##############ECHO OF PROBLEM################# ##############temp/sing1postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001); ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-2.0; x_end=-1.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=500; glob_max_h=0.5; /* # Not Given = 0 */ /* # No Pole = 3 */ /* # Pole = 4 */ glob_type_given_pole=4; /* # Real Part */ array_given_rad_poles[1][1]=0.0; /* # Imag Part */ array_given_rad_poles[1][2]=0.001; /* # Order */ array_given_ord_poles[1][1]=1.0; /* # Not Used */ array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.1; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(1.0 / (x * x + 0.000001)) ; } /* 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 = 1e-10 range = 0.5 estimated_steps = 500000 step_error = 2e-16 est_needed_step_err = 2e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.484894657593405e-101 estimated_step_error = 6.484894657593405e-101 best_h = 2e-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 = 4.249941687783492e-96 estimated_step_error = 4.249941687783492e-96 best_h = 4e-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 = 2.785243259044777e-91 estimated_step_error = 2.785243259044777e-91 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.825338954958387e-86 estimated_step_error = 1.825338954958387e-86 best_h = 1.6e-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 = 1.196256670772253e-81 estimated_step_error = 1.196256670772253e-81 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.839820921607218e-77 estimated_step_error = 7.839820921607218e-77 best_h = 6.4e-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 = 5.137948560927449e-72 estimated_step_error = 5.137948560927449e-72 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 = 3.367263015153421e-67 estimated_step_error = 3.367263015153421e-67 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 = 2.206844265078339e-62 estimated_step_error = 2.206844265078339e-62 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.446375477192988e-57 estimated_step_error = 1.446375477192988e-57 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 = 9.480251350568087e-53 estimated_step_error = 9.480251350568087e-53 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 = 6.214662513191828e-48 estimated_step_error = 6.214662513191828e-48 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 = 4.075051561168922e-43 estimated_step_error = 4.075051561168922e-43 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.6735276130217e-38 estimated_step_error = 2.6735276130217e-38 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.755938825983392e-33 estimated_step_error = 1.755938825983392e-33 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.155805701139686e-28 estimated_step_error = 1.155805701139686e-28 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.641509870515368e-24 estimated_step_error = 7.641509870515368e-24 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 = 5.097738956153388e-19 estimated_step_error = 5.097738956153388e-19 best_h = 0.262144 opt_iter = 19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.464361060665141e-14 estimated_step_error = 3.464361060665141e-14 best_h = 0.131072 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = 0.2499999375000156 y[1] (numeric) = 0.2499999375000156 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.778 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 18 Radius of convergence (six term test) for eq 1 = 2 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = 0.2770082335157248 y[1] (numeric) = 0.2770082335157248 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.689 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 18 Radius of convergence (six term test) for eq 1 = 1.9 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = 0.3086418800488025 y[1] (numeric) = 0.3086418800488024 absolute error = 5.551115123125783e-17 relative error = 1.798561855004266e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.6 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 18 Radius of convergence (six term test) for eq 1 = 1.8 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = 0.3460206415153491 y[1] (numeric) = 0.3460206415153489 absolute error = 1.110223024625157e-16 relative error = 3.208545651389726e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.511 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 18 Radius of convergence (six term test) for eq 1 = 1.7 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = 0.3906248474121691 y[1] (numeric) = 0.390624847412169 absolute error = 1.665334536937735e-16 relative error = 4.263258079895136e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.422 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 18 Radius of convergence (six term test) for eq 1 = 1.6 Order of pole (six term test) = 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001); Iterations = 5 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 120 %