##############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_type_given_pole=1; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=2.0; 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); } /* 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 = 4.385290096535146e-15 est_needed_step_err = 4.385290096535146e-15 opt_iter = 1 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 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 = 4.385290096535146e-15 est_needed_step_err = 4.385290096535146e-15 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 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 650000 step_error = 6.201736729460423e-15 est_needed_step_err = 6.201736729460423e-15 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 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 325000 step_error = 8.770580193070292e-15 est_needed_step_err = 8.770580193070292e-15 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 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 162500 step_error = 1.240347345892085e-14 est_needed_step_err = 1.240347345892085e-14 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 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 81250 step_error = 1.754116038614058e-14 est_needed_step_err = 1.754116038614058e-14 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 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 40625 step_error = 2.480694691784169e-14 est_needed_step_err = 2.480694691784169e-14 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 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 20312.5 step_error = 3.508232077228117e-14 est_needed_step_err = 3.508232077228117e-14 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 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 10156.25 step_error = 4.961389383568339e-14 est_needed_step_err = 4.961389383568339e-14 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 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 5078.125 step_error = 7.016464154456234e-14 est_needed_step_err = 7.016464154456234e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.434035767329203e-63 estimated_step_error = 2.434035767329203e-63 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 2539.0625 step_error = 9.922778767136677e-14 est_needed_step_err = 9.922778767136677e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.595265777628918e-58 estimated_step_error = 1.595265777628918e-58 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 1269.53125 step_error = 1.403292830891247e-13 est_needed_step_err = 1.403292830891247e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.045599359331682e-53 estimated_step_error = 1.045599359331682e-53 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 634.765625 step_error = 1.984555753427335e-13 est_needed_step_err = 1.984555753427335e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.854091796399115e-49 estimated_step_error = 6.854091796399115e-49 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 317.3828125 step_error = 2.806585661782493e-13 est_needed_step_err = 2.806585661782493e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.494064264907686e-44 estimated_step_error = 4.494064264907686e-44 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.25 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 158.69140625 step_error = 3.969111506854671e-13 est_needed_step_err = 3.969111506854671e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.948073975815616e-39 estimated_step_error = 2.948073975815616e-39 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.221 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 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 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 6.584e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.99 y[1] (analytic) = 0.252518875785965 y[1] (numeric) = 0.2525188757859571 absolute error = 7.882583474838611e-15 relative error = 3.121581881870839e-12 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.99 Order of pole (three term test) = 2.832e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.98 y[1] (analytic) = 0.2550760126517703 y[1] (numeric) = 0.2550760126517541 absolute error = 1.615374500829603e-14 relative error = 6.332914193052374e-12 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 1.98 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.98 Order of pole (three term test) = 9.74e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.97 y[1] (analytic) = 0.2576721894405937 y[1] (numeric) = 0.257672189440569 absolute error = 2.464695114667848e-14 relative error = 9.565235270514449e-12 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 14 h = 0.01 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.97 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.96 y[1] (analytic) = 0.2603082049146189 y[1] (numeric) = 0.2603082049145853 absolute error = 3.358424649491099e-14 relative error = 1.2901724133485e-11 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.96 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.96 Order of pole (three term test) = 3.591e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (analytic) = 0.2629848783694938 y[1] (numeric) = 0.2629848783694509 absolute error = 4.29101199017623e-14 relative error = 1.631657309264511e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.95 Order of pole (three term test) = 3.08e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.94 y[1] (analytic) = 0.2657030502710171 y[1] (numeric) = 0.2657030502709646 absolute error = 5.256906021600116e-14 relative error = 1.978489150289419e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.94 Order of pole (three term test) = 2.64e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.93 y[1] (analytic) = 0.2684635829149776 y[1] (numeric) = 0.268463582914915 absolute error = 6.261657858885883e-14 relative error = 2.332404935856402e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.93 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.93 