##############ECHO OF PROBLEM################# ##############temp/sing4postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0); ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=20; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-2.0; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=50; /* # Not Given = 0 */ /* # No Pole = 3 */ /* # Pole = 4 */ glob_max_h=0.5; glob_type_given_pole=4; /* # Real Part */ array_given_rad_poles[1][1]=0.0; /* # Imag Part */ array_given_rad_poles[1][2]=1.0; /* # 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 + 1.0)); } /* 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 = 3 estimated_steps = 3000000 step_error = 3.333333333333333e-17 est_needed_step_err = 3.333333333333333e-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 = 1.144417382795083e-102 estimated_step_error = 1.144417382795083e-102 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 = 7.500055238870521e-98 estimated_step_error = 7.500055238870521e-98 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 = 4.915238139881815e-93 estimated_step_error = 4.915238139881815e-93 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 = 3.221253008232601e-88 estimated_step_error = 3.221253008232601e-88 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 = 2.111083701862951e-83 estimated_step_error = 2.111083701862951e-83 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 = 1.383524180073924e-78 estimated_step_error = 1.383524180073924e-78 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 = 9.067121282759621e-74 estimated_step_error = 9.067121282759621e-74 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 = 5.942303599376916e-69 estimated_step_error = 5.942303599376916e-69 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 = 3.894446387763168e-64 estimated_step_error = 3.894446387763168e-64 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 = 2.552393236853233e-59 estimated_step_error = 2.552393236853233e-59 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 = 1.67290533981166e-54 estimated_step_error = 1.67290533981166e-54 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 = 1.096576684522375e-49 estimated_step_error = 1.096576684522375e-49 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 = 7.189428736648961e-45 estimated_step_error = 7.189428736648961e-45 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 = 4.715473476845421e-40 estimated_step_error = 4.715473476845421e-40 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 = 3.095334802326781e-35 estimated_step_error = 3.095334802326781e-35 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 = 2.035138486570559e-30 estimated_step_error = 2.035138486570559e-30 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 = 1.34243436188061e-25 estimated_step_error = 1.34243436188061e-25 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 = 8.913242752753631e-21 estimated_step_error = 8.913242752753631e-21 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 = 5.996960503691097e-16 estimated_step_error = 5.996960503691097e-16 best_h = 0.131072 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = 0.2 y[1] (numeric) = 0.2 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = 0.2169197396963124 y[1] (numeric) = 0.2169197396963124 absolute error = 2.775557561562891e-17 relative error = 1.279532035880493e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.147 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = 0.2358490566037736 y[1] (numeric) = 0.2358490566037736 absolute error = 2.775557561562891e-17 relative error = 1.176836406102666e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.059 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = 0.2570694087403599 y[1] (numeric) = 0.2570694087403599 absolute error = 5.551115123125783e-17 relative error = 2.159383782895929e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.972 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = 0.2808988764044945 y[1] (numeric) = 0.2808988764044944 absolute error = 5.551115123125783e-17 relative error = 1.976196983832778e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.887 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (analytic) = 0.3076923076923078 y[1] (numeric) = 0.3076923076923077 absolute error = 1.110223024625157e-16 relative error = 3.608224830031757e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.803 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.803 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.399999999999999 y[1] (analytic) = 0.3378378378378381 y[1] (numeric) = 0.3378378378378379 absolute error = 1.665334536937735e-16 relative error = 4.929390229335692e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.72 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.299999999999999 y[1] (analytic) = 0.371747211895911 y[1] (numeric) = 0.3717472118959109 absolute error = 1.110223024625157e-16 relative error = 2.986499936241669e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.64 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.199999999999999 y[1] (analytic) = 0.4098360655737707 y[1] (numeric) = 0.4098360655737706 absolute error = 1.110223024625157e-16 relative error = 2.70894418008538e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.562 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.562 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.099999999999999 y[1] (analytic) = 0.4524886877828058 y[1] (numeric) = 0.4524886877828056 absolute error = 2.220446049250313e-16 relative error = 4.907185768843187e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.487 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.487 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.9999999999999992 y[1] (analytic) = 0.5000000000000004 y[1] (numeric) = 0.5000000000000002 absolute error = 2.220446049250313e-16 relative error = 4.440892098500622e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO 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) = 1.32 TOP MAIN SOLVE Loop x[1] = -0.8999999999999992 y[1] (analytic) = 0.5524861878453042 