##############ECHO OF PROBLEM################# ##############temp/sing4postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-2.0; x_end=-1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.05; glob_type_given_pole=2; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=1.0; array_given_ord_poles[1][1]=1.0; 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=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(1.0 / (x * x + 1.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1000000 step_error = 2.5e-15 est_needed_step_err = 2.5e-15 opt_iter = 1 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1000000 step_error = 2.5e-15 est_needed_step_err = 2.5e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.163371676992207e-229 estimated_step_error = 1.163371676992207e-229 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 500000 step_error = 3.535533905932737e-15 est_needed_step_err = 3.535533905932737e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.99463098764576e-219 estimated_step_error = 7.99463098764576e-219 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 250000 step_error = 5e-15 est_needed_step_err = 5e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.493870915958275e-208 estimated_step_error = 5.493870915958275e-208 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 125000 step_error = 7.071067811865475e-15 est_needed_step_err = 7.071067811865475e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.775362554202742e-197 estimated_step_error = 3.775362554202742e-197 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 62500 step_error = 1e-14 est_needed_step_err = 1e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.594413801466996e-186 estimated_step_error = 2.594413801466996e-186 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 31250 step_error = 1.414213562373095e-14 est_needed_step_err = 1.414213562373095e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.782873648898369e-175 estimated_step_error = 1.782873648898369e-175 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 15625 step_error = 2e-14 est_needed_step_err = 2e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.225189771478359e-164 estimated_step_error = 1.225189771478359e-164 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 7812.5 step_error = 2.82842712474619e-14 est_needed_step_err = 2.82842712474619e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.4195544757987e-154 estimated_step_error = 8.4195544757987e-154 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 3906.25 step_error = 4e-14 est_needed_step_err = 4e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.786031118819402e-143 estimated_step_error = 5.786031118819402e-143 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1953.125 step_error = 5.65685424949238e-14 est_needed_step_err = 5.65685424949238e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.976346568135108e-132 estimated_step_error = 3.976346568135108e-132 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 976.5625 step_error = 8e-14 est_needed_step_err = 8e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.732821817210943e-121 estimated_step_error = 2.732821817210943e-121 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 488.28125 step_error = 1.131370849898476e-13 est_needed_step_err = 1.131370849898476e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.878389510546474e-110 estimated_step_error = 1.878389510546474e-110 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 244.140625 step_error = 1.6e-13 est_needed_step_err = 1.6e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.291381381612364e-99 estimated_step_error = 1.291381381612364e-99 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 min_size = 0.2 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 122.0703125 step_error = 2.262741699796952e-13 est_needed_step_err = 2.262741699796952e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.882036325997041e-89 estimated_step_error = 8.882036325997041e-89 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.365 Order of pole (six term test) = 1 START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (analytic) = 0.2 y[1] (numeric) = 0.2 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.236 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (analytic) = 0.2016088385314812 y[1] (numeric) = 0.2016088385314812 absolute error = 2.775557561562891e-17 relative error = 1.37670430611081e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.227 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.227 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (analytic) = 0.2032355093081863 y[1] (numeric) = 0.2032355093081863 absolute error = 2.775557561562891e-17 relative error = 1.365685342591405e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.218 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.218 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (analytic) = 0.204880247495339 y[1] (numeric) = 0.204880247495339 absolute error = 5.551115123125783e-17 relative error = 2.709443780446463e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.209 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.209 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (analytic) = 0.2065432914738929 y[1] (numeric) = 0.206543291473893 absolute error = 2.775557561562891e-17 relative error = 1.343813949006289e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.2 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (analytic) = 0.2082248828735034 y[1] (numeric) = 0.2082248828735034 absolute error = 5.551115123125783e-17 relative error = 2.665923037881157e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.191 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (analytic) = 0.2099252666050886 y[1] (numeric) = 0.2099252666050886 absolute error = 5.551115123125783e-17 relative error = 2.644329200052198e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.183 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.183 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (analytic) = 0.2116446908929289 y[1] (numeric) = 0.211644690892929 absolute error = 5.551115123125783e-17 relative error = 2.622846384525701e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.174 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.174 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.92 y[1] (analytic) = 0.2133834073062479 y[1] (numeric) = 0.2133834073062479 absolute error = 5.551115123125783e-17 relative error = 