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.92 y[1] (analytic) = 0.2712673611111112 y[1] (numeric) = 0.2712673611110381 absolute error = 7.310818617156656e-14 relative error = 2.695060175028629e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.92 Order of pole (three term test) = 7.739e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.91 y[1] (analytic) = 0.2741152928921904 y[1] (numeric) = 0.2741152928921065 absolute error = 8.398837181289309e-14 relative error = 3.063979792106153e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.91 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.91 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (analytic) = 0.2770083102493075 y[1] (numeric) = 0.2770083102492121 absolute error = 9.54236689665322e-14 relative error = 3.444794449691813e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 2.826e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.89 y[1] (analytic) = 0.2799473698944599 y[1] (numeric) = 0.2799473698943525 absolute error = 1.073585664812526e-13 relative error = 3.834955353276825e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.89 Order of pole (three term test) = 7.237e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.88 y[1] (analytic) = 0.2829334540516071 y[1] (numeric) = 0.2829334540514873 absolute error = 1.197375532058231e-13 relative error = 4.232004080506613e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.88 Order of pole (three term test) = 4.115e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.87 y[1] (analytic) = 0.2859675712774172 y[1] (numeric) = 0.2859675712772845 absolute error = 1.326716514427062e-13 relative error = 4.639394979299993e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.87 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.86 y[1] (analytic) = 0.2890507573129842 y[1] (numeric) = 0.289050757312838 absolute error = 1.462163723431331e-13 relative error = 5.058501617583032e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.86 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (analytic) = 0.2921840759678598 y[1] (numeric) = 0.2921840759676995 absolute error = 1.602606936046413e-13 relative error = 5.484922238618849e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.85 Order of pole (three term test) = 5.079e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.84 y[1] (analytic) = 0.2953686200378072 y[1] (numeric) = 0.2953686200376322 absolute error = 1.750266598321559e-13 relative error = 5.925702595277471e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.84 Order of pole (three term test) = 4.317e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.83 y[1] (analytic) = 0.2986055122577563 y[1] (numeric) = 0.2986055122575659 absolute error = 1.904032487232143e-13 relative error = 6.376414396491724e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.83 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.83 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.82 y[1] (analytic) = 0.3018959062915108 y[1] (numeric) = 0.3018959062913043 absolute error = 2.065014825802791e-13 relative error = 6.840155108989164e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.82 Order of pole (three term test) = 3.11e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81 y[1] (analytic) = 0.3052409877598364 y[1] (numeric) = 0.3052409877596132 absolute error = 2.23265850252119e-13 relative error = 7.314412520109668e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.81 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.81 Order of pole (three term test) = 2.636e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (analytic) = 0.308641975308642 y[1] (numeric) = 0.3086419753084012 absolute error = 2.408073740411965e-13 relative error = 7.802158918934764e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.79 y[1] (analytic) = 0.3121001217190476 y[1] (numeric) = 0.3121001217187884 absolute error = 2.591815650987428e-13 relative error = 8.304436527328815e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.79 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.79 Order of pole (three term test) = 3.778e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.78 y[1] (analytic) = 0.3156167150612297 y[1] (numeric) = 0.3156167150609513 absolute error = 2.783329122735267e-13 relative error = 8.81869999247442e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.78 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.77 y[1] (analytic) = 0.319193079894028 y[1] (numeric) = 0.3191930798937295 absolute error = 2.984279490192421e-13 relative error = 9.349449214823834e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.77 Order of pole (three term test) = 1.079e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.76 y[1] (analytic) = 0.3228305785123968 y[1] (numeric) = 0.3228305785120774 absolute error = 3.194111641846575e-13 relative error = 9.894080221783949e-11 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 13 h = 0.01 Radius of convergence (given) for eq 1 = 1.76 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.76 Order of pole (three term test) = 4.551e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (analytic) = 0.326530612244898 y[1] (numeric) = 0.3265306122445567 absolute error = 3.413935800722356e-13 relative error = 1.045517838971221e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.75 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.75 Order of pole (three term test) = 3.836e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.74 y[1] (analytic) = 0.3302946228035408 y[1] (numeric) = 0.3302946228031765 absolute error = 3.643751966819764e-13 relative error = 1.103182345474351e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.74 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.74 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.73 y[1] (analytic) = 0.334124093688396 y[1] (numeric) = 0.3341240936880075 absolute error = 3.884670363163423e-13 relative error = 1.16264299299118e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.73 