##############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=30; ! /* 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=0.001; /* # 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=0.01; 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 = 1.005794611214363e-163 estimated_step_error = 1.005794611214363e-163 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 = 6.74977512752968e-156 estimated_step_error = 6.74977512752968e-156 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 = 4.529699759368465e-148 estimated_step_error = 4.529699759368465e-148 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 = 3.039833203538167e-140 estimated_step_error = 3.039833203538167e-140 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 = 2.040001761502553e-132 estimated_step_error = 2.040001761502553e-132 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 = 1.369027686663758e-124 estimated_step_error = 1.369027686663758e-124 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 = 9.187465506037023e-117 estimated_step_error = 9.187465506037023e-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 = 6.165706037985226e-109 estimated_step_error = 6.165706037985226e-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 = 4.137872599946438e-101 estimated_step_error = 4.137872599946438e-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 = 2.777063622068331e-93 estimated_step_error = 2.777063622068331e-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 = 1.863903297323974e-85 estimated_step_error = 1.863903297323974e-85 best_h = 0.001 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 = 0.001 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 2.003 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 2 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.989000000000001 y[1] (analytic) = 0.2527727911323258 y[1] (numeric) = 0.2527727911323261 absolute error = 3.33066907387547e-16 relative error = 1.317653319787839e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.989 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.89 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.992 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.989 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.979000000000002 y[1] (analytic) = 0.2553337953172797 y[1] (numeric) = 0.2553337953172803 absolute error = 6.106226635438361e-16 relative error = 2.391468245654954e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.979 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.88 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.982 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.979 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.969000000000003 y[1] (analytic) = 0.2579339183618505 y[1] (numeric) = 0.2579339183618513 absolute error = 8.326672684688674e-16 relative error = 3.228219358497608e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.969 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.871 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.972 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.969 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.959000000000005 y[1] (analytic) = 0.26057396105253 y[1] (numeric) = 0.2605739610525311 absolute error = 1.054711873393899e-15 relative error = 4.047648771710063e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.959 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.861 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.962 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.959 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.949000000000006 y[1] (analytic) = 0.2632547447718909 y[1] (numeric) = 0.2632547447718923 absolute error = 1.387778780781446e-15 relative error = 5.271619252233992e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.949 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.852 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.952 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.949 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.939000000000007 y[1] (analytic) = 0.2659771121375445 y[1] (numeric) = 0.2659771121375462 absolute error = 1.665334536937735e-15 relative error = 6.261194895884658e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.939 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.842 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.942 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.939 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.929000000000008 y[1] (analytic) = 0.2687419276643456 y[1] (numeric) = 0.2687419276643476 absolute error = 1.942890293094024e-15 relative error = 7.229576381995231e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.929 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.833 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.932 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.929 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.919000000000009 y[1] (analytic) = 0.2715500784508151 y[1] (numeric) = 0.2715500784508174 absolute error = 2.275957200481571e-15 relative error = 8.381353500119893e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.919 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.823 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.922 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.919 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.90900000000001 y[1] (analytic) = 0.2744024748907987 y[1] (numeric) = 0.2744024748908012 absolute error = 2.498001805406602e-15 relative error = 9.103423015410878e-13 % Correct digits = 15 h = 0.001 Radius of convergence (given) for eq 1 = 1.909 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.814 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.912 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.909 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.899000000000011 y[1] (analytic) = 0.2773000514114263 y[1] (numeric) = 0.2773000514114291 absolute error = 2.831068712794149e-15 relative error = 1.020940565421581e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.899 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.804 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.902 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.899 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.889000000000012 y[1] (analytic) = 0.2802437672384911 y[1] (numeric) = 0.2802437672384942 absolute error = 3.108624468950438e-15 relative error = 1.109257308229431e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.889 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.795 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.892 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.889 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.879000000000013 y[1] (analytic) = 0.2832346071904163 y[1] (numeric) = 0.2832346071904198 absolute error = 3.497202527569243e-15 relative error = 1.23473701263423e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.879 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.785 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.882 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.879 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.869000000000014 y[1] (analytic) = 0.2862735825020382 y[1] (numeric) = 0.286273582502042 absolute error = 3.885780586188048e-15 relative error = 1.357366108401002e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.869 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.776 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.872 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.869 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.859000000000016 y[1] (analytic) = 0.2893617316794911 y[1] (numeric) = 0.2893617316794954 absolute error = 4.274358644806853e-15 relative error = 1.477167910213264e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.859 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.766 