##############ECHO OF PROBLEM################# ##############temp/sing3postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=20; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-2.0; x_end=-0.7; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; glob_max_h=0.0001; // # 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]=0.0; // # Order array_given_ord_poles[1][1]=2.0; // # 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=1000000000; glob_max_minutes=30.0; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(1.0/x/x); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 1300000 step_error = 7.692307692307693e-17 est_needed_step_err = 7.692307692307693e-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 = 7.152559056001943e-102 estimated_step_error = 7.152559056001943e-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 = 4.68750220588339e-97 estimated_step_error = 4.68750220588339e-97 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 = 3.072002891296846e-92 estimated_step_error = 3.072002891296846e-92 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 = 2.013269709684182e-87 estimated_step_error = 2.013269709684182e-87 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.319418920555435e-82 estimated_step_error = 1.319418920555435e-82 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 = 8.646976391198815e-78 estimated_step_error = 8.646976391198815e-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 = 5.666925116673318e-73 estimated_step_error = 5.666925116673318e-73 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.713931972760191e-68 estimated_step_error = 3.713931972760191e-68 best_h = 0.0001 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = 0.25 y[1] (numeric) = 0.25 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.143 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 2.749e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.989900000000001 y[1] (analytic) = 0.2525442564805524 y[1] (numeric) = 0.2525442564805529 absolute error = 4.996003610813204e-16 relative error = 1.978268553970433e-13 % Correct digits = 15 h = 0.0001 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.132 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.99 Order of pole (three term test) = 4.724e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.979900000000002 y[1] (analytic) = 0.2551017798576175 y[1] (numeric) = 0.2551017798576184 absolute error = 9.436895709313831e-16 relative error = 3.69926690224621e-13 % Correct digits = 15 h = 0.0001 Radius of convergence (given) for eq 1 = 1.98 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.121 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.98 Order of pole (three term test) = 4.061e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.969900000000003 y[1] (analytic) = 0.2576983510457175 y[1] (numeric) = 0.257698351045719 absolute error = 1.443289932012704e-15 relative error = 5.600695255347806e-13 % Correct digits = 15 h = 0.0001 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.111 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.97 Order of pole (three term test) = 3.489e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.959900000000004 y[1] (analytic) = 0.2603347690092929 y[1] (numeric) = 0.2603347690092949 absolute error = 2.05391259555654e-15 relative error = 7.889505513891706e-13 % Correct digits = 15 h = 0.0001 Radius of convergence (given) for eq 1 = 1.96 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.1 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.96 Order of pole (three term test) = 2.995e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.949900000000006 y[1] (analytic) = 0.2630118532525034 y[1] (numeric) = 0.2630118532525055 absolute error = 2.109423746787797e-15 relative error = 8.020261142993635e-13 % Correct digits = 15 h = 0.0001 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.089 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.95 Order of pole (three term test) = 7.707e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.939900000000007 y[1] (analytic) = 0.2657304444561424 y[1] (numeric) = 0.2657304444561446 absolute error = 2.220446049250313e-15 relative error = 8.356009240095888e-13 % Correct digits = 15 h = 0.0001 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.078 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.94 Order of pole (three term test) = 4.403e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.929900000000008 y[1] (analytic) = 0.2684914051377114 y[1] (numeric) = 0.2684914051377139 absolute error = 2.55351295663786e-15 relative error = 9.51059478171431e-13 % Correct digits = 15 h = 0.0001 Radius of convergence (given) for eq 1 = 1.93 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.068 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.93 Order of pole (three term test) = 3.771e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.919900000000009 y[1] (analytic) = 0.2712956203356238 y[1] (numeric) = 0.2712956203356263 absolute error = 2.442490654175344e-15 relative error = 9.003059655565774e-13 % Correct digits = 15 h = 0.0001 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.057 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.92 Order of pole (three term test) = 3.227e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.90990000000001 y[1] (analytic) = 0.2741439983185514 y[1] (numeric) = 0.2741439983185539 absolute error = 2.498001805406602e-15 relative error = 9.112006174594271e-13 % Correct digits = 15 h = 0.0001 Radius of convergence (given) for eq 1 = 1.91 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.046 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.91 Order of pole (three term test) = 2.759e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.899900000000011 y[1] (analytic) = 0.2770374713209739 y[1] (numeric) = 0.2770374713209768 absolute error = 2.886579864025407e-15 relative error = 1.041945643764931e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.036 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.889900000000012 y[1] (analytic) = 0.2799769963060443 y[1] (numeric) = 0.2799769963060474 absolute error = 3.164135620181696e-15 relative error = 1.130141283722811e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.025 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.89 Order of pole (three term test) = 4.023e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.879900000000013 y[1] (analytic) = 0.2829635557569361 y[1] (numeric) = 0.2829635557569396 absolute error = 3.497202527569243e-15 relative error = 1.235919770026257e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.014 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.88 Order of pole (three term test) = 6.863e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.869900000000014 y[1] (analytic) = 0.2859981584978928 y[1] (numeric) = 