##############ECHO OF PROBLEM################# ##############temp/mtest8postode.ode################# diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 3 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(1.4); 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); array_y2_init[3 + 1] = exact_soln_y2ppp(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=true; glob_h=c(0.001); glob_display_interval=c(0.01); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y1 (double x) { return(c(1.0) + sin(c(x))); } double exact_soln_y2 (double x) { return(c(1.0) + sin(c(x))); } double exact_soln_y2p (double x) { return( cos(c(x))); } double exact_soln_y2pp (double x) { return(neg(sin(c(x)))); } double exact_soln_y2ppp (double x) { return( neg(cos(c(x)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (closed_form) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.099833416646828 y1[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (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) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.11 y2[1] (closed_form) = 1.109778300837175 y2[1] (numeric) = 1.109778300837175 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.109778300837175 y1[1] (numeric) = 1.109778300837175 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1091 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1091 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.12 y2[1] (closed_form) = 1.119712207288919 y2[1] (numeric) = 1.119712207288919 absolute error = 2.220446049250313e-16 relative error = 1.983050675696859e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.119712207288919 y1[1] (numeric) = 1.119712207288919 absolute error = 2.220446049250313e-16 relative error = 1.983050675696859e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1189 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1189 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.13 y2[1] (closed_form) = 1.129634142619695 y2[1] (numeric) = 1.129634142619694 absolute error = 6.661338147750939e-16 relative error = 5.896898735995057e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.129634142619695 y1[1] (numeric) = 1.129634142619694 absolute error = 6.661338147750939e-16 relative error = 5.896898735995057e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1285 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1285 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.14 y2[1] (closed_form) = 1.139543114644237 y2[1] (numeric) = 1.139543114644236 absolute error = 6.661338147750939e-16 relative error = 5.845621865593561e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.139543114644237 y1[1] (numeric) = 1.139543114644236 absolute error = 6.661338147750939e-16 relative error = 5.845621865593561e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1382 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1382 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.15 y2[1] (closed_form) = 1.149438132473599 y2[1] (numeric) = 1.149438132473598 absolute error = 6.661338147750939e-16 relative error = 5.79529942461165e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.149438132473599 y1[1] (numeric) = 1.149438132473598 absolute error = 6.661338147750939e-16 relative error = 5.79529942461165e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1478 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1478 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y2[1] (closed_form) = 1.159318206614246 y2[1] (numeric) = 1.159318206614245 absolute error = 8.881784197001252e-16 relative error = 7.66121341520223e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.159318206614246 y1[1] (numeric) = 1.159318206614245 absolute error = 8.881784197001252e-16 relative error = 7.66121341520223e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1573 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1573 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y2[1] (closed_form) = 1.169182349066996 y2[1] (numeric) = 1.169182349066995 absolute error = 1.110223024625157e-15 relative error = 9.49572173674287e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.169182349066996 y1[1] (numeric) = 1.169182349066995 absolute error = 1.110223024625157e-15 relative error = 9.49572173674287e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1667 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1667 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y2[1] (closed_form) = 1.179029573425824 y2[1] (numeric) = 1.179029573425823 absolute error = 8.881784197001252e-16 relative error = 7.533130972443778e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.179029573425824 y1[1] (numeric) = 1.179029573425823 absolute error = 8.881784197001252e-16 relative error = 7.533130972443778e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1761 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1761 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y2[1] (closed_form) = 1.188858894976501 y2[1] (numeric) = 1.1888588949765 absolute error = 1.110223024625157e-15 relative error = 9.338560104284719e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.188858894976501 y1[1] (numeric) = 1.1888588949765 absolute error = 1.110223024625157e-15 relative error = 9.338560104284719e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1855 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1855 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y2[1] (closed_form) = 1.198669330795061 y2[1] (numeric) = 1.19866933079506 absolute error = 1.110223024625157e-15 relative error = 9.262129230325435e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.198669330795061 y1[1] (numeric) = 1.19866933079506 absolute error = 1.110223024625157e-15 relative error = 9.262129230325435e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (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) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y2[1] (closed_form) = 1.2084598998461 y2[1] (numeric) = 1.208459899846098 absolute error = 1.110223024625157e-15 relative error = 9.187090318566187e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.2084598998461 y1[1] (numeric) = 1.208459899846098 absolute error = 1.110223024625157e-15 relative error = 9.187090318566187e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2039 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2039 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y2[1] (closed_form) = 1.218229623080869 y2[1] (numeric) = 1.218229623080868 absolute error = 1.110223024625157e-15 relative error = 9.113413461556065e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.218229623080869 y1[1] (numeric) = 1.218229623080868 absolute error = 1.110223024625157e-15 relative error = 9.113413461556065e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.213 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.213 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y2[1] (closed_form) = 1.227977523535189 y2[1] (numeric) = 1.227977523535187 absolute error = 1.332267629550188e-15 relative error = 1.084928350899096e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.227977523535189 y1[1] (numeric) = 1.227977523535187 absolute error = 1.332267629550188e-15 relative error = 1.084928350899096e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.222 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.222 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y2[1] (closed_form) = 1.237702626427135 y2[1] (numeric) = 1.237702626427134 absolute error = 8.881784197001252e-16 relative error = 7.176024359453951e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.237702626427135 y1[1] (numeric) = 1.237702626427134 absolute error = 8.881784197001252e-16 relative error = 7.176024359453951e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2309 Order of pole (three term test) = 32.94 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2309 Order of pole (three term test) = 32.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y2[1] (closed_form) = 1.247403959254523 y2[1] (numeric) = 1.247403959254522 absolute error = 8.881784197001252e-16 relative error = 7.120214851898666e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.247403959254523 y1[1] (numeric) = 1.247403959254522 absolute error = 8.881784197001252e-16 relative error = 7.120214851898666e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2397 Order of pole (three term test) = 32.94 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2397 Order of pole (three term test) = 32.