##############ECHO OF PROBLEM################# ##############temp/lin_tanhpostode.ode################# diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=1.1; x_end=2.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=10; // 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(ln(cosh(3.0*x + 1.0))/3.0); } // 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 = 0.8999999999999999 estimated_steps = 900000 step_error = 1.111111111111111e-16 est_needed_step_err = 1.111111111111111e-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 = 4.114948349382778e-163 estimated_step_error = 4.114948349382778e-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 = 2.761494174509256e-155 estimated_step_error = 2.761494174509256e-155 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 = 1.853206139233278e-147 estimated_step_error = 1.853206139233278e-147 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 = 1.243663935794903e-139 estimated_step_error = 1.243663935794903e-139 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 = 8.346065222584092e-132 estimated_step_error = 8.346065222584092e-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 = 5.600919803295137e-124 estimated_step_error = 5.600919803295137e-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 = 3.758673715901579e-116 estimated_step_error = 3.758673715901579e-116 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 = 2.522349630323399e-108 estimated_step_error = 2.522349630323399e-108 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.692648243838111e-100 estimated_step_error = 1.692648243838111e-100 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 = 1.135820463698909e-92 estimated_step_error = 1.135820463698909e-92 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.621066599557378e-85 estimated_step_error = 7.621066599557378e-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 = 5.112673208511047e-77 estimated_step_error = 5.112673208511047e-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 = 3.428726294988962e-69 estimated_step_error = 3.428726294988962e-69 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 = 2.29785681466537e-61 estimated_step_error = 2.29785681466537e-61 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 = 1.537889880466759e-53 estimated_step_error = 1.537889880466759e-53 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 = 1.02649655928412e-45 estimated_step_error = 1.02649655928412e-45 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 = 6.815117159456676e-38 estimated_step_error = 6.815117159456676e-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 = 4.477716319822724e-30 estimated_step_error = 4.477716319822724e-30 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 1.20234563609611 y[1] (numeric) = 1.20234563609611 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = -249.5 Radius of convergence (six term test) for eq 1 = 1.527 Order of pole (six term test) = 0.03164 TOP MAIN SOLVE Loop x[1] = 1.11 y[1] (analytic) = 1.212342062905879 y[1] (numeric) = 1.212342062905879 absolute error = 4.440892098500626e-16 relative error = 3.663068563220675e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.713 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4703 Order of pole (three term test) = -239.4 Radius of convergence (six term test) for eq 1 = 1.538 Order of pole (six term test) = 0.04924 TOP MAIN SOLVE Loop x[1] = 1.12 y[1] (analytic) = 1.222338697767025 y[1] (numeric) = 1.222338697767025 absolute error = 4.440892098500626e-16 relative error = 3.633110942665296e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.698 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4377 Order of pole (three term test) = -227.5 Radius of convergence (six term test) for eq 1 = 1.549 Order of pole (six term test) = 0.07192 TOP MAIN SOLVE Loop x[1] = 1.13 y[1] (analytic) = 1.232335528567539 y[1] (numeric) = 1.232335528567539 absolute error = 2.220446049250313e-16 relative error = 1.801819389100426e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4029 Order of pole (three term test) = -214.3 Radius of convergence (six term test) for eq 1 = 1.561 Order of pole (six term test) = 0.1002 TOP MAIN SOLVE Loop x[1] = 1.14 y[1] (analytic) = 1.242332543900312 y[1] (numeric) = 1.242332543900312 absolute error = 4.440892098500626e-16 relative error = 3.574640397456235e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3668 Order of pole (three term test) = -200 Radius of convergence (six term test) for eq 1 = 1.572 Order of pole (six term test) = 0.1345 TOP MAIN SOLVE Loop