##############ECHO OF PROBLEM################# ##############temp/mtest4postode.ode################# diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; 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); array_y2_init[2 + 1] = exact_soln_y2pp(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_y2 (double x) { return(sin(x)); } double exact_soln_y2p (double x) { return( cos(x)); } double exact_soln_y2pp (double x) { return( -sin(x)); } double exact_soln_y1 (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 = 4.9 estimated_steps = 4900000.000000001 step_error = 2.040816326530612e-17 est_needed_step_err = 2.040816326530612e-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 = 2.467208605532302e-183 estimated_step_error = 2.467208605532302e-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 = 1.655715664606566e-175 estimated_step_error = 1.655715664606566e-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 = 1.111131969458436e-167 estimated_step_error = 1.111131969458436e-167 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 = 7.456680367024187e-160 estimated_step_error = 7.456680367024187e-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 = 5.004093412037817e-152 estimated_step_error = 5.004093412037817e-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 = 3.358190142481625e-144 estimated_step_error = 3.358190142481625e-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 = 2.25364312158092e-136 estimated_step_error = 2.25364312158092e-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 = 1.512394117654307e-128 estimated_step_error = 1.512394117654307e-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 = 1.014950270158056e-120 estimated_step_error = 1.014950270158056e-120 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 = 6.811212724408108e-113 estimated_step_error = 6.811212724408108e-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 = 4.570923134360026e-105 estimated_step_error = 4.570923134360026e-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 = 3.067488750234022e-97 estimated_step_error = 3.067488750234022e-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 = 2.058549011618091e-89 estimated_step_error = 2.058549011618091e-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 = 1.381458319740245e-81 estimated_step_error = 1.381458319740245e-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 = 9.270668118428106e-74 estimated_step_error = 9.270668118428106e-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 = 6.221249002016116e-66 estimated_step_error = 6.221249002016116e-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 = 4.174750875079242e-58 estimated_step_error = 4.174750875079242e-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 = 2.801274754399603e-50 estimated_step_error = 2.801274754399603e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (analytic) = 0.09983341664682815 y2[1] (numeric) = 0.09983341664682815 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.9950041652780258 y1[1] (numeric) = 0.9950041652780258 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 = 0.09933 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 = 0.09933 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2 y2[1] (analytic) = 0.1986693307950612 y2[1] (numeric) = 0.1986693307950612 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.9800665778412416 y1[1] (numeric) = 0.9800665778412417 absolute error = 1.110223024625157e-16 relative error = 1.132803678573149e-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 = 0.1947 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 = 0.1947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3 y2[1] (analytic) = 0.2955202066613396 y2[1] (numeric) = 0.2955202066613396 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.955336489125606 y1[1] (numeric) = 0.9553364891256061 absolute error = 1.110223024625157e-16 relative error = 1.16212772909084e-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 = 0.2823 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 = 0.2823 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4 y2[1] (analytic) = 0.3894183423086505 y2[1] (numeric) = 0.3894183423086505 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.9210609940028851 y1[1] (numeric) = 0.9210609940028851 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 = 0.3587 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 = 0.3587 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5 y2[1] (analytic) = 0.479425538604203 y2[1] (numeric) = 0.4794255386042031 absolute error = 5.551115123125783e-17 relative error = 1.157868047515214e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.8775825618903728 y1[1] (numeric) = 0.8775825618903728 