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.862 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.859 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.849000000000017 y[1] (analytic) = 0.2925001213875451 y[1] (numeric) = 0.2925001213875497 absolute error = 4.6074255521944e-15 relative error = 1.57518756926936e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.849 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.757 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.852 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.849 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.839000000000018 y[1] (analytic) = 0.2956898473708089 y[1] (numeric) = 0.2956898473708137 absolute error = 4.829470157119431e-15 relative error = 1.633289137270597e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.747 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.842 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.839 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.829000000000019 y[1] (analytic) = 0.298932035410287 y[1] (numeric) = 0.2989320354102923 absolute error = 5.273559366969494e-15 relative error = 1.764133228388013e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.829 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.738 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.832 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.829 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.81900000000002 y[1] (analytic) = 0.3022278423168479 y[1] (numeric) = 0.3022278423168534 absolute error = 5.551115123125783e-15 relative error = 1.836731877702431e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.819 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.728 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.822 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.819 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.809000000000021 y[1] (analytic) = 0.3055784569632398 y[1] (numeric) = 0.3055784569632456 absolute error = 5.88418203051333e-15 relative error = 1.925587977957877e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.809 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.719 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.812 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.809 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.799000000000022 y[1] (analytic) = 0.3089851013563752 y[1] (numeric) = 0.3089851013563815 absolute error = 6.272760089132134e-15 relative error = 2.030117329798792e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.799 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.709 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.802 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.799 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.789000000000023 y[1] (analytic) = 0.3124490317516874 y[1] (numeric) = 0.312449031751694 absolute error = 6.661338147750939e-15 relative error = 2.131975929131669e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.789 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.792 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.789 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.779000000000024 y[1] (analytic) = 0.3159715398114575 y[1] (numeric) = 0.3159715398114645 absolute error = 6.994405055138486e-15 relative error = 2.21361868835152e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.779 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.782 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.779 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.769000000000025 y[1] (analytic) = 0.3195539538091059 y[1] (numeric) = 0.3195539538091132 absolute error = 7.327471962526033e-15 relative error = 2.293031231559505e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.769 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.681 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.772 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.769 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.759000000000027 y[1] (analytic) = 0.3231976398815448 y[1] (numeric) = 0.3231976398815525 absolute error = 7.771561172376096e-15 relative error = 2.40458475353485e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.759 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.671 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.762 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.759 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.749000000000028 y[1] (analytic) = 0.3269040033317953 y[1] (numeric) = 0.3269040033318035 absolute error = 8.271161533457416e-15 relative error = 2.53014996731701e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.749 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.662 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.752 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.749 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.739000000000029 y[1] (analytic) = 0.3306744899841895 y[1] (numeric) = 0.3306744899841981 absolute error = 8.604228440844963e-15 relative error = 2.602023652098581e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.739 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.652 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.741 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.739 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.72900000000003 y[1] (analytic) = 0.3345105875945964 y[1] (numeric) = 0.3345105875946054 absolute error = 8.992806499463768e-15 relative error = 2.68834734473709e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.729 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.643 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.731 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.729 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.719000000000031 y[1] (analytic) = 0.338413827318241 y[1] (numeric) = 0.3384138273182504 absolute error = 9.436895709313831e-15 relative error = 2.788566821898642e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.719 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.633 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.721 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.719 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.709000000000032 y[1] (analytic) = 0.3423857852378186 y[1] (numeric) = 0.3423857852378284 absolute error = 9.825473767932635e-15 relative error = 2.86970843754741e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.709 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.624 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.711 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.709 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.699000000000033 y[1] (analytic) = 0.3464280839547541 y[1] (numeric) = 0.3464280839547644 absolute error = 1.032507412901396e-14 relative error = 2.980437963096111e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.699 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.614 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.701 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.699 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.689000000000034 y[1] (analytic) = 0.3505423942466036 y[1] (numeric) = 0.3505423942466144 absolute error = 1.082467449009528e-14 relative error = 3.087978706073483e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.689 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.605 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.691 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.689 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.679000000000035 y[1] (analytic) = 0.3547304367937611 y[1] (numeric) = 0.3547304367937723 absolute error = 1.121325254871408e-14 relative error = 3.161062989143337e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.679 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.595 