x[1] = 1.15 y[1] (analytic) = 1.252329733022138 y[1] (numeric) = 1.252329733022138 absolute error = 2.220446049250313e-16 relative error = 1.773052248701231e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3301 Order of pole (three term test) = -185.1 Radius of convergence (six term test) for eq 1 = 1.585 Order of pole (six term test) = 0.1753 TOP MAIN SOLVE Loop x[1] = 1.16 y[1] (analytic) = 1.262327085815092 y[1] (numeric) = 1.262327085815092 absolute error = 2.220446049250313e-16 relative error = 1.759010064983719e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2934 Order of pole (three term test) = -169.7 Radius of convergence (six term test) for eq 1 = 1.598 Order of pole (six term test) = 0.2227 TOP MAIN SOLVE Loop x[1] = 1.17 y[1] (analytic) = 1.272324592750161 y[1] (numeric) = 1.272324592750161 absolute error = 2.220446049250313e-16 relative error = 1.745188344155767e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2575 Order of pole (three term test) = -154.3 Radius of convergence (six term test) for eq 1 = 1.611 Order of pole (six term test) = 0.2772 TOP MAIN SOLVE Loop x[1] = 1.18 y[1] (analytic) = 1.28232224485298 y[1] (numeric) = 1.28232224485298 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.625 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2227 Order of pole (three term test) = -139 Radius of convergence (six term test) for eq 1 = 1.625 Order of pole (six term test) = 0.3387 TOP MAIN SOLVE Loop x[1] = 1.19 y[1] (analytic) = 1.292320033671564 y[1] (numeric) = 1.292320033671565 absolute error = 2.220446049250313e-16 relative error = 1.718185891571984e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 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 = 0.1895 Order of pole (three term test) = -124 Radius of convergence (six term test) for eq 1 = 1.639 Order of pole (six term test) = 0.4073 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 1.302317951245919 y[1] (numeric) = 1.302317951245919 absolute error = 2.220446049250313e-16 relative error = 1.704995348582908e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.604 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1582 Order of pole (three term test) = -109.5 Radius of convergence (six term test) for eq 1 = 1.654 Order of pole (six term test) = 0.4829 TOP MAIN SOLVE Loop x[1] = 1.21 y[1] (analytic) = 1.312315990079407 y[1] (numeric) = 1.312315990079407 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.594 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1291 Order of pole (three term test) = -95.67 Radius of convergence (six term test) for eq 1 = 1.669 Order of pole (six term test) = 0.5654 TOP MAIN SOLVE Loop x[1] = 1.22 y[1] (analytic) = 1.32231414311179 y[1] (numeric) = 1.322314143111791 absolute error = 2.220446049250313e-16 relative error = 1.679212205977739e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.584 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1024 Order of pole (three term test) = -82.6 Radius of convergence (six term test) for eq 1 = 1.684 Order of pole (six term test) = 0.6543 TOP MAIN SOLVE Loop x[1] = 1.23 y[1] (analytic) = 1.332312403693838 y[1] (numeric) = 1.332312403693838 absolute error = 2.220446049250313e-16 relative error = 1.666610656099968e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.575 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.07822 Order of pole (three term test) = -70.38 Radius of convergence (six term test) for eq 1 = 1.7 Order of pole (six term test) = 0.7491 TOP MAIN SOLVE Loop x[1] = 1.24 y[1] (analytic) = 1.342310765563402 y[1] (numeric) = 1.342310765563402 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.565 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.05669 Order of pole (three term test) = -59.07 Radius of convergence (six term test) for eq 1 = 1.717 Order of pole (six term test) = 0.8493 TOP MAIN SOLVE Loop x[1] = 1.25 y[1] (analytic) = 1.352309222822895 y[1] (numeric) = 1.352309222822895 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.555 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.03788 Order of pole (three term test) = -48.71 Radius of convergence (six term test) for eq 1 = 1.733 Order of pole (six term test) = 0.954 TOP MAIN SOLVE Loop x[1] = 1.26 y[1] (analytic) = 1.362307769918072 y[1] (numeric) = 1.362307769918072 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.546 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.02183 Order of pole (three term test) = -39.34 Radius of convergence (six term test) for eq 1 = 1.75 Order of pole (six term test) = 1.062 