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.73 Order of pole (three term test) = 5.434e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72 y[1] (analytic) = 0.3380205516495404 y[1] (numeric) = 0.3380205516491267 absolute error = 4.136690989753333e-13 relative error = 1.223798662408626e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.72 Order of pole (three term test) = 4.567e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.71 y[1] (analytic) = 0.3419855682090217 y[1] (numeric) = 0.3419855682085816 absolute error = 4.400368958101808e-13 relative error = 1.286711887038549e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.71 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.71 Order of pole (three term test) = 7.668e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (analytic) = 0.3460207612456749 y[1] (numeric) = 0.3460207612452071 absolute error = 4.677369602745785e-13 relative error = 1.351759815193531e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 3.215e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.69 y[1] (analytic) = 0.3501277966457759 y[1] (numeric) = 0.3501277966452791 absolute error = 4.967692923685263e-13 relative error = 1.418822775933747e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.69 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.69 Order of pole (three term test) = 2.694e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.68 y[1] (analytic) = 0.3543083900226758 y[1] (numeric) = 0.3543083900221488 absolute error = 5.270783809407931e-13 relative error = 1.487626022367294e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.68 Order of pole (three term test) = 9.017e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.67 y[1] (analytic) = 0.3585643085087311 y[1] (numeric) = 0.3585643085081722 absolute error = 5.589417817475351e-13 relative error = 1.5588327351157e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.67 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.67 Order of pole (three term test) = 3.769e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.66 y[1] (analytic) = 0.3628973726230224 y[1] (numeric) = 0.3628973726224299 absolute error = 5.924150059399835e-13 relative error = 1.632458790368218e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.66 Order of pole (given) = 2 NO POLE (ratio test) for Equation 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] = -1.65 y[1] (analytic) = 0.3673094582185493 y[1] (numeric) = 0.3673094582179218 absolute error = 6.274980535181385e-13 relative error = 1.708363450703131e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.65 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.64 y[1] (analytic) = 0.3718024985127901 y[1] (numeric) = 0.3718024985121258 absolute error = 6.643019467844624e-13 relative error = 1.78670651607149e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.64 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.63 y[1] (analytic) = 0.3763784862057286 y[1] (numeric) = 0.3763784862050256 absolute error = 7.029932191926491e-13 relative error = 1.867782684072949e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.63 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.63 Order of pole (three term test) = 3.643e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.62 y[1] (analytic) = 0.3810394756896816 y[1] (numeric) = 0.381039475688938 absolute error = 7.435718707426986e-13 relative error = 1.951430017577138e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.62 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.62 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.61 y[1] (analytic) = 0.3857875853555034 y[1] (numeric) = 0.3857875853547171 absolute error = 7.863154571907671e-13 relative error = 2.038208296584186e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.61 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.61 Order of pole (three term test) = 5.03e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (analytic) = 0.3906250000000002 y[1] (numeric) = 0.3906249999991691 absolute error = 8.311129562343922e-13 relative error = 2.127649167960043e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 4.173e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.59 y[1] (analytic) = 0.3955539733396624 y[1] (numeric) = 0.3955539733387842 absolute error = 8.782419236297301e-13 relative error = 2.220283407128319e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.59 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.59 Order of pole (three term test) = 3.457e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.58 y[1] (analytic) = 0.4005768306361162 y[1] (numeric) = 0.4005768306351885 absolute error = 9.277578705280121e-13 relative error = 2.316054747986128e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.58 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.58 Order of pole (three term test) = 2.861e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.57 y[1] (analytic) = 0.4056959714390038 y[1] (numeric) = 0.4056959714380239 absolute error = 9.798828415341632e-13 relative error = 2.415313216097557e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.57 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.57 Order of pole (three term test) = 2.365e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.56 y[1] (analytic) = 0.4109138724523342 y[1] (numeric) = 0.4109138724512995 absolute error = 1.034672347799415e-12 relative error = 2.517978625604654e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.56 Order of pole (given) = 2 NO POLE (ratio test) for Equation 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] = -1.55 y[1] (analytic) = 0.4162330905306974 y[1] (numeric) = 0.416233090529605 absolute error = 1.092403945079923e-12 relative error = 2.624500478054513e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.55 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.55 Order of pole (three term test) = 6.439e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54 y[1] (analytic) = 0.4216562658121102 y[1] (numeric) = 0.421656265810957 absolute