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y2[1] (closed_form) = 1.257080551892155 y2[1] (numeric) = 1.257080551892154 absolute error = 8.881784197001252e-16 relative error = 7.065405779790649e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.257080551892155 y1[1] (numeric) = 1.257080551892154 absolute error = 8.881784197001252e-16 relative error = 7.065405779790649e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2484 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2484 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y2[1] (closed_form) = 1.266731436688831 y2[1] (numeric) = 1.26673143668883 absolute error = 1.110223024625157e-15 relative error = 8.764470451031203e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.266731436688831 y1[1] (numeric) = 1.26673143668883 absolute error = 1.110223024625157e-15 relative error = 8.764470451031203e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2571 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2571 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y2[1] (closed_form) = 1.276355648564114 y2[1] (numeric) = 1.276355648564113 absolute error = 1.110223024625157e-15 relative error = 8.698382977143912e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.276355648564114 y1[1] (numeric) = 1.276355648564113 absolute error = 1.110223024625157e-15 relative error = 8.698382977143912e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2656 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2656 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y2[1] (closed_form) = 1.285952225104836 y2[1] (numeric) = 1.285952225104835 absolute error = 8.881784197001252e-16 relative error = 6.906776180022688e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.285952225104836 y1[1] (numeric) = 1.285952225104835 absolute error = 8.881784197001252e-16 relative error = 6.906776180022688e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.274 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.274 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y2[1] (closed_form) = 1.29552020666134 y2[1] (numeric) = 1.295520206661339 absolute error = 1.110223024625157e-15 relative error = 8.569708283333465e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.29552020666134 y1[1] (numeric) = 1.295520206661339 absolute error = 1.110223024625157e-15 relative error = 8.569708283333465e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (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) = 32.91 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y2[1] (closed_form) = 1.305058636443444 y2[1] (numeric) = 1.305058636443443 absolute error = 8.881784197001252e-16 relative error = 6.805659109084909e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.305058636443444 y1[1] (numeric) = 1.305058636443443 absolute error = 8.881784197001252e-16 relative error = 6.805659109084909e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2905 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2905 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y2[1] (closed_form) = 1.314566560616118 y2[1] (numeric) = 1.314566560616117 absolute error = 6.661338147750939e-16 relative error = 5.067326636263187e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.314566560616118 y1[1] (numeric) = 1.314566560616117 absolute error = 6.661338147750939e-16 relative error = 5.067326636263187e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2986 Order of pole (three term test) = 32.9 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2986 Order of pole (three term test) = 32.9 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y2[1] (closed_form) = 1.324043028394869 y2[1] (numeric) = 1.324043028394868 absolute error = 8.881784197001252e-16 relative error = 6.708078216890428e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.324043028394869 y1[1] (numeric) = 1.324043028394868 absolute error = 8.881784197001252e-16 relative error = 6.708078216890428e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3066 Order of pole (three term test) = 32.89 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3066 Order of pole (three term test) = 32.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y2[1] (closed_form) = 1.333487092140815 y2[1] (numeric) = 1.333487092140814 absolute error = 1.110223024625157e-15 relative error = 8.325712570961417e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.333487092140815 y1[1] (numeric) = 1.333487092140814 absolute error = 1.110223024625157e-15 relative error = 8.325712570961417e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3144 Order of pole (three term test) = 32.89 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3144 Order of pole (three term test) = 32.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y2[1] (closed_form) = 1.342897807455452 y2[1] (numeric) = 1.342897807455451 absolute error = 1.110223024625157e-15 relative error = 8.267367914829114e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.342897807455452 y1[1] (numeric) = 1.342897807455451 absolute error = 1.110223024625157e-15 relative error = 8.267367914829114e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3221 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3221 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y2[1] (closed_form) = 1.35227423327509 y2[1] (numeric) = 1.352274233275089 absolute error = 8.881784197001252e-16 relative error = 6.568034780556565e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.35227423327509 y1[1] (numeric) = 1.352274233275089 absolute error = 8.881784197001252e-16 relative error = 6.568034780556565e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3297 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3297 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y2[1] (closed_form) = 1.361615431964962 y2[1] (numeric) = 1.361615431964961 absolute error = 1.110223024625157e-15 relative error = 8.153719461176946e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.361615431964962 y1[1] (numeric) = 1.361615431964961 absolute error = 1.110223024625157e-15 relative error = 8.153719461176946e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3371 Order of pole (three term test) = 32.87 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3371 Order of pole (three term test) = 32.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y2[1] (closed_form) = 1.370920469412983 y2[1] (numeric) = 1.370920469412982 absolute error = 8.881784197001252e-16 relative error = 6.478701277838795e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.370920469412983 y1[1] (numeric) = 1.370920469412982 absolute error = 8.881784197001252e-16 relative error = 6.478701277838795e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3445 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3445 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y2[1] (closed_form) = 1.380188415123162 y2[1] (numeric) = 1.380188415123161 absolute error = 8.881784197001252e-16 relative error = 6.435196890280146e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.380188415123162 y1[1] (numeric) = 1.380188415123161 absolute error = 8.881784197001252e-16 relative error = 6.435196890280146e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3516 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3516 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y2[1] (closed_form) = 1.389418342308651 y2[1] (numeric) = 1.389418342308649 absolute error = 1.332267629550188e-15 relative error = 9.588671669156882e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.389418342308651 y1[1] (numeric) = 1.389418342308649 absolute error = 1.332267629550188e-15 relative error = 9.588671669156882e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (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) = 32.85 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y2[1] (closed_form) = 1.398609327984423 y2[1] (numeric) = 1.398609327984422 absolute error = 1.332267629550188e-15 relative error = 9.525659545472629e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.398609327984423 y1[1] (numeric) = 1.398609327984422 absolute error = 1.332267629550188e-15 relative error = 9.525659545472629e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3656 Order of pole (three term test) = 32.84 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3656 Order of pole (three term test) = 32.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y2[1] (closed_form) = 1.40776045305957 y2[1] (numeric) = 1.407760453059569 absolute error = 1.110223024625157e-15 relative error = 7.886448452307651e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.40776045305957 y1[1] (numeric) = 1.407760453059569 absolute error = 1.110223024625157e-15 relative error = 7.886448452307651e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3723 Order of pole (three term test) = 32.83 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3723 Order of pole (three term test) = 32.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y2[1] (closed_form) = 1.416870802429211 y2[1] (numeric) = 1.41687080242921 absolute error = 1.110223024625157e-15 relative error = 7.835739311740281e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.416870802429211 y1[1] (numeric) = 1.41687080242921 absolute error = 1.110223024625157e-15 relative error = 7.835739311740281e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3789 Order of pole (three term test) = 32.83 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3789 Order of pole (three term test) = 32.