TOP MAIN SOLVE Loop x[1] = 1.27 y[1] (analytic) = 1.372306401618049 y[1] (numeric) = 1.37230640161805 absolute error = 2.220446049250313e-16 relative error = 1.618039562179587e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.536 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.008571 Order of pole (three term test) = -30.97 Radius of convergence (six term test) for eq 1 = 1.767 Order of pole (six term test) = 1.173 TOP MAIN SOLVE Loop x[1] = 1.28 y[1] (analytic) = 1.382305112996481 y[1] (numeric) = 1.382305112996481 absolute error = 2.220446049250313e-16 relative error = 1.606335698518078e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.526 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 = 1.784 Order of pole (six term test) = 1.286 TOP MAIN SOLVE Loop x[1] = 1.29 y[1] (analytic) = 1.392303899413835 y[1] (numeric) = 1.392303899413835 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.516 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 = 1.801 Order of pole (six term test) = 1.398 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 1.402302756500701 y[1] (numeric) = 1.402302756500702 absolute error = 2.220446049250313e-16 relative error = 1.583428427960309e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.505 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 = 1.818 Order of pole (six term test) = 1.509 TOP MAIN SOLVE Loop x[1] = 1.31 y[1] (analytic) = 1.412301680142064 y[1] (numeric) = 1.412301680142064 absolute error = 2.220446049250313e-16 relative error = 1.57221794781619e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.495 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 = 1.835 Order of pole (six term test) = 1.617 TOP MAIN SOLVE Loop x[1] = 1.32 y[1] (analytic) = 1.422300666462496 y[1] (numeric) = 1.422300666462496 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.483 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 = 1.851 Order of pole (six term test) = 1.72 TOP MAIN SOLVE Loop x[1] = 1.33 y[1] (analytic) = 1.432299711812211 y[1] (numeric) = 1.432299711812211 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.472 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 = 1.867 Order of pole (six term test) = 1.818 TOP MAIN SOLVE Loop x[1] = 1.34 y[1] (analytic) = 1.442298812753932 y[1] (numeric) = 1.442298812753932 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.46 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 = 1.883 Order of pole (six term test) = 1.907 TOP MAIN SOLVE Loop x[1] = 1.35 y[1] (analytic) = 1.452297966050513 y[1] (numeric) = 1.452297966050513 absolute error = 2.220446049250313e-16 relative error = 1.528919065616238e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.447 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.003242 Order of pole (three term test) = -0.9452 Radius of convergence (six term test) for eq 1 = 1.897 Order of pole (six term test) = 1.987 TOP MAIN SOLVE Loop x[1] = 1.36 y[1] (analytic) = 1.462297168653296 y[1] (numeric) = 1.462297168653296 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 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 = 0.01521 Order of pole (three term test) = -1.779 Radius of convergence (six term test) for eq 1 = 1.912 Order of pole (six term test) = 2.057 TOP MAIN SOLVE Loop x[1] = 1.37 y[1] (analytic) = 1.472296417691135 y[1] (numeric) = 1.472296417691134 absolute error = 2.220446049250313e-16 relative error = 1.508151498957276e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.03004 Order of pole (three term test) = -3.63 Radius of convergence (six term test) for eq 1 = 1.925 Order of pole (six term test) = 2.114 TOP MAIN SOLVE Loop x[1] = 1.38 y[1] (analytic) = 1.482295710460057 y[1] (numeric) = 1.482295710460057 absolute error = 2.220446049250313e-16 relative error = 1.49797778782019e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.405 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.04776 Order of pole (three term test) = -6.502 Radius of convergence (six term test) for eq 1 = 1.937 Order of pole (six term test) = 2.158 TOP MAIN SOLVE Loop x[1] = 1.39 y[1] (analytic) = 1.49229504441354 y[1] (numeric) = 1.49229504441354 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.389 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.06842 Order of pole (three term test) = -10.4 Radius of convergence (six term test) for eq 1 = 1.949 Order of pole (six term test) = 2.187 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 1.502294417153335 y[1] (numeric) = 1.502294417153335 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.373 