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 y2[1] (analytic) = 0.5646424733950354 y2[1] (numeric) = 0.5646424733950355 absolute error = 1.110223024625157e-16 relative error = 1.966240722115182e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.8253356149096783 y1[1] (numeric) = 0.8253356149096783 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 y2[1] (analytic) = 0.644217687237691 y2[1] (numeric) = 0.6442176872376912 absolute error = 2.220446049250313e-16 relative error = 3.446732514860393e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.7648421872844885 y1[1] (numeric) = 0.7648421872844884 absolute error = 1.110223024625157e-16 relative error = 1.451571373915598e-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 = 0.4927 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 y2[1] (analytic) = 0.7173560908995227 y2[1] (numeric) = 0.717356090899523 absolute error = 3.33066907387547e-16 relative error = 4.642978732778312e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.6967067093471655 y1[1] (numeric) = 0.6967067093471654 absolute error = 1.110223024625157e-16 relative error = 1.593529974277796e-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 = 0.4998 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 y2[1] (analytic) = 0.7833269096274833 y2[1] (numeric) = 0.7833269096274836 absolute error = 3.33066907387547e-16 relative error = 4.25195283468481e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.6216099682706645 y1[1] (numeric) = 0.6216099682706644 absolute error = 1.110223024625157e-16 relative error = 1.786044435088174e-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 = 0.4869 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 y2[1] (analytic) = 0.8414709848078964 y2[1] (numeric) = 0.8414709848078967 absolute error = 3.33066907387547e-16 relative error = 3.958150826360156e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.5403023058681398 y1[1] (numeric) = 0.5403023058681397 absolute error = 1.110223024625157e-16 relative error = 2.054818224107497e-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 = 0.4546 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 y2[1] (analytic) = 0.8912073600614353 y2[1] (numeric) = 0.8912073600614355 absolute error = 2.220446049250313e-16 relative error = 2.491503267092909e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.4535961214255775 y1[1] (numeric) = 0.4535961214255773 absolute error = 1.665334536937735e-16 relative error = 3.67140382881552e-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 y2[1] (analytic) = 0.9320390859672263 y2[1] (numeric) = 0.9320390859672265 absolute error = 2.220446049250313e-16 relative error = 2.382352932061898e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.3623577544766736 y1[1] (numeric) = 0.3623577544766735 absolute error = 1.665334536937735e-16 relative error = 4.595829719010302e-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 y2[1] (analytic) = 0.963558185417193 y2[1] (numeric) = 0.9635581854171931 absolute error = 1.110223024625157e-16 relative error = 1.152211710125696e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.2674988286245873 y1[1] (numeric) = 0.2674988286245873 absolute error = 5.551115123125783e-17 relative error = 2.075192310810571e-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 y2[1] (analytic) = 0.9854497299884603 y2[1] (numeric) = 0.9854497299884603 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.1699671429002408 y1[1] (numeric) = 0.1699671429002408 absolute error = 2.775557561562891e-17 relative error = 1.632996539332285e-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 y2[1] (analytic) = 0.9974949866040544 y2[1] (numeric) = 0.9974949866040546 absolute error = 1.110223024625157e-16 relative error = 1.11301113242171e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = 0.07073720166770268 y1[1] (numeric) = 0.07073720166770275 absolute error = 6.938893903907228e-17 relative error = 9.809398365097331e-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 y2[1] (analytic) = 0.9995736030415051 y2[1] (numeric) = 0.9995736030415053 absolute error = 2.220446049250313e-16 relative error = 2.22139324457342e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = -0.02919952230128904 y1[1] (numeric) = -0.0291995223012889 absolute error = 1.35308431126191e-16 relative error = 4.633926189957486e-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 = 0.02919 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 y2[1] (analytic) = 0.9916648104524686 y2[1] (numeric) = 0.9916648104524688 absolute error = 2.220446049250313e-16 relative error = 2.23910945094158e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = -0.1288444942955251 y1[1] (numeric) = -0.1288444942955249 absolute error = 