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y2[1] (closed_form) = 1.425939465066 y2[1] (numeric) = 1.425939465065999 absolute error = 1.110223024625157e-15 relative error = 7.785905726185717e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.425939465066 y1[1] (numeric) = 1.425939465065999 absolute error = 1.110223024625157e-15 relative error = 7.785905726185717e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3854 Order of pole (three term test) = 32.82 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3854 Order of pole (three term test) = 32.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y2[1] (closed_form) = 1.43496553411123 y2[1] (numeric) = 1.434965534111229 absolute error = 1.332267629550188e-15 relative error = 9.284317970573069e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.43496553411123 y1[1] (numeric) = 1.434965534111229 absolute error = 1.332267629550188e-15 relative error = 9.284317970573069e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3917 Order of pole (three term test) = 32.81 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3917 Order of pole (three term test) = 32.81 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y2[1] (closed_form) = 1.44394810696552 y2[1] (numeric) = 1.443948106965519 absolute error = 1.110223024625157e-15 relative error = 7.688801413773159e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.44394810696552 y1[1] (numeric) = 1.443948106965519 absolute error = 1.110223024625157e-15 relative error = 7.688801413773159e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3978 Order of pole (three term test) = 32.8 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3978 Order of pole (three term test) = 32.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y2[1] (closed_form) = 1.452886285379068 y2[1] (numeric) = 1.452886285379067 absolute error = 1.110223024625157e-15 relative error = 7.641499791124336e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.452886285379068 y1[1] (numeric) = 1.452886285379067 absolute error = 1.110223024625157e-15 relative error = 7.641499791124336e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4038 Order of pole (three term test) = 32.79 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4038 Order of pole (three term test) = 32.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y2[1] (closed_form) = 1.461779175541483 y2[1] (numeric) = 1.461779175541482 absolute error = 6.661338147750939e-16 relative error = 4.557007145271034e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.461779175541483 y1[1] (numeric) = 1.461779175541482 absolute error = 6.661338147750939e-16 relative error = 4.557007145271034e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4096 Order of pole (three term test) = 32.79 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4096 Order of pole (three term test) = 32.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y2[1] (closed_form) = 1.470625888171158 y2[1] (numeric) = 1.470625888171158 absolute error = 6.661338147750939e-16 relative error = 4.529593964944307e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.470625888171158 y1[1] (numeric) = 1.470625888171158 absolute error = 6.661338147750939e-16 relative error = 4.529593964944307e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4152 Order of pole (three term test) = 32.78 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4152 Order of pole (three term test) = 32.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y2[1] (closed_form) = 1.479425538604203 y2[1] (numeric) = 1.479425538604202 absolute error = 1.332267629550188e-15 relative error = 9.005303712731262e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.479425538604203 y1[1] (numeric) = 1.479425538604202 absolute error = 1.332267629550188e-15 relative error = 9.005303712731262e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (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) = 32.77 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y2[1] (closed_form) = 1.488177246882908 y2[1] (numeric) = 1.488177246882906 absolute error = 1.332267629550188e-15 relative error = 8.952345107686039e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.488177246882908 y1[1] (numeric) = 1.488177246882906 absolute error = 1.332267629550188e-15 relative error = 8.952345107686039e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4261 Order of pole (three term test) = 32.76 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4261 Order of pole (three term test) = 32.76 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y2[1] (closed_form) = 1.496880137843737 y2[1] (numeric) = 1.496880137843736 absolute error = 1.332267629550188e-15 relative error = 8.900295994770334e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.496880137843737 y1[1] (numeric) = 1.496880137843736 absolute error = 1.332267629550188e-15 relative error = 8.900295994770334e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4312 Order of pole (three term test) = 32.75 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4312 Order of pole (three term test) = 32.75 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y2[1] (closed_form) = 1.505533341204847 y2[1] (numeric) = 1.505533341204846 absolute error = 1.332267629550188e-15 relative error = 8.849140653929334e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.505533341204847 y1[1] (numeric) = 1.505533341204846 absolute error = 1.332267629550188e-15 relative error = 8.849140653929334e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4362 Order of pole (three term test) = 32.74 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4362 Order of pole (three term test) = 32.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y2[1] (closed_form) = 1.514135991653113 y2[1] (numeric) = 1.514135991653112 absolute error = 1.332267629550188e-15 relative error = 8.798863753946143e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.514135991653113 y1[1] (numeric) = 1.514135991653112 absolute error = 1.332267629550188e-15 relative error = 8.798863753946143e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.441 Order of pole (three term test) = 32.74 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.441 Order of pole (three term test) = 32.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y2[1] (closed_form) = 1.522687228930659 y2[1] (numeric) = 1.522687228930658 absolute error = 1.554312234475219e-15 relative error = 1.020769206534141e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.522687228930659 y1[1] (numeric) = 1.522687228930658 absolute error = 1.332267629550188e-15 relative error = 8.749450341721209e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4456 Order of pole (three term test) = 32.73 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4456 Order of pole (three term test) = 32.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y2[1] (closed_form) = 1.531186197920884 y2[1] (numeric) = 1.531186197920882 absolute error = 1.554312234475219e-15 relative error = 1.015103347055856e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.531186197920884 y1[1] (numeric) = 1.531186197920882 absolute error = 1.332267629550188e-15 relative error = 8.700885831907336e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4501 Order of pole (three term test) = 32.72 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4501 Order of pole (three term test) = 32.72 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y2[1] (closed_form) = 1.539632048733969 y2[1] (numeric) = 1.539632048733968 absolute error = 1.554312234475219e-15 relative error = 1.009534866303492e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.539632048733969 y1[1] (numeric) = 1.539632048733968 absolute error = 1.332267629550188e-15 relative error = 8.653155996887074e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4543 Order of pole (three term test) = 32.71 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4543 Order of pole (three term test) = 32.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y2[1] (closed_form) = 1.548023936791874 y2[1] (numeric) = 1.548023936791872 absolute error = 1.998401444325282e-15 relative error = 1.290937043561982e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.548023936791874 y1[1] (numeric) = 1.548023936791872 absolute error = 1.77635683940025e-15 relative error = 1.147499594277317e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4584 Order of pole (three term test) = 32.7 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4584 Order of pole (three term test) = 32.7 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y2[1] (closed_form) = 1.556361022912784 y2[1] (numeric) = 1.556361022912782 absolute error = 1.77635683940025e-15 relative error = 1.141352689542261e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.556361022912784 y1[1] (numeric) = 1.556361022912782 absolute error = 1.554312234475219e-15 relative error = 9.986836033494783e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4623 Order of pole (three term test) = 32.69 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4623 Order of pole (three term test) = 32.