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.09206 Order of pole (three term test) = -15.34 Radius of convergence (six term test) for eq 1 = 1.959 Order of pole (six term test) = 2.201 TOP MAIN SOLVE Loop x[1] = 1.41 y[1] (analytic) = 1.512293826420842 y[1] (numeric) = 1.512293826420842 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.355 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1188 Order of pole (three term test) = -21.33 Radius of convergence (six term test) for eq 1 = 1.969 Order of pole (six term test) = 2.199 TOP MAIN SOLVE Loop x[1] = 1.42 y[1] (analytic) = 1.522293270088974 y[1] (numeric) = 1.522293270088974 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.336 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1486 Order of pole (three term test) = -28.38 Radius of convergence (six term test) for eq 1 = 1.977 Order of pole (six term test) = 2.18 TOP MAIN SOLVE Loop x[1] = 1.43 y[1] (analytic) = 1.532292746154502 y[1] (numeric) = 1.532292746154502 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.315 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.1816 Order of pole (three term test) = -36.51 Radius of convergence (six term test) for eq 1 = 1.985 Order of pole (six term test) = 2.146 TOP MAIN SOLVE Loop x[1] = 1.44 y[1] (analytic) = 1.542292252730846 y[1] (numeric) = 1.542292252730846 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.293 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2179 Order of pole (three term test) = -45.75 Radius of convergence (six term test) for eq 1 = 1.991 Order of pole (six term test) = 2.097 TOP MAIN SOLVE Loop x[1] = 1.45 y[1] (analytic) = 1.552291788041279 y[1] (numeric) = 1.552291788041279 absolute error = 2.220446049250313e-16 relative error = 1.430430841905134e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.269 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.2576 Order of pole (three term test) = -56.12 Radius of convergence (six term test) for eq 1 = 1.997 Order of pole (six term test) = 2.032 TOP MAIN SOLVE Loop x[1] = 1.46 y[1] (analytic) = 1.562291350412533 y[1] (numeric) = 1.562291350412533 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.244 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3007 Order of pole (three term test) = -67.64 Radius of convergence (six term test) for eq 1 = 2.002 Order of pole (six term test) = 1.953 TOP MAIN SOLVE Loop x[1] = 1.47 y[1] (analytic) = 1.572290938268776 y[1] (numeric) = 1.572290938268776 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.216 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.3475 Order of pole (three term test) = -80.35 Radius of convergence (six term test) for eq 1 = 2.006 Order of pole (six term test) = 1.862 TOP MAIN SOLVE Loop x[1] = 1.48 y[1] (analytic) = 1.582290550125937 y[1] (numeric) = 1.582290550125936 absolute error = 2.220446049250313e-16 relative error = 1.403311199118003e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.186 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.398 Order of pole (three term test) = -94.27 Radius of convergence (six term test) for eq 1 = 2.009 Order of pole (six term test) = 1.759 TOP MAIN SOLVE Loop x[1] = 1.49 y[1] (analytic) = 1.592290184586364 y[1] (numeric) = 1.592290184586363 absolute error = 2.220446049250313e-16 relative error = 1.394498358869887e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.153 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4523 Order of pole (three term test) = -109.4 Radius of convergence (six term test) for eq 1 = 2.012 Order of pole (six term test) = 1.646 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 1.602289840333792 y[1] (numeric) = 1.602289840333791 absolute error = 2.220446049250313e-16 relative error = 1.38579549926357e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.117 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.5106 Order of pole (three term test) = -125.9 Radius of convergence (six term test) for eq 1 = 2.014 Order of pole (six term test) = 1.525 TOP MAIN SOLVE Loop x[1] = 1.51 y[1] (analytic) = 1.612289516128603 y[1] (numeric) = 1.612289516128603 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.077 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.573 Order of pole (three term test) = -143.7 Radius of convergence (six term test) for eq 1 = 2.016 Order of pole (six term test) = 1.397 TOP MAIN SOLVE Loop x[1] = 1.52 y[1] (analytic) = 1.622289210803368 y[1] (numeric) = 1.622289210803367 absolute error = 2.220446049250313e-16 relative error = 