SOLVE Loop bytes used=224068644, alloc=4717728, time=7.71 x[1] = 4.74 y[1] (analytic) = 0 y[1] (numeric) = 3.6986680226999207511188087752528 absolute error = 3.6986680226999207511188087752528 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 = 0.1112 Order of pole (three term test) = -18.67 Radius of convergence (six term test) for eq 1 = 4.199 Order of pole (six term test) = 6.601 TOP MAIN SOLVE Loop x[1] = 4.75 y[1] (analytic) = 0 y[1] (numeric) = 3.7066753837790417995978865656103 absolute error = 3.7066753837790417995978865656103 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 = 0.1136 Order of pole (three term test) = -20.68 Radius of convergence (six term test) for eq 1 = 4.152 Order of pole (six term test) = 6.179 TOP MAIN SOLVE Loop x[1] = 4.76 y[1] (analytic) = 0 y[1] (numeric) = 3.7146706234775004455601877424281 absolute error = 3.7146706234775004455601877424281 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 = 0.1146 Order of pole (three term test) = -22.61 Radius of convergence (six term test) for eq 1 = 4.09 Order of pole (six term test) = 5.634 TOP MAIN SOLVE Loop x[1] = 4.77 y[1] (analytic) = 0 y[1] (numeric) = 3.7226539700169246179220562929847 absolute error = 3.7226539700169246179220562929847 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 = 0.1141 Order of pole (three term test) = -24.41 Radius of convergence (six term test) for eq 1 = 4.013 Order of pole (six term test) = 4.975 TOP MAIN SOLVE Loop x[1] = 4.78 y[1] (analytic) = 0 y[1] (numeric) = 3.7306256542912633151684562860562 absolute error = 3.7306256542912633151684562860562 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 = 0.1121 Order of pole (three term test) = -26.06 Radius of convergence (six term test) for eq 1 = 3.922 Order of pole (six term test) = 4.215 TOP MAIN SOLVE Loop x[1] = 4.79 y[1] (analytic) = 0 y[1] (numeric) = 3.7385859098329476267560347822042 absolute error = 3.7385859098329476267560347822042 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 = 0.1087 Order of pole (three term test) = -27.51 Radius of convergence (six term test) for eq 1 = 3.819 Order of pole (six term test) = 3.375 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (analytic) = 0 y[1] (numeric) = 3.746534972779654967804878939605 absolute error = 3.746534972779654967804878939605 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) = -28.75 Radius of convergence (six term test) for eq 1 = 3.705 Order of pole (six term test) = 2.48 TOP MAIN SOLVE Loop x[1] = 4.81 y[1] (analytic) = 0 y[1] (numeric) = 3.7544730818416820592001224677477 absolute error = 3.7544730818416820592001224677477 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 = 0.09786 Order of pole (three term test) = -29.74 Radius of convergence (six term test) for eq 1 = 3.584 Order of pole (six term test) = 1.554 TOP MAIN SOLVE Loop x[1] = 4.82 y[1] (analytic) = 0 y[1] (numeric) = 3.7624004782699316235294222962666 absolute error = 3.7624004782699316235294222962666 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 = 0.09062 Order of pole (three term test) = -30.48 Radius of convergence (six term test) for eq 1 = 3.457 Order of pole (six term test) = 0.6222 TOP MAIN SOLVE Loop bytes used=228070068, alloc=4717728, time=7.85 x[1] = 4.83 y[1] (analytic) = 0 y[1] (numeric) = 3.7703174058245172134126443161396 absolute error = 3.7703174058245172134126443161396 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 = 0.08235 Order of pole (three term test) = -30.95 Radius of convergence (six term test) for eq 1 = 3.328 Order of pole (six term test) = -0.2933 TOP MAIN SOLVE Loop x[1] = 4.84 y[1] (analytic) = 0 y[1] (numeric) = 3.7782241107439900428111707387691 absolute error = 3.7782241107439900428111707387691 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 = 0.0732 Order of pole (three term test) = -31.13 Radius of convergence (six term test) for eq 1 = 3.199 Order of pole (six term test) = -1.175 TOP MAIN SOLVE Loop x[1] = 4.85 y[1] (analytic) = 0 y[1] (numeric) = 3.7861208417151911538964714612598 absolute error = 3.7861208417151911538964714612598 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 = 0.06336 Order of pole (three term test) = -31.03 Radius of convergence (six term test) for eq 1 = 3.071 Order of pole (six term test) = -2.008 TOP MAIN SOLVE Loop x[1] = 4.86 y[1] (analytic) = 0 y[1] (numeric) = 