2.601474591301667e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.165 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.165 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (analytic) = 0.2151416707902154 y[1] (numeric) = 0.2151416707902154 absolute error = 2.775557561562891e-17 relative error = 1.290106910190047e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.156 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.156 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = 0.2169197396963124 y[1] (numeric) = 0.2169197396963124 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.147 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (analytic) = 0.2187178758119901 y[1] (numeric) = 0.2187178758119901 absolute error = 2.775557561562891e-17 relative error = 1.269012672722169e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.138 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.138 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (analytic) = 0.2205363443895554 y[1] (numeric) = 0.2205363443895554 absolute error = 2.775557561562891e-17 relative error = 1.258548820715077e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.129 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.129 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (analytic) = 0.2223754141742089 y[1] (numeric) = 0.2223754141742089 absolute error = 5.551115123125783e-17 relative error = 2.496280959718433e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.121 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.121 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.86 y[1] (analytic) = 0.2242353574311597 y[1] (numeric) = 0.2242353574311598 absolute error = 5.551115123125783e-17 relative error = 2.475575300309174e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.112 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.112 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (analytic) = 0.2261164499717355 y[1] (numeric) = 0.2261164499717355 absolute error = 2.775557561562891e-17 relative error = 1.227490331601189e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.103 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (analytic) = 0.2280189711784021 y[1] (numeric) = 0.2280189711784021 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.094 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (analytic) = 0.229943204028605 y[1] (numeric) = 0.229943204028605 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.085 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.085 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (analytic) = 0.2318894351173361 y[1] (numeric) = 0.2318894351173361 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.077 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (analytic) = 0.2338579546783284 y[1] (numeric) = 0.2338579546783284 absolute error = 2.775557561562891e-17 relative error = 1.186856168899908e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.068 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = 0.2358490566037736 y[1] (numeric) = 0.2358490566037736 absolute error = 2.775557561562891e-17 relative error = 1.176836406102666e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.059 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (analytic) = 0.2378630384624534 y[1] (numeric) = 0.2378630384624534 absolute error = 2.775557561562891e-17 relative error = 1.166872154456655e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.05 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (analytic) = 0.2399002015161693 y[1] (numeric) = 0.2399002015161693 absolute error = 2.775557561562891e-17 relative error = 1.156963413961875e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.042 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.042 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (analytic) = 0.2419608507343512 y[1] (numeric) = 0.2419608507343513 absolute error = 2.775557561562891e-17 relative error = 1.147110184618327e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.033 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.033 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (analytic) = 0.2440452948067161 y[1] (numeric) = 0.2440452948067162 absolute error = 5.551115123125783e-17 relative error = 2.274624932852021e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.024 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.024 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (analytic) = 0.2461538461538462 y[1] (numeric) = 0.2461538461538462 absolute error = 2.775557561562891e-17 relative error = 1.127570259384924e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.016 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.016 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (analytic) = 0.2482868209355448 y[1] (numeric) = 0.2482868209355448 absolute error = 2.775557561562891e-17 relative error = 1.11788356349507e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2.007 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.007 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (analytic) = 0.2504445390568259 y[1] (numeric) = 0.2504445390568259 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.998 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.998 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (analytic) = 0.2526273241713825 y[1] (numeric) = 0.2526273241713824 absolute error = 5.551115123125783e-17 relative error = 2.197353410338109e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.99 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (analytic) = 0.2548355036823731 y[1] (numeric) = 0.2548355036823731 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.981 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.981 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = 0.2570694087403599 y[1] (numeric) = 0.2570694087403599 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.972 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (analytic) = 0.25932937423822 y[1] (numeric) = 0.25932937423822 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.964 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.964 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (analytic) = 0.2616157388028464 y[1] (numeric) = 0.2616157388028464 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.955 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.955 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (analytic) = 0.2639288447834465 y[1] (numeric) = 0.2639288447834465 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.947 