1.368711592522233e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.033 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.6397 Order of pole (three term test) = -162.8 Radius of convergence (six term test) for eq 1 = 2.018 Order of pole (six term test) = 1.265 TOP MAIN SOLVE Loop x[1] = 1.53 y[1] (analytic) = 1.632288923258633 y[1] (numeric) = 1.632288923258633 absolute error = 2.220446049250313e-16 relative error = 1.360326604935545e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9854 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7108 Order of pole (three term test) = -183.4 Radius of convergence (six term test) for eq 1 = 2.02 Order of pole (six term test) = 1.13 TOP MAIN SOLVE Loop x[1] = 1.54 y[1] (analytic) = 1.642288652458974 y[1] (numeric) = 1.642288652458974 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9321 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.7863 Order of pole (three term test) = -205.4 Radius of convergence (six term test) for eq 1 = 2.022 Order of pole (six term test) = 0.9949 TOP MAIN SOLVE Loop x[1] = 1.55 y[1] (analytic) = 1.652288397429258 y[1] (numeric) = 1.652288397429258 absolute error = 2.220446049250313e-16 relative error = 1.343861067296141e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8727 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.8666 Order of pole (three term test) = -228.9 Radius of convergence (six term test) for eq 1 = 2.024 Order of pole (six term test) = 0.8603 TOP MAIN SOLVE Loop x[1] = 1.56 y[1] (analytic) = 1.662288157251138 y[1] (numeric) = 1.662288157251138 absolute error = 2.220446049250313e-16 relative error = 1.335776856476063e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8063 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.9516 Order of pole (three term test) = -253.9 Radius of convergence (six term test) for eq 1 = 2.027 Order of pole (six term test) = 0.7285 TOP MAIN SOLVE Loop x[1] = 1.570000000000001 y[1] (analytic) = 1.672287931059745 y[1] (numeric) = 1.672287931059744 absolute error = 2.220446049250313e-16 relative error = 1.327789316665818e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7316 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 1.041 Order of pole (three term test) = -280.4 Radius of convergence (six term test) for eq 1 = 2.03 Order of pole (six term test) = 0.6009 TOP MAIN SOLVE Loop x[1] = 1.580000000000001 y[1] (analytic) = 1.682287718040573 y[1] (numeric) = 1.682287718040572 absolute error = 4.440892098500626e-16 relative error = 2.639793449644339e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.136 Order of pole (three term test) = -308.6 Radius of convergence (six term test) for eq 1 = 2.034 Order of pole (six term test) = 0.4791 TOP MAIN SOLVE Loop x[1] = 1.590000000000001 y[1] (analytic) = 1.692287517426546 y[1] (numeric) = 1.692287517426546 absolute error = 2.220446049250313e-16 relative error = 1.312097398571453e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.236 Order of pole (three term test) = -338.3 Radius of convergence (six term test) for eq 1 = 2.038 Order of pole (six term test) = 0.3643 TOP MAIN SOLVE Loop x[1] = 1.600000000000001 y[1] (analytic) = 1.702287328495261 y[1] (numeric) = 1.702287328495261 absolute error = 2.220446049250313e-16 relative error = 1.304389695018807e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.341 Order of pole (three term test) = -369.7 Radius of convergence (six term test) for eq 1 = 2.044 Order of pole (six term test) = 0.2578 TOP MAIN SOLVE Loop x[1] = 1.610000000000001 y[1] (analytic) = 1.71228715056638 y[1] (numeric) = 1.71228715056638 absolute error = 4.440892098500626e-16 relative error = 2.59354401919777e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.452 Order of pole (three term test) = -402.7 Radius of convergence (six term test) for eq 1 = 2.05 Order of pole (six term test) = 0.1605 TOP MAIN SOLVE Loop x[1] = 1.620000000000001 y[1] (analytic) = 1.722286982999183 y[1] (numeric) = 1.722286982999183 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.567 Order of pole (three term test) = -437.3 Radius of convergence (six term test) for eq 1 = 2.057 Order of pole (six term test) = 0.0733 TOP MAIN SOLVE Loop x[1] = 1.630000000000001 y[1] (analytic) = 1.732286825190263 y[1] (numeric) = 1.732286825190263 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.687 Order of pole (three term test) = -473.6 Radius of convergence (six term test) for eq 1 = 2.065 Order of pole (six term test) = -0.003108 TOP MAIN SOLVE Loop x[1] = 1.640000000000001 y[1] (analytic) = 1.742286676571351 y[1] (numeric) = 