2.220446049250313e-16 relative error = 1.723353459060013e-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 = 0.1278 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 y2[1] (analytic) = 0.973847630878195 y2[1] (numeric) = 0.9738476308781954 absolute error = 3.33066907387547e-16 relative error = 3.420113135020869e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = -0.2272020946930875 y1[1] (numeric) = -0.2272020946930873 absolute error = 2.498001805406602e-16 relative error = 1.099462489014897e-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 = 0.2213 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 y2[1] (analytic) = 0.9463000876874142 y2[1] (numeric) = 0.9463000876874147 absolute error = 4.440892098500626e-16 relative error = 4.692900440655523e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = -0.323289566863504 y1[1] (numeric) = -0.3232895668635037 absolute error = 2.775557561562891e-16 relative error = 8.585360760295611e-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 y2[1] (analytic) = 0.9092974268256815 y2[1] (numeric) = 0.9092974268256819 absolute error = 4.440892098500626e-16 relative error = 4.883871841586081e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = -0.4161468365471428 y1[1] (numeric) = -0.4161468365471427 absolute error = 1.110223024625157e-16 relative error = 2.667863665231505e-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 y2[1] (analytic) = 0.8632093666488735 y2[1] (numeric) = 0.863209366648874 absolute error = 5.551115123125783e-16 relative error = 6.430786478460217e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = -0.5048461045998579 y1[1] (numeric) = -0.5048461045998578 absolute error = 1.110223024625157e-16 relative error = 2.199131605670448e-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 y2[1] (analytic) = 0.8084964038195899 y2[1] (numeric) = 0.8084964038195904 absolute error = 5.551115123125783e-16 relative error = 6.865973796420836e-14 % Correct digits = 16 h = 0.1 y1[1] (analytic) = -0.5885011172553463 y1[1] (numeric) = -0.588501117255346 absolute error = 2.220446049250313e-16 relative error = 3.773053243477324e-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 y2[1] (analytic) = 0.7457052121767197 y2[1] (numeric) = 0.7457052121767205 absolute error = 7.771561172376096e-16 relative error = 1.042176056365604e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.6662760212798248 y1[1] (numeric) = -0.6662760212798245 absolute error = 2.220446049250313e-16 relative error = 3.332621883923034e-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 y2[1] (analytic) = 0.6754631805511503 y2[1] (numeric) = 0.6754631805511513 absolute error = 9.992007221626409e-16 relative error = 1.47928229240761e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.737393715541246 y1[1] (numeric) = -0.7373937155412459 absolute error = 1.110223024625157e-16 relative error = 1.505604131451343e-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 y2[1] (analytic) = 0.5984721441039558 y2[1] (numeric) = 0.5984721441039569 absolute error = 1.110223024625157e-15 relative error = 1.855095572221501e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.8011436155469343 y1[1] (numeric) = -0.8011436155469341 absolute error = 1.110223024625157e-16 relative error = 1.38579775595817e-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 = 0.4795 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 y2[1] (analytic) = 0.5155013718214634 y2[1] (numeric) = 0.5155013718214646 absolute error = 1.221245327087672e-15 relative error = 2.369043796668369e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.8568887533689478 y1[1] (numeric) = -0.8568887533689477 absolute error = 1.110223024625157e-16 relative error = 1.29564429485181e-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 = 0.4417 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 y2[1] (analytic) = 0.4273798802338289 y2[1] (numeric) = 0.4273798802338303 absolute error = 1.387778780781446e-15 relative error = 3.247178552303775e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.9040721420170617 y1[1] (numeric) = -0.9040721420170617 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 = 0.3864 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 y2[1] (analytic) = 0.3349881501559038 y2[1] (numeric) = 0.3349881501559053 absolute error = 1.498801083243961e-15 relative error = 4.47419134839969e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.9422223406686585 y1[1] (numeric) = -0.9422223406686587 absolute error = 2.220446049250313e-16 relative error = 2.356605180550643e-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 = 0.3156 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 y2[1] (analytic) = 0.2392493292139811 y2[1] (numeric) = 