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y2[1] (closed_form) = 1.564642473395036 y2[1] (numeric) = 1.564642473395034 absolute error = 1.998401444325282e-15 relative error = 1.277225614353326e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.564642473395036 y1[1] (numeric) = 1.564642473395034 absolute error = 1.77635683940025e-15 relative error = 1.135311657202956e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (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) = 32.68 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y2[1] (closed_form) = 1.572867460100482 y2[1] (numeric) = 1.57286746010048 absolute error = 1.998401444325282e-15 relative error = 1.270546625840689e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.572867460100482 y1[1] (numeric) = 1.57286746010048 absolute error = 1.77635683940025e-15 relative error = 1.129374778525057e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4695 Order of pole (three term test) = 32.67 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4695 Order of pole (three term test) = 32.67 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y2[1] (closed_form) = 1.581035160537305 y2[1] (numeric) = 1.581035160537304 absolute error = 1.77635683940025e-15 relative error = 1.123540376418046e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.581035160537305 y1[1] (numeric) = 1.581035160537304 absolute error = 1.554312234475219e-15 relative error = 9.830978293657906e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4729 Order of pole (three term test) = 32.66 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4729 Order of pole (three term test) = 32.66 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y2[1] (closed_form) = 1.58914475794227 y2[1] (numeric) = 1.589144757942268 absolute error = 2.220446049250313e-15 relative error = 1.397258517924757e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.58914475794227 y1[1] (numeric) = 1.589144757942268 absolute error = 1.998401444325282e-15 relative error = 1.257532666132282e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.476 Order of pole (three term test) = 32.65 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.476 Order of pole (three term test) = 32.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y2[1] (closed_form) = 1.597195441362393 y2[1] (numeric) = 1.597195441362391 absolute error = 1.77635683940025e-15 relative error = 1.112172495236422e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.597195441362393 y1[1] (numeric) = 1.597195441362391 absolute error = 1.554312234475219e-15 relative error = 9.731509333318693e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.479 Order of pole (three term test) = 32.64 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.479 Order of pole (three term test) = 32.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y2[1] (closed_form) = 1.60518640573604 y2[1] (numeric) = 1.605186405736039 absolute error = 1.332267629550188e-15 relative error = 8.299768953869826e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.60518640573604 y1[1] (numeric) = 1.605186405736039 absolute error = 1.110223024625157e-15 relative error = 6.916474128224855e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = 32.63 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = 32.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y2[1] (closed_form) = 1.613116851973434 y2[1] (numeric) = 1.613116851973433 absolute error = 1.332267629550188e-15 relative error = 8.258965417913373e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.613116851973434 y1[1] (numeric) = 1.613116851973433 absolute error = 1.110223024625157e-15 relative error = 6.882471181594477e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4844 Order of pole (three term test) = 32.62 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4844 Order of pole (three term test) = 32.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y2[1] (closed_form) = 1.62098598703656 y2[1] (numeric) = 1.620985987036559 absolute error = 1.110223024625157e-15 relative error = 6.849059976482797e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.62098598703656 y1[1] (numeric) = 1.620985987036559 absolute error = 8.881784197001252e-16 relative error = 5.479247981186237e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4867 Order of pole (three term test) = 32.61 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4867 Order of pole (three term test) = 32.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y2[1] (closed_form) = 1.628793024018469 y2[1] (numeric) = 1.628793024018468 absolute error = 8.881784197001252e-16 relative error = 5.452985165106246e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.628793024018469 y1[1] (numeric) = 1.628793024018468 absolute error = 6.661338147750939e-16 relative error = 4.089738873829684e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4889 Order of pole (three term test) = 32.6 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4889 Order of pole (three term test) = 32.6 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y2[1] (closed_form) = 1.636537182221968 y2[1] (numeric) = 1.636537182221968 absolute error = 4.440892098500626e-16 relative error = 2.713590712599095e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.636537182221968 y1[1] (numeric) = 1.636537182221968 absolute error = 2.220446049250313e-16 relative error = 1.356795356299548e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4909 Order of pole (three term test) = 32.59 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4909 Order of pole (three term test) = 32.59 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y2[1] (closed_form) = 1.644217687237691 y2[1] (numeric) = 1.644217687237691 absolute error = 6.661338147750939e-16 relative error = 4.051372393969365e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.644217687237691 y1[1] (numeric) = 1.644217687237691 absolute error = 2.220446049250313e-16 relative error = 1.350457464656455e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (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) = 32.58 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y2[1] (closed_form) = 1.651833771021537 y2[1] (numeric) = 1.651833771021536 absolute error = 8.881784197001252e-16 relative error = 5.376923727324284e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.651833771021537 y1[1] (numeric) = 1.651833771021537 absolute error = 4.440892098500626e-16 relative error = 2.688461863662142e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4943 Order of pole (three term test) = 32.58 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4943 Order of pole (three term test) = 32.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y2[1] (closed_form) = 1.659384671971474 y2[1] (numeric) = 1.659384671971473 absolute error = 6.661338147750939e-16 relative error = 4.014342340427172e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.659384671971474 y1[1] (numeric) = 1.659384671971473 absolute error = 2.220446049250313e-16 relative error = 1.338114113475724e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4957 Order of pole (three term test) = 32.57 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4957 Order of pole (three term test) = 32.57 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y2[1] (closed_form) = 1.666869635003698 y2[1] (numeric) = 1.666869635003698 absolute error = 6.661338147750939e-16 relative error = 3.996316213256929e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.666869635003698 y1[1] (numeric) = 1.666869635003698 absolute error = 2.220446049250313e-16 relative error = 1.332105404418976e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4969 Order of pole (three term test) = 32.56 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4969 Order of pole (three term test) = 32.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y2[1] (closed_form) = 1.674287911628145 y2[1] (numeric) = 1.674287911628145 absolute error = 6.661338147750939e-16 relative error = 3.978609713112713e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.674287911628145 y1[1] (numeric) = 1.674287911628145 absolute error = 2.220446049250313e-16 relative error = 1.326203237704238e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4979 Order of pole (three term test) = 32.55 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4979 Order of pole (three term test) = 32.