1.742286676571351 absolute error = 2.220446049250313e-16 relative error = 1.274443568391358e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.813 Order of pole (three term test) = -511.5 Radius of convergence (six term test) for eq 1 = 2.075 Order of pole (six term test) = -0.06822 TOP MAIN SOLVE Loop x[1] = 1.650000000000001 y[1] (analytic) = 1.75228653660727 y[1] (numeric) = 1.75228653660727 absolute error = 2.220446049250313e-16 relative error = 1.267170638398832e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.943 Order of pole (three term test) = -550.9 Radius of convergence (six term test) for eq 1 = 2.085 Order of pole (six term test) = -0.1217 TOP MAIN SOLVE Loop x[1] = 1.660000000000001 y[1] (analytic) = 1.762286404794009 y[1] (numeric) = 1.762286404794008 absolute error = 4.440892098500626e-16 relative error = 2.519960482257546e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8009 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 2.078 Order of pole (three term test) = -591.7 Radius of convergence (six term test) for eq 1 = 2.096 Order of pole (six term test) = -0.1633 TOP MAIN SOLVE Loop x[1] = 1.670000000000001 y[1] (analytic) = 1.772286280656906 y[1] (numeric) = 1.772286280656906 absolute error = 2.220446049250313e-16 relative error = 1.252870979979202e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8899 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 2.217 Order of pole (three term test) = -633.9 Radius of convergence (six term test) for eq 1 = 2.109 Order of pole (six term test) = -0.1931 TOP MAIN SOLVE Loop x[1] = 1.680000000000001 y[1] (analytic) = 1.782286163748944 y[1] (numeric) = 1.782286163748943 absolute error = 2.220446049250313e-16 relative error = 1.245841489662762e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.359 Order of pole (three term test) = -677.4 Radius of convergence (six term test) for eq 1 = 2.122 Order of pole (six term test) = -0.2112 TOP MAIN SOLVE Loop x[1] = 1.690000000000001 y[1] (analytic) = 1.792286053649133 y[1] (numeric) = 1.792286053649133 absolute error = 2.220446049250313e-16 relative error = 1.23889043533505e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.505 Order of pole (three term test) = -721.9 Radius of convergence (six term test) for eq 1 = 2.136 Order of pole (six term test) = -0.218 TOP MAIN SOLVE Loop x[1] = 1.700000000000001 y[1] (analytic) = 1.802285949961004 y[1] (numeric) = 1.802285949961004 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.653 Order of pole (three term test) = -767.3 Radius of convergence (six term test) for eq 1 = 2.151 Order of pole (six term test) = -0.2139 TOP MAIN SOLVE Loop x[1] = 1.710000000000001 y[1] (analytic) = 1.812285852311171 y[1] (numeric) = 1.812285852311171 absolute error = 2.220446049250313e-16 relative error = 1.22521844245411e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.803 Order of pole (three term test) = -813.4 Radius of convergence (six term test) for eq 1 = 2.167 Order of pole (six term test) = -0.1997 TOP MAIN SOLVE Loop x[1] = 1.720000000000001 y[1] (analytic) = 1.822285760347996 y[1] (numeric) = 1.822285760347996 absolute error = 2.220446049250313e-16 relative error = 1.218494978979741e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.954 Order of pole (three term test) = -859.8 Radius of convergence (six term test) for eq 1 = 2.184 Order of pole (six term test) = -0.1763 TOP MAIN SOLVE Loop x[1] = 1.730000000000001 y[1] (analytic) = 1.832285673740316 y[1] (numeric) = 1.832285673740316 absolute error = 2.220446049250313e-16 relative error = 1.211844900100993e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.104 Order of pole (three term test) = -906.3 Radius of convergence (six term test) for eq 1 = 2.201 Order of pole (six term test) = -0.1447 TOP MAIN SOLVE Loop x[1] = 1.740000000000001 y[1] (analytic) = 1.842285592176254 y[1] (numeric) = 1.842285592176254 absolute error = 2.220446049250313e-16 relative error = 1.205267011086672e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.253 Order of pole (three term test) = -952.6 Radius of convergence (six term test) for eq 1 = 2.218 Order of pole (six term test) = -0.1061 TOP MAIN SOLVE Loop x[1] = 1.750000000000001 y[1] (analytic) = 1.852285515362095 y[1] (numeric) = 1.852285515362095 absolute error = 2.220446049250313e-16 relative error = 1.198760142988133e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = -998.1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = -0.0621 TOP MAIN SOLVE Loop x[1] = 1.760000000000001 y[1] (analytic) = 1.862285443021228 y[1] (numeric) = 