0.2859981584978963 absolute error = 3.552713678800501e-15 relative error = 1.242215578400893e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 2.003 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.87 Order of pole (three term test) = 2.924e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.859900000000015 y[1] (analytic) = 0.2890818405462621 y[1] (numeric) = 0.2890818405462662 absolute error = 4.163336342344337e-15 relative error = 1.440192969048872e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.993 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.86 Order of pole (three term test) = 4.979e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.849900000000017 y[1] (analytic) = 0.2922156659968573 y[1] (numeric) = 0.2922156659968616 absolute error = 4.274358644806853e-15 relative error = 1.462741099189672e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.982 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.85 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.839900000000018 y[1] (analytic) = 0.2954007279400566 y[1] (numeric) = 0.2954007279400612 absolute error = 4.6074255521944e-15 relative error = 1.559720446298071e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.971 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.84 Order of pole (three term test) = 7.2e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.829900000000019 y[1] (analytic) = 0.2986381494151166 y[1] (numeric) = 0.2986381494151216 absolute error = 4.996003610813204e-15 relative error = 1.672928800489116e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.83 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.961 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.83 Order of pole (three term test) = 3.057e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81990000000002 y[1] (analytic) = 0.3019290844002563 y[1] (numeric) = 0.3019290844002616 absolute error = 5.218048215738236e-15 relative error = 1.728236359244166e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.95 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.82 Order of pole (three term test) = 2.594e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.809900000000021 y[1] (analytic) = 0.3052747188411374 y[1] (numeric) = 0.3052747188411431 absolute error = 5.717648576819556e-15 relative error = 1.872951877091066e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.81 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.939 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.81 Order of pole (three term test) = 4.397e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.799900000000022 y[1] (analytic) = 0.3086762717194543 y[1] (numeric) = 0.3086762717194607 absolute error = 6.439293542825908e-15 relative error = 2.086099299747397e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.928 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 7.447e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.789900000000023 y[1] (analytic) = 0.3121349961634314 y[1] (numeric) = 0.3121349961634381 absolute error = 6.661338147750939e-15 relative error = 2.134120886676582e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.79 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.918 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.79 Order of pole (three term test) = 3.15e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.779900000000024 y[1] (analytic) = 0.3156521806021163 y[1] (numeric) = 0.3156521806021235 absolute error = 7.16093850883226e-15 relative error = 2.268616834888499e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.907 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.78 Order of pole (three term test) = 1.065e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.769900000000025 y[1] (analytic) = 0.319229149965453 y[1] (numeric) = 0.3192291499654604 absolute error = 7.438494264988549e-15 relative error = 2.330142553019843e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.896 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.77 Order of pole (three term test) = 4.498e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.759900000000026 y[1] (analytic) = 0.3228672669322241 y[1] (numeric) = 0.3228672669322319 absolute error = 7.771561172376096e-15 relative error = 2.407045237573585e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.76 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.886 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.76 Order of pole (three term test) = 3.795e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.749900000000028 y[1] (analytic) = 0.3265679332280552 y[1] (numeric) = 0.3265679332280632 absolute error = 7.938094626069869e-15 relative error = 2.430763653860156e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.75 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.875 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.75 Order of pole (three term test) = 3.198e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.739900000000029 y[1] (analytic) = 0.3303325909757896 y[1] (numeric) = 0.3303325909757981 absolute error = 8.493206138382448e-15 relative error = 2.571107535376345e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.74 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.864 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.74 Order of pole (three term test) = 5.386e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72990000000003 y[1] (analytic) = 0.3341627241006639 y[1] (numeric) = 0.3341627241006728 absolute error = 8.881784197001252e-15 relative error = 2.657921891469164e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.73 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.853 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.73 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.719900000000031 y[1] (analytic) = 0.3380598597928388 y[1] (numeric) = 0.3380598597928482 absolute error = 9.436895709313831e-15 relative error = 2.791486606867999e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.843 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.72 Order of pole (three term test) = 3.808e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.709900000000032 y[1] (analytic) = 0.3420255700299775 y[1] (numeric) = 0.3420255700299874 absolute error = 9.936496070395151e-15 relative error = 2.905190997715243e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.71 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.832 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.71 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.699900000000033 y[1] (analytic) = 0.3460614731627065 y[1] (numeric) = 0.3460614731627168 absolute error = 1.032507412901396e-14 relative error = 2.983595381089837e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.821 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.689900000000034 y[1] (analytic) = 0.3501692355659426 