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y2[1] (closed_form) = 1.681638760023334 y2[1] (numeric) = 1.681638760023334 absolute error = 2.220446049250313e-16 relative error = 1.320406083658242e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.681638760023334 y1[1] (numeric) = 1.681638760023335 absolute error = 2.220446049250313e-16 relative error = 1.320406083658242e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4987 Order of pole (three term test) = 32.54 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4987 Order of pole (three term test) = 32.54 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y2[1] (closed_form) = 1.688921445110552 y2[1] (numeric) = 1.688921445110551 absolute error = 2.220446049250313e-16 relative error = 1.314712448988395e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.688921445110552 y1[1] (numeric) = 1.688921445110552 absolute error = 2.220446049250313e-16 relative error = 1.314712448988395e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4994 Order of pole (three term test) = 32.53 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4994 Order of pole (three term test) = 32.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y2[1] (closed_form) = 1.696135238627357 y2[1] (numeric) = 1.696135238627357 absolute error = 4.440892098500626e-16 relative error = 2.61824175181605e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.696135238627357 y1[1] (numeric) = 1.696135238627357 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (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) = 32.52 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.52 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y2[1] (closed_form) = 1.703279419200411 y2[1] (numeric) = 1.70327941920041 absolute error = 6.661338147750939e-16 relative error = 3.910889823865802e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.703279419200411 y1[1] (numeric) = 1.70327941920041 absolute error = 2.220446049250313e-16 relative error = 1.303629941288601e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (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) = 32.51 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y2[1] (closed_form) = 1.710353272417608 y2[1] (numeric) = 1.710353272417608 absolute error = 4.440892098500626e-16 relative error = 2.596476511676072e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.710353272417608 y1[1] (numeric) = 1.710353272417608 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (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) = 32.5 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.5 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y2[1] (closed_form) = 1.717356090899523 y2[1] (numeric) = 1.717356090899523 absolute error = 4.440892098500626e-16 relative error = 2.585888926608435e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.717356090899523 y1[1] (numeric) = 1.717356090899523 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (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) = 32.49 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y2[1] (closed_form) = 1.724287174370143 y2[1] (numeric) = 1.724287174370143 absolute error = 2.220446049250313e-16 relative error = 1.287747239702928e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.724287174370143 y1[1] (numeric) = 1.724287174370143 absolute error = 2.220446049250313e-16 relative error = 1.287747239702928e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4994 Order of pole (three term test) = 32.48 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4994 Order of pole (three term test) = 32.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y2[1] (closed_form) = 1.731145829726896 y2[1] (numeric) = 1.731145829726896 absolute error = 2.220446049250313e-16 relative error = 1.282645292569378e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.731145829726896 y1[1] (numeric) = 1.731145829726896 absolute error = 2.220446049250313e-16 relative error = 1.282645292569378e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4988 Order of pole (three term test) = 32.47 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4988 Order of pole (three term test) = 32.47 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y2[1] (closed_form) = 1.737931371109963 y2[1] (numeric) = 1.737931371109963 absolute error = 2.220446049250313e-16 relative error = 1.277637360232575e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.737931371109963 y1[1] (numeric) = 1.737931371109963 absolute error = 2.220446049250313e-16 relative error = 1.277637360232575e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.498 Order of pole (three term test) = 32.46 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.498 Order of pole (three term test) = 32.46 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y2[1] (closed_form) = 1.74464311997086 y2[1] (numeric) = 1.744643119970859 absolute error = 6.661338147750939e-16 relative error = 3.818166633335419e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.74464311997086 y1[1] (numeric) = 1.74464311997086 absolute error = 2.220446049250313e-16 relative error = 1.272722211111806e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.497 Order of pole (three term test) = 32.45 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.497 Order of pole (three term test) = 32.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y2[1] (closed_form) = 1.751280405140293 y2[1] (numeric) = 1.751280405140292 absolute error = 8.881784197001252e-16 relative error = 5.071594572138059e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.751280405140293 y1[1] (numeric) = 1.751280405140293 absolute error = 2.220446049250313e-16 relative error = 1.267898643034515e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4958 Order of pole (three term test) = 32.44 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4958 Order of pole (three term test) = 32.44 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y2[1] (closed_form) = 1.757842562895277 y2[1] (numeric) = 1.757842562895277 absolute error = 8.881784197001252e-16 relative error = 5.052661930299602e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.757842562895277 y1[1] (numeric) = 1.757842562895277 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4944 Order of pole (three term test) = 32.43 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4944 Order of pole (three term test) = 32.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y2[1] (closed_form) = 1.764328937025506 y2[1] (numeric) = 1.764328937025504 absolute error = 1.110223024625157e-15 relative error = 6.292607922062931e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.764328937025506 y1[1] (numeric) = 1.764328937025505 absolute error = 2.220446049250313e-16 relative error = 1.258521584412586e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4929 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4929 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y2[1] (closed_form) = 1.77073887889897 y2[1] (numeric) = 1.770738878898969 absolute error = 1.110223024625157e-15 relative error = 6.269829153553593e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.77073887889897 y1[1] (numeric) = 1.77073887889897 absolute error = 2.220446049250313e-16 relative error = 1.253965830710718e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4911 Order of pole (three term test) = 32.41 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4911 Order of pole (three term test) = 32.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y2[1] (closed_form) = 1.777071747526824 y2[1] (numeric) = 1.777071747526823 absolute error = 1.110223024625157e-15 relative error = 6.247485652564504e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.777071747526824 y1[1] (numeric) = 1.777071747526824 absolute error = 2.220446049250313e-16 relative error = 1.249497130512901e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4891 Order of pole (three term test) = 32.4 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4891 Order of pole (three term test) = 32.