1.862285443021228 absolute error = 2.220446049250313e-16 relative error = 1.192323151948196e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.542 Order of pole (three term test) = -1043 Radius of convergence (six term test) for eq 1 = 2.253 Order of pole (six term test) = -0.0143 TOP MAIN SOLVE Loop x[1] = 1.770000000000001 y[1] (analytic) = 1.872285374893151 y[1] (numeric) = 1.872285374893151 absolute error = 2.220446049250313e-16 relative error = 1.185954918532134e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.679 Order of pole (three term test) = -1085 Radius of convergence (six term test) for eq 1 = 2.271 Order of pole (six term test) = 0.03542 TOP MAIN SOLVE Loop x[1] = 1.780000000000001 y[1] (analytic) = 1.882285310732531 y[1] (numeric) = 1.882285310732531 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.808 Order of pole (three term test) = -1126 Radius of convergence (six term test) for eq 1 = 2.288 Order of pole (six term test) = 0.08503 TOP MAIN SOLVE Loop x[1] = 1.790000000000001 y[1] (analytic) = 1.892285250308325 y[1] (numeric) = 1.892285250308324 absolute error = 2.220446049250313e-16 relative error = 1.173420365078954e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.929 Order of pole (three term test) = -1165 Radius of convergence (six term test) for eq 1 = 2.304 Order of pole (six term test) = 0.1323 TOP MAIN SOLVE Loop x[1] = 1.800000000000001 y[1] (analytic) = 1.902285193402939 y[1] (numeric) = 1.902285193402939 absolute error = 2.220446049250313e-16 relative error = 1.167251922556484e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.039 Order of pole (three term test) = -1200 Radius of convergence (six term test) for eq 1 = 2.319 Order of pole (six term test) = 0.1748 TOP MAIN SOLVE Loop x[1] = 1.810000000000001 y[1] (analytic) = 1.912285139811457 y[1] (numeric) = 1.912285139811456 absolute error = 4.440892098500626e-16 relative error = 2.322295982982161e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.138 Order of pole (three term test) = -1232 Radius of convergence (six term test) for eq 1 = 2.333 Order of pole (six term test) = 0.2101 TOP MAIN SOLVE Loop x[1] = 1.820000000000001 y[1] (analytic) = 1.922285089340892 y[1] (numeric) = 1.922285089340891 absolute error = 6.661338147750939e-16 relative error = 3.465322695727179e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.223 Order of pole (three term test) = -1260 Radius of convergence (six term test) for eq 1 = 2.345 Order of pole (six term test) = 0.2355 TOP MAIN SOLVE Loop x[1] = 1.830000000000001 y[1] (analytic) = 1.932285041809496 y[1] (numeric) = 1.932285041809495 absolute error = 4.440892098500626e-16 relative error = 2.298259315997155e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.293 Order of pole (three term test) = -1284 Radius of convergence (six term test) for eq 1 = 2.356 Order of pole (six term test) = 0.2484 TOP MAIN SOLVE Loop x[1] = 1.840000000000001 y[1] (analytic) = 1.942284997046107 y[1] (numeric) = 1.942284997046107 absolute error = 6.661338147750939e-16 relative error = 3.429639912722246e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.348 Order of pole (three term test) = -1303 Radius of convergence (six term test) for eq 1 = 2.364 Order of pole (six term test) = 0.2461 TOP MAIN SOLVE Loop x[1] = 1.850000000000001 y[1] (analytic) = 1.95228495488953 y[1] (numeric) = 1.952284954889529 absolute error = 6.661338147750939e-16 relative error = 3.412072674671547e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.386 Order of pole (three term test) = -1317 Radius of convergence (six term test) for eq 1 = 2.37 Order of pole (six term test) = 0.226 TOP MAIN SOLVE Loop x[1] = 1.860000000000001 y[1] (analytic) = 1.962284915187956 y[1] (numeric) = 1.962284915187955 absolute error = 4.440892098500626e-16 relative error = 2.263122986946704e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.407 Order of pole (three term test) = -1326 Radius of convergence (six term test) for eq 1 = 2.374 Order of pole (six term test) = 0.1856 TOP MAIN SOLVE Loop x[1] = 1.870000000000001 y[1] (analytic) = 1.972284877798417 y[1] (numeric) = 1.972284877798416 absolute error = 6.661338147750939e-16 relative error = 3.377472606891722e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.411 Order of pole (three term test) = -1330 Radius of convergence (six term test) for eq 1 = 2.374 Order of pole (six term test) = 0.1227 TOP MAIN SOLVE Loop x[1] = 1.880000000000001 y[1] (analytic) = 1.982284842586271 y[1] (numeric) = 1.982284842586271 absolute error = 6.661338147750939e-16 