##############ECHO OF PROBLEM################# ##############temp/mtest4postode.ode################# diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; diff ( y1 , x , 1 ) = neg ( y2 ) ; ! // 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(5.0); array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); glob_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_y2 (double x) { return(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_y1 (double x) { return( 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) = 0.09983341664682815 y2[1] (numeric) = 0.09983341664682815 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9950041652780258 y1[1] (numeric) = 0.9950041652780258 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) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.11 y2[1] (closed_form) = 0.1097783008371748 y2[1] (numeric) = 0.1097783008371748 absolute error = 1.387778780781446e-17 relative error = 1.264164930772452e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9939560979566968 y1[1] (numeric) = 0.9939560979566969 absolute error = 1.110223024625157e-16 relative error = 1.116973905494893e-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 = 0.1091 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) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.12 y2[1] (closed_form) = 0.1197122072889194 y2[1] (numeric) = 0.1197122072889194 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9928086358538663 y1[1] (numeric) = 0.9928086358538663 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 = 0.1189 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) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.13 y2[1] (closed_form) = 0.1296341426196949 y2[1] (numeric) = 0.1296341426196949 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9915618937147881 y1[1] (numeric) = 0.9915618937147881 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 = 0.1285 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) = 32.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.14 y2[1] (closed_form) = 0.1395431146442365 y2[1] (numeric) = 0.1395431146442365 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9902159962126371 y1[1] (numeric) = 0.9902159962126372 absolute error = 1.110223024625157e-16 relative error = 1.121192779021467e-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) = 32.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.15 y2[1] (closed_form) = 0.1494381324735993 y2[1] (numeric) = 0.1494381324735993 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9887710779360422 y1[1] (numeric) = 0.9887710779360421 absolute error = 1.110223024625157e-16 relative error = 1.122831208759294e-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) = 32.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y2[1] (closed_form) = 0.159318206614246 y2[1] (numeric) = 0.159318206614246 absolute error = 2.775557561562891e-17 relative error = 1.742147128409054e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9872272833756269 y1[1] (numeric) = 0.9872272833756267 absolute error = 2.220446049250313e-16 relative error = 2.249174112832397e-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) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y2[1] (closed_form) = 0.1691823490669961 y2[1] (numeric) = 0.1691823490669961 absolute error = 2.775557561562891e-17 relative error = 1.640571594418383e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9855847669095607 y1[1] (numeric) = 0.9855847669095603 absolute error = 3.33066907387547e-16 relative error = 3.379383677285567e-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) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y2[1] (closed_form) = 0.1790295734258243 y2[1] (numeric) = 0.1790295734258242 absolute error = 5.551115123125783e-17 relative error = 3.100669356968404e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9838436927881214 y1[1] (numeric) = 0.9838436927881212 absolute error = 2.220446049250313e-16 relative error = 2.256909370387664e-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) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y2[1] (closed_form) = 0.1888588949765007 y2[1] (numeric) = 0.1888588949765006 absolute error = 8.326672684688674e-17 relative error = 4.408938581222105e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9820042351172703 y1[1] (numeric) = 0.9820042351172701 absolute error = 2.220446049250313e-16 relative error = 2.261136937953377e-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) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y2[1] (closed_form) = 0.1986693307950613 y2[1] (numeric) = 0.1986693307950612 absolute error = 8.326672684688674e-17 relative error = 4.191221992526924e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9800665778412416 y1[1] (numeric) = 0.9800665778412414 absolute error = 2.220446049250313e-16 relative error = 2.265607357146299e-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) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y2[1] (closed_form) = 0.2084598998460997 y2[1] (numeric) = 0.2084598998460996 absolute error = 1.110223024625157e-16 relative error = 5.325834970873556e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9780309147241483 y1[1] (numeric) = 0.978030914724148 absolute error = 2.220446049250313e-16 relative error = 2.27032296814113e-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) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y2[1] (closed_form) = 0.2182296230808694 y2[1] (numeric) = 0.2182296230808693 absolute error = 1.387778780781446e-16 relative error = 6.359259394711854e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9758974493306055 y1[1] (numeric) = 0.9758974493306055 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 = 0.213 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) = 32.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y2[1] (closed_form) = 0.2279775235351885 y2[1] (numeric) = 0.2279775235351884 absolute error = 1.110223024625157e-16 relative error = 4.869879308316079e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9736663950053748 y1[1] (numeric) = 0.9736663950053749 absolute error = 1.110223024625157e-16 relative error = 1.140249915494956e-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 = 0.222 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) = 32.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y2[1] (closed_form) = 0.2377026264271347 y2[1] (numeric) = 0.2377026264271346 absolute error = 1.110223024625157e-16 relative error = 4.670638441454007e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9713379748520296 y1[1] (numeric) = 0.9713379748520296 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 = 0.2309 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) = 32.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y2[1] (closed_form) = 0.247403959254523 y2[1] (numeric) = 0.2474039592545229 absolute error = 1.110223024625157e-16 relative error = 4.487490935757365e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9689124217106447 y1[1] (numeric) = 0.9689124217106446 absolute error = 1.110223024625157e-16 relative error = 1.145844556998272e-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) = 32.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y2[1] (closed_form) = 0.2570805518921552 y2[1] (numeric) = 0.2570805518921551 absolute error = 1.665334536937735e-16 relative error = 6.477870553336681e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9663899781345132 y1[1] (numeric) = 0.9663899781345132 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 = 0.2484 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) = 32.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y2[1] (closed_form) = 0.2667314366888313 y2[1] (numeric) = 0.266731436688831 absolute error = 2.220446049250313e-16 relative error = 8.324650730392475e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9637708963658905 y1[1] (numeric) = 0.9637708963658905 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 = 0.2571 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) = 32.