error = 1.153244166829381e-12 relative error = 2.735033866052559e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.54 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.54 Order of pole (three term test) = 2.651e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.53 y[1] (analytic) = 0.4271861249946605 y[1] (numeric) = 0.4271861249934432 absolute error = 1.217248524199022e-12 relative error = 2.849457070297488e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.53 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.53 Order of pole (three term test) = 4.362e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.52 y[1] (analytic) = 0.4328254847645432 y[1] (numeric) = 0.4328254847632586 absolute error = 1.284639061793769e-12 relative error = 2.968030088368321e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.52 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.52 Order of pole (three term test) = 3.583e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.51 y[1] (analytic) = 0.438577255383536 y[1] (numeric) = 0.4385772553821804 absolute error = 1.355637824218547e-12 relative error = 3.090989803000708e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.51 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.51 Order of pole (three term test) = 8.817e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (analytic) = 0.4444444444444447 y[1] (numeric) = 0.4444444444430141 absolute error = 1.430577878380745e-12 relative error = 3.218800226356675e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.5 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.5 Order of pole (three term test) = 4.816e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.49 y[1] (analytic) = 0.4504301608035677 y[1] (numeric) = 0.4504301608020581 absolute error = 1.509681268885288e-12 relative error = 3.351643385052225e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.49 Order of pole (given) = 2 NO POLE (ratio test) for Equation 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] = -1.48 y[1] (analytic) = 0.4565376186997812 y[1] (numeric) = 0.4565376186981882 absolute error = 1.593003506883406e-12 relative error = 3.48931488147741e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.48 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.48 Order of pole (three term test) = 6.439e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.47 y[1] (analytic) = 0.4627701420704339 y[1] (numeric) = 0.4627701420687529 absolute error = 1.680933170433718e-12 relative error = 3.63232848799022e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.47 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.47 Order of pole (three term test) = 5.254e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.46 y[1] (analytic) = 0.4691311690748736 y[1] (numeric) = 0.4691311690730998 absolute error = 1.773858837594844e-12 relative error = 3.781157498217167e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.46 Order of pole (three term test) = 8.562e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45 y[1] (analytic) = 0.475624256837099 y[1] (numeric) = 0.475624256835227 absolute error = 1.872002552971708e-12 relative error = 3.935885367623013e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.45 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.45 Order of pole (three term test) = 6.967e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.44 y[1] (analytic) = 0.4822530864197534 y[1] (numeric) = 0.4822530864177778 absolute error = 1.975641872320466e-12 relative error = 4.096690986443716e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.44 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.44 Order of pole (three term test) = 2.83e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.429999999999999 y[1] (analytic) = 0.4890214680424474 y[1] (numeric) = 0.4890214680403622 absolute error = 2.0852763960022e-12 relative error = 4.264181702184896e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.43 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.43 Order of pole (three term test) = 9.185e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.419999999999999 y[1] (analytic) = 0.495933346558223 y[1] (numeric) = 0.4959333465560218 absolute error = 2.201128168621835e-12 relative error = 4.438354839209065e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.42 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.42 Order of pole (three term test) = 7.442e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.409999999999999 y[1] (analytic) = 0.5029928072028573 y[1] (numeric) = 0.5029928072005337 absolute error = 2.32358576823799e-12 relative error = 4.619520865833945e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.41 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.41 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.399999999999999 y[1] (analytic) = 0.5102040816326534 y[1] (numeric) = 0.5102040816302 absolute error = 2.453370839816671e-12 relative error = 4.808606846040672e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.4 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.4 Order of pole (three term test) = 4.862e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.389999999999999 y[1] (analytic) = 0.5175715542673779 y[1] (numeric) = 0.5175715542647871 absolute error = 2.590816450265265e-12 relative error = 5.005716463557515e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.39 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.39 Order of pole (three term test) = 3.922e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.379999999999999 y[1] (analytic) = 0.5250997689561021 y[1] (numeric) = 0.5250997689533659 absolute error = 2.736255666491161e-12 relative error = 5.210925291265762e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.38 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.38 Order of pole (three term test) = 3.158e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.369999999999999 y[1] (analytic) = 0.5327934359848692 y[1] (numeric) = 0.5327934359819787 absolute error = 