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y2[1] (closed_form) = 1.783326909627484 y2[1] (numeric) = 1.783326909627482 absolute error = 1.332267629550188e-15 relative error = 7.470686514950212e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.783326909627484 y1[1] (numeric) = 1.783326909627484 absolute error = 2.220446049250313e-16 relative error = 1.245114419158369e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (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) = 32.39 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.39 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y2[1] (closed_form) = 1.789503739689951 y2[1] (numeric) = 1.789503739689949 absolute error = 1.554312234475219e-15 relative error = 8.685716604003963e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.789503739689951 y1[1] (numeric) = 1.78950373968995 absolute error = 4.440892098500626e-16 relative error = 2.481633315429704e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4846 Order of pole (three term test) = 32.38 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4846 Order of pole (three term test) = 32.38 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y2[1] (closed_form) = 1.795601620036366 y2[1] (numeric) = 1.795601620036365 absolute error = 1.332267629550188e-15 relative error = 7.419616994571464e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.795601620036366 y1[1] (numeric) = 1.795601620036366 absolute error = 2.220446049250313e-16 relative error = 1.236602832428577e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.482 Order of pole (three term test) = 32.37 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.482 Order of pole (three term test) = 32.37 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y2[1] (closed_form) = 1.801619940883778 y2[1] (numeric) = 1.801619940883776 absolute error = 1.554312234475219e-15 relative error = 8.62730367933626e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.801619940883778 y1[1] (numeric) = 1.801619940883777 absolute error = 4.440892098500626e-16 relative error = 2.464943908381789e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4792 Order of pole (three term test) = 32.36 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4792 Order of pole (three term test) = 32.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y2[1] (closed_form) = 1.807558100405115 y2[1] (numeric) = 1.807558100405113 absolute error = 1.77635683940025e-15 relative error = 9.827384464168143e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.807558100405115 y1[1] (numeric) = 1.807558100405114 absolute error = 6.661338147750939e-16 relative error = 3.685269174063054e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = 32.35 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4763 Order of pole (three term test) = 32.35 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y2[1] (closed_form) = 1.813415504789374 y2[1] (numeric) = 1.813415504789372 absolute error = 2.220446049250313e-15 relative error = 1.224455202564409e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.813415504789374 y1[1] (numeric) = 1.813415504789373 absolute error = 1.110223024625157e-15 relative error = 6.122276012822044e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4732 Order of pole (three term test) = 32.34 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4732 Order of pole (three term test) = 32.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y2[1] (closed_form) = 1.819191568300999 y2[1] (numeric) = 1.819191568300996 absolute error = 2.442490654175344e-15 relative error = 1.342624216566958e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.819191568300999 y1[1] (numeric) = 1.819191568300998 absolute error = 1.110223024625157e-15 relative error = 6.102837348031628e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4698 Order of pole (three term test) = 32.33 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4698 Order of pole (three term test) = 32.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y2[1] (closed_form) = 1.824885713338451 y2[1] (numeric) = 1.824885713338448 absolute error = 2.220446049250313e-15 relative error = 1.216758963600095e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.824885713338451 y1[1] (numeric) = 1.82488571333845 absolute error = 8.881784197001252e-16 relative error = 4.86703585440038e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4663 Order of pole (three term test) = 32.32 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4663 Order of pole (three term test) = 32.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y2[1] (closed_form) = 1.830497370491971 y2[1] (numeric) = 1.830497370491969 absolute error = 1.77635683940025e-15 relative error = 9.704230489677407e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.830497370491971 y1[1] (numeric) = 1.83049737049197 absolute error = 4.440892098500626e-16 relative error = 2.426057622419352e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4626 Order of pole (three term test) = 32.31 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4626 Order of pole (three term test) = 32.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y2[1] (closed_form) = 1.836025978600521 y2[1] (numeric) = 1.836025978600519 absolute error = 1.554312234475219e-15 relative error = 8.465633126062666e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.836025978600521 y1[1] (numeric) = 1.836025978600521 absolute error = 2.220446049250313e-16 relative error = 1.209376160866095e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4587 Order of pole (three term test) = 32.3 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4587 Order of pole (three term test) = 32.3 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y2[1] (closed_form) = 1.841470984807897 y2[1] (numeric) = 1.841470984807895 absolute error = 1.554312234475219e-15 relative error = 8.440601276361495e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.841470984807897 y1[1] (numeric) = 1.841470984807897 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (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) = 32.29 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.01 y2[1] (closed_form) = 1.846831844618015 y2[1] (numeric) = 1.846831844618014 absolute error = 8.881784197001252e-16 relative error = 4.809200265245748e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.846831844618015 y1[1] (numeric) = 1.846831844618016 absolute error = 6.661338147750939e-16 relative error = 3.606900198934311e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4504 Order of pole (three term test) = 32.28 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4504 Order of pole (three term test) = 32.28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y2[1] (closed_form) = 1.852108021949362 y2[1] (numeric) = 1.852108021949362 absolute error = 4.440892098500626e-16 relative error = 2.397750047983995e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.852108021949362 y1[1] (numeric) = 1.852108021949363 absolute error = 1.110223024625157e-15 relative error = 5.994375119959989e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.446 Order of pole (three term test) = 32.27 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.446 Order of pole (three term test) = 32.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y2[1] (closed_form) = 1.857298989188602 y2[1] (numeric) = 1.857298989188602 absolute error = 2.220446049250313e-16 relative error = 1.19552428670645e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.857298989188602 y1[1] (numeric) = 1.857298989188604 absolute error = 1.77635683940025e-15 relative error = 9.564194293651596e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4414 Order of pole (three term test) = 32.27 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4414 Order of pole (three term test) = 32.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y2[1] (closed_form) = 1.862404227243337 y2[1] (numeric) = 1.862404227243337 absolute error = 4.440892098500626e-16 relative error = 2.384494211052063e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.862404227243337 y1[1] (numeric) = 1.862404227243339 absolute error = 2.220446049250313e-15 relative error = 1.192247105526031e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4366 Order of pole (three term test) = 32.26 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4366 Order of pole (three term test) = 32.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y2[1] (closed_form) = 1.867423225594015 y2[1] (numeric) = 1.867423225594016 absolute error = 8.881784197001252e-16 relative error = 4.756171003590264e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.867423225594015 y1[1] (numeric) = 1.867423225594017 absolute error = 2.664535259100376e-15 relative error = 1.426851301077079e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4316 Order of pole (three term test) = 32.25 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4316 Order of pole (three term test) = 32.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y2[1] (closed_form) = 1.872355482344983 y2[1] (numeric) = 1.872355482344985 absolute error = 1.554312234475219e-15 relative error = 8.301373586006013e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 1.872355482344983 y1[1] (numeric) = 1.872355482344987 absolute error = 3.33066907387547e-15 relative error = 1.77886576842986e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4265 Order of pole (three term test) = 32.24 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4265 Order of pole (three term test) = 32.