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.947 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (analytic) = 0.266269038236234 y[1] (numeric) = 0.266269038236234 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.938 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.938 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (analytic) = 0.2686366689053057 y[1] (numeric) = 0.2686366689053057 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.929 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.929 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (analytic) = 0.2710320901994797 y[1] (numeric) = 0.2710320901994797 absolute error = 5.551115123125783e-17 relative error = 2.048139435828488e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.921 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.921 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (analytic) = 0.2734556591648665 y[1] (numeric) = 0.2734556591648665 absolute error = 5.551115123125783e-17 relative error = 2.029987289375867e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.912 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.912 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (analytic) = 0.2759077364529303 y[1] (numeric) = 0.2759077364529303 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.904 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.904 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (analytic) = 0.2783886862837895 y[1] (numeric) = 0.2783886862837895 absolute error = 5.551115123125783e-17 relative error = 1.994016063378012e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.895 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.895 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = 0.2808988764044945 y[1] (numeric) = 0.2808988764044945 absolute error = 5.551115123125783e-17 relative error = 1.976196983832778e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.887 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (analytic) = 0.2834386780420057 y[1] (numeric) = 0.2834386780420057 absolute error = 5.551115123125783e-17 relative error = 1.958488926590007e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.878 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.878 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (analytic) = 0.2860084658505893 y[1] (numeric) = 0.2860084658505893 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.87 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (analytic) = 0.2886086178533292 y[1] (numeric) = 0.2886086178533293 absolute error = 5.551115123125783e-17 relative error = 1.923405879011852e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.861 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.861 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.56 y[1] (analytic) = 0.2912395153774465 y[1] (numeric) = 0.2912395153774466 absolute error = 5.551115123125783e-17 relative error = 1.906030888676468e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.853 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.853 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (analytic) = 0.2939015429831007 y[1] (numeric) = 0.2939015429831008 absolute error = 1.110223024625157e-16 relative error = 3.777533841287094e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.845 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = 0.2965950883853364 y[1] (numeric) = 0.2965950883853365 absolute error = 5.551115123125783e-17 relative error = 1.871613974913088e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.836 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = 0.2993205423688229 y[1] (numeric) = 0.2993205423688229 absolute error = 5.551115123125783e-17 relative error = 1.854572051485092e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.828 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.828 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = 0.3020782986950219 y[1] (numeric) = 0.3020782986950219 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.819 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.819 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = 0.3048687540014025 y[1] (numeric) = 0.3048687540014026 absolute error = 5.551115123125783e-17 relative error = 1.820821271536487e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.811 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.811 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (analytic) = 0.3076923076923078 y[1] (numeric) = 0.3076923076923079 absolute error = 5.551115123125783e-17 relative error = 1.804112415015879e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.803 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.803 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.49 y[1] (analytic) = 0.3105493618210616 y[1] (numeric) = 0.3105493618210616 absolute error = 5.551115123125783e-17 relative error = 1.787514580797733e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.794 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.794 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.48 y[1] (analytic) = 0.3134403209628888 y[1] (numeric) = 0.3134403209628888 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.786 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.786 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.47 y[1] (analytic) = 0.3163655920782057 y[1] (numeric) = 0.3163655920782057 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.778 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.778 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.46 y[1] (analytic) = 0.3193255843658195 y[1] (numeric) = 0.3193255843658196 absolute error = 5.551115123125783e-17 relative error = 1.738387211958069e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.77 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.45 y[1] (analytic) = 0.3223207091055602 y[1] (numeric) = 0.3223207091055602 absolute error = 5.551115123125783e-17 relative error = 1.722233466949773e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.761 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.761 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.44 y[1] (analytic) = 0.3253513794898492 y[1] (numeric) = 0.3253513794898492 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.753 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.753 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.429999999999999 y[1] (analytic) = 0.3284180104436929 y[1] (numeric) = 0.3284180104436929 