2.890465644611595e-12 relative error = 5.425114968371498e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.37 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.37 Order of pole (three term test) = 5.078e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.359999999999999 y[1] (analytic) = 0.5406574394463672 y[1] (numeric) = 0.5406574394433135 absolute error = 3.053779451533956e-12 relative error = 5.6482704735572e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.36 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.36 Order of pole (three term test) = 4.076e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.349999999999999 y[1] (analytic) = 0.5486968449931418 y[1] (numeric) = 0.5486968449899148 absolute error = 3.22697424337548e-12 relative error = 5.881160558551807e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.35 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.35 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.339999999999999 y[1] (analytic) = 0.5569169079973273 y[1] (numeric) = 0.5569169079939165 absolute error = 3.410827176253406e-12 relative error = 6.12448127768061e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.34 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.34 Order of pole (three term test) = 2.613e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.329999999999999 y[1] (analytic) = 0.5653230821414443 y[1] (numeric) = 0.5653230821378384 absolute error = 3.605893361680046e-12 relative error = 6.378464767475828e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.33 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.33 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.319999999999999 y[1] (analytic) = 0.5739210284664835 y[1] (numeric) = 0.5739210284626705 absolute error = 3.8130609780751e-12 relative error = 6.643877448198049e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.32 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.32 Order of pole (three term test) = 3.329e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.309999999999999 y[1] (analytic) = 0.5827166249053091 y[1] (numeric) = 0.582716624901276 absolute error = 4.033107181555806e-12 relative error = 6.921215234267912e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.31 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.31 Order of pole (three term test) = 5.3e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.299999999999999 y[1] (analytic) = 0.5917159763313615 y[1] (numeric) = 0.5917159763270945 absolute error = 4.267031172844327e-12 relative error = 7.211282682106905e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.3 Order of pole (given) = 2 NO POLE (ratio test) for Equation 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] = -1.289999999999999 y[1] (analytic) = 0.6009254251547389 y[1] (numeric) = 0.6009254251502232 absolute error = 4.515721130360362e-12 relative error = 7.514611533032671e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.29 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.29 Order of pole (three term test) = 3.34e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.279999999999999 y[1] (analytic) = 0.6103515625000007 y[1] (numeric) = 0.6103515624952203 absolute error = 4.780398299430999e-12 relative error = 7.83220457378774e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.28 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.28 Order of pole (three term test) = 5.29e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.269999999999999 y[1] (analytic) = 0.6200012400024806 y[1] (numeric) = 0.6200012399974186 absolute error = 5.061950858475939e-12 relative error = 8.164420539635834e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.27 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.27 Order of pole (three term test) = 8.361e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.259999999999999 y[1] (analytic) = 0.6298815822625353 y[1] (numeric) = 0.6298815822571734 absolute error = 5.361933119729656e-12 relative error = 8.512605020882793e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.26 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.26 Order of pole (three term test) = 6.596e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.249999999999999 y[1] (analytic) = 0.6400000000000007 y[1] (numeric) = 0.6399999999943192 absolute error = 5.681455306216776e-12 relative error = 8.877273915963703e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.25 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.25 Order of pole (three term test) = 2.597e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.239999999999999 y[1] (analytic) = 0.650364203954215 y[1] (numeric) = 0.6503642039481931 absolute error = 6.021960707869312e-12 relative error = 9.259366784419844e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.24 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.24 Order of pole (three term test) = 4.081e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.229999999999999 y[1] (analytic) = 0.6609822195782941 y[1] (numeric) = 0.6609822195719088 absolute error = 6.385225681526663e-12 relative error = 9.660207933581677e-10 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 12 h = 0.01 Radius of convergence (given) for eq 1 = 1.23 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.23 Order of pole (three term test) = 3.201e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.219999999999999 y[1] (analytic) = 0.6718624025799524 y[1] (numeric) = 0.6718624025731795 absolute error = 6.772915561725767e-12 relative error = 1.008080752207262e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.22 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.22 Order of pole (three term test) = 2.506e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.209999999999999 y[1] (analytic) = 0.6830134553650715 y[1] (numeric) = 0.6830134553578848 absolute error = 7.186695683003563e-12 relative error = 1.05220411494855e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.21 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.21 Order of pole (three term test) = 3.915e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.199999999999999 y[1] (analytic) = 0.6944444444444453 y[1] (numeric) = 0.6944444444368166 absolute error = 7.628675469106838e-12 relative error = 1.098529267551383e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.2 Order of pole (three term test) = 3.052e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.189999999999999 y[1] (analytic) = 0.7061648188687247 y[1] (numeric) = 0.7061648188606238 absolute error = 8.10096434378238e-12 relative error = 1.147177560723021e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.19 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.19 Order of pole (three term test) = 9.499e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.179999999999999 y[1] (analytic) = 0.7181844297615636 y[1] (numeric) = 0.7181844297529574 absolute error = 8.606226842289288e-12 relative error = 1.198331025520359e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.18 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.18 Order of pole (three term test) = 3.687e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.169999999999999 y[1] (analytic) = 0.7305135510263724 y[1] (numeric) = 0.7305135510172256 absolute error = 9.146794432979277e-12 relative error = 1.252104689930532e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.17 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.17 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.159999999999999 y[1] (analytic) = 0.7431629013079676 y[1] (numeric) = 0.743162901298242 absolute error = 9.725553695716371e-12 relative error = 1.308670505295593e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.16 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.16 Order of pole (three term test) = 4.416e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.149999999999999 y[1] (analytic) = 0.7561436672967874 y[1] (numeric) = 0.7561436672864418 absolute error = 1.034561325496952e-11 relative error = 1.368207352969717e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.15 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.15 Order of pole (three term test) = 3.406e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.139999999999999 y[1] (analytic) = 0.7694675284702996 y[1] (numeric) = 0.7694675284592895 absolute error = 1.101019275751014e-11 relative error = 1.430884650766016e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.14 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.14 Order of pole (three term test) = 2.621e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.129999999999999 y[1] (analytic) = 0.783146683373797 y[1] (numeric) = 0.7831466833620742 absolute error = 1.172284491701703e-11 relative error = 1.496890067453902e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.13 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.13 Order of pole (three term test) = 4.024e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.119999999999999 y[1] (analytic) = 0.7971938775510216 y[1] (numeric) = 0.7971938775385339 absolute error = 1.24876775586813e-11 relative error = 1.56645427296098e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.12 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.12 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.109999999999999 y[1] (analytic) = 0.811622433244056 y[1] (numeric) = 0.811622433230747 absolute error = 1.330902055229899e-11 relative error = 1.639804422248756e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.11 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.11 Order of pole (three term test) = 2.355e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.099999999999999 y[1] (analytic) = 0.8264462809917367 y[1] (numeric) = 0.8264462809775451 absolute error = 1.419153683457353e-11 relative error = 1.717175956983394e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.1 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.089999999999999 y[1] (analytic) = 0.8416799932665613 y[1] (numeric) = 0.8416799932514207 absolute error = 1.514055547602311e-11 relative error = 1.798849396106303e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.09 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.09 Order of pole (three term test) = 5.459e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.079999999999999 y[1] (analytic) = 0.8573388203017845 y[1] (numeric) = 0.8573388202856229 absolute error = 1.616162759177087e-11 relative error = 1.885092242304151e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.08 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.08 Order of pole (three term test) = 4.141e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.069999999999999 y[1] (analytic) = 0.873438728273213 y[1] (numeric) = 0.8734387282559519 absolute error = 1.726108145305716e-11 relative error = 1.976221215560511e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.07 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.07 Order of pole (three term test) = 6.264e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.059999999999999 y[1] (analytic) = 0.8899964400142414 y[1] (numeric) = 0.8899964399957958 absolute error = 1.844557839802974e-11 relative error = 2.072545188802618e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.06 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.06 Order of pole (three term test) = 4.727e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.049999999999999 y[1] (analytic) = 0.9070294784580513 y[1] (numeric) = 0.9070294784383287 absolute error = 1.972255692095359e-11 relative error = 2.17441190053513e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.05 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.05 Order of pole (three term test) = 3.557e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.039999999999999 y[1] (analytic) = 0.924556213017753 y[1] (numeric) = 0.9245562129966524 absolute error = 2.11006767614208e-11 relative error = 2.28224919851527e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.04 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.04 Order of pole (three term test) = 8.007e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.029999999999999 y[1] (analytic) = 0.9425959091337559 y[1] (numeric) = 0.9425959091111674 absolute error = 2.258848663672097e-11 relative error = 2.396412547289724e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.03 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.03 Order of pole (three term test) = 7.99e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.019999999999999 y[1] (analytic) = 0.961168781237987 y[1] (numeric) = 0.9611687812137908 absolute error = 2.419620059868066e-11 relative error = 2.517372710286732e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.02 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.02 Order of pole (three term test) = 5.963e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.009999999999999 y[1] (analytic) = 0.9802960494069226 y[1] (numeric) = 0.9802960493809878 absolute error = 2.593480985524366e-11 relative error = 2.645609953333401e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.01 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.01 Order of pole (three term test) = 8.874e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9999999999999991 y[1] (analytic) = 1.000000000000002 y[1] (numeric) = 0.9999999999721856 absolute error = 2.781619379277345e-11 relative error = 2.78161937927734e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 6.584e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9899999999999991 y[1] (analytic) = 1.020304050607083 y[1] (numeric) = 1.020304050577229 absolute error = 2.985389713217046e-11 relative error = 2.925980457924021e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.99 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.99 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9799999999999991 y[1] (analytic) = 1.041232819658477 y[1] (numeric) = 1.041232819626415 absolute error = 3.206235277275482e-11 relative error = 3.079268360295368e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.98 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.98 Order of pole (three term test) = 7.182e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9699999999999991 y[1] (analytic) = 1.06281220108407 y[1] (numeric) = 1.062812201049612 absolute error = 3.445843610450083e-11 relative error = 3.242194253072478e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.97 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.97 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9599999999999991 y[1] (analytic) = 1.085069444444446 y[1] (numeric) = 1.085069444407387 absolute error = 3.70599106958025e-11 relative error = 3.415441369725152e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.96 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.96 Order of pole (three term test) = 3.869e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9499999999999991 y[1] (analytic) = 1.108033240997232 y[1] (numeric) = 1.108033240957345 absolute error = 3.9886982605708e-11 relative error = 3.599800180165139e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.95 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.95 Order of pole (three term test) = 2.826e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9399999999999991 y[1] (analytic) = 1.131733816206431 y[1] (numeric) = 1.131733816163469 absolute error = 4.296141220549998e-11 relative error = 3.796070382477971e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.94 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.94 Order of pole (three term test) = 4.115e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.929999999999999 y[1] (analytic) = 1.156203029251939 y[1] (numeric) = 1.156203029205631 absolute error = 4.630829053553498e-11 relative error = 4.005204048418412e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.93 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.93 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.919999999999999 y[1] (analytic) = 1.181474480151231 y[1] (numeric) = 1.181474480101276 absolute error = 4.995492908221877e-11 relative error = 4.228185197518988e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.92 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.92 Order of pole (three term test) = 4.317e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.909999999999999 y[1] (analytic) = 1.207583625166045 y[1] (numeric) = 1.207583625112113 absolute error = 5.3931970001031e-11 relative error = 4.466106435785368e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.91 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.91 Order of pole (three term test) = 3.11e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.899999999999999 y[1] (analytic) = 1.23456790123457 y[1] (numeric) = 1.234567901176298 absolute error = 5.827294202731537e-11 relative error = 4.720108304212535e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.889999999999999 y[1] (analytic) = 1.262466860244921 y[1] (numeric) = 1.262466860181905 absolute error = 6.301648092232881e-11 relative error = 4.991535453857654e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.89 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.89 Order of pole (three term test) = 6.387e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.879999999999999 y[1] (analytic) = 1.29132231404959 y[1] (numeric) = 1.291322313981385 absolute error = 6.820455311640217e-11 relative error = 5.281760593334173e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.88 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.88 Order of pole (three term test) = 9.102e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.869999999999999 y[1] (analytic) = 1.321178491214166 y[1] (numeric) = 1.321178491140281 absolute error = 7.388512024419924e-11 relative error = 5.592364751283428e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.87 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.87 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.859999999999999 y[1] (analytic) = 1.352082206598164 