##############ECHO OF PROBLEM################# ##############temp/mtest1postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=10.0; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_display_interval=0.1; glob_max_minutes=10; /* 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(1.0 + cos(x)); } double exact_soln_y2 (double x) { return(1.0 + sin(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 = 9.9 estimated_steps = 9900000 step_error = 1.01010101010101e-17 est_needed_step_err = 1.01010101010101e-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 = 7.456680367024186e-160 estimated_step_error = 7.456680367024186e-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 = 5.004093412037816e-152 estimated_step_error = 5.004093412037816e-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 = 3.358190142481624e-144 estimated_step_error = 3.358190142481624e-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 = 1.014950270158055e-120 estimated_step_error = 1.014950270158055e-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 = 6.811212724408107e-113 estimated_step_error = 6.811212724408107e-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 = 4.570923134360025e-105 estimated_step_error = 4.570923134360025e-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 = 2.05854901161809e-89 estimated_step_error = 2.05854901161809e-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 = 1.381458319740244e-81 estimated_step_error = 1.381458319740244e-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 = 9.270668118428105e-74 estimated_step_error = 9.270668118428105e-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 = 6.221249002016115e-66 estimated_step_error = 6.221249002016115e-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 = 4.174750875079241e-58 estimated_step_error = 4.174750875079241e-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 y1[1] (analytic) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 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 y1[1] (analytic) = 1.980066577841242 y1[1] (numeric) = 1.980066577841242 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.198669330795061 y2[1] (numeric) = 1.198669330795061 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 = 0.1947 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 y1[1] (analytic) = 1.955336489125606 y1[1] (numeric) = 1.955336489125606 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.29552020666134 y2[1] (numeric) = 1.29552020666134 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 = 0.2823 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 y1[1] (analytic) = 1.921060994002885 y1[1] (numeric) = 1.921060994002885 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.389418342308651 y2[1] (numeric) = 1.389418342308651 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 y1[1] (analytic) = 1.877582561890373 y1[1] (numeric) = 1.877582561890373 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.479425538604203 y2[1] (numeric) = 1.479425538604203 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) = 1.825335614909678 y1[1] (numeric) = 1.825335614909678 absolute error = 2.220446049250313e-16 relative error = 1.216459061617655e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.564642473395035 y2[1] (numeric) = 1.564642473395035 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) = 1.764842187284489 y1[1] (numeric) = 1.764842187284489 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.644217687237691 y2[1] (numeric) = 1.644217687237691 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) = 1.696706709347165 y1[1] (numeric) = 1.696706709347165 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.717356090899523 y2[1] (numeric) = 1.717356090899523 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) = 1.621609968270664 y1[1] (numeric) = 1.621609968270665 absolute error = 2.220446049250313e-16 relative error = 1.369284903704845e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.783326909627483 y2[1] (numeric) = 1.783326909627483 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) = 1.54030230586814 y1[1] (numeric) = 1.54030230586814 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.841470984807896 y2[1] (numeric) = 1.841470984807897 absolute error = 2.220446049250313e-16 relative error = 1.205800182337357e-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 y1[1] (analytic) = 1.453596121425577 y1[1] (numeric) = 1.453596121425577 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.891207360061435 y2[1] (numeric) = 1.891207360061435 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 = 0.4042 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) = 1.362357754476674 y1[1] (numeric) = 1.362357754476674 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.932039085967226 y2[1] (numeric) = 1.932039085967227 absolute error = 2.220446049250313e-16 relative error = 1.149275946526052e-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) = 1.267498828624587 y1[1] (numeric) = 1.267498828624587 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.963558185417193 y2[1] (numeric) = 1.963558185417193 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 = 0.2578 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) = 1.169967142900241 y1[1] (numeric) = 1.169967142900241 absolute error = 2.220446049250313e-16 relative error = 1.897870433990165e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.98544972998846 y2[1] (numeric) = 1.98544972998846 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 = 0.1675 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) = 1.070737201667703 y1[1] (numeric) = 1.070737201667703 absolute error = 2.220446049250313e-16 relative error = 2.073754461684816e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.997494986604055 y2[1] (numeric) = 1.997494986604055 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 = 0.07056 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) = 0.9708004776987109 y1[1] (numeric) = 0.9708004776987111 absolute error = 2.220446049250313e-16 relative error = 2.287232134984004e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.999573603041505 y2[1] (numeric) = 1.999573603041505 absolute error = 2.220446049250313e-16 relative error = 1.110459772960017e-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 = 0.02919 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) = 0.8711555057044749 y1[1] (numeric) = 0.8711555057044752 absolute error = 3.33066907387547e-16 relative error = 3.823277304758657e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.991664810452469 y2[1] (numeric) = 1.991664810452469 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) = 0.7727979053069125 y1[1] (numeric) = 0.7727979053069128 absolute error = 3.33066907387547e-16 relative error = 4.309883672048402e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.973847630878195 y2[1] (numeric) = 1.973847630878195 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 = 0.2213 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) = 0.676710433136496 y1[1] (numeric) = 0.6767104331364965 absolute error = 4.440892098500626e-16 relative error = 6.562470269473258e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.946300087687414 y2[1] (numeric) = 1.946300087687414 absolute error = 2.220446049250313e-16 relative error = 1.140854929461899e-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) = 0.5838531634528572 y1[1] (numeric) = 0.5838531634528575 absolute error = 3.33066907387547e-16 relative error = 5.704634799233048e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.909297426825681 y2[1] (numeric) = 1.909297426825681 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 = 0.3784 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) = 0.4951538954001421 y1[1] (numeric) = 0.4951538954001425 absolute error = 3.885780586188048e-16 relative error = 7.847621966192721e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.863209366648873 y2[1] (numeric) = 1.863209366648874 absolute error = 2.220446049250313e-16 relative error = 1.191731905708459e-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) = 0.4114988827446537 y1[1] (numeric) = 0.4114988827446542 absolute error = 4.996003610813204e-16 relative error = 1.214098949064064e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.80849640381959 y2[1] (numeric) = 1.80849640381959 absolute error = 2.220446049250313e-16 relative error = 1.227785714453551e-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) = 0.3337239787201752 y1[1] (numeric) = 0.3337239787201758 absolute error = 5.551115123125783e-16 relative error = 1.663385155724859e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.74570521217672 y2[1] (numeric) = 1.74570521217672 absolute error = 2.220446049250313e-16 relative error = 1.271947883160433e-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) = 0.262606284458754 y1[1] (numeric) = 0.2626062844587545 absolute error = 4.996003610813204e-16 relative error = 1.902469173999489e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.67546318055115 y2[1] (numeric) = 1.675463180551151 absolute error = 6.661338147750939e-16 relative error = 3.975818881056918e-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) = 0.1988563844530657 y1[1] (numeric) = 0.1988563844530663 absolute error = 5.551115123125783e-16 relative error = 2.791519688137527e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.598472144103956 y2[1] (numeric) = 1.598472144103956 absolute error = 6.661338147750939e-16 relative error = 4.167315753559808e-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 y1[1] (analytic) = 0.1431112466310522 y1[1] (numeric) = 0.1431112466310528 absolute error = 5.551115123125783e-16 relative error = 3.878881117873865e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.515501371821463 y2[1] (numeric) = 1.515501371821464 absolute error = 8.881784197001252e-16 relative error = 5.860624320205227e-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 y1[1] (analytic) = 0.09592785798293835 y1[1] (numeric) = 0.09592785798293887 absolute error = 5.273559366969494e-16 relative error = 5.497422206495474e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.427379880233829 y2[1] (numeric) = 1.42737988023383 absolute error = 1.110223024625157e-15 relative error = 7.778048717089127e-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 = 0.3864 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) = 0.05777765933134149 y1[1] (numeric) = 0.05777765933134187 absolute error = 3.747002708109903e-16 relative error = 6.485210289710268e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.334988150155904 y2[1] (numeric) = 1.334988150155905 absolute error = 1.332267629550188e-15 relative error = 9.979621387610083e-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 y1[1] (analytic) = 0.02904183485040923 y1[1] (numeric) = 0.02904183485040948 absolute error = 2.498001805406602e-16 relative error = 8.601391125159582e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.239249329213981 y2[1] (numeric) = 1.239249329213983 absolute error = 1.554312234475219e-15 relative error = 1.254236897962312e-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) = 0.01000750339955436 y1[1] (numeric) = 0.01000750339955452 absolute error = 1.595945597898663e-16 relative error = 1.594748994009565e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.141120008059866 y2[1] (numeric) = 1.141120008059867 