y[1] (numeric) = 0.3501692355659532 absolute error = 1.060262988517024e-14 relative error = 3.027858763216107e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.69 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.811 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.69 Order of pole (three term test) = 4.492e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.679900000000035 y[1] (analytic) = 0.3543505733592336 y[1] (numeric) = 0.3543505733592445 absolute error = 1.088018564132653e-14 relative error = 3.070458032050767e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.8 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.68 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.669900000000036 y[1] (analytic) = 0.3586072541994286 y[1] (numeric) = 0.35860725419944 absolute error = 1.13242748511766e-14 relative error = 3.157848793789024e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.67 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.789 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.67 Order of pole (three term test) = 3.143e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.659900000000037 y[1] (analytic) = 0.3629410991491731 y[1] (numeric) = 0.3629410991491852 absolute error = 1.215694211964546e-14 relative error = 3.349563372168226e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.66 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.778 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.66 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.649900000000039 y[1] (analytic) = 0.3673539846249181 y[1] (numeric) = 0.3673539846249306 absolute error = 1.249000902703301e-14 relative error = 3.399992799802013e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.768 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.65 Order of pole (three term test) = 4.379e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.63990000000004 y[1] (analytic) = 0.3718478444283335 y[1] (numeric) = 0.3718478444283466 absolute error = 1.315614284180811e-14 relative error = 3.538044670403811e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.757 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.64 Order of pole (three term test) = 7.297e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.629900000000041 y[1] (analytic) = 0.3764246718652307 y[1] (numeric) = 0.3764246718652444 absolute error = 1.376676550535194e-14 relative error = 3.657243144328431e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.63 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.746 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.63 Order of pole (three term test) = 6.074e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.619900000000042 y[1] (analytic) = 0.3810865219563317 y[1] (numeric) = 0.381086521956346 absolute error = 1.432187701766452e-14 relative error = 3.758169390022576e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.62 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.736 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.62 Order of pole (three term test) = 2.525e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.609900000000043 y[1] (analytic) = 0.3858355137444609 y[1] (numeric) = 0.3858355137444758 absolute error = 1.48769885299771e-14 relative error = 3.855785172701893e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.61 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.725 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.61 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.599900000000044 y[1] (analytic) = 0.3906738327029967 y[1] (numeric) = 0.3906738327030118 absolute error = 1.509903313490213e-14 relative error = 3.864869328573875e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.714 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 3.479e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.589900000000045 y[1] (analytic) = 0.395603733250694 y[1] (numeric) = 0.3956037332507097 absolute error = 1.570965579844597e-14 relative error = 3.971058531060615e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.59 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.703 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.59 Order of pole (three term test) = 2.882e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.579900000000046 y[1] (analytic) = 0.4006275413782813 y[1] (numeric) = 0.4006275413782977 absolute error = 1.637578961322106e-14 relative error = 4.087534660468757e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.58 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.693 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.58 Order of pole (three term test) = 2.385e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.569900000000047 y[1] (analytic) = 0.4057476573925451 y[1] (numeric) = 0.4057476573925622 absolute error = 1.709743457922741e-14 relative error = 4.213809807085665e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.57 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.682 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.57 Order of pole (three term test) = 3.943e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.559900000000048 y[1] (analytic) = 0.4109665587839467 y[1] (numeric) = 0.4109665587839644 absolute error = 1.770805724277125e-14 relative error = 4.308880336923161e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.56 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.671 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.56 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54990000000005 y[1] (analytic) = 0.4162868032241696 y[1] (numeric) = 0.4162868032241877 absolute error = 1.809663530139005e-14 relative error = 4.34715565356153e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.55 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.661 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.55 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.539900000000051 y[1] (analytic) = 0.4217110317003658 y[1] (numeric) = 0.4217110317003844 absolute error = 1.859623566247137e-14 relative error = 4.409710504249832e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.54 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.65 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.54 Order of pole (three term test) = 8.841e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.529900000000052 y[1] (analytic) = 0.4272419717932767 y[1] (numeric) = 0.4272419717932961 absolute error = 1.942890293094024e-14 relative error = 4.547517382103324e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.53 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.639 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.53 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.519900000000053 y[1] (analytic) = 0.4328824411068224 y[1] (numeric) = 0.4328824411068427 absolute error = 2.026157019940911e-14 relative error = 