0.2392493292139828 absolute error = 1.665334536937735e-15 relative error = 6.96066543805556e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.9709581651495908 y1[1] (numeric) = -0.9709581651495911 absolute error = 3.33066907387547e-16 relative error = 3.43029101914224e-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 = 0.2323 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 y2[1] (analytic) = 0.1411200080598659 y2[1] (numeric) = 0.1411200080598677 absolute error = 1.831867990631508e-15 relative error = 1.298092322850771e-12 % Correct digits = 14 h = 0.1 y1[1] (analytic) = -0.9899924966004456 y1[1] (numeric) = -0.9899924966004461 absolute error = 4.440892098500626e-16 relative error = 4.485783593057817e-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 = 0.1397 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 y2[1] (analytic) = 0.04158066243328916 y2[1] (numeric) = 0.04158066243329116 absolute error = 1.998401444325282e-15 relative error = 4.806083711464339e-12 % Correct digits = 14 h = 0.1 y1[1] (analytic) = -0.9991351502732795 y1[1] (numeric) = -0.9991351502732801 absolute error = 6.661338147750939e-16 relative error = 6.667104190988532e-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 = 0.04154 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 y2[1] (analytic) = -0.05837414342758142 y2[1] (numeric) = -0.05837414342757927 absolute error = 2.151057110211241e-15 relative error = 3.684948478738413e-12 % Correct digits = 14 h = 0.1 y1[1] (analytic) = -0.998294775794753 y1[1] (numeric) = -0.9982947757947538 absolute error = 7.771561172376096e-16 relative error = 7.784836063265055e-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 = 0.05827 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 y2[1] (analytic) = -0.15774569414325 y2[1] (numeric) = -0.1577456941432477 absolute error = 2.275957200481571e-15 relative error = 1.442801474133905e-12 % Correct digits = 14 h = 0.1 y1[1] (analytic) = -0.9874797699088647 y1[1] (numeric) = -0.9874797699088657 absolute error = 9.992007221626409e-16 relative error = 1.011869561899843e-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 y2[1] (analytic) = -0.2555411020268329 y2[1] (numeric) = -0.2555411020268306 absolute error = 2.386979502944087e-15 relative error = 9.340882871724655e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.9667981925794605 y1[1] (numeric) = -0.9667981925794619 absolute error = 1.332267629550188e-15 relative error = 1.378020397406452e-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 y2[1] (analytic) = -0.3507832276896215 y2[1] (numeric) = -0.350783227689619 absolute error = 2.498001805406602e-15 relative error = 7.121212213763177e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.9364566872907957 y1[1] (numeric) = -0.9364566872907972 absolute error = 1.554312234475219e-15 relative error = 1.659780164496345e-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 y2[1] (analytic) = -0.4425204432948541 y2[1] (numeric) = -0.4425204432948514 absolute error = 2.664535259100376e-15 relative error = 6.021270428234158e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.8967584163341462 y1[1] (numeric) = -0.896758416334148 absolute error = 1.77635683940025e-15 relative error = 1.98086441905035e-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 y2[1] (analytic) = -0.5298361409084948 y2[1] (numeric) = -0.5298361409084922 absolute error = 2.664535259100376e-15 relative error = 5.028979817291387e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.8481000317104072 y1[1] (numeric) = -0.8481000317104093 absolute error = 2.109423746787797e-15 relative error = 2.487234604311491e-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 y2[1] (analytic) = -0.6118578909427207 y2[1] (numeric) = -0.6118578909427179 absolute error = 2.775557561562891e-15 relative error = 4.536278117270741e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.7909677119144155 y1[1] (numeric) = -0.7909677119144179 absolute error = 2.442490654175344e-15 relative error = 3.087977697931148e-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 y2[1] (analytic) = -0.6877661591839753 y2[1] (numeric) = -0.6877661591839725 absolute error = 2.775557561562891e-15 relative error = 4.035612285512929e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.7259323042001387 y1[1] (numeric) = -0.7259323042001415 absolute error = 2.886579864025407e-15 relative error = 3.976376099154255e-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 y2[1] (analytic) = -0.7568024953079294 y2[1] (numeric) = -0.7568024953079269 absolute error = 2.55351295663786e-15 relative error = 3.374081048185341e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.6536436208636106 y1[1] (numeric) = -0.6536436208636135 absolute