absolute error = 1.332267629550188e-15 relative error = 1.16750878096977e-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) = 0.000864849726720518 y1[1] (numeric) = 0.0008648497267205041 absolute error = 1.387778780781446e-17 relative error = 1.604647302189547e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.041580662433289 y2[1] (numeric) = 1.041580662433291 absolute error = 1.554312234475219e-15 relative error = 1.49226295239018e-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 = 0.04154 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) = 0.001705224205246991 y1[1] (numeric) = 0.00170522420524688 absolute error = 1.110223024625157e-16 relative error = 6.5107158414066e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 0.9416258565724186 y2[1] (numeric) = 0.9416258565724202 absolute error = 1.554312234475219e-15 relative error = 1.650668600088171e-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 = 0.05827 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) = 0.01252023009113534 y1[1] (numeric) = 0.01252023009113508 absolute error = 2.671474153004283e-16 relative error = 2.133726084551559e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 0.84225430585675 y2[1] (numeric) = 0.8422543058567517 absolute error = 1.665334536937735e-15 relative error = 1.97723481537294e-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) = 0.03320180742053946 y1[1] (numeric) = 0.03320180742053894 absolute error = 5.204170427930421e-16 relative error = 1.567435881430657e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 0.744458897973167 y2[1] (numeric) = 0.7444588979731687 absolute error = 1.665334536937735e-15 relative error = 2.236973110902033e-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) = 0.06354331270920432 y1[1] (numeric) = 0.06354331270920363 absolute error = 6.938893903907228e-16 relative error = 1.091994359132951e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 0.6492167723103786 y2[1] (numeric) = 0.6492167723103801 absolute error = 1.554312234475219e-15 relative error = 2.394134441326681e-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) = 0.1032415836658538 y1[1] (numeric) = 0.103241583665853 absolute error = 8.187894806610529e-16 relative error = 7.930810934778988e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.5574795567051459 y2[1] (numeric) = 0.5574795567051476 absolute error = 1.665334536937735e-15 relative error = 2.987256692927557e-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) = 0.1518999682895928 y1[1] (numeric) = 0.1518999682895918 absolute error = 1.02695629777827e-15 relative error = 6.7607406989079e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.4701638590915052 y2[1] (numeric) = 0.4701638590915068 absolute error = 1.609823385706477e-15 relative error = 3.423962421988643e-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) = 0.2090322880855845 y1[1] (numeric) = 0.2090322880855833 absolute error = 1.221245327087672e-15 relative error = 5.842376497298136e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.3881421090572793 y2[1] (numeric) = 0.3881421090572809 absolute error = 1.609823385706477e-15 relative error = 4.147510275595762e-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) = 0.2740676957998613 y1[1] (numeric) = 0.2740676957998598 absolute error = 1.498801083243961e-15 relative error = 5.468725815604568e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.3122338408160247 y2[1] (numeric) = 0.3122338408160262 absolute error = 1.498801083243961e-15 relative error = 4.800251885980191e-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) = 0.3463563791363894 y1[1] (numeric) = 0.3463563791363881 absolute error = 1.332267629550188e-15 relative error = 3.846522569822694e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.2431975046920706 y2[1] (numeric) = 0.2431975046920717 absolute error = 1.165734175856414e-15 relative error = 4.793364049242331e-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) = 0.4251760534667323 y1[1] (numeric) = 0.425176053466731 absolute error = 1.221245327087672e-15 relative error = 2.872328573375847e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.1817228889355886 y2[1] (numeric) = 0.1817228889355895 absolute error = 8.604228440844963e-16 relative error = 4.734807206314399e-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 y1[1] (analytic) = 0.5097391786593013 y1[1] (numeric) = 0.5097391786593004 absolute error = 8.881784197001252e-16 relative error = 1.742417410480752e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.1284242275864114 y2[1] (numeric) = 0.1284242275864119 absolute error = 5.551115123125783e-16 relative error = 4.322482780276538e-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 y1[1] (analytic) = 0.5992008279200254 y1[1] (numeric) = 0.5992008279200247 absolute error = 6.661338147750939e-16 relative error = 1.111703762305218e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.08383406325054477 y2[1] (numeric) = 0.08383406325054499 absolute error = 2.220446049250313e-16 relative error = 2.648620337790778e-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 y1[1] (analytic) = 0.6926671300215806 y1[1] (numeric) = 0.6926671300215803 absolute error = 3.33066907387547e-16 relative error = 4.80846994106924e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.04839792611048399 y2[1] (numeric) = 0.04839792611048402 absolute error = 2.775557561562891e-17 relative error = 5.734868794226388e-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) = 0.7892042005692204 y1[1] (numeric) = 0.7892042005692204 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.02246988233490299 y2[1] (numeric) = 0.02246988233490291 absolute error = 7.632783294297951e-17 relative