4.680617247399314e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.52 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.628 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.52 Order of pole (three term test) = 2.986e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.509900000000054 y[1] (analytic) = 0.4386353508572141 y[1] (numeric) = 0.438635350857235 absolute error = 2.09277040141842e-14 relative error = 4.771093796540957e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.51 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.618 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.51 Order of pole (three term test) = 2.45e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.499900000000055 y[1] (analytic) = 0.4445037096301238 y[1] (numeric) = 0.4445037096301453 absolute error = 2.159383782895929e-14 relative error = 4.857965717975167e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.5 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.607 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.5 Order of pole (three term test) = 4.014e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.489900000000056 y[1] (analytic) = 0.450490627314967 y[1] (numeric) = 0.450490627314989 absolute error = 2.19824158875781e-14 relative error = 4.879661097190548e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.49 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.596 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.49 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.479900000000057 y[1] (analytic) = 0.4565993192259041 y[1] (numeric) = 0.4565993192259269 absolute error = 2.281508315604697e-14 relative error = 4.996740510854578e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.48 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.586 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.48 Order of pole (three term test) = 5.367e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.469900000000058 y[1] (analytic) = 0.462833110419757 y[1] (numeric) = 0.4628331104197807 absolute error = 2.370326157574709e-14 relative error = 5.12134094171653e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.47 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.575 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.47 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.459900000000059 y[1] (analytic) = 0.4691954402216686 y[1] (numeric) = 0.4691954402216928 absolute error = 2.420286193682841e-14 relative error = 5.158375351089071e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.564 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.46 Order of pole (three term test) = 3.568e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.449900000000061 y[1] (analytic) = 0.4756898669700067 y[1] (numeric) = 0.4756898669700318 absolute error = 2.509104035652854e-14 relative error = 5.274663619881266e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.45 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.553 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.45 Order of pole (three term test) = 5.807e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.439900000000062 y[1] (analytic) = 0.4823200729927351 y[1] (numeric) = 0.4823200729927608 absolute error = 2.570166302007237e-14 relative error = 5.328756661649349e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.44 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.543 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.44 Order of pole (three term test) = 4.718e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.429900000000063 y[1] (analytic) = 0.489089869828248 y[1] (numeric) = 0.4890898698282744 absolute error = 2.636779683484747e-14 relative error = 5.391196682136752e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.43 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.532 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.43 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.419900000000064 y[1] (analytic) = 0.4960032037044882 y[1] (numeric) = 0.4960032037045156 absolute error = 2.736699755701011e-14 relative error = 5.517504192032394e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.42 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.521 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.42 Order of pole (three term test) = 3.101e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.409900000000065 y[1] (analytic) = 0.5030641612910569 y[1] (numeric) = 0.5030641612910853 absolute error = 2.842170943040401e-14 relative error = 5.649718588074914e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.41 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.511 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.41 Order of pole (three term test) = 5.017e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.399900000000066 y[1] (analytic) = 0.5102769757399709 y[1] (numeric) = 0.5102769757400001 absolute error = 2.919886554764162e-14 relative error = 5.722160108301829e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.4 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.4 Order of pole (three term test) = 4.053e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.389900000000067 y[1] (analytic) = 0.5176460330317405 y[1] (numeric) = 0.5176460330317704 absolute error = 2.986499936241671e-14 relative error = 5.769386309695815e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.39 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.489 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.39 Order of pole (three term test) = 3.268e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.379900000000068 y[1] (analytic) = 0.5251758786445327 y[1] (numeric) = 0.5251758786445634 absolute error = 3.064215547965432e-14 relative error = 5.834646396696863e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.38 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.478 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.38 Order of pole (three term test) = 5.264e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.369900000000069 y[1] (analytic) = 0.5328712245653564 y[1] (numeric) = 0.5328712245653878 absolute error = 3.141931159689193e-14 relative error = 5.8962297359028e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.37 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.468 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.37 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.35990000000007 y[1] (analytic) = 0.540736956663462 y[1] (numeric) = 0.5407369566634945 absolute error = 3.252953462151709e-14 relative error = 6.015777952784252e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.36 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.457 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.36 Order of pole (three term test) = 3.397e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.349900000000072 