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y2[1] (closed_form) = 1.877200504274678 y2[1] (numeric) = 1.87720050427468 absolute error = 2.220446049250313e-15 relative error = 1.182849697831431e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.877200504274678 y1[1] (numeric) = 1.877200504274682 absolute error = 3.996802888650564e-15 relative error = 2.129129456096576e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4212 Order of pole (three term test) = 32.23 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4212 Order of pole (three term test) = 32.23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y2[1] (closed_form) = 1.881957806884944 y2[1] (numeric) = 1.881957806884946 absolute error = 2.442490654175344e-15 relative error = 1.297845597409119e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.881957806884944 y1[1] (numeric) = 1.881957806884948 absolute error = 4.218847493575595e-15 relative error = 2.24173330461575e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4157 Order of pole (three term test) = 32.22 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4157 Order of pole (three term test) = 32.22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y2[1] (closed_form) = 1.886626914449483 y2[1] (numeric) = 1.886626914449486 absolute error = 2.886579864025407e-15 relative error = 1.530021564898384e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.886626914449483 y1[1] (numeric) = 1.886626914449488 absolute error = 4.662936703425657e-15 relative error = 2.471573297143543e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4101 Order of pole (three term test) = 32.21 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4101 Order of pole (three term test) = 32.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y2[1] (closed_form) = 1.891207360061431 y2[1] (numeric) = 1.891207360061434 absolute error = 3.33066907387547e-15 relative error = 1.761133730870888e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.891207360061431 y1[1] (numeric) = 1.891207360061436 absolute error = 5.10702591327572e-15 relative error = 2.700405054002028e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (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) = 32.21 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y2[1] (closed_form) = 1.895698685680042 y2[1] (numeric) = 1.895698685680046 absolute error = 3.996802888650564e-15 relative error = 2.108353462943291e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.895698685680042 y1[1] (numeric) = 1.895698685680048 absolute error = 5.995204332975845e-15 relative error = 3.162530194414937e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3983 Order of pole (three term test) = 32.2 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3983 Order of pole (three term test) = 32.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y2[1] (closed_form) = 1.9001004421765 y2[1] (numeric) = 1.900100442176504 absolute error = 4.440892098500626e-15 relative error = 2.337188076970151e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.9001004421765 y1[1] (numeric) = 1.900100442176506 absolute error = 6.439293542825908e-15 relative error = 3.388922711606719e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3922 Order of pole (three term test) = 32.19 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3922 Order of pole (three term test) = 32.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y2[1] (closed_form) = 1.90441218937882 y2[1] (numeric) = 1.904412189378825 absolute error = 4.662936703425657e-15 relative error = 2.448491313714292e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.90441218937882 y1[1] (numeric) = 1.904412189378827 absolute error = 6.661338147750939e-15 relative error = 3.49784473387756e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3859 Order of pole (three term test) = 32.18 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3859 Order of pole (three term test) = 32.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y2[1] (closed_form) = 1.908633496115877 y2[1] (numeric) = 1.908633496115882 absolute error = 5.10702591327572e-15 relative error = 2.675749914097527e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.908633496115877 y1[1] (numeric) = 1.908633496115884 absolute error = 7.105427357601002e-15 relative error = 3.722782489179167e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3794 Order of pole (three term test) = 32.17 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3794 Order of pole (three term test) = 32.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y2[1] (closed_form) = 1.912763940260515 y2[1] (numeric) = 1.91276394026052 absolute error = 5.329070518200751e-15 relative error = 2.786057602839869e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.912763940260515 y1[1] (numeric) = 1.912763940260522 absolute error = 7.327471962526033e-15 relative error = 3.83082920390482e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3729 Order of pole (three term test) = 32.17 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3729 Order of pole (three term test) = 32.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y2[1] (closed_form) = 1.91680310877176 y2[1] (numeric) = 1.916803108771766 absolute error = 5.329070518200751e-15 relative error = 2.780186704525687e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.91680310877176 y1[1] (numeric) = 1.916803108771768 absolute error = 7.327471962526033e-15 relative error = 3.822756718722819e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3661 Order of pole (three term test) = 32.16 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3661 Order of pole (three term test) = 32.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y2[1] (closed_form) = 1.920750597736129 y2[1] (numeric) = 1.920750597736134 absolute error = 5.551115123125783e-15 relative error = 2.890075957632679e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.920750597736129 y1[1] (numeric) = 1.920750597736136 absolute error = 7.549516567451064e-15 relative error = 3.930503302380443e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3592 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3592 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y2[1] (closed_form) = 1.924606012408013 y2[1] (numeric) = 1.924606012408019 absolute error = 5.773159728050814e-15 relative error = 2.99965795120197e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.924606012408013 y1[1] (numeric) = 1.924606012408021 absolute error = 7.771561172376096e-15 relative error = 4.038001088156498e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3522 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3522 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y2[1] (closed_form) = 1.928368967249159 y2[1] (numeric) = 1.928368967249165 absolute error = 5.551115123125783e-15 relative error = 2.87865819114716e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.928368967249159 y1[1] (numeric) = 1.928368967249167 absolute error = 7.771561172376096e-15 relative error = 4.030121467606024e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.345 Order of pole (three term test) = 32.14 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.345 Order of pole (three term test) = 32.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y2[1] (closed_form) = 1.932039085967219 y2[1] (numeric) = 1.932039085967224 absolute error = 5.551115123125783e-15 relative error = 2.873189866315142e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.932039085967219 y1[1] (numeric) = 1.932039085967227 absolute error = 7.993605777301127e-15 relative error = 4.137393407493805e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (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) = 32.13 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y2[1] (closed_form) = 1.935616001553378 y2[1] (numeric) = 1.935616001553383 absolute error = 5.551115123125783e-15 relative error = 2.867880364013772e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.935616001553378 y1[1] (numeric) = 1.935616001553386 absolute error = 7.993605777301127e-15 relative error = 4.129747724179831e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3303 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3303 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y2[1] (closed_form) = 1.939099356319059 y2[1] (numeric) = 1.939099356319065 absolute error = 5.551115123125783e-15 relative error = 2.862728567794131e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.939099356319059 y1[1] (numeric) = 1.939099356319067 absolute error = 7.993605777301127e-15 relative error = 4.122329137623549e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3227 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3227 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y2[1] (closed_form) = 1.942488801931689 y2[1] (numeric) = 1.942488801931695 absolute error = 5.995204332975845e-15 relative error = 3.086352069064168e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.942488801931689 y1[1] (numeric) = 1.942488801931698 absolute error = 8.43769498715119e-15 relative error = 4.343754763868088e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.315 Order of pole (three term test) = 32.11 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.315 Order of pole (three term test) = 32.