error = 3.396895088516673e-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 = 0.2061 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) = 0.8878474730649452 y1[1] (numeric) = 0.8878474730649456 absolute error = 4.440892098500626e-16 relative error = 5.001863758388801e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.006308996366535591 y2[1] (numeric) = 0.006308996366535521 absolute error = 6.938893903907228e-17 relative error = 1.099841163439682e-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 y1[1] (analytic) = 0.9876113365371085 y1[1] (numeric) = 0.9876113365371094 absolute error = 8.881784197001252e-16 relative error = 8.993197899229995e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 7.674243589916863e-05 y2[1] (numeric) = 7.674243589910444e-05 absolute error = 6.418476861114186e-17 relative error = 8.363660582193898e-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 y1[1] (analytic) = 1.087498983439446 y1[1] (numeric) = 1.087498983439447 absolute error = 1.332267629550188e-15 relative error = 1.225074827506146e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.003835391164159208 y2[1] (numeric) = 0.003835391164159333 absolute error = 1.257674520083185e-16 relative error = 3.279129732153127e-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 y1[1] (analytic) = 1.186512369422574 y1[1] (numeric) = 1.186512369422576 absolute error = 1.554312234475219e-15 relative error = 1.309984012414163e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.01754738737566719 y2[1] (numeric) = 0.01754738737566752 absolute error = 3.295974604355933e-16 relative error = 1.878327829547111e-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 = 0.1832 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) = 1.283662185463225 y1[1] (numeric) = 1.283662185463226 absolute error = 1.77635683940025e-15 relative error = 1.383819559005885e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.04107572533686099 y2[1] (numeric) = 0.04107572533686159 absolute error = 5.967448757360216e-16 relative error = 1.452792058672444e-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 = 0.272 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 TOP MAIN SOLVE Loop x[1] = 5.099999999999998 y1[1] (analytic) = 1.377977742712979 y1[1] (numeric) = 1.377977742712981 absolute error = 1.998401444325282e-15 relative error = 1.450242179086874e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.07418531767226688 y2[1] (numeric) = 0.07418531767226777 absolute error = 8.881784197001252e-16 relative error = 1.197242860944381e-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 = 0.3499 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 = 0.3499 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.199999999999998 y1[1] (analytic) = 1.468516671300375 y1[1] (numeric) = 1.468516671300377 absolute error = 2.220446049250313e-15 relative error = 1.512033259577573e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.1165453442798455 y2[1] (numeric) = 0.1165453442798468 absolute error = 1.290634266126744e-15 relative error = 1.107409544415355e-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 = 0.4139 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 = 0.4139 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.299999999999997 y1[1] (analytic) = 1.554374336179158 y1[1] (numeric) = 1.554374336179161 absolute error = 2.442490654175344e-15 relative error = 1.571365788359118e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.1677325577760973 y2[1] (numeric) = 0.1677325577760989 absolute error = 1.609823385706477e-15 relative error = 9.597560587225986e-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 = 0.4614 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 = 0.4614 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.399999999999997 y1[1] (analytic) = 1.634692875942632 y1[1] (numeric) = 1.634692875942634 absolute error = 2.220446049250313e-15 relative error = 1.358326130815191e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.2272355124440106 y2[1] (numeric) = 0.2272355124440127 absolute error = 2.081668171172169e-15 relative error = 9.160839997159678e-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 = 0.4905 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 = 0.4905 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.499999999999996 y1[1] (analytic) = 1.708669774291258 y1[1] (numeric) = 1.70866977429126 absolute error = 2.442490654175344e-15 relative error = 1.429469105689816e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.2944596744296055 y2[1] (numeric) = 0.2944596744296082 absolute error = 2.664535259100376e-15 relative error = 9.04889698143495e-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 = 0.5 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 = 0.5 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.599999999999996 y1[1] (analytic) = 1.775565878510247 y1[1] (numeric) = 1.77556587851025 absolute error = 2.442490654175344e-15 relative error = 1.375612520907795e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.3687333621276757 y2[1] (numeric) = 0.3687333621276788 absolute error = 3.05311331771918e-15 relative error = 8.280002927052815e-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 = 0.4896 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 = 0.4896 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.699999999999996 y1[1] (analytic) = 1.834712784839157 y1[1] (numeric) = 1.83471278483916 absolute error = 2.220446049250313e-15 relative error = 1.210241770591342e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.4493144574023586 y2[1] (numeric) = 0.4493144574023623 absolute error = 3.663735981263017e-15 relative error = 