y[1] (analytic) = 0.5487781424475026 y[1] (numeric) = 0.5487781424475354 absolute error = 3.286260152890463e-14 relative error = 5.988321871264825e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.35 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.446 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.35 Order of pole (three term test) = 5.444e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.339900000000073 y[1] (analytic) = 0.5570000392294523 y[1] (numeric) = 0.5570000392294862 absolute error = 3.386180225106727e-14 relative error = 6.079317749763773e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.34 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.436 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.34 Order of pole (three term test) = 4.356e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.329900000000074 y[1] (analytic) = 0.5654081027198437 y[1] (numeric) = 0.5654081027198783 absolute error = 3.463895836830488e-14 relative error = 6.126363984116493e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.33 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.425 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.33 Order of pole (three term test) = 3.479e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.319900000000075 y[1] (analytic) = 0.5740079960805623 y[1] (numeric) = 0.5740079960805977 absolute error = 3.541611448554249e-14 relative error = 6.169968837955321e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.32 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.414 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.32 Order of pole (three term test) = 2.774e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.309900000000076 y[1] (analytic) = 0.5828055994632524 y[1] (numeric) = 0.5828055994632888 absolute error = 3.641531520770513e-14 relative error = 6.248278197951876e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.31 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.403 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.31 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.299900000000077 y[1] (analytic) = 0.59180702006333 y[1] (numeric) = 0.5918070200633677 absolute error = 3.774758283725532e-14 relative error = 6.37836010009072e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.3 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.393 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.3 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.289900000000078 y[1] (analytic) = 0.6010186027217084 y[1] (numeric) = 0.6010186027217476 absolute error = 3.919087276926803e-14 relative error = 6.520742052208108e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.29 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.382 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.29 Order of pole (three term test) = 2.784e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.279900000000079 y[1] (analytic) = 0.6104469411086002 y[1] (numeric) = 0.6104469411086406 absolute error = 4.04121180963557e-14 relative error = 6.620086919096589e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.28 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.371 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.28 Order of pole (three term test) = 8.816e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.26990000000008 y[1] (analytic) = 0.6200988895262101 y[1] (numeric) = 0.6200988895262514 absolute error = 4.130029651605582e-14 relative error = 6.660275838844275e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.27 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.361 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.27 Order of pole (three term test) = 6.967e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.259900000000082 y[1] (analytic) = 0.6299815753697707 y[1] (numeric) = 0.6299815753698135 absolute error = 4.274358644806853e-14 relative error = 6.784894688861333e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.26 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.35 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.26 Order of pole (three term test) = 8.244e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.249900000000083 y[1] (analytic) = 0.6401024122892263 y[1] (numeric) = 0.6401024122892697 absolute error = 4.340972026284362e-14 relative error = 6.781683591473361e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.25 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.339 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.25 Order of pole (three term test) = 4.327e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.239900000000084 y[1] (analytic) = 0.6504691140969496 y[1] (numeric) = 0.6504691140969949 absolute error = 4.529709940470639e-14 relative error = 6.963758681700458e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.24 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.328 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.24 Order of pole (three term test) = 3.401e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.229900000000085 y[1] (analytic) = 0.6610897094702192 y[1] (numeric) = 0.6610897094702655 absolute error = 4.629630012686903e-14 relative error = 7.00302840350816e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.23 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.318 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.23 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.219900000000086 y[1] (analytic) = 0.6719725575007819 y[1] (numeric) = 0.671972557500829 absolute error = 4.707345624410664e-14 relative error = 7.005264682114918e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.22 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.307 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.22 Order of pole (three term test) = 4.176e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.209900000000087 y[1] (analytic) = 0.6831263641477469 y[1] (numeric) = 0.6831263641477953 absolute error = 4.840572387365683e-14 relative error = 7.085910662231097e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.21 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.296 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.21 Order of pole (three term test) = 3.262e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.199900000000088 y[1] (analytic) = 0.6945601996542834 y[1] (numeric) = 0.6945601996543334 absolute error = 4.996003610813204e-14 relative error = 7.193046208665512e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.2 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.286 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.189900000000089 y[1] (analytic) = 0.706283516993192 y[1] (numeric) = 0.7062835169932431 absolute error = 5.10702591327572e-14 relative error = 7.230843974693731e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.19 