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.681 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.679 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.669000000000036 y[1] (analytic) = 0.3589939839788008 y[1] (numeric) = 0.3589939839788125 absolute error = 1.176836406102666e-14 relative error = 3.278150773056298e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.669 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.586 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.671 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.669 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.659000000000038 y[1] (analytic) = 0.3633348617619687 y[1] (numeric) = 0.363334861761981 absolute error = 1.226796442210798e-14 relative error = 3.376489765560972e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.659 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.576 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.661 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.659 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.649000000000039 y[1] (analytic) = 0.367754951636529 y[1] (numeric) = 0.3677549516365419 absolute error = 1.287858708565182e-14 relative error = 3.501947976048023e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.649 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.567 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.651 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.649 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.63900000000004 y[1] (analytic) = 0.3722561926678751 y[1] (numeric) = 0.3722561926678884 absolute error = 1.332267629550188e-14 relative error = 3.578899843148693e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.639 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.557 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.641 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.639 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.629000000000041 y[1] (analytic) = 0.3768405836205297 y[1] (numeric) = 0.3768405836205437 absolute error = 1.398881011027697e-14 relative error = 3.712129403865747e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.629 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.548 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.631 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.629 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.619000000000042 y[1] (analytic) = 0.3815101851773939 y[1] (numeric) = 0.3815101851774084 absolute error = 1.448841047135829e-14 relative error = 3.797647096792842e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.619 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.538 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.621 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.619 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.609000000000043 y[1] (analytic) = 0.3862671222558411 y[1] (numeric) = 0.3862671222558561 absolute error = 1.493249968120836e-14 relative error = 3.865847963968812e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.609 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.529 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.611 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.609 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.599000000000044 y[1] (analytic) = 0.3911135864255209 y[1] (numeric) = 0.3911135864255365 absolute error = 1.554312234475219e-14 relative error = 3.974068629730929e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.599 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.519 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.601 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.599 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.589000000000045 y[1] (analytic) = 0.3960518384330062 y[1] (numeric) = 0.3960518384330223 absolute error = 1.609823385706477e-14 relative error = 4.064678482685001e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.589 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.51 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.591 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.589 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.579000000000046 y[1] (analytic) = 0.4010842108387157 y[1] (numeric) = 0.4010842108387323 absolute error = 1.659783421814609e-14 relative error = 4.138241738172143e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.579 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.5 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.581 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.579 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.569000000000047 y[1] (analytic) = 0.4062131107718535 y[1] (numeric) = 0.4062131107718706 absolute error = 1.709743457922741e-14 relative error = 4.208981474463057e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.569 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.491 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.571 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.569 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.559000000000049 y[1] (analytic) = 0.4114410228094418 y[1] (numeric) = 0.4114410228094595 absolute error = 1.770805724277125e-14 relative error = 4.303911438352782e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.559 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.481 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.561 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.559 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.54900000000005 y[1] (analytic) = 0.4167705119858764 y[1] (numeric) = 0.4167705119858947 absolute error = 1.826316875508383e-14 relative error = 4.382068363728845e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.549 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.472 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.551 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.549 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.539000000000051 y[1] (analytic) = 0.4222042269398106 y[1] (numeric) = 0.4222042269398294 absolute error = 1.88182802673964e-14 relative error = 4.45715108154972e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.539 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.462 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.541 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.539 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.529000000000052 y[1] (analytic) = 0.4277449032055768 y[1] (numeric) = 0.4277449032055962 absolute error = 1.937339177970898e-14 relative error = 4.529192898506148e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.529 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.453 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.531 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.529 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.519000000000053 y[1] (analytic) = 0.4333953666567839 y[1] (numeric) = 0.4333953666568039 absolute error = 2.003952559448408e-14 relative error = 4.623843985474319e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.519 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.443 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.521 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.519 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.509000000000054 y[1] (analytic) = 0.4391585371101824 y[1] (numeric) = 0.4391585371102031 absolute error = 2.070565940925917e-14 relative error = 4.714848433895807e-12 % Correct digits = 14 h = 0.001 Radius of convergence (given) for eq 1 = 1.509 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.434 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.511 Order of pole (three term test) = 677 Radius of convergence (six term test) for eq 1 = 1.509 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 = 501 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 100.4 %