relative error = 3.36043438593817e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.397 Order of pole (three term test) = -1328 Radius of convergence (six term test) for eq 1 = 2.372 Order of pole (six term test) = 0.03517 TOP MAIN SOLVE Loop x[1] = 1.890000000000001 y[1] (analytic) = 1.992284809424718 y[1] (numeric) = 1.992284809424717 absolute error = 8.881784197001252e-16 relative error = 4.458089603948699e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.367 Order of pole (three term test) = -1322 Radius of convergence (six term test) for eq 1 = 2.366 Order of pole (six term test) = -0.07851 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (analytic) = 2.00228477819434 y[1] (numeric) = 2.00228477819434 absolute error = 8.881784197001252e-16 relative error = 4.435824660771202e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.319 Order of pole (three term test) = -1310 Radius of convergence (six term test) for eq 1 = 2.356 Order of pole (six term test) = -0.2196 TOP MAIN SOLVE Loop x[1] = 1.910000000000001 y[1] (analytic) = 2.012284748782676 y[1] (numeric) = 2.012284748782675 absolute error = 8.881784197001252e-16 relative error = 4.413781003098223e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.256 Order of pole (three term test) = -1294 Radius of convergence (six term test) for eq 1 = 2.343 Order of pole (six term test) = -0.389 TOP MAIN SOLVE Loop x[1] = 1.920000000000001 y[1] (analytic) = 2.02228472108381 y[1] (numeric) = 2.02228472108381 absolute error = 8.881784197001252e-16 relative error = 4.391955348523429e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.179 Order of pole (three term test) = -1273 Radius of convergence (six term test) for eq 1 = 2.326 Order of pole (six term test) = -0.5868 TOP MAIN SOLVE Loop x[1] = 1.930000000000001 y[1] (analytic) = 2.032284694998 y[1] (numeric) = 2.032284694997998 absolute error = 1.332267629550188e-15 relative error = 6.555516718839921e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.088 Order of pole (three term test) = -1248 Radius of convergence (six term test) for eq 1 = 2.305 Order of pole (six term test) = -0.8129 TOP MAIN SOLVE Loop x[1] = 1.940000000000001 y[1] (analytic) = 2.042284670431306 y[1] (numeric) = 2.042284670431305 absolute error = 8.881784197001252e-16 relative error = 4.348945240393704e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.985 Order of pole (three term test) = -1219 Radius of convergence (six term test) for eq 1 = 2.281 Order of pole (six term test) = -1.066 TOP MAIN SOLVE Loop x[1] = 1.950000000000001 y[1] (analytic) = 2.052284647295264 y[1] (numeric) = 2.052284647295263 absolute error = 1.332267629550188e-15 relative error = 6.491631808024304e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.872 Order of pole (three term test) = -1187 Radius of convergence (six term test) for eq 1 = 2.252 Order of pole (six term test) = -1.346 TOP MAIN SOLVE Loop x[1] = 1.960000000000001 y[1] (analytic) = 2.062284625506559 y[1] (numeric) = 2.062284625506558 absolute error = 8.881784197001252e-16 relative error = 4.306769340735216e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.75 Order of pole (three term test) = -1153 Radius of convergence (six term test) for eq 1 = 2.22 Order of pole (six term test) = -1.65 TOP MAIN SOLVE Loop x[1] = 1.970000000000001 y[1] (analytic) = 2.072284604986728 y[1] (numeric) = 2.072284604986726 absolute error = 1.332267629550188e-15 relative error = 6.428980007592734e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.62 Order of pole (three term test) = -1116 Radius of convergence (six term test) for eq 1 = 2.184 Order of pole (six term test) = -1.976 TOP MAIN SOLVE Loop x[1] = 1.980000000000001 y[1] (analytic) = 2.082284585661877 y[1] (numeric) = 2.082284585661876 absolute error = 1.332267629550188e-15 relative error = 6.398105420958643e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.485 Order of pole (three term test) = -1077 Radius of convergence (six term test) for eq 1 = 2.145 Order of pole (six term test) = -2.322 TOP MAIN SOLVE Loop x[1] = 1.990000000000001 y[1] (analytic) = 2.092284567462417 y[1] (numeric) = 2.092284567462416 absolute error = 8.881784197001252e-16 relative error = 4.245017305544311e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.346 Order of pole (three term test) = -1037 Radius of convergence (six term test) for eq 1 = 2.102 Order of pole (six term test) = -2.685 Finished! diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ; Iterations = 90 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 101.1 %