8.154057633587697e-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 = 0.4597 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 = 0.4597 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.799999999999995 y1[1] (analytic) = 1.885519516941317 y1[1] (numeric) = 1.885519516941319 absolute error = 1.998401444325282e-15 relative error = 1.05986781169313e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 0.5353978205862386 y2[1] (numeric) = 0.5353978205862429 absolute error = 4.218847493575595e-15 relative error = 7.879836882705518e-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 = 0.4114 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 = 0.4114 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.899999999999995 y1[1] (analytic) = 1.927478430744034 y1[1] (numeric) = 1.927478430744036 absolute error = 1.554312234475219e-15 relative error = 8.063966940866013e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.626123335169759 y2[1] (numeric) = 0.6261233351697637 absolute error = 4.662936703425657e-15 relative error = 7.44731339898298e-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 = 0.3468 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 = 0.3468 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.999999999999995 y1[1] (analytic) = 1.960170286650365 y1[1] (numeric) = 1.960170286650366 absolute error = 1.332267629550188e-15 relative error = 6.796693321103404e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.720584501801069 y2[1] (numeric) = 0.7205845018010741 absolute error = 5.10702591327572e-15 relative error = 7.087337988134543e-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 = 0.2683 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 = 0.2683 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.099999999999994 y1[1] (analytic) = 1.983268438442584 y1[1] (numeric) = 1.983268438442584 absolute error = 8.881784197001252e-16 relative error = 4.478357051845145e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.8178374957278989 y2[1] (numeric) = 0.8178374957279044 absolute error = 5.551115123125783e-15 relative error = 6.787552725477731e-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 = 0.1791 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 = 0.1791 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.199999999999994 y1[1] (analytic) = 1.996542097023217 y1[1] (numeric) = 1.996542097023217 absolute error = 4.440892098500626e-16 relative error = 2.22429174176786e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 0.9169105971824973 y2[1] (numeric) = 0.9169105971825033 absolute error = 5.995204332975845e-15 relative error = 6.538482979036384e-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 = 0.0828 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 = 0.0828 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.299999999999994 y1[1] (analytic) = 1.999858636383415 y1[1] (numeric) = 1.999858636383415 absolute error = 2.220446049250313e-16 relative error = 1.11030150274312e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.016813900484344 y2[1] (numeric) = 1.01681390048435 absolute error = 6.217248937900877e-15 relative error = 6.1144413298632e-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 = 0.01681 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 = 0.01681 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.399999999999993 y1[1] (analytic) = 1.993184918758193 y1[1] (numeric) = 1.993184918758192 absolute error = 8.881784197001252e-16 relative error = 4.456076359706172e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.116549204850487 y2[1] (numeric) = 1.116549204850493 absolute error = 6.439293542825908e-15 relative error = 5.767138174343308e-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 = 0.1158 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 = 0.1158 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.499999999999993 y1[1] (analytic) = 1.976587625728025 y1[1] (numeric) = 1.976587625728023 absolute error = 1.77635683940025e-15 relative error = 8.986987555110163e-14 % Correct digits = 16 h = 0.1 y2[1] (analytic) = 1.215119988087809 y2[1] (numeric) = 1.215119988087815 absolute error = 6.661338147750939e-15 relative error = 5.482041455209417e-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 = 0.2101 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 = 0.2101 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.599999999999993 y1[1] (analytic) = 1.950232591958532 y1[1] (numeric) = 1.950232591958529 absolute error = 2.442490654175344e-15 relative error = 1.252409924973339e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.311541363513371 y2[1] (numeric) = 1.311541363513378 absolute error = 6.883382752675971e-15 relative error = 5.248315412818313e-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 = 0.296 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 = 0.296 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.699999999999992 y1[1] (analytic) = 1.914383148235323 y1[1] (numeric) = 1.914383148235319 absolute error = 3.33066907387547e-15 relative error = 1.73981320141983e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.404849920616591 y2[1] (numeric) = 1.404849920616598 absolute error = 6.883382752675971e-15 relative error = 4.899728185666155e-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 = 0.3702 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 = 0.3702 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.799999999999992 y1[1] (analytic) = 1.869397490349829 y1[1] (numeric) = 1.869397490349825 absolute error = 3.996802888650564e-15 relative error = 2.138016611920573e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.494113351138601 y2[1] (numeric) = 1.494113351138608 absolute error = 6.661338147750939e-15 