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.275 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.19 Order of pole (three term test) = 7.914e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.17990000000009 y[1] (analytic) = 0.7183061714114035 y[1] (numeric) = 0.7183061714114563 absolute error = 5.273559366969494e-14 relative error = 7.341659555294436e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.18 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.264 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.18 Order of pole (three term test) = 3.072e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.169900000000091 y[1] (analytic) = 0.73063844114887 y[1] (numeric) = 0.7306384411489243 absolute error = 5.428990590417015e-14 relative error = 7.430474889714762e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.17 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.253 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.17 Order of pole (three term test) = 4.759e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.159900000000093 y[1] (analytic) = 0.7432910494131939 y[1] (numeric) = 0.7432910494132501 absolute error = 5.617728504603292e-14 relative error = 7.557912218959614e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.16 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.243 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.16 Order of pole (three term test) = 7.357e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.149900000000094 y[1] (analytic) = 0.7562751876977359 y[1] (numeric) = 0.7562751876977934 absolute error = 5.750955267558311e-14 relative error = 7.604315679145119e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.15 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.232 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.15 Order of pole (three term test) = 2.837e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.139900000000095 y[1] (analytic) = 0.769602540537897 y[1] (numeric) = 0.7696025405379561 absolute error = 5.906386491005833e-14 relative error = 7.674593286656371e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.14 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.221 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.14 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.129900000000096 y[1] (analytic) = 0.7832853118078517 y[1] (numeric) = 0.7832853118079123 absolute error = 6.061817714453355e-14 relative error = 7.738965129401512e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.13 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.211 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.13 Order of pole (three term test) = 6.704e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.119900000000097 y[1] (analytic) = 0.7973362526682575 y[1] (numeric) = 0.7973362526683198 absolute error = 6.228351168147128e-14 relative error = 7.811448616946956e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.12 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.2 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.12 Order of pole (three term test) = 5.135e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.109900000000098 y[1] (analytic) = 0.8117686912844749 y[1] (numeric) = 0.8117686912845388 absolute error = 6.38378239159465e-14 relative error = 7.864041148832048e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.11 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.189 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.11 Order of pole (three term test) = 3.923e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.099900000000099 y[1] (analytic) = 0.8265965644446545 y[1] (numeric) = 0.8265965644447203 absolute error = 6.583622536027178e-14 relative error = 7.964734937472622e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.178 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.1 Order of pole (three term test) = 5.981e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.0899000000001 y[1] (analytic) = 0.8418344512177738 y[1] (numeric) = 0.8418344512178412 absolute error = 6.7390537594747e-14 relative error = 8.005200725304336e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.09 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.168 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.09 Order of pole (three term test) = 9.095e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.079900000000101 y[1] (analytic) = 0.8574976088034446 y[1] (numeric) = 0.8574976088035143 absolute error = 6.972200594645983e-14 relative error = 8.130868847990162e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.08 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.157 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.08 Order of pole (three term test) = 1.035e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.069900000000102 y[1] (analytic) = 0.8736020107381312 y[1] (numeric) = 0.8736020107382028 absolute error = 7.16093850883226e-14 relative error = 8.197026129532119e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.07 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.146 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.07 Order of pole (three term test) = 5.218e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.059900000000104 y[1] (analytic) = 0.8901643876364718 y[1] (numeric) = 0.890164387636545 absolute error = 7.327471962526033e-14 relative error = 8.231594146314524e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.06 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.136 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.06 Order of pole (three term test) = 3.937e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.049900000000105 y[1] (analytic) = 0.9072022706617842 y[1] (numeric) = 0.9072022706618595 absolute error = 7.538414337204813e-14 relative error = 8.309518815143292e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.05 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.125 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.05 Order of pole (three term test) = 2.962e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.039900000000106 y[1] (analytic) = 0.9247340379367115 y[1] (numeric) = 0.9247340379367884 absolute error = 7.693845560652335e-14 relative error = 8.320063115465097e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.04 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.114 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.04 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.029900000000107 y[1] (analytic) = 0.9427789641234917 y[1] (numeric) = 0.9427789641235703 absolute error = 7.860379014346108e-14 relative error = 8.337456936848351e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.03 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.103 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.03 Order of pole (three term test) = 