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y2[1] (closed_form) = 1.945783999449531 y2[1] (numeric) = 1.945783999449537 absolute error = 6.439293542825908e-15 relative error = 3.309356816916784e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.945783999449531 y1[1] (numeric) = 1.94578399944954 absolute error = 8.881784197001252e-15 relative error = 4.564630092299012e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3072 Order of pole (three term test) = 32.11 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3072 Order of pole (three term test) = 32.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y2[1] (closed_form) = 1.948984619355578 y2[1] (numeric) = 1.948984619355584 absolute error = 6.661338147750939e-15 relative error = 3.417850547201075e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.948984619355578 y1[1] (numeric) = 1.948984619355587 absolute error = 9.103828801926284e-15 relative error = 4.671062414508135e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2992 Order of pole (three term test) = 32.1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2992 Order of pole (three term test) = 32.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y2[1] (closed_form) = 1.952090341590507 y2[1] (numeric) = 1.952090341590514 absolute error = 7.105427357601002e-15 relative error = 3.639907030025928e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.952090341590507 y1[1] (numeric) = 1.952090341590517 absolute error = 9.547918011776346e-15 relative error = 4.89112507159734e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2912 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2912 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y2[1] (closed_form) = 1.955100855584684 y2[1] (numeric) = 1.95510085558469 absolute error = 6.883382752675971e-15 relative error = 3.520730264637656e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.955100855584684 y1[1] (numeric) = 1.955100855584693 absolute error = 9.547918011776346e-15 relative error = 4.88359359288449e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.283 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.283 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y2[1] (closed_form) = 1.958015860289216 y2[1] (numeric) = 1.958015860289223 absolute error = 6.883382752675971e-15 relative error = 3.515488762005857e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.958015860289216 y1[1] (numeric) = 1.958015860289226 absolute error = 9.547918011776346e-15 relative error = 4.876323121491995e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2747 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2747 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y2[1] (closed_form) = 1.960835064206064 y2[1] (numeric) = 1.960835064206071 absolute error = 7.105427357601002e-15 relative error = 3.623674161741884e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.960835064206064 y1[1] (numeric) = 1.960835064206074 absolute error = 9.769962616701378e-15 relative error = 4.982551972395091e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2663 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2663 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y2[1] (closed_form) = 1.963558185417184 y2[1] (numeric) = 1.963558185417191 absolute error = 7.105427357601002e-15 relative error = 3.618648742049556e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.963558185417184 y1[1] (numeric) = 1.963558185417194 absolute error = 9.769962616701378e-15 relative error = 4.975642020318139e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (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) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y2[1] (closed_form) = 1.966184951612725 y2[1] (numeric) = 1.966184951612732 absolute error = 6.883382752675971e-15 relative error = 3.500882634174373e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.966184951612725 y1[1] (numeric) = 1.966184951612735 absolute error = 9.769962616701378e-15 relative error = 4.968994706570078e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2491 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2491 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y2[1] (closed_form) = 1.968715100118257 y2[1] (numeric) = 1.968715100118264 absolute error = 6.883382752675971e-15 relative error = 3.496383378307252e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.968715100118257 y1[1] (numeric) = 1.968715100118267 absolute error = 9.769962616701378e-15 relative error = 4.962608665984486e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2404 Order of pole (three term test) = 32.06 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2404 Order of pole (three term test) = 32.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y2[1] (closed_form) = 1.971148377921036 y2[1] (numeric) = 1.971148377921043 absolute error = 6.661338147750939e-15 relative error = 3.379419947460592e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.971148377921036 y1[1] (numeric) = 1.971148377921046 absolute error = 9.547918011776346e-15 relative error = 4.843835258026849e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2316 Order of pole (three term test) = 32.06 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2316 Order of pole (three term test) = 32.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y2[1] (closed_form) = 1.973484541695311 y2[1] (numeric) = 1.973484541695318 absolute error = 6.883382752675971e-15 relative error = 3.487933453364088e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.973484541695311 y1[1] (numeric) = 1.973484541695321 absolute error = 9.769962616701378e-15 relative error = 4.950615224129674e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2227 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2227 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y2[1] (closed_form) = 1.975723357826651 y2[1] (numeric) = 1.975723357826658 absolute error = 6.661338147750939e-15 relative error = 3.371594571356686e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.975723357826651 y1[1] (numeric) = 1.97572335782666 absolute error = 9.547918011776346e-15 relative error = 4.83261888561125e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2137 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2137 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y2[1] (closed_form) = 1.977864602435308 y2[1] (numeric) = 1.977864602435315 absolute error = 6.439293542825908e-15 relative error = 3.255679653145784e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.977864602435308 y1[1] (numeric) = 1.977864602435317 absolute error = 9.325873406851315e-15 relative error = 4.715122256280101e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2046 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2046 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y2[1] (closed_form) = 1.979908061398606 y2[1] (numeric) = 1.979908061398612 absolute error = 5.995204332975845e-15 relative error = 3.028021578305427e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.979908061398606 y1[1] (numeric) = 1.979908061398615 absolute error = 9.103828801926284e-15 relative error = 4.598106841130463e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1954 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1954 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y2[1] (closed_form) = 1.981853530372352 y2[1] (numeric) = 1.981853530372357 absolute error = 5.551115123125783e-15 relative error = 2.800971433082058e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.981853530372352 y1[1] (numeric) = 1.981853530372361 absolute error = 8.881784197001252e-15 relative error = 4.481554292931293e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1862 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1862 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y2[1] (closed_form) = 1.983700814811269 y2[1] (numeric) = 1.983700814811274 absolute error = 5.10702591327572e-15 relative error = 2.57449403415283e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.983700814811269 y1[1] (numeric) = 1.983700814811277 absolute error = 8.43769498715119e-15 relative error = 4.253511882513372e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1769 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1769 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y2[1] (closed_form) = 1.985449729988453 y2[1] (numeric) = 1.985449729988457 absolute error = 4.662936703425657e-15 relative error = 2.348554402056191e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 1.985449729988453 y1[1] (numeric) = 1.985449729988461 absolute error = 7.993605777301127e-15 relative error = 4.026093260667757e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (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) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (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) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 3 ) ) ; Iterations = 1301 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %