##############ECHO OF PROBLEM################# ##############temp/mtest5postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 2 ) = diff ( y1, x , 1) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.5; x_end=5.0; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); glob_max_iter=20; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.1; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y1 (double x) { return( - cos(x)); } double exact_soln_y2 (double x) { return( - sin(x)); } double exact_soln_y2p (double x) { return( - cos(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 4.5 estimated_steps = 4500000 step_error = 2.222222222222222e-17 est_needed_step_err = 2.222222222222222e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.176050419120135e-183 estimated_step_error = 2.176050419120135e-183 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.460322701565095e-175 estimated_step_error = 1.460322701565095e-175 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.800059559255629e-168 estimated_step_error = 9.800059559255629e-168 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.576708375401056e-160 estimated_step_error = 6.576708375401056e-160 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.413553922118907e-152 estimated_step_error = 4.413553922118907e-152 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.961885419727831e-144 estimated_step_error = 2.961885419727831e-144 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.987687014675068e-136 estimated_step_error = 1.987687014675068e-136 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.33391331174907e-128 estimated_step_error = 1.33391331174907e-128 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.951729110475025e-121 estimated_step_error = 8.951729110475025e-121 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.00738815552068e-113 estimated_step_error = 6.00738815552068e-113 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.03146906394583e-105 estimated_step_error = 4.03146906394583e-105 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.705445060834664e-97 estimated_step_error = 2.705445060834664e-97 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.815555820804895e-89 estimated_step_error = 1.815555820804895e-89 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.218348376174881e-81 estimated_step_error = 1.218348376174881e-81 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.17551933611488e-74 estimated_step_error = 8.17551933611488e-74 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.485587141141666e-66 estimated_step_error = 5.485587141141666e-66 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.680090513956989e-58 estimated_step_error = 3.680090513956989e-58 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.468017908338341e-50 estimated_step_error = 2.468017908338341e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.5 y1[1] (analytic) = -0.8775825618903728 y1[1] (numeric) = -0.8775825618903728 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.479425538604203 y2[1] (numeric) = -0.479425538604203 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4207 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4207 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6 y1[1] (analytic) = -0.8253356149096783 y1[1] (numeric) = -0.8253356149096783 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.5646424733950354 y2[1] (numeric) = -0.5646424733950354 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.466 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.466 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7 y1[1] (analytic) = -0.7648421872844885 y1[1] (numeric) = -0.7648421872844885 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.644217687237691 y2[1] (numeric) = -0.644217687237691 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4927 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4927 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y1[1] (analytic) = -0.6967067093471655 y1[1] (numeric) = -0.6967067093471655 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.7173560908995227 y2[1] (numeric) = -0.7173560908995227 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4998 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4998 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y1[1] (analytic) = -0.6216099682706645 y1[1] (numeric) = -0.6216099682706645 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.7833269096274833 y2[1] (numeric) = -0.7833269096274833 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4869 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4869 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y1[1] (analytic) = -0.5403023058681398 y1[1] (numeric) = -0.5403023058681398 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.8414709848078964 y2[1] (numeric) = -0.8414709848078964 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4546 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4546 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.1 y1[1] (analytic) = -0.4535961214255775 y1[1] (numeric) = -0.4535961214255774 absolute error = 5.551115123125783e-17 relative error = 1.22380127627184e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.8912073600614353 y2[1] (numeric) = -0.8912073600614352 absolute error = 1.110223024625157e-16 relative error = 1.245751633546455e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4042 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4042 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.2 y1[1] (analytic) = -0.3623577544766736 y1[1] (numeric) = -0.3623577544766736 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.9320390859672263 y2[1] (numeric) = -0.9320390859672262 absolute error = 1.110223024625157e-16 relative error = 1.191176466030949e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3377 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3377 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.3 y1[1] (analytic) = -0.2674988286245873 y1[1] (numeric) = -0.2674988286245875 absolute error = 1.110223024625157e-16 relative error = 4.150384621621142e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.963558185417193 y2[1] (numeric) = -0.9635581854171928 absolute error = 1.110223024625157e-16 relative error = 1.152211710125696e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2578 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2578 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.4 y1[1] (analytic) = -0.1699671429002408 y1[1] (numeric) = -0.169967142900241 absolute error = 1.942890293094024e-16 relative error = 1.143097577532599e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = -0.9854497299884603 y2[1] (numeric) = -0.98544972998846 absolute error = 2.220446049250313e-16 relative error = 2.253231171189539e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1675 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1675 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.5 y1[1] (analytic) = -0.07073720166770268 y1[1] (numeric) = -0.07073720166770299 absolute error = 3.05311331771918e-16 relative error = 4.316135280642825e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = -0.9974949866040544 y2[1] (numeric) = -0.9974949866040543 absolute error = 1.110223024625157e-16 relative error = 1.11301113242171e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07056 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07056 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.6 y1[1] (analytic) = 0.02919952230128904 y1[1] (numeric) = 0.02919952230128865 absolute error = 3.851086116668512e-16 relative error = 1.318886684834054e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = -0.9995736030415051 y2[1] (numeric) = -0.9995736030415051 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02919 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02919 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.7 y1[1] (analytic) = 0.1288444942955251 y1[1] (numeric) = 0.1288444942955246 absolute error = 4.718447854656915e-16 relative error = 3.662126100502528e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = -0.9916648104524686 y2[1] (numeric) = -0.9916648104524686 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1278 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1278 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.8 y1[1] (analytic) = 0.2272020946930875 y1[1] (numeric) = 0.227202094693087 absolute error = 5.273559366969494e-16 relative error = 2.321087476809226e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = -0.973847630878195 y2[1] (numeric) = -0.9738476308781951 absolute error = 1.110223024625157e-16 relative error = 1.140037711673623e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2213 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2213 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y1[1] (analytic) = 0.323289566863504 y1[1] (numeric) = 0.3232895668635034 absolute error = 6.106226635438361e-16 relative error = 1.888779367265034e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = -0.9463000876874142 y2[1] (numeric) = -0.9463000876874145 absolute error = 2.220446049250313e-16 relative error = 2.346450220327762e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3059 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3059 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2 y1[1] (analytic) = 0.4161468365471428 y1[1] (numeric) = 0.4161468365471423 absolute error = 4.996003610813204e-16 relative error = 1.200538649354177e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = -0.9092974268256815 y2[1] (numeric) = -0.9092974268256817 absolute error = 2.220446049250313e-16 relative error = 2.441935920793041e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3784 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3784 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y1[1] (analytic) = 0.5048461045998579 y1[1] (numeric) = 0.5048461045998573 absolute error = 5.551115123125783e-16 relative error = 1.099565802835224e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = -0.8632093666488735 y2[1] (numeric) = -0.8632093666488738 absolute error = 3.33066907387547e-16 relative error = 3.85847188707613e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4358 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4358 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.200000000000001 y1[1] (analytic) = 0.5885011172553463 y1[1] (numeric) = 0.5885011172553456 absolute error = 6.661338147750939e-16 relative error = 1.131915973043197e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = -0.8084964038195899 y2[1] (numeric) = -0.8084964038195902 absolute error = 3.33066907387547e-16 relative error = 4.119584277852502e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4758 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4758 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.300000000000001 y1[1] (analytic) = 0.6662760212798248 y1[1] (numeric) = 0.6662760212798241 absolute error = 6.661338147750939e-16 relative error = 9.997865651769101e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.7457052121767197 y2[1] (numeric) = -0.7457052121767203 absolute error = 5.551115123125783e-16 relative error = 7.444114688325742e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4968 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4968 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y1[1] (analytic) = 0.737393715541246 y1[1] (numeric) = 0.7373937155412454 absolute error = 5.551115123125783e-16 relative error = 7.528020657256716e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.6754631805511503 y2[1] (numeric) = -0.675463180551151 absolute error = 6.661338147750939e-16 relative error = 9.861881949384066e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4981 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4981 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.500000000000001 y1[1] (analytic) = 0.8011436155469343 y1[1] (numeric) = 0.8011436155469337 absolute error = 5.551115123125783e-16 relative error = 6.928988779790851e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.5984721441039558 y2[1] (numeric) = -0.5984721441039565 absolute error = 7.771561172376096e-16 relative error = 1.298566900555051e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4795 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4795 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y1[1] (analytic) = 0.8568887533689478 y1[1] (numeric) = 0.8568887533689472 absolute error = 5.551115123125783e-16 relative error = 6.478221474259049e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.5155013718214634 y2[1] (numeric) = -0.5155013718214643 absolute error = 8.881784197001252e-16 relative error = 1.722940943031541e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4417 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4417 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y1[1] (analytic) = 0.9040721420170617 y1[1] (numeric) = 0.9040721420170611 absolute error = 5.551115123125783e-16 relative error = 6.140124073219173e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.4273798802338289 y2[1] (numeric) = -0.4273798802338299 absolute error = 9.992007221626409e-16 relative error = 2.337968557658718e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3864 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3864 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.800000000000001 y1[1] (analytic) = 0.9422223406686585 y1[1] (numeric) = 0.9422223406686581 absolute error = 4.440892098500626e-16 relative error = 4.713210361101285e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.3349881501559038 y2[1] (numeric) = -0.3349881501559049 absolute error = 1.110223024625157e-15 relative error = 3.3142158136294e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3156 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3156 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.900000000000001 y1[1] (analytic) = 0.9709581651495908 y1[1] (numeric) = 0.9709581651495904 absolute error = 3.33066907387547e-16 relative error = 3.43029101914224e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.2392493292139811 y2[1] (numeric) = -0.2392493292139823 absolute error = 1.221245327087672e-15 relative error = 5.10448798790741e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2323 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2323 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.000000000000001 y1[1] (analytic) = 0.9899924966004456 y1[1] (numeric) = 0.9899924966004454 absolute error = 2.220446049250313e-16 relative error = 2.242891796528909e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.1411200080598659 y2[1] (numeric) = -0.1411200080598672 absolute error = 1.332267629550188e-15 relative error = 9.440671438914697e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1397 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1397 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y1[1] (analytic) = 0.9991351502732795 y1[1] (numeric) = 0.9991351502732794 absolute error = 1.110223024625157e-16 relative error = 1.111184031831422e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = -0.04158066243328916 y2[1] (numeric) = -0.04158066243329059 absolute error = 1.429412144204889e-15 relative error = 3.437684876950187e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04154 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04154 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.200000000000002 y1[1] (analytic) = 0.998294775794753 y1[1] (numeric) = 0.998294775794753 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.05837414342758142 y2[1] (numeric) = 0.05837414342757991 absolute error = 1.512678871051776e-15 relative error = 2.591350865693465e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05827 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05827 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.300000000000002 y1[1] (analytic) = 0.9874797699088647 y1[1] (numeric) = 0.9874797699088648 absolute error = 1.110223024625157e-16 relative error = 1.124299513222048e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.15774569414325 y2[1] (numeric) = 0.1577456941432484 absolute error = 1.554312234475219e-15 relative error = 9.85327835993886e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1558 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1558 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.400000000000002 y1[1] (analytic) = 0.9667981925794605 y1[1] (numeric) = 0.9667981925794609 absolute error = 3.33066907387547e-16 relative error = 3.44505099351613e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.2555411020268329 y2[1] (numeric) = 0.2555411020268313 absolute error = 1.609823385706477e-15 relative error = 6.299665192558489e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2471 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2471 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.500000000000002 y1[1] (analytic) = 0.9364566872907957 y1[1] (numeric) = 0.9364566872907962 absolute error = 5.551115123125783e-16 relative error = 5.92778630177266e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.3507832276896215 y2[1] (numeric) = 0.3507832276896199 absolute error = 1.609823385706477e-15 relative error = 4.589225648869603e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3285 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3285 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.600000000000002 y1[1] (analytic) = 0.8967584163341462 y1[1] (numeric) = 0.8967584163341469 absolute error = 6.661338147750939e-16 relative error = 7.428241571438813e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.4425204432948541 y2[1] (numeric) = 0.4425204432948524 absolute error = 1.665334536937735e-15 relative error = 3.763294017646349e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3968 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3968 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.700000000000002 y1[1] (analytic) = 0.8481000317104072 y1[1] (numeric) = 0.848100031710408 absolute error = 8.881784197001252e-16 relative error = 1.047256675499575e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.5298361409084948 y2[1] (numeric) = 0.5298361409084933 absolute error = 1.554312234475219e-15 relative error = 2.933571560086642e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4494 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4494 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.800000000000002 y1[1] (analytic) = 0.7909677119144155 y1[1] (numeric) = 0.7909677119144166 absolute error = 1.110223024625157e-15 relative error = 1.40362622633234e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.6118578909427207 y2[1] (numeric) = 0.6118578909427191 absolute error = 1.554312234475219e-15 