relative error = 4.458388744518354e-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 = 0.4296 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 = 0.4296 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.899999999999991 y1[1] (analytic) = 1.815725100125362 y1[1] (numeric) = 1.815725100125357 absolute error = 4.884981308350689e-15 relative error = 2.690374940575211e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.578439764388193 y2[1] (numeric) = 1.5784397643882 absolute error = 6.661338147750939e-15 relative error = 4.220204215605839e-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 = 0.4718 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 = 0.4718 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.999999999999991 y1[1] (analytic) = 1.75390225434331 y1[1] (numeric) = 1.753902254343305 absolute error = 5.773159728050814e-15 relative error = 3.291608590931642e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.656986598718782 y2[1] (numeric) = 1.656986598718789 absolute error = 6.439293542825908e-15 relative error = 3.88614702605616e-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 = 0.4953 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 = 0.4953 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.099999999999991 y1[1] (analytic) = 1.684546666442813 y1[1] (numeric) = 1.684546666442806 absolute error = 6.661338147750939e-15 relative error = 3.954380297351696e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.72896904012587 y2[1] (numeric) = 1.728969040125876 absolute error = 5.995204332975845e-15 relative error = 3.467502421292281e-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 = 0.499 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 = 0.499 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.19999999999999 y1[1] (analytic) = 1.608351314532262 y1[1] (numeric) = 1.608351314532255 absolute error = 7.549516567451064e-15 relative error = 4.693947459884783e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.793667863849147 y2[1] (numeric) = 1.793667863849153 absolute error = 5.551115123125783e-15 relative error = 3.09484003979047e-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 = 0.4828 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 = 0.4828 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.29999999999999 y1[1] (analytic) = 1.526077517381114 y1[1] (numeric) = 1.526077517381105 absolute error = 8.215650382226158e-15 relative error = 5.383507907465247e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.850436620628559 y2[1] (numeric) = 1.850436620628564 absolute error = 4.884981308350689e-15 relative error = 2.639907389365949e-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 = 0.4474 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 = 0.4474 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.39999999999999 y1[1] (analytic) = 1.4385473275744 y1[1] (numeric) = 1.438547327574391 absolute error = 8.881784197001252e-15 relative error = 6.174134160728123e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.898708095811622 y2[1] (numeric) = 1.898708095811626 absolute error = 4.218847493575595e-15 relative error = 2.221956867873471e-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 = 0.3941 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 = 0.3941 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.499999999999989 y1[1] (analytic) = 1.346635317835036 y1[1] (numeric) = 1.346635317835026 absolute error = 9.769962616701378e-15 relative error = 7.255091625257825e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.937999976774735 y2[1] (numeric) = 1.937999976774739 absolute error = 3.552713678800501e-15 relative error = 1.833185614745471e-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 = 0.3251 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 = 0.3251 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.599999999999989 y1[1] (analytic) = 1.251259842582266 y1[1] (numeric) = 1.251259842582256 absolute error = 1.043609643147647e-14 relative error = 8.340471000762844e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.967919672031484 y2[1] (numeric) = 1.967919672031486 absolute error = 2.664535259100376e-15 relative error = 1.353985783550695e-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 = 0.2432 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 = 0.2432 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.699999999999989 y1[1] (analytic) = 1.153373862037876 y1[1] (numeric) = 1.153373862037865 absolute error = 1.088018564132653e-14 relative error = 9.433355479464853e-13 % Correct digits = 15 h = 0.1 y2[1] (analytic) = 1.988168233876999 y2[1] (numeric) = 1.988168233877 absolute error = 1.554312234475219e-15 relative error = 7.817810424645278e-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 = 0.1516 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 = 0.1516 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.799999999999988 y1[1] (analytic) = 1.053955420562661 y1[1] (numeric) = 1.05395542056265 absolute error = 1.154631945610163e-14 relative error = 1.095522564885861e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.998543345374604 y2[1] (numeric) = 1.998543345374605 absolute error = 6.661338147750939e-16 relative error = 3.333096659208233e-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 = 0.05388 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 = 0.05388 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.899999999999988 y1[1] (analytic) = 0.9539978743604755 y1[1] (numeric) = 0.9539978743604636 absolute error = 1.187938636348917e-14 relative error = 1.245221470902403e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.998941341839773 y2[1] (numeric) = 