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.745 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.745 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.419999999999999 y[1] (analytic) = 0.3315210184325688 y[1] (numeric) = 0.3315210184325688 absolute error = 5.551115123125783e-17 relative error = 1.67443836573966e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.737 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.737 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.409999999999999 y[1] (analytic) = 0.3346608212576556 y[1] (numeric) = 0.3346608212576556 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.729 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.729 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.399999999999999 y[1] (analytic) = 0.3378378378378381 y[1] (numeric) = 0.3378378378378381 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.72 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.389999999999999 y[1] (analytic) = 0.3410524879779 y[1] (numeric) = 0.3410524879779 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.712 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.712 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.379999999999999 y[1] (analytic) = 0.3443051921222974 y[1] (numeric) = 0.3443051921222974 absolute error = 5.551115123125783e-17 relative error = 1.612265876360651e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.704 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.704 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.369999999999999 y[1] (analytic) = 0.347596371093886 y[1] (numeric) = 0.347596371093886 absolute error = 5.551115123125783e-17 relative error = 1.597000309772055e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.696 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.696 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.359999999999999 y[1] (analytic) = 0.350926445816957 y[1] (numeric) = 0.350926445816957 absolute error = 5.551115123125783e-17 relative error = 1.581845765485922e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.688 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.688 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.349999999999999 y[1] (analytic) = 0.3542958370239151 y[1] (numeric) = 0.3542958370239153 absolute error = 1.110223024625157e-16 relative error = 3.133604487004502e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.68 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.339999999999999 y[1] (analytic) = 0.3577049649449136 y[1] (numeric) = 0.3577049649449137 absolute error = 1.110223024625157e-16 relative error = 3.103739487642086e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.672 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.672 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.329999999999999 y[1] (analytic) = 0.3611542489797394 y[1] (numeric) = 0.3611542489797395 absolute error = 1.110223024625157e-16 relative error = 3.074096532884595e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.664 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.664 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.319999999999999 y[1] (analytic) = 0.3646441073512254 y[1] (numeric) = 0.3646441073512255 absolute error = 5.551115123125783e-17 relative error = 1.522337811366014e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.656 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.656 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.309999999999999 y[1] (analytic) = 0.3681749567394428 y[1] (numeric) = 0.3681749567394429 absolute error = 5.551115123125783e-17 relative error = 1.507738378592193e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.648 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.648 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.299999999999999 y[1] (analytic) = 0.371747211895911 y[1] (numeric) = 0.3717472118959111 absolute error = 1.110223024625157e-16 relative error = 2.986499936241669e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.64 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.289999999999999 y[1] (analytic) = 0.3753612852370409 y[1] (numeric) = 0.375361285237041 absolute error = 1.110223024625157e-16 relative error = 2.957745159903878e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.632 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.632 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.279999999999999 y[1] (analytic) = 0.37901758641601 y[1] (numeric) = 0.37901758641601 absolute error = 5.551115123125783e-17 relative error = 1.464606214085505e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.624 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.624 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.269999999999999 y[1] (analytic) = 0.3827165218722495 y[1] (numeric) = 0.3827165218722495 absolute error = 5.551115123125783e-17 relative error = 1.450450870521535e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.616 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.616 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.259999999999999 y[1] (analytic) = 0.3864584943577062 y[1] (numeric) = 0.3864584943577063 absolute error = 5.551115123125783e-17 relative error = 1.436406549260027e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.609 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.609 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.249999999999999 y[1] (analytic) = 0.3902439024390247 y[1] (numeric) = 0.3902439024390247 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.601 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.601 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.239999999999999 y[1] (analytic) = 0.3940731399747796 y[1] (numeric) = 0.3940731399747796 absolute error = 5.551115123125783e-17 relative error = 1.408650973644398e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.593 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.593 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.229999999999999 y[1] (analytic) = 0.3979465955668752 y[1] (numeric) = 0.3979465955668752 absolute error = 5.551115123125783e-17 relative error = 1.394939719290277e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.585 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.585 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.219999999999999 y[1] (analytic) = 0.4018646519852116 y[1] (numeric) = 0.4018646519852117 absolute error = 1.110223024625157e-16 relative error = 2.762678974477238e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.577 