relative error = 2.540315745671615e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.484 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.484 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.900000000000002 y1[1] (analytic) = 0.7259323042001387 y1[1] (numeric) = 0.72593230420014 absolute error = 1.332267629550188e-15 relative error = 1.835250507301964e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.6877661591839753 y2[1] (numeric) = 0.6877661591839739 absolute error = 1.443289932012704e-15 relative error = 2.098518388466723e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4993 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4993 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.000000000000002 y1[1] (analytic) = 0.6536436208636106 y1[1] (numeric) = 0.6536436208636118 absolute error = 1.221245327087672e-15 relative error = 1.868365708938048e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.7568024953079294 y2[1] (numeric) = 0.7568024953079283 absolute error = 1.110223024625157e-15 relative error = 1.466991760080583e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y1[1] (analytic) = 0.5748239465332677 y1[1] (numeric) = 0.5748239465332688 absolute error = 1.110223024625157e-15 relative error = 1.931414011752384e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.8182771110644114 y2[1] (numeric) = 0.8182771110644106 absolute error = 7.771561172376096e-16 relative error = 9.497468604818827e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4704 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4704 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.200000000000001 y1[1] (analytic) = 0.4902608213406986 y1[1] (numeric) = 0.4902608213406995 absolute error = 8.326672684688674e-16 relative error = 1.698416908354623e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.8715757724135886 y2[1] (numeric) = 0.8715757724135882 absolute error = 4.440892098500626e-16 relative error = 5.095245002282247e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4273 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4273 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.300000000000001 y1[1] (analytic) = 0.4007991720799746 y1[1] (numeric) = 0.4007991720799752 absolute error = 5.551115123125783e-16 relative error = 1.385011624230133e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.9161659367494552 y2[1] (numeric) = 0.9161659367494551 absolute error = 1.110223024625157e-16 relative error = 1.211814345078375e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3672 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3672 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.4 y1[1] (analytic) = 0.3073328699784194 y1[1] (numeric) = 0.3073328699784196 absolute error = 2.220446049250313e-16 relative error = 7.224889577890679e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.951602073889516 y2[1] (numeric) = 0.9516020738895161 absolute error = 1.110223024625157e-16 relative error = 1.166688319716774e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2925 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2925 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.5 y1[1] (analytic) = 0.2107957994307797 y1[1] (numeric) = 0.2107957994307796 absolute error = 1.110223024625157e-16 relative error = 5.266817591352086e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.977530117665097 y2[1] (numeric) = 0.9775301176650972 absolute error = 2.220446049250313e-16 relative error = 2.271486074059808e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2061 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2061 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.6 y1[1] (analytic) = 0.1121525269350549 y1[1] (numeric) = 0.1121525269350544 absolute error = 4.996003610813204e-16 relative error = 4.454650953791066e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.9936910036334644 y2[1] (numeric) = 0.9936910036334646 absolute error = 2.220446049250313e-16 relative error = 2.234543777825479e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1114 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1114 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.699999999999999 y1[1] (analytic) = 0.01238866346289145 y1[1] (numeric) = 0.01238866346289057 absolute error = 8.795048023202412e-16 relative error = 7.099271079198156e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 0.9999232575641008 y2[1] (numeric) = 0.9999232575641011 absolute error = 2.220446049250313e-16 relative error = 2.220616464767017e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01239 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01239 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.799999999999999 y1[1] (analytic) = -0.08749898343944551 y1[1] (numeric) = -0.08749898343944676 absolute error = 1.249000902703301e-15 relative error = 1.427446186923627e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 0.9961646088358408 y2[1] (numeric) = 0.9961646088358408 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08716 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08716 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.899999999999999 y1[1] (analytic) = -0.186512369422574 y1[1] (numeric) = -0.1865123694225756 absolute error = 1.582067810090848e-15 relative error = 8.482374734655892e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.9824526126243328 y2[1] (numeric) = 0.9824526126243326 absolute error = 2.220446049250313e-16 relative error = 2.260104986966288e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1832 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1832 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.999999999999998 y1[1] (analytic) = -0.2836621854632246 y1[1] (numeric) = -0.2836621854632265 absolute error = 1.887379141862766e-15 relative error = 6.653615598359181e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.958924274663139 y2[1] (numeric) = 0.9589242746631386 absolute error = 4.440892098500626e-16 relative error = 4.631118656434753e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.272 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.272 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 2 ) = diff ( y1, x , 1) ; Iterations = 46 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 104.4 %