1.998941341839772 absolute error = 6.661338147750939e-16 relative error = 3.332433027584501e-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 = 0.04595 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 = 0.04595 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.999999999999988 y1[1] (analytic) = 0.8544999661913988 y1[1] (numeric) = 0.8544999661913867 absolute error = 1.210143096841421e-14 relative error = 1.416200286391072e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.989358246623384 y2[1] (numeric) = 1.989358246623382 absolute error = 1.998401444325282e-15 relative error = 1.004545786419941e-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 = 0.144 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 = 0.144 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.099999999999987 y1[1] (analytic) = 0.7564558462642209 y1[1] (numeric) = 0.7564558462642088 absolute error = 1.210143096841421e-14 relative error = 1.599753776532692e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.96988981084509 y2[1] (numeric) = 1.969889810845086 absolute error = 3.33066907387547e-15 relative error = 1.690789533271712e-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 = 0.2362 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 = 0.2362 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.199999999999987 y1[1] (analytic) = 0.6608451390161771 y1[1] (numeric) = 0.660845139016165 absolute error = 1.210143096841421e-14 relative error = 1.83120526337381e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.940730556679777 y2[1] (numeric) = 1.940730556679773 absolute error = 4.440892098500626e-15 relative error = 2.288257936278466e-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 = 0.3191 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 = 0.3191 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.299999999999986 y1[1] (analytic) = 0.568623155029392 y1[1] (numeric) = 0.5686231550293801 absolute error = 1.187938636348917e-14 relative error = 2.089149247338535e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.9021718337563 y2[1] (numeric) = 1.902171833756294 absolute error = 5.995204332975845e-15 relative error = 3.151768008853785e-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 = 0.3892 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 = 0.3892 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.399999999999986 y1[1] (analytic) = 0.4807113458833265 y1[1] (numeric) = 0.480711345883315 absolute error = 1.154631945610163e-14 relative error = 2.40192363982689e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.854598908088288 y2[1] (numeric) = 1.854598908088281 absolute error = 7.105427357601002e-15 relative error = 3.831247460899912e-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 = 0.4438 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 = 0.4438 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.499999999999986 y1[1] (analytic) = 0.3979880973151877 y1[1] (numeric) = 0.3979880973151766 absolute error = 1.104671909502031e-14 relative error = 2.77564057054496e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.798487112623499 y2[1] (numeric) = 1.79848711262349 absolute error = 8.215650382226158e-15 relative error = 4.568089659670556e-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 = 0.4807 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 = 0.4807 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.599999999999985 y1[1] (analytic) = 0.321279952679998 y1[1] (numeric) = 0.3212799526799875 absolute error = 1.043609643147647e-14 relative error = 3.248287465315664e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.734397097874123 y2[1] (numeric) = 1.734397097874113 absolute error = 9.547918011776346e-15 relative error = 5.505035740361521e-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 = 0.4985 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 = 0.4985 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.699999999999985 y1[1] (analytic) = 0.2513533544026108 y1[1] (numeric) = 0.251353354402601 absolute error = 9.71445146547012e-15 relative error = 3.864858493159309e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.662969230082194 y2[1] (numeric) = 1.662969230082183 absolute error = 1.110223024625157e-14 relative error = 6.676148930129528e-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 = 0.4963 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 = 0.4963 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.799999999999985 y1[1] (analytic) = 0.1889069859383534 y1[1] (numeric) = 0.1889069859383446 absolute error = 8.826273045769994e-15 relative error = 4.672285147067191e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.584917192891775 y2[1] (numeric) = 1.584917192891762 absolute error = 1.221245327087672e-14 relative error = 7.705420400288789e-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 = 0.4744 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 = 0.4744 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.899999999999984 y1[1] (analytic) = 0.1345647907588958 y1[1] (numeric) = 0.1345647907588881 absolute error = 7.743805596760467e-15 relative error = 5.754704148899766e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.501020856457898 y2[1] (numeric) = 1.501020856457885 absolute error = 1.310063169057685e-14 relative error = 8.727814563144481e-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 = 0.4336 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 = 0.4336 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.999999999999984 y1[1] (analytic) = 0.08886973811532961 y1[1] (numeric) = 0.08886973811532312 absolute error = 6.494804694057166e-15 relative error = 7.308229811174432e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.412118485241771 