3.327e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.019900000000108 y[1] (analytic) = 0.9613572734236775 y[1] (numeric) = 0.9613572734237578 absolute error = 8.026912468039882e-14 relative error = 8.349562321876105e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.02 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.093 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.02 Order of pole (three term test) = 4.966e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.009900000000109 y[1] (analytic) = 0.9804901962695114 y[1] (numeric) = 0.9804901962695942 absolute error = 8.282263763703668e-14 relative error = 8.447064330898305e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 1.01 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.082 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.01 Order of pole (three term test) = 3.695e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9999000000001101 y[1] (analytic) = 1.00020003000378 y[1] (numeric) = 1.000200030003865 absolute error = 8.526512829121202e-14 relative error = 8.524807611822385e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9999 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.071 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9999 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9899000000001112 y[1] (analytic) = 1.020510203872095 y[1] (numeric) = 1.020510203872183 absolute error = 8.815170815523743e-14 relative error = 8.638003600626996e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9899 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.061 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9899 Order of pole (three term test) = 8.11e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9799000000001123 y[1] (analytic) = 1.041445348681444 y[1] (numeric) = 1.041445348681535 absolute error = 9.081624341433781e-14 relative error = 8.720212109960324e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9799 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.05 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9799 Order of pole (three term test) = 2.99e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9699000000001134 y[1] (analytic) = 1.063031371511878 y[1] (numeric) = 1.063031371511972 absolute error = 9.481304630298837e-14 relative error = 8.919120248365032e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9699 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.039 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9699 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9599000000001146 y[1] (analytic) = 1.085295535904622 y[1] (numeric) = 1.085295535904719 absolute error = 9.636735853746359e-14 relative error = 8.879365605898202e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9599 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.028 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9599 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9499000000001157 y[1] (analytic) = 1.108266547990259 y[1] (numeric) = 1.108266547990359 absolute error = 9.925393840148899e-14 relative error = 8.955782215160874e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9499 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.018 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9499 Order of pole (three term test) = 2.353e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9399000000001168 y[1] (analytic) = 1.131974649065221 y[1] (numeric) = 1.131974649065323 absolute error = 1.014743844507393e-13 relative error = 8.964368993116262e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9399 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 1.007 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9399 Order of pole (three term test) = 3.426e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9299000000001179 y[1] (analytic) = 1.1564517151743 y[1] (numeric) = 1.156451715174404 absolute error = 1.039168751049147e-13 relative error = 8.98583777786627e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9299 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.9963 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9299 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.919900000000119 y[1] (analytic) = 1.181731364311745 y[1] (numeric) = 1.181731364311852 absolute error = 1.072475441787901e-13 relative error = 9.075458891729798e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9199 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.9856 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9199 Order of pole (three term test) = 7.188e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9099000000001201 y[1] (analytic) = 1.207849071914423 y[1] (numeric) = 1.207849071914534 absolute error = 1.103561686477406e-13 relative error = 9.136585953808586e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.9099 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.9749 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.9099 Order of pole (three term test) = 5.178e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8999000000001212 y[1] (analytic) = 1.234842295388244 y[1] (numeric) = 1.234842295388358 absolute error = 1.13464793116691e-13 relative error = 9.188605989643137e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8999 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.9642 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8999 Order of pole (three term test) = 3.717e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8899000000001223 y[1] (analytic) = 1.262750608484446 y[1] (numeric) = 1.262750608484562 absolute error = 1.165734175856414e-13 relative error = 9.231705516701587e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8899 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.9535 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8899 Order of pole (three term test) = 5.317e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8799000000001234 y[1] (analytic) = 1.291615846426307 y[1] (numeric) = 1.291615846426427 absolute error = 1.199040866595169e-13 relative error = 9.283262278894472e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8799 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.9428 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8799 Order of pole (three term test) = 3.788e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8699000000001245 y[1] (analytic) = 1.321482262780572 y[1] (numeric) = 1.321482262780697 absolute error = 1.245670233629426e-13 relative error = 9.426310656704329e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8699 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.932 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8699 Order of pole (three term test) = 5.377e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8599000000001256 y[1] (analytic) = 1.352396699172524 y[1] (numeric) = 1.352396699172652 absolute error = 1.285638262515931e-13 relative