3.7940078498437317220568899324187 absolute error = 3.7940078498437317220568899324187 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 = 0.05301 Order of pole (three term test) = -30.66 Radius of convergence (six term test) for eq 1 = 2.948 Order of pole (six term test) = -2.785 TOP MAIN SOLVE Loop x[1] = 4.87 y[1] (analytic) = 0 y[1] (numeric) = 3.8018853886251037796598552299724 absolute error = 3.8018853886251037796598552299724 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 = 0.04235 Order of pole (three term test) = -30.01 Radius of convergence (six term test) for eq 1 = 2.83 Order of pole (six term test) = -3.499 TOP MAIN SOLVE Loop x[1] = 4.88 y[1] (analytic) = 0 y[1] (numeric) = 3.8097537139164231252822106818229 absolute error = 3.8097537139164231252822106818229 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) = -29.12 Radius of convergence (six term test) for eq 1 = 2.719 Order of pole (six term test) = -4.149 TOP MAIN SOLVE Loop x[1] = 4.89 y[1] (analytic) = 0 y[1] (numeric) = 3.8176130839088056792791406752232 absolute error = 3.8176130839088056792791406752232 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 = 0.02089 Order of pole (three term test) = -27.99 Radius of convergence (six term test) for eq 1 = 2.614 Order of pole (six term test) = -4.734 TOP MAIN SOLVE Loop x[1] = 4.9 y[1] (analytic) = 0 y[1] (numeric) = 3.8254637591003780487746531504347 absolute error = 3.8254637591003780487746531504347 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 = 0.01047 Order of pole (three term test) = -26.65 Radius of convergence (six term test) for eq 1 = 2.518 Order of pole (six term test) = -5.257 TOP MAIN SOLVE Loop x[1] = 4.91 y[1] (analytic) = 0 y[1] (numeric) = 3.833306002269922575403832985671 absolute error = 3.833306002269922575403832985671 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 = 0.0005216 Order of pole (three term test) = -25.12 Radius of convergence (six term test) for eq 1 = 2.43 Order of pole (six term test) = -5.719 TOP MAIN SOLVE Loop bytes used=232070908, alloc=4717728, time=7.99 x[1] = 4.92 y[1] (analytic) = 0 y[1] (numeric) = 3.8411400784511566573873953184612 absolute error = 3.8411400784511566573873953184612 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 = 2.35 Order of pole (six term test) = -6.125 TOP MAIN SOLVE Loop x[1] = 4.93 y[1] (analytic) = 0 y[1] (numeric) = 3.8489662549076456637293424541721 absolute error = 3.8489662549076456637293424541721 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 = 2.279 Order of pole (six term test) = -6.478 TOP MAIN SOLVE Loop x[1] = 4.94 y[1] (analytic) = 0 y[1] (numeric) = 3.8567848011083482924447530861896 absolute error = 3.8567848011083482924447530861896 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 = 2.218 Order of pole (six term test) = -6.782 TOP MAIN SOLVE Loop x[1] = 4.95 y[1] (analytic) = 0 y[1] (numeric) = 3.8645959887037927666824382175395 absolute error = 3.8645959887037927666824382175395 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 = 2.165 Order of pole (six term test) = -7.038 TOP MAIN SOLVE Loop x[1] = 4.96 y[1] (analytic) = 0 y[1] (numeric) = 3.8724000915028818123319104263783 absolute error = 3.8724000915028818123319104263783 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 = 2.121 Order of pole (six term test) = -7.25 TOP MAIN SOLVE Loop x[1] = 4.97 y[1] (analytic) = 0 y[1] (numeric) = 3.8801973854503239181118088191589 absolute error = 3.8801973854503239181118088191589 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 = 2.087 Order of pole (six term test) = -7.419 TOP MAIN SOLVE Loop x[1] = 4.98 y[1] (analytic) = 0 y[1] (numeric) = 3.8879881486046879441344829139755 absolute error = 3.8879881486046879441344829139755 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 = 2.064 Order of pole (six term test) = -7.545 TOP MAIN SOLVE Loop x[1] = 4.99 y[1] (analytic) = 0 y[1] (numeric) = 3.8957726611170777174271039966579 absolute error = 3.8957726611170777174271039966579 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 = 2.051 Order of pole (six term test) = -7.627 Finished! diff ( y , x , 1 ) = expt((0.2 * x + 0.3) , sin(x)); Iterations = 490 Total Elapsed Time = 8 Seconds Elapsed Time(since restart) = 7 Seconds Time to Timeout = 2 Minutes 51 Seconds Percent Done = 100.2 % > quit bytes used=235662308, alloc=4717728, time=8.10