y2[1] (numeric) = 1.412118485241757 absolute error = 1.4210854715202e-14 relative error = 1.006350024004462e-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 = 0.3755 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 = 0.3755 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.099999999999984 y1[1] (analytic) = 0.05227839786889321 y1[1] (numeric) = 0.05227839786888804 absolute error = 5.176414852314792e-15 relative error = 9.901632535290207e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 1.319098362349367 y2[1] (numeric) = 1.319098362349352 absolute error = 1.509903313490213e-14 relative error = 1.144648008508641e-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 = 0.3024 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 = 0.3024 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.199999999999983 y1[1] (analytic) = 0.02515637859583997 y1[1] (numeric) = 0.02515637859583628 absolute error = 3.691491556878645e-15 relative error = 1.467417713887124e-11 % Correct digits = 13 h = 0.1 y2[1] (analytic) = 1.222889914100263 y2[1] (numeric) = 1.222889914100247 absolute error = 1.576516694967722e-14 relative error = 1.28917302922368e-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 = 0.2173 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 = 0.2173 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.299999999999983 y1[1] (analytic) = 0.007774674547398663 y1[1] (numeric) = 0.007774674547396564 absolute error = 2.099015405931937e-15 relative error = 2.699811282305378e-11 % Correct digits = 13 h = 0.1 y2[1] (analytic) = 1.124454423507079 y2[1] (numeric) = 1.124454423507063 absolute error = 1.643130076445232e-14 relative error = 1.461268720274537e-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 = 0.1235 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 = 0.1235 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.399999999999983 y1[1] (analytic) = 0.0003069579647939635 y1[1] (numeric) = 0.0003069579647934596 absolute error = 5.039371697712625e-16 relative error = 1.641713939918501e-10 % Correct digits = 12 h = 0.1 y2[1] (analytic) = 1.024775425453376 y2[1] (numeric) = 1.024775425453359 absolute error = 1.709743457922741e-14 relative error = 1.668407941346101e-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 = 0.02477 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 = 0.02477 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.499999999999982 y1[1] (analytic) = 0.002827843803620222 y1[1] (numeric) = 0.002827843803621419 absolute error = 1.196091836686008e-15 relative error = 4.229695555160312e-11 % Correct digits = 13 h = 0.1 y2[1] (analytic) = 0.9248488795382084 y2[1] (numeric) = 0.9248488795381911 absolute error = 1.731947918415244e-14 relative error = 1.872682074589346e-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 = 0.07494 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 = 0.07494 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.599999999999982 y1[1] (analytic) = 0.0153121442058699 y1[1] (numeric) = 0.01531214420587295 absolute error = 3.04270497686332e-15 relative error = 1.987118809720261e-11 % Correct digits = 13 h = 0.1 y2[1] (analytic) = 0.8256732187770379 y2[1] (numeric) = 0.8256732187770204 absolute error = 1.754152378907747e-14 relative error = 2.124511657900137e-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 = 0.1717 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 = 0.1717 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.699999999999982 y1[1] (analytic) = 0.03763512016868498 y1[1] (numeric) = 0.03763512016868979 absolute error = 4.815592369311616e-15 relative error = 1.279547493864128e-11 % Correct digits = 13 h = 0.1 y2[1] (analytic) = 0.7282393735890746 y2[1] (numeric) = 0.7282393735890572 absolute error = 1.743050148661496e-14 relative error = 2.393512644161219e-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 = 0.2615 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 = 0.2615 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.799999999999981 y1[1] (analytic) = 0.06957372789523963 y1[1] (numeric) = 0.06957372789524627 absolute error = 6.63358257213531e-15 relative error = 9.534608497799344e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 0.6335208707480897 y2[1] (numeric) = 0.6335208707480726 absolute error = 1.709743457922741e-14 relative error = 2.698795788533059e-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 = 0.341 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 = 0.341 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.899999999999981 y1[1] (analytic) = 0.1108088473746301 y1[1] (numeric) = 0.1108088473746387 absolute error = 8.548717289613705e-15 relative error = 7.714832788316637e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 0.542464106224696 y2[1] (numeric) = 0.5424641062246793 absolute error = 1.665334536937735e-14 relative error = 3.069944200599202e-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 = 0.4068 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 = 0.4068 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.99999999999998 y1[1] (analytic) = 0.1609284709235369 y1[1] (numeric) = 0.1609284709235473 absolute error = 1.038058528024521e-14 relative error = 6.450434295853973e-12 % Correct digits = 14 h = 0.1 y2[1] (analytic) = 0.4559788891106465 y2[1] (numeric) = 0.4559788891106306 absolute error = 1.598721155460225e-14 relative error = 3.506129765302104e-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 = 0.4565 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 = 0.4565 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; Iterations = 100 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 102 %