error = 2.886579864025407e-15 relative error = 4.416137130217203e-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 y2[1] (analytic) = -0.8182771110644114 y2[1] (numeric) = -0.818277111064409 absolute error = 2.331468351712829e-15 relative error = 2.849240581445648e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.5748239465332677 y1[1] (numeric) = -0.5748239465332706 absolute error = 2.886579864025407e-15 relative error = 5.021676430556199e-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 = 0.4704 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 y2[1] (analytic) = -0.8715757724135886 y2[1] (numeric) = -0.8715757724135864 absolute error = 2.220446049250313e-15 relative error = 2.547622501141123e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.4902608213406986 y1[1] (numeric) = -0.4902608213407014 absolute error = 2.775557561562891e-15 relative error = 5.661389694515409e-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 = 0.4273 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 y2[1] (analytic) = -0.9161659367494552 y2[1] (numeric) = -0.9161659367494532 absolute error = 1.998401444325282e-15 relative error = 2.181265821141074e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.4007991720799746 y1[1] (numeric) = -0.4007991720799773 absolute error = 2.664535259100376e-15 relative error = 6.648055796304639e-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 = 0.3672 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 y2[1] (analytic) = -0.951602073889516 y2[1] (numeric) = -0.9516020738895141 absolute error = 1.887379141862766e-15 relative error = 1.983370143518515e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.3073328699784194 y1[1] (numeric) = -0.3073328699784219 absolute error = 2.498001805406602e-15 relative error = 8.128000775127013e-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 = 0.2925 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 y2[1] (analytic) = -0.977530117665097 y2[1] (numeric) = -0.9775301176650951 absolute error = 1.887379141862766e-15 relative error = 1.930763162950837e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.2107957994307797 y1[1] (numeric) = -0.2107957994307821 absolute error = 2.359223927328458e-15 relative error = 1.119198738162318e-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 = 0.2061 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 y2[1] (analytic) = -0.9936910036334644 y2[1] (numeric) = -0.9936910036334624 absolute error = 1.998401444325282e-15 relative error = 2.011089400042931e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.1121525269350549 y1[1] (numeric) = -0.1121525269350571 absolute error = 2.192690473634684e-15 relative error = 1.95509680749719e-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 = 0.1114 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 y2[1] (analytic) = -0.9999232575641008 y2[1] (numeric) = -0.9999232575640987 absolute error = 2.109423746787797e-15 relative error = 2.109585641528666e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = -0.01238866346289145 y1[1] (numeric) = -0.0123886634628935 absolute error = 2.048708425128609e-15 relative error = 1.653696083734324e-11 % Correct digits = 13 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 y2[1] (analytic) = -0.9961646088358408 y2[1] (numeric) = -0.9961646088358383 absolute error = 2.442490654175344e-15 relative error = 2.451894629171518e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = 0.08749898343944551 y1[1] (numeric) = 0.08749898343944358 absolute error = 1.929012505286209e-15 relative error = 2.204611333137602e-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 = 0.08716 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 y2[1] (analytic) = -0.9824526126243328 y2[1] (numeric) = -0.98245261262433 absolute error = 2.775557561562891e-15 relative error = 2.82513123370786e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = 0.186512369422574 y1[1] (numeric) = 0.1865123694225722 absolute error = 1.831867990631508e-15 relative error = 9.821697061180506e-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 = 0.1832 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 y2[1] (analytic) = -0.958924274663139 y2[1] (numeric) = -0.9589242746631359 absolute error = 3.108624468950438e-15 relative error = 3.241783059504327e-13 % Correct digits = 15 h = 0.1 y1[1] (analytic) = 0.2836621854632246 y1[1] (numeric) = 0.2836621854632228 absolute error = 1.77635683940025e-15 relative error = 6.262226445514523e-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 = 0.272 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 ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2; Iterations = 50 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 104.1 %