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.577 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.209999999999999 y[1] (analytic) = 0.4058276855647095 y[1] (numeric) = 0.4058276855647096 absolute error = 5.551115123125783e-17 relative error = 1.367850277489423e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.57 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.57 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.199999999999999 y[1] (analytic) = 0.4098360655737707 y[1] (numeric) = 0.4098360655737708 absolute error = 1.110223024625157e-16 relative error = 2.70894418008538e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.562 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.562 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.189999999999999 y[1] (analytic) = 0.4138901535532473 y[1] (numeric) = 0.4138901535532473 absolute error = 5.551115123125783e-17 relative error = 1.341204924898419e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.554 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.554 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.179999999999999 y[1] (analytic) = 0.4179903026249794 y[1] (numeric) = 0.4179903026249794 absolute error = 5.551115123125783e-17 relative error = 1.328048782056611e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.547 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.547 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.169999999999999 y[1] (analytic) = 0.4221368567689648 y[1] (numeric) = 0.4221368567689648 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.539 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.539 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.159999999999999 y[1] (analytic) = 0.4263301500682131 y[1] (numeric) = 0.4263301500682132 absolute error = 5.551115123125783e-17 relative error = 1.302069563280383e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.532 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.532 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.149999999999999 y[1] (analytic) = 0.4305705059203448 y[1] (numeric) = 0.4305705059203448 absolute error = 5.551115123125783e-17 relative error = 1.289246487345962e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.524 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.524 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.139999999999999 y[1] (analytic) = 0.4348582362149943 y[1] (numeric) = 0.4348582362149943 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.516 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.516 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.129999999999999 y[1] (analytic) = 0.4391936404760863 y[1] (numeric) = 0.4391936404760863 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.509 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.509 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.119999999999999 y[1] (analytic) = 0.4435770049680628 y[1] (numeric) = 0.4435770049680628 absolute error = 5.551115123125783e-17 relative error = 1.251443393357475e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.501 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.501 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.109999999999999 y[1] (analytic) = 0.4480086017651543 y[1] (numeric) = 0.4480086017651543 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.494 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.494 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.099999999999999 y[1] (analytic) = 0.4524886877828058 y[1] (numeric) = 0.4524886877828058 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.487 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.487 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.089999999999999 y[1] (analytic) = 0.4570175037703948 y[1] (numeric) = 0.4570175037703948 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.479 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.479 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.079999999999999 y[1] (analytic) = 0.4615952732644021 y[1] (numeric) = 0.4615952732644021 absolute error = 5.551115123125783e-17 relative error = 1.202593580273969e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.472 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.472 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.069999999999999 y[1] (analytic) = 0.4662222015012359 y[1] (numeric) = 0.4662222015012358 absolute error = 1.110223024625157e-16 relative error = 2.381317365518496e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.465 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.465 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.059999999999999 y[1] (analytic) = 0.4708984742889438 y[1] (numeric) = 0.4708984742889437 absolute error = 1.110223024625157e-16 relative error = 2.35766961509398e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.457 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.049999999999999 y[1] (analytic) = 0.4756242568370991 y[1] (numeric) = 0.4756242568370991 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.45 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.039999999999999 y[1] (analytic) = 0.4803996925441972 y[1] (numeric) = 0.4803996925441972 absolute error = 5.551115123125783e-17 relative error = 1.155520124029862e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.443 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.443 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.029999999999999 y[1] (analytic) = 0.4852249017419578 y[1] (numeric) = 0.4852249017419578 absolute error = 5.551115123125783e-17 relative error = 1.144029315724992e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.436 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.436 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.019999999999999 y[1] (analytic) = 0.4900999803960012 y[1] (numeric) = 0.4900999803960012 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.428 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.428 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.009999999999999 y[1] (analytic) = 0.4950249987624379 y[1] (numeric) = 0.4950249987624379 absolute error = 5.551115123125783e-17 relative error = 1.121380766022639e-14 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.421 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.421 Order of pole (six term test) = 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; Iterations = 100 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 101 %