y[1] (numeric) = 0.5524861878453041 absolute error = 1.110223024625157e-16 relative error = 2.009503674571532e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.345 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.345 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.7999999999999993 y[1] (analytic) = 0.609756097560976 y[1] (numeric) = 0.6097560975609759 absolute error = 1.110223024625157e-16 relative error = 1.820765760385255e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.281 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.281 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.6999999999999993 y[1] (analytic) = 0.6711409395973159 y[1] (numeric) = 0.6711409395973158 absolute error = 1.110223024625157e-16 relative error = 1.654232306691482e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.221 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.221 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.5999999999999993 y[1] (analytic) = 0.7352941176470592 y[1] (numeric) = 0.7352941176470592 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.166 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.166 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.4999999999999993 y[1] (analytic) = 0.8000000000000004 y[1] (numeric) = 0.8000000000000004 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.118 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.118 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.3999999999999994 y[1] (analytic) = 0.8620689655172418 y[1] (numeric) = 0.8620689655172418 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.077 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.077 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.2999999999999994 y[1] (analytic) = 0.9174311926605507 y[1] (numeric) = 0.9174311926605508 absolute error = 1.110223024625157e-16 relative error = 1.21014309684142e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.044 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.044 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.1999999999999994 y[1] (analytic) = 0.9615384615384617 y[1] (numeric) = 0.9615384615384618 absolute error = 1.110223024625157e-16 relative error = 1.154631945610163e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.02 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -0.09999999999999937 y[1] (analytic) = 0.9900990099009903 y[1] (numeric) = 0.9900990099009902 absolute error = 1.110223024625157e-16 relative error = 1.121325254871408e-14 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.005 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.005 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 6.38378239159465e-16 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.384e-16 Order of pole (three term test) = 18 Radius of convergence (six term test) for eq 1 = 1 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000000004 y[1] (analytic) = 0.9615384615384615 y[1] (numeric) = 0.9615384615384613 absolute error = 1.110223024625157e-16 relative error = 1.154631945610163e-14 % Correct digits = 16 h = 0.09999999999999987 Radius of convergence (given) for eq 1 = 1.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.02 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000003 y[1] (analytic) = 0.9174311926605504 y[1] (numeric) = 0.9174311926605503 absolute error = 1.110223024625157e-16 relative error = 1.210143096841421e-14 % Correct digits = 16 h = 0.09999999999999987 Radius of convergence (given) for eq 1 = 1.044 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.044 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000001 y[1] (analytic) = 0.8620689655172413 y[1] (numeric) = 0.8620689655172412 absolute error = 1.110223024625157e-16 relative error = 1.287858708565182e-14 % Correct digits = 16 h = 0.09999999999999987 Radius of convergence (given) for eq 1 = 1.077 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.077 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0.8 y[1] (numeric) = 0.7999999999999999 absolute error = 1.110223024625157e-16 relative error = 1.387778780781446e-14 % Correct digits = 16 h = 0.09999999999999987 Radius of convergence (given) for eq 1 = 1.118 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.118 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.5999999999999999 y[1] (analytic) = 0.7352941176470589 y[1] (numeric) = 0.7352941176470589 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.09999999999999987 Radius of convergence (given) for eq 1 = 1.166 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.166 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.6999999999999997 y[1] (analytic) = 0.6711409395973157 y[1] (numeric) = 0.6711409395973156 absolute error = 1.110223024625157e-16 relative error = 1.654232306691483e-14 % Correct digits = 16 h = 0.09999999999999987 Radius of convergence (given) for eq 1 = 1.221 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.221 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999996 y[1] (analytic) = 0.6097560975609759 y[1] (numeric) = 0.6097560975609758 absolute error = 1.110223024625157e-16 relative error = 1.820765760385256e-14 % Correct digits = 16 h = 0.09999999999999987 Radius of convergence (given) for eq 1 = 1.281 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.281 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.8999999999999995 y[1] (analytic) = 0.5524861878453041 y[1] (numeric) = 0.5524861878453041 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.09999999999999987 Radius of convergence (given) for eq 1 = 1.345 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.345 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = 0.9999999999999993 y[1] (analytic) = 0.5000000000000003 y[1] (numeric) = 0.5000000000000003 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.09999999999999987 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.296 Order of pole (six term test) = 2.28 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0); Iterations = 31 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 106.7 %