error = 9.506369420322903e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8599 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.9213 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8599 Order of pole (three term test) = 3.801e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8499000000001267 y[1] (analytic) = 1.384408769060699 y[1] (numeric) = 1.38440876906083 absolute error = 1.316724507205436e-13 relative error = 9.511096264572308e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8499 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.9106 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8499 Order of pole (three term test) = 5.352e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8399000000001278 y[1] (analytic) = 1.417571056918293 y[1] (numeric) = 1.41757105691843 absolute error = 1.374456104485944e-13 relative error = 9.695853324445843e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8399 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.8999 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8399 Order of pole (three term test) = 7.505e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8299000000001289 y[1] (analytic) = 1.451939334315274 y[1] (numeric) = 1.451939334315416 absolute error = 1.4166445794217e-13 relative error = 9.756913019301738e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8299 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.8892 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8299 Order of pole (three term test) = 5.239e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.81990000000013 y[1] (analytic) = 1.487572794560177 y[1] (numeric) = 1.487572794560323 absolute error = 1.465494392505207e-13 relative error = 9.851581030953863e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8199 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.8785 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8199 Order of pole (three term test) = 7.284e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8099000000001311 y[1] (analytic) = 1.524534307746057 y[1] (numeric) = 1.524534307746208 absolute error = 1.507682867440963e-13 relative error = 9.889464997806389e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.8099 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.8678 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.8099 Order of pole (three term test) = 5.041e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7999000000001322 y[1] (analytic) = 1.56289069825388 y[1] (numeric) = 1.562890698254035 absolute error = 1.552091788425969e-13 relative error = 9.93090425427718e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7999 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.857 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7999 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7899000000001333 y[1] (analytic) = 1.602713047002016 y[1] (numeric) = 1.602713047002176 absolute error = 1.592059817312474e-13 relative error = 9.933530024545133e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7899 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.8463 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7899 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7799000000001344 y[1] (analytic) = 1.644077020996319 y[1] (numeric) = 1.644077020996483 absolute error = 1.63424829224823e-13 relative error = 9.940217346130581e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7799 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.8356 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7799 Order of pole (three term test) = 6.498e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7699000000001355 y[1] (analytic) = 1.687063233035762 y[1] (numeric) = 1.687063233035929 absolute error = 1.669775429036235e-13 relative error = 9.89752723157615e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7699 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.8249 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7699 Order of pole (three term test) = 4.412e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7599000000001366 y[1] (analytic) = 1.731757634768956 y[1] (numeric) = 1.731757634769127 absolute error = 1.707523011873491e-13 relative error = 9.86005765235908e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7599 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.8142 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7599 Order of pole (three term test) = 5.961e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7499000000001377 y[1] (analytic) = 1.778251946682872 y[1] (numeric) = 1.778251946683049 absolute error = 1.767475055203249e-13 relative error = 9.939396149686628e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7499 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.8035 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7499 Order of pole (three term test) = 4.006e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7399000000001388 y[1] (analytic) = 1.826644129043612 y[1] (numeric) = 1.826644129043794 absolute error = 1.811883976188255e-13 relative error = 9.919195246514245e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7399 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.7928 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7399 Order of pole (three term test) = 2.678e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7299000000001399 y[1] (analytic) = 1.877038898308089 y[1] (numeric) = 1.877038898308277 absolute error = 1.880717803715015e-13 relative error = 1.001959951607951e-11 % Correct digits = 13 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7299 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.782 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7299 Order of pole (three term test) = 7.122e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.719900000000141 y[1] (analytic) = 1.92954829409428 y[1] (numeric) = 1.929548294094473 absolute error = 1.925126724700021e-13 relative error = 9.977084950877924e-12 % Correct digits = 14 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7199 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.7713 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7199 Order of pole (three term test) = 2.354e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7099000000001421 y[1] (analytic) = 1.984292302447181 y[1] (numeric) = 1.98429230244738 absolute error = 1.989519660128281e-13 relative error = 1.002634368774526e-11 % Correct digits = 13 h = 0.0001 Radius of convergence (given) for eq 1 = 0.7099 Order of pole (given) = 2 Radius of convergence (ratio test) for eq 1 = 0.7606 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 0.7099 Order of pole (three term test) = 6.189e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations = 13001 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 29 Minutes 59.0 Seconds Percent Done = 100 %