y[1] (numeric) = 1.352082206518053 absolute error = 8.01110289216922e-11 relative error = 5.925011699048341e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.86 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.86 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.849999999999999 y[1] (analytic) = 1.384083044982702 y[1] (numeric) = 1.38408304489576 absolute error = 8.694178710300093e-11 relative error = 6.281544118191803e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.85 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.85 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.839999999999999 y[1] (analytic) = 1.417233560090706 y[1] (numeric) = 1.417233559996262 absolute error = 9.444467430341774e-11 relative error = 6.66401621884914e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.84 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.84 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.829999999999999 y[1] (analytic) = 1.451589490492092 y[1] (numeric) = 1.451589490389398 absolute error = 1.026945195548024e-10 relative error = 7.074625452130317e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.83 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.83 Order of pole (three term test) = 3.148e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.819999999999999 y[1] (analytic) = 1.487209994051164 y[1] (numeric) = 1.487209993939387 absolute error = 1.11776587985446e-10 relative error = 7.515857776141368e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.82 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.82 Order of pole (three term test) = 4.376e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8099999999999989 y[1] (analytic) = 1.52415790275873 y[1] (numeric) = 1.524157902636944 absolute error = 1.217863587754664e-10 relative error = 7.990402999258329e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.81 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.81 Order of pole (three term test) = 9.086e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7999999999999989 y[1] (analytic) = 1.562500000000004 y[1] (numeric) = 1.562499999867173 absolute error = 1.328313015136473e-10 relative error = 8.501203296873404e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.8 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8 Order of pole (three term test) = 4.173e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7899999999999989 y[1] (analytic) = 1.602307322544468 y[1] (numeric) = 1.602307322399434 absolute error = 1.450339848219073e-10 relative error = 9.051570992735211e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.79 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.79 Order of pole (three term test) = 2.861e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7799999999999989 y[1] (analytic) = 1.643655489809341 y[1] (numeric) = 1.643655489650808 absolute error = 1.585327424891148e-10 relative error = 9.645132053037713e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.78 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.78 Order of pole (three term test) = 3.905e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7699999999999989 y[1] (analytic) = 1.686625063248445 y[1] (numeric) = 1.686625063074961 absolute error = 1.734836718725319e-10 relative error = 1.028584690532239e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 Radius of convergence (given) for eq 1 = 0.77 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.77 Order of pole (three term test) = 7.954e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7599999999999989 y[1] (analytic) = 1.731301939058177 y[1] (numeric) = 1.731301938868111 absolute error = 1.900661850129381e-10 relative error = 1.097822284634728e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 Radius of convergence (given) for eq 1 = 0.76 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.76 Order of pole (three term test) = 3.583e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7499999999999989 y[1] (analytic) = 1.777777777777783 y[1] (numeric) = 1.7777777775693 absolute error = 2.084825645454202e-10 relative error = 1.172714425567985e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 Radius of convergence (given) for eq 1 = 0.75 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.75 Order of pole (three term test) = 2.408e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7399999999999989 y[1] (analytic) = 1.826150474799129 y[1] (numeric) = 1.826150474570165 absolute error = 2.289641809483101e-10 relative error = 1.253807854872942e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 Radius of convergence (given) for eq 1 = 0.74 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.74 Order of pole (three term test) = 6.439e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7299999999999989 y[1] (analytic) = 1.876524676299499 y[1] (numeric) = 1.876524676047724 absolute error = 2.517754893460733e-10 relative error = 1.34171158272522e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 Radius of convergence (given) for eq 1 = 0.73 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.73 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7199999999999989 y[1] (analytic) = 1.929012345679018 y[1] (numeric) = 1.9290123454018 absolute error = 2.772186924460129e-10 relative error = 1.437101701640126e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 Radius of convergence (given) for eq 1 = 0.72 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.72 Order of pole (three term test) = 2.83e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7099999999999989 y[1] (analytic) = 1.983733386232897 y[1] (numeric) = 1.983733385927256 absolute error = 3.056404018764169e-10 relative error = 1.540733265859013e-08 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 10 h = 0.01 Radius of convergence (given) for eq 1 = 0.71 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.71 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations = 130 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 100.8 %