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y2[1] (closed_form) = 0.2763556485641139 y2[1] (numeric) = 0.2763556485641137 absolute error = 2.220446049250313e-16 relative error = 8.034740960741299e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9610554383107709 y1[1] (numeric) = 0.961055438310771 absolute error = 1.110223024625157e-16 relative error = 1.155212259738704e-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) = 32.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y2[1] (closed_form) = 0.2859522251048357 y2[1] (numeric) = 0.2859522251048353 absolute error = 3.885780586188048e-16 relative error = 1.358891536781518e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9582438755126971 y1[1] (numeric) = 0.9582438755126974 absolute error = 3.33066907387547e-16 relative error = 3.475805229742204e-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) = 32.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y2[1] (closed_form) = 0.2955202066613397 y2[1] (numeric) = 0.2955202066613393 absolute error = 3.885780586188048e-16 relative error = 1.314895055768919e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.955336489125606 y1[1] (numeric) = 0.9553364891256064 absolute error = 4.440892098500626e-16 relative error = 4.64851091636336e-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) = 32.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y2[1] (closed_form) = 0.3050586364434437 y2[1] (numeric) = 0.3050586364434433 absolute error = 3.33066907387547e-16 relative error = 1.091812745479494e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9523335698857134 y1[1] (numeric) = 0.9523335698857137 absolute error = 3.33066907387547e-16 relative error = 3.49737652771725e-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) = 32.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y2[1] (closed_form) = 0.3145665606161179 y2[1] (numeric) = 0.3145665606161176 absolute error = 3.33066907387547e-16 relative error = 1.058812185043425e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9492354180824408 y1[1] (numeric) = 0.9492354180824413 absolute error = 4.440892098500626e-16 relative error = 4.678388536609509e-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) = 32.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y2[1] (closed_form) = 0.3240430283948685 y2[1] (numeric) = 0.3240430283948683 absolute error = 2.775557561562891e-16 relative error = 8.565398167371418e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9460423435283869 y1[1] (numeric) = 0.9460423435283875 absolute error = 5.551115123125783e-16 relative error = 5.86772374524187e-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) = 32.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y2[1] (closed_form) = 0.3334870921408146 y2[1] (numeric) = 0.3334870921408142 absolute error = 3.33066907387547e-16 relative error = 9.987400269360645e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.9427546655283462 y1[1] (numeric) = 0.9427546655283467 absolute error = 5.551115123125783e-16 relative error = 5.888186318351214e-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) = 32.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y2[1] (closed_form) = 0.3428978074554516 y2[1] (numeric) = 0.3428978074554511 absolute error = 4.440892098500626e-16 relative error = 1.29510658917747e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9393727128473789 y1[1] (numeric) = 0.9393727128473793 absolute error = 4.440892098500626e-16 relative error = 4.727508088924171e-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) = 32.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y2[1] (closed_form) = 0.3522742332750902 y2[1] (numeric) = 0.3522742332750897 absolute error = 4.440892098500626e-16 relative error = 1.260634948294031e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9358968236779348 y1[1] (numeric) = 0.9358968236779351 absolute error = 3.33066907387547e-16 relative error = 3.558799420631045e-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) = 32.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y2[1] (closed_form) = 0.3616154319649622 y2[1] (numeric) = 0.3616154319649617 absolute error = 4.996003610813204e-16 relative error = 1.381579205197548e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9323273456060344 y1[1] (numeric) = 0.9323273456060348 absolute error = 4.440892098500626e-16 relative error = 4.763232698719078e-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) = 32.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y2[1] (closed_form) = 0.3709204694129829 y2[1] (numeric) = 0.3709204694129824 absolute error = 4.996003610813204e-16 relative error = 1.346920437882508e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9286646355765101 y1[1] (numeric) = 0.9286646355765106 absolute error = 4.440892098500626e-16 relative error = 4.782019179338884e-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) = 32.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y2[1] (closed_form) = 0.3801884151231616 y2[1] (numeric) = 0.3801884151231611 absolute error = 4.996003610813204e-16 relative error = 1.314086229901233e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.924909059857313 y1[1] (numeric) = 0.9249090598573132 absolute error = 2.220446049250313e-16 relative error = 2.400718238821084e-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) = 32.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y2[1] (closed_form) = 0.3894183423086507 y2[1] (numeric) = 0.3894183423086502 absolute error = 4.440892098500626e-16 relative error = 1.140391095132546e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.921060994002885 y1[1] (numeric) = 0.9210609940028852 absolute error = 2.220446049250313e-16 relative error = 2.410748108657132e-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) = 32.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y2[1] (closed_form) = 0.3986093279844231 y2[1] (numeric) = 0.3986093279844226 absolute error = 4.996003610813204e-16 relative error = 1.253358428934819e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.917120822816605 y1[1] (numeric) = 0.9171208228166053 absolute error = 3.33066907387547e-16 relative error = 3.631657891755771e-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) = 32.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y2[1] (closed_form) = 0.4077604530595704 y2[1] (numeric) = 0.4077604530595698 absolute error = 6.106226635438361e-16 relative error = 1.497503396815751e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9130889403123081 y1[1] (numeric) = 0.9130889403123086 absolute error = 4.440892098500626e-16 relative error = 4.863592036260659e-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) = 32.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y2[1] (closed_form) = 0.416870802429211 y2[1] (numeric) = 0.4168708024292104 absolute error = 5.551115123125783e-16 relative error = 1.331615236849892e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.908965749674885 y1[1] (numeric) = 0.9089657496748855 absolute error = 5.551115123125783e-16 relative error = 6.107067428130578e-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) = 32.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y2[1] (closed_form) = 0.4259394650659998 y2[1] (numeric) = 0.4259394650659993 absolute error = 4.996003610813204e-16 relative error = 1.172937475995343e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9047516632199633 y1[1] (numeric) = 0.9047516632199637 absolute error = 4.440892098500626e-16 relative error = 4.908409985891296e-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) = 32.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y2[1] (closed_form) = 0.4349655341112305 y2[1] (numeric) = 0.4349655341112299 absolute error = 5.551115123125783e-16 relative error = 1.276219536444062e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.9004471023526768 y1[1] (numeric) = 0.9004471023526771 absolute error = 3.33066907387547e-16 relative error = 3.698905871508875e-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) = 32.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y2[1] (closed_form) = 0.44394810696552 y2[1] (numeric) = 0.4439481069655195 absolute error = 4.996003610813204e-16 relative error = 1.125357565991655e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8960524975255251 y1[1] (numeric) = 0.8960524975255255 absolute error = 4.440892098500626e-16 relative error = 4.956062407910562e-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) = 32.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y2[1] (closed_form) = 0.4528862853790686 y2[1] (numeric) = 0.452886285379068 absolute error = 5.551115123125783e-16 relative error = 1.225719413975953e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8915682881953289 y1[1] (numeric) = 0.8915682881953292 absolute error = 3.33066907387547e-16 relative error = 3.735741970609178e-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) = 32.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y2[1] (closed_form) = 0.4617791755414832 y2[1] (numeric) = 0.4617791755414826 absolute error = 6.106226635438361e-16 relative error = 1.322326115784279e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.886994922779284 y1[1] (numeric) = 0.8869949227792844 absolute error = 3.33066907387547e-16 relative error = 3.755003538734188e-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) = 32.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y2[1] (closed_form) = 0.4706258881711583 y2[1] (numeric) = 0.4706258881711577 absolute error = 5.551115123125783e-16 relative error = 1.179517587674e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8823328586101213 y1[1] (numeric) = 0.8823328586101219 absolute error = 5.551115123125783e-16 relative error = 6.2914070001542e-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) = 32.22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y2[1] (closed_form) = 0.4794255386042033 y2[1] (numeric) = 0.4794255386042027 absolute error = 5.551115123125783e-16 relative error = 1.157868047515213e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8775825618903725 y1[1] (numeric) = 0.8775825618903731 absolute error = 5.551115123125783e-16 relative error = 6.325461972681297e-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) = 32.23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y2[1] (closed_form) = 0.4881772468829078 y2[1] (numeric) = 0.4881772468829073 absolute error = 5.551115123125783e-16 relative error = 1.137110579931893e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8727445076457511 y1[1] (numeric) = 0.8727445076457516 absolute error = 5.551115123125783e-16 relative error = 6.360527135369831e-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) = 32.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y2[1] (closed_form) = 0.496880137843737 y2[1] (numeric) = 0.4968801378437365 absolute error = 5.551115123125783e-16 relative error = 1.117194007233902e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8678191796776498 y1[1] (numeric) = 0.8678191796776501 absolute error = 3.33066907387547e-16 relative error = 3.837975873168236e-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) = 32.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y2[1] (closed_form) = 0.5055333412048473 y2[1] (numeric) = 0.5055333412048468 absolute error = 4.440892098500626e-16 relative error = 8.78456817094707e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8628070705147608 y1[1] (numeric) = 0.8628070705147614 absolute error = 5.551115123125783e-16 relative error = 6.433784924611156e-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) = 32.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y2[1] (closed_form) = 0.5141359916531134 y2[1] (numeric) = 0.514135991653113 absolute error = 4.440892098500626e-16 relative error = 8.637582605764911e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8577086813638239 y1[1] (numeric) = 0.8577086813638244 absolute error = 4.440892098500626e-16 relative error = 5.177622886408542e-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) = 32.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y2[1] (closed_form) = 0.5226872289306594 y2[1] (numeric) = 0.522687228930659 absolute error = 4.440892098500626e-16 relative error = 8.496270527952314e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8525245220595056 y1[1] (numeric) = 0.852524522059506 absolute error = 4.440892098500626e-16 relative error = 5.209107754193908e-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) = 32.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y2[1] (closed_form) = 0.5311861979208837 y2[1] (numeric) = 0.5311861979208832 absolute error = 5.551115123125783e-16 relative error = 1.045041295284668e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.8472551110134159 y1[1] (numeric) = 0.8472551110134163 absolute error = 4.440892098500626e-16 relative error = 5.24150523351674e-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) = 32.28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y2[1] (closed_form) = 0.5396320487339695 y2[1] (numeric) = 0.5396320487339691 absolute error = 4.440892098500626e-16 relative error = 8.229481753204616e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8419009751622685 y1[1] (numeric) = 0.841900975162269 absolute error = 5.551115123125783e-16 relative error = 6.593548750856189e-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) = 32.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y2[1] (closed_form) = 0.5480239367918739 y2[1] (numeric) = 0.5480239367918734 absolute error = 4.440892098500626e-16 relative error = 8.103463736452024e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8364626499151867 y1[1] (numeric) = 0.8364626499151873 absolute error = 5.551115123125783e-16 relative error = 6.636417207258015e-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 = 0.4584 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) = 32.3 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y2[1] (closed_form) = 0.5563610229127841 y2[1] (numeric) = 0.5563610229127838 absolute error = 3.33066907387547e-16 relative error = 5.986524822386038e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8309406791001632 y1[1] (numeric) = 0.8309406791001639 absolute error = 6.661338147750939e-16 relative error = 8.016622985607819e-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) = 32.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y2[1] (closed_form) = 0.5646424733950357 y2[1] (numeric) = 0.5646424733950353 absolute error = 4.440892098500626e-16 relative error = 7.864962888460721e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8253356149096781 y1[1] (numeric) = 0.8253356149096787 absolute error = 5.551115123125783e-16 relative error = 6.725888260296725e-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 = 0.466 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) = 32.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y2[1] (closed_form) = 0.5728674601004816 y2[1] (numeric) = 0.5728674601004813 absolute error = 3.33066907387547e-16 relative error = 5.814030828860948e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8196480178454792 y1[1] (numeric) = 0.8196480178454798 absolute error = 5.551115123125783e-16 relative error = 6.772559686921958e-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 = 0.4695 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) = 32.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y2[1] (closed_form) = 0.5810351605373054 y2[1] (numeric) = 0.5810351605373052 absolute error = 2.220446049250313e-16 relative error = 3.82153473672227e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8138784566625337 y1[1] (numeric) = 0.8138784566625342 absolute error = 5.551115123125783e-16 relative error = 6.820570169517947e-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) = 32.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y2[1] (closed_form) = 0.5891447579422698 y2[1] (numeric) = 0.5891447579422696 absolute error = 2.220446049250313e-16 relative error = 3.768931182559879e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8080275083121516 y1[1] (numeric) = 0.8080275083121521 absolute error = 4.440892098500626e-16 relative error = 5.495966477399989e-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 = 0.476 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) = 32.35 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y2[1] (closed_form) = 0.5971954413623924 y2[1] (numeric) = 0.5971954413623919 absolute error = 5.551115123125783e-16 relative error = 9.295307262329275e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.8020957578842923 y1[1] (numeric) = 0.8020957578842927 absolute error = 3.33066907387547e-16 relative error = 4.152458158687757e-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) = 32.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y2[1] (closed_form) = 0.6051864057360399 y2[1] (numeric) = 0.6051864057360393 absolute error = 5.551115123125783e-16 relative error = 9.172570749295673e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.7960837985490555 y1[1] (numeric) = 0.7960837985490558 absolute error = 2.220446049250313e-16 relative error = 2.789211453991783e-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) = 32.37 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y2[1] (closed_form) = 0.6131168519734341 y2[1] (numeric) = 0.6131168519734334 absolute error = 7.771561172376096e-16 relative error = 1.267549757825419e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7899922314973647 y1[1] (numeric) = 0.7899922314973651 absolute error = 3.33066907387547e-16 relative error = 4.216078261380448e-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) = 32.38 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y2[1] (closed_form) = 0.62098598703656 y2[1] (numeric) = 0.6209859870365592 absolute error = 8.881784197001252e-16 relative error = 1.43027127542547e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.783821665880849 y1[1] (numeric) = 0.7838216658808494 absolute error = 4.440892098500626e-16 relative error = 5.665691944748691e-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) = 32.39 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y2[1] (closed_form) = 0.6287930240184689 y2[1] (numeric) = 0.6287930240184679 absolute error = 9.992007221626409e-16 relative error = 1.589077302061946e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7775727187509276 y1[1] (numeric) = 0.7775727187509281 absolute error = 5.551115123125783e-16 relative error = 7.139030201629178e-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) = 32.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y2[1] (closed_form) = 0.6365371822219683 y2[1] (numeric) = 0.6365371822219672 absolute error = 1.110223024625157e-15 relative error = 1.744160522955921e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7712460149971063 y1[1] (numeric) = 0.7712460149971068 absolute error = 4.440892098500626e-16 relative error = 5.758074611921708e-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) = 32.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y2[1] (closed_form) = 0.6442176872376915 y2[1] (numeric) = 0.6442176872376904 absolute error = 1.110223024625157e-15 relative error = 1.723366257430196e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7648421872844881 y1[1] (numeric) = 0.7648421872844888 absolute error = 7.771561172376096e-16 relative error = 1.01609996174092e-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 = 0.4927 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) = 32.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y2[1] (closed_form) = 0.6518337710215371 y2[1] (numeric) = 0.6518337710215361 absolute error = 9.992007221626409e-16 relative error = 1.532907263452643e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7583618759905079 y1[1] (numeric) = 0.7583618759905086 absolute error = 7.771561172376096e-16 relative error = 1.024782682044181e-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 = 0.4943 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) = 32.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y2[1] (closed_form) = 0.6593846719714735 y2[1] (numeric) = 0.6593846719714724 absolute error = 1.110223024625157e-15 relative error = 1.683725861120999e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7518057291408946 y1[1] (numeric) = 0.7518057291408955 absolute error = 8.881784197001252e-16 relative error = 1.181393523982674e-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 = 0.4957 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) = 32.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y2[1] (closed_form) = 0.6668696350036982 y2[1] (numeric) = 0.6668696350036971 absolute error = 1.110223024625157e-15 relative error = 1.664827675980478e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.74517440234487 y1[1] (numeric) = 0.745174402344871 absolute error = 9.992007221626409e-16 relative error = 1.340895123367652e-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 = 0.4969 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) = 32.44 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y2[1] (closed_form) = 0.6742879116281455 y2[1] (numeric) = 0.6742879116281443 absolute error = 1.221245327087672e-15 relative error = 1.811163015126336e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7384685587295875 y1[1] (numeric) = 0.7384685587295887 absolute error = 1.221245327087672e-15 relative error = 1.653753992165383e-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 = 0.4979 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) = 32.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y2[1] (closed_form) = 0.6816387600233346 y2[1] (numeric) = 0.6816387600233332 absolute error = 1.332267629550188e-15 relative error = 1.954506855661466e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7316888688738205 y1[1] (numeric) = 0.7316888688738217 absolute error = 1.221245327087672e-15 relative error = 1.669077362031423e-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 = 0.4987 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) = 32.46 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y2[1] (closed_form) = 0.6889214451105518 y2[1] (numeric) = 0.6889214451105504 absolute error = 1.332267629550188e-15 relative error = 1.93384548994029e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7248360107409048 y1[1] (numeric) = 0.7248360107409061 absolute error = 1.332267629550188e-15 relative error = 1.838026270505497e-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 = 0.4994 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) = 32.47 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y2[1] (closed_form) = 0.6961352386273572 y2[1] (numeric) = 0.6961352386273557 absolute error = 1.443289932012704e-15 relative error = 2.073289573529692e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.717910669610943 y1[1] (numeric) = 0.7179106696109443 absolute error = 1.332267629550188e-15 relative error = 1.855756831518026e-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 = 0.4998 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) = 32.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y2[1] (closed_form) = 0.7032794192004106 y2[1] (numeric) = 0.7032794192004094 absolute error = 1.221245327087672e-15 relative error = 1.736500875393396e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.710913538012277 y1[1] (numeric) = 0.7109135380122783 absolute error = 1.332267629550188e-15 relative error = 1.874022027031901e-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 = 0.5 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) = 32.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y2[1] (closed_form) = 0.7103532724176083 y2[1] (numeric) = 0.710353272417607 absolute error = 1.221245327087672e-15 relative error = 1.719208419961662e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.7038453156522356 y1[1] (numeric) = 0.703845315652237 absolute error = 1.332267629550188e-15 relative error = 1.892841509239298e-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 = 0.5 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) = 0.7173560908995231 y2[1] (numeric) = 0.7173560908995219 absolute error = 1.221245327087672e-15 relative error = 1.702425535352047e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6967067093471649 y1[1] (numeric) = 0.6967067093471663 absolute error = 1.332267629550188e-15 relative error = 1.912235969133357e-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 = 0.4998 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) = 32.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y2[1] (closed_form) = 0.7242871743701429 y2[1] (numeric) = 0.7242871743701417 absolute error = 1.221245327087672e-15 relative error = 1.686134133397703e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6894984329517466 y1[1] (numeric) = 0.689498432951748 absolute error = 1.332267629550188e-15 relative error = 1.932227204414001e-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 = 0.4994 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) = 32.52 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y2[1] (closed_form) = 0.7311458297268963 y2[1] (numeric) = 0.7311458297268949 absolute error = 1.443289932012704e-15 relative error = 1.974011029443761e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6822212072876132 y1[1] (numeric) = 0.6822212072876146 absolute error = 1.443289932012704e-15 relative error = 2.115574708899714e-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 = 0.4988 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) = 32.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y2[1] (closed_form) = 0.7379313711099631 y2[1] (numeric) = 0.7379313711099617 absolute error = 1.443289932012704e-15 relative error = 1.955859296023385e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6748757600712666 y1[1] (numeric) = 0.6748757600712681 absolute error = 1.554312234475219e-15 relative error = 2.303108700053302e-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 = 0.498 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) = 32.54 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y2[1] (closed_form) = 0.7446431199708597 y2[1] (numeric) = 0.7446431199708582 absolute error = 1.554312234475219e-15 relative error = 2.087325045769636e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6674628258413077 y1[1] (numeric) = 0.6674628258413091 absolute error = 1.443289932012704e-15 relative error = 2.162352532807351e-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 = 0.497 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) = 32.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y2[1] (closed_form) = 0.7512804051402932 y2[1] (numeric) = 0.7512804051402917 absolute error = 1.443289932012704e-15 relative error = 1.921106849237184e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6599831458849816 y1[1] (numeric) = 0.6599831458849831 absolute error = 1.443289932012704e-15 relative error = 2.186858772093905e-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 = 0.4958 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) = 32.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y2[1] (closed_form) = 0.7578425628952774 y2[1] (numeric) = 0.757842562895276 absolute error = 1.443289932012704e-15 relative error = 1.904471987557322e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6524374681640513 y1[1] (numeric) = 0.6524374681640527 absolute error = 1.332267629550188e-15 relative error = 2.041985162653469e-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 = 0.4944 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) = 32.57 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y2[1] (closed_form) = 0.7643289370255055 y2[1] (numeric) = 0.7643289370255041 absolute error = 1.443289932012704e-15 relative error = 1.888309943660476e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6448265472400007 y1[1] (numeric) = 0.644826547240002 absolute error = 1.332267629550188e-15 relative error = 2.066086818622134e-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 = 0.4929 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) = 32.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y2[1] (closed_form) = 0.7707388788989697 y2[1] (numeric) = 0.7707388788989683 absolute error = 1.443289932012704e-15 relative error = 1.872605588645663e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6371511441985797 y1[1] (numeric) = 0.637151144198581 absolute error = 1.332267629550188e-15 relative error = 2.090975809556049e-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 = 0.4911 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) = 32.59 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y2[1] (closed_form) = 0.7770717475268243 y2[1] (numeric) = 0.7770717475268228 absolute error = 1.443289932012704e-15 relative error = 1.857344494387092e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6294120265736963 y1[1] (numeric) = 0.6294120265736975 absolute error = 1.221245327087672e-15 relative error = 1.940295506801346e-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 = 0.4891 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) = 32.6 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y2[1] (closed_form) = 0.7833269096274839 y2[1] (numeric) = 0.7833269096274823 absolute error = 1.554312234475219e-15 relative error = 1.984244656186243e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6216099682706639 y1[1] (numeric) = 0.6216099682706653 absolute error = 1.332267629550188e-15 relative error = 2.14325332210581e-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 = 0.4869 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) = 32.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y2[1] (closed_form) = 0.7895037396899508 y2[1] (numeric) = 0.7895037396899494 absolute error = 1.443289932012704e-15 relative error = 1.828097651037731e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.613745749488811 y1[1] (numeric) = 0.6137457494888126 absolute error = 1.554312234475219e-15 relative error = 2.532501831205848e-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 = 0.4846 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) = 32.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y2[1] (closed_form) = 0.7956016200363665 y2[1] (numeric) = 0.7956016200363649 absolute error = 1.554312234475219e-15 relative error = 1.953631309101875e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.6058201566434622 y1[1] (numeric) = 0.6058201566434638 absolute error = 1.554312234475219e-15 relative error = 2.565633080098991e-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 = 0.482 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) = 32.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y2[1] (closed_form) = 0.8016199408837775 y2[1] (numeric) = 0.8016199408837762 absolute error = 1.332267629550188e-15 relative error = 1.661969172175753e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5978339822872977 y1[1] (numeric) = 0.5978339822872991 absolute error = 1.443289932012704e-15 relative error = 2.414198548049599e-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 = 0.4792 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) = 32.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y2[1] (closed_form) = 0.8075581004051147 y2[1] (numeric) = 0.8075581004051134 absolute error = 1.221245327087672e-15 relative error = 1.512269304802998e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5897880250310976 y1[1] (numeric) = 0.589788025031099 absolute error = 1.332267629550188e-15 relative error = 2.258892301992638e-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 = 0.4763 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) = 32.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y2[1] (closed_form) = 0.8134155047893742 y2[1] (numeric) = 0.813415504789373 absolute error = 1.221245327087672e-15 relative error = 1.501379454776807e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5816830894638829 y1[1] (numeric) = 0.5816830894638843 absolute error = 1.332267629550188e-15 relative error = 2.290366788517254e-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 = 0.4732 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) = 32.66 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y2[1] (closed_form) = 0.8191915683009987 y2[1] (numeric) = 0.8191915683009974 absolute error = 1.332267629550188e-15 relative error = 1.626319997791613e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.573519986072456 y1[1] (numeric) = 0.5735199860724575 absolute error = 1.443289932012704e-15 relative error = 2.5165468807749e-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 = 0.4698 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) = 32.67 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y2[1] (closed_form) = 0.8248857133384505 y2[1] (numeric) = 0.8248857133384494 absolute error = 1.110223024625157e-15 relative error = 1.345911326469576e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5652995311603537 y1[1] (numeric) = 0.565299531160355 absolute error = 1.332267629550188e-15 relative error = 2.356746390387992e-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 = 0.4663 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) = 32.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y2[1] (closed_form) = 0.8304973704919709 y2[1] (numeric) = 0.8304973704919697 absolute error = 1.221245327087672e-15 relative error = 1.470498728206965e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5570225467662167 y1[1] (numeric) = 0.5570225467662182 absolute error = 1.554312234475219e-15 relative error = 2.790393752458941e-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 = 0.4626 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) = 32.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y2[1] (closed_form) = 0.836025978600521 y2[1] (numeric) = 0.8360259786005197 absolute error = 1.221245327087672e-15 relative error = 1.460774375853721e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.548689860581587 y1[1] (numeric) = 0.5486898605815885 absolute error = 1.554312234475219e-15 relative error = 2.832770105916878e-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 = 0.4587 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) = 32.7 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y2[1] (closed_form) = 0.8414709848078968 y2[1] (numeric) = 0.8414709848078956 absolute error = 1.221245327087672e-15 relative error = 1.45132196966539e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5403023058681392 y1[1] (numeric) = 0.5403023058681409 absolute error = 1.665334536937735e-15 relative error = 3.082227336161248e-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 = 0.4546 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) = 32.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.01 y2[1] (closed_form) = 0.846831844618015 y2[1] (numeric) = 0.8468318446180143 absolute error = 6.661338147750939e-16 relative error = 7.866187590944582e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.5318607213743558 y1[1] (numeric) = 0.5318607213743567 absolute error = 8.881784197001252e-16 relative error = 1.669945502659091e-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 = 0.4504 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) = 32.72 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y2[1] (closed_form) = 0.8521080219493621 y2[1] (numeric) = 0.8521080219493622 absolute error = 1.110223024625157e-16 relative error = 1.302913475788324e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.5233659512516509 y1[1] (numeric) = 0.5233659512516508 absolute error = 1.110223024625157e-16 relative error = 2.121313054412526e-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) = 32.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y2[1] (closed_form) = 0.857298989188602 y2[1] (numeric) = 0.8572989891886026 absolute error = 5.551115123125783e-16 relative error = 6.475121507351458e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.5148188449699576 y1[1] (numeric) = 0.5148188449699566 absolute error = 9.992007221626409e-16 relative error = 1.940878295201004e-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 = 0.4414 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) = 32.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y2[1] (closed_form) = 0.8624042272433365 y2[1] (numeric) = 0.8624042272433377 absolute error = 1.110223024625157e-15 relative error = 1.287358050381976e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.5062202572327816 y1[1] (numeric) = 0.5062202572327795 absolute error = 2.109423746787797e-15 relative error = 4.167007773096276e-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) = 32.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y2[1] (closed_form) = 0.8674232255940145 y2[1] (numeric) = 0.8674232255940163 absolute error = 1.77635683940025e-15 relative error = 2.04785482678746e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4975710478917312 y1[1] (numeric) = 0.4975710478917282 absolute error = 2.997602166487923e-15 relative error = 6.024470634272485e-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) = 32.75 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y2[1] (closed_form) = 0.8723554823449834 y2[1] (numeric) = 0.8723554823449857 absolute error = 2.331468351712829e-15 relative error = 2.672612712246155e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4888720818605328 y1[1] (numeric) = 0.4888720818605288 absolute error = 3.996802888650564e-15 relative error = 8.175559695369936e-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) = 32.76 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y2[1] (closed_form) = 0.8772005042746782 y2[1] (numeric) = 0.8772005042746809 absolute error = 2.664535259100376e-15 relative error = 3.037544148818716e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4801242290285403 y1[1] (numeric) = 0.4801242290285352 absolute error = 5.051514762044462e-15 relative error = 1.052126607371065e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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) = 32.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y2[1] (closed_form) = 0.8819578068849436 y2[1] (numeric) = 0.8819578068849467 absolute error = 3.108624468950438e-15 relative error = 3.524686152424949e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4713283641737472 y1[1] (numeric) = 0.4713283641737411 absolute error = 6.106226635438361e-15 relative error = 1.295535575530821e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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) = 32.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y2[1] (closed_form) = 0.8866269144494829 y2[1] (numeric) = 0.8866269144494865 absolute error = 3.552713678800501e-15 relative error = 4.006999585622124e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4624853668753091 y1[1] (numeric) = 0.462485366875302 absolute error = 7.049916206369744e-15 relative error = 1.524354436120024e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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) = 32.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y2[1] (closed_form) = 0.8912073600614306 y2[1] (numeric) = 0.8912073600614349 absolute error = 4.218847493575595e-15 relative error = 4.733856207476553e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4535961214255866 y1[1] (numeric) = 0.4535961214255785 absolute error = 8.049116928532385e-15 relative error = 1.774511850594133e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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) = 32.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y2[1] (closed_form) = 0.8956986856800425 y2[1] (numeric) = 0.8956986856800473 absolute error = 4.773959005888173e-15 relative error = 5.32987162112852e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4446615167417171 y1[1] (numeric) = 0.444661516741708 absolute error = 9.159339953157541e-15 relative error = 2.059845434854164e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 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) = 32.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y2[1] (closed_form) = 0.9001004421764995 y2[1] (numeric) = 0.9001004421765045 absolute error = 4.996003610813204e-15 relative error = 5.550495674385575e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4356824462767235 y1[1] (numeric) = 0.4356824462767133 absolute error = 1.015854067532018e-14 relative error = 2.331638734159143e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.81 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y2[1] (closed_form) = 0.9044121893788201 y2[1] (numeric) = 0.9044121893788255 absolute error = 5.440092820663267e-15 relative error = 6.015059156157218e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4266598079301697 y1[1] (numeric) = 0.4266598079301584 absolute error = 1.126876369994534e-14 relative error = 2.641158949237063e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y2[1] (closed_form) = 0.9086334961158771 y2[1] (numeric) = 0.9086334961158827 absolute error = 5.662137425588298e-15 relative error = 6.23148656723768e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4175945039583715 y1[1] (numeric) = 0.4175945039583592 absolute error = 1.226796442210798e-14 relative error = 2.937769608033665e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y2[1] (closed_form) = 0.9127639402605146 y2[1] (numeric) = 0.9127639402605204 absolute error = 5.88418203051333e-15 relative error = 6.446554000406621e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.4084874408841718 y1[1] (numeric) = 0.4084874408841584 absolute error = 1.337818744673314e-14 relative error = 3.27505477714958e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y2[1] (closed_form) = 0.9168031087717602 y2[1] (numeric) = 0.9168031087717663 absolute error = 6.106226635438361e-15 relative error = 6.660346782221173e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3993395294062887 y1[1] (numeric) = 0.3993395294062743 absolute error = 1.443289932012704e-14 relative error = 3.614192499696913e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y2[1] (closed_form) = 0.9207505977361286 y2[1] (numeric) = 0.9207505977361351 absolute error = 6.550315845288424e-15 relative error = 7.114104363759135e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3901516843082468 y1[1] (numeric) = 0.3901516843082313 absolute error = 1.548761119352093e-14 relative error = 3.96963842946905e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y2[1] (closed_form) = 0.9246060124080131 y2[1] (numeric) = 0.9246060124080199 absolute error = 6.772360450213455e-15 relative error = 7.324590538380499e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3809248243668995 y1[1] (numeric) = 0.3809248243668829 absolute error = 1.665334536937735e-14 relative error = 4.371819399550911e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y2[1] (closed_form) = 0.9283689672491592 y2[1] (numeric) = 0.9283689672491664 absolute error = 7.216449660063518e-15 relative error = 7.773256016351459e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3716598722605517 y1[1] (numeric) = 0.371659872260534 absolute error = 1.770805724277125e-14 relative error = 4.764586807573628e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y2[1] (closed_form) = 0.9320390859672186 y2[1] (numeric) = 0.9320390859672261 absolute error = 7.438494264988549e-15 relative error = 7.980882322407424e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3623577544766935 y1[1] (numeric) = 0.3623577544766747 absolute error = 1.88182802673964e-14 relative error = 5.193287582481356e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y2[1] (closed_form) = 0.935616001553378 y2[1] (numeric) = 0.9356160015533855 absolute error = 7.549516567451064e-15 relative error = 8.069033187671871e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3530194012193514 y1[1] (numeric) = 0.3530194012193315 absolute error = 1.98729921407903e-14 relative error = 5.629433417015532e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y2[1] (closed_form) = 0.9390993563190595 y2[1] (numeric) = 0.9390993563190673 absolute error = 7.771561172376096e-15 relative error = 8.275547331687984e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3436457463160691 y1[1] (numeric) = 0.3436457463160482 absolute error = 2.09277040141842e-14 relative error = 6.08990631734341e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y2[1] (closed_form) = 0.9424888019316893 y2[1] (numeric) = 0.9424888019316972 absolute error = 7.882583474838611e-15 relative error = 8.363583162667575e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3342377271245258 y1[1] (numeric) = 0.3342377271245038 absolute error = 2.19824158875781e-14 relative error = 6.576880496613773e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y2[1] (closed_form) = 0.9457839994495306 y2[1] (numeric) = 0.9457839994495387 absolute error = 8.104628079763643e-15 relative error = 8.569216739213958e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3247962844388006 y1[1] (numeric) = 0.3247962844387774 absolute error = 2.314815006343451e-14 relative error = 7.126975021722017e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y2[1] (closed_form) = 0.9489846193555778 y2[1] (numeric) = 0.9489846193555859 absolute error = 8.104628079763643e-15 relative error = 8.540315527207608e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3153223623952942 y1[1] (numeric) = 0.3153223623952698 absolute error = 2.436939539052219e-14 relative error = 7.728406956425198e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.9 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y2[1] (closed_form) = 0.9520903415905072 y2[1] (numeric) = 0.9520903415905153 absolute error = 8.104628079763643e-15 relative error = 8.512456986197884e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.3058169083783159 y1[1] (numeric) = 0.3058169083782904 absolute error = 2.55351295663786e-14 relative error = 8.349809597443822e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y2[1] (closed_form) = 0.9551008555846836 y2[1] (numeric) = 0.9551008555846918 absolute error = 8.215650382226158e-15 relative error = 8.601866843891359e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2962808729253465 y1[1] (numeric) = 0.2962808729253198 absolute error = 2.664535259100376e-14 relative error = 8.993274634275009e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y2[1] (closed_form) = 0.9580158602892163 y2[1] (numeric) = 0.9580158602892246 absolute error = 8.326672684688674e-15 relative error = 8.691581246029609e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2867152096319844 y1[1] (numeric) = 0.2867152096319566 absolute error = 2.781108676686017e-14 relative error = 9.699899353981713e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 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) = 32.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y2[1] (closed_form) = 0.960835064206064 y2[1] (numeric) = 0.9608350642060723 absolute error = 8.326672684688674e-15 relative error = 8.666079116886711e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2771208750565877 y1[1] (numeric) = 0.2771208750565588 absolute error = 2.886579864025407e-14 relative error = 1.0416320544008e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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) = 32.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y2[1] (closed_form) = 0.9635581854171843 y2[1] (numeric) = 0.9635581854171926 absolute error = 8.326672684688674e-15 relative error = 8.641587825942799e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2674988286246186 y1[1] (numeric) = 0.2674988286245886 absolute error = 2.997602166487923e-14 relative error = 1.120603847837577e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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) = 32.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y2[1] (closed_form) = 0.9661849516127254 y2[1] (numeric) = 0.9661849516127338 absolute error = 8.326672684688674e-15 relative error = 8.618093948565494e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.257850032532702 y1[1] (numeric) = 0.257850032532671 absolute error = 3.103073353827313e-14 relative error = 1.203441133339304e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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) = 32.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y2[1] (closed_form) = 0.9687151001182567 y2[1] (numeric) = 0.9687151001182649 absolute error = 8.215650382226158e-15 relative error = 8.480976895294836e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2481754516524065 y1[1] (numeric) = 0.2481754516523743 absolute error = 3.219646771412954e-14 relative error = 1.29732685081294e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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) = 32.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y2[1] (closed_form) = 0.971148377921036 y2[1] (numeric) = 0.9711483779210444 absolute error = 8.326672684688674e-15 relative error = 8.57404787362546e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2384760534337579 y1[1] (numeric) = 0.2384760534337245 absolute error = 3.333444631437033e-14 relative error = 1.397811052069835e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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) = 32.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y2[1] (closed_form) = 0.973484541695311 y2[1] (numeric) = 0.9734845416953191 absolute error = 8.104628079763643e-15 relative error = 8.325379328211557e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2287528078084953 y1[1] (numeric) = 0.2287528078084608 absolute error = 3.447242491461111e-14 relative error = 1.506972755651172e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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) = 32.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y2[1] (closed_form) = 0.9757233578266508 y2[1] (numeric) = 0.9757233578266589 absolute error = 8.104628079763643e-15 relative error = 8.306276584190916e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2190066870930786 y1[1] (numeric) = 0.219006687093043 absolute error = 3.558264793923627e-14 relative error = 1.624728834152609e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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) = 32.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y2[1] (closed_form) = 0.977864602435308 y2[1] (numeric) = 0.977864602435316 absolute error = 7.993605777301127e-15 relative error = 8.1745527523888e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.2092386658914575 y1[1] (numeric) = 0.2092386658914207 absolute error = 3.674838211509268e-14 relative error = 1.756290213308658e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y2[1] (closed_form) = 0.9799080613986062 y2[1] (numeric) = 0.9799080613986141 absolute error = 7.882583474838611e-15 relative error = 8.044207191833827e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1994497209976122 y1[1] (numeric) = 0.1994497209975744 absolute error = 3.785860513971784e-14 relative error = 1.898152825201048e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y2[1] (closed_form) = 0.9818535303723519 y2[1] (numeric) = 0.9818535303723596 absolute error = 7.66053886991358e-15 relative error = 7.802119799893622e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1896408312978748 y1[1] (numeric) = 0.1896408312978358 absolute error = 3.899658373995862e-14 relative error = 2.056339000049281e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y2[1] (closed_form) = 0.9837008148112689 y2[1] (numeric) = 0.9837008148112765 absolute error = 7.549516567451064e-15 relative error = 7.674606398389028e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1798129776730411 y1[1] (numeric) = 0.1798129776730009 absolute error = 4.016231791581504e-14 relative error = 2.233560582531662e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y2[1] (closed_form) = 0.9854497299884528 y2[1] (numeric) = 0.9854497299884601 absolute error = 7.327471962526033e-15 relative error = 7.435662864925534e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1699671429002837 y1[1] (numeric) = 0.1699671429002424 absolute error = 4.130029651605582e-14 relative error = 2.429898850525826e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y2[1] (closed_form) = 0.9871001010138433 y2[1] (numeric) = 0.9871001010138504 absolute error = 7.105427357601002e-15 relative error = 7.198284500531476e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1601043115548751 y1[1] (numeric) = 0.1601043115548327 absolute error = 4.246603069191224e-14 relative error = 2.652397694946346e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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 = 0.158 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 = 0.158 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y2[1] (closed_form) = 0.988651762851713 y2[1] (numeric) = 0.9886517628517199 absolute error = 6.883382752675971e-15 relative error = 6.962393646900727e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1502254699117309 y1[1] (numeric) = 0.1502254699116873 absolute error = 4.360400929215302e-14 relative error = 2.902571003290838e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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 = 0.1485 Order of pole (three term test) = 32.02 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 = 0.1485 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y2[1] (closed_form) = 0.9901045603371712 y2[1] (numeric) = 0.9901045603371776 absolute error = 6.439293542825908e-15 relative error = 6.503650019178847e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1403316058467829 y1[1] (numeric) = 0.1403316058467381 absolute error = 4.474198789239381e-14 relative error = 3.188304418125457e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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 = 0.1389 Order of pole (three term test) = 32.02 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 = 0.1389 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y2[1] (closed_form) = 0.9914583481916802 y2[1] (numeric) = 0.9914583481916864 absolute error = 6.217248937900877e-15 relative error = 6.270812030823595e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1304237087381929 y1[1] (numeric) = 0.130423708738147 absolute error = 4.590772206825022e-14 relative error = 3.519890862818775e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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 = 0.1293 Order of pole (three term test) = 32.02 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 = 0.1293 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y2[1] (closed_form) = 0.9927129910375826 y2[1] (numeric) = 0.9927129910375885 absolute error = 5.88418203051333e-15 relative error = 5.927374864272893e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1205027693674151 y1[1] (numeric) = 0.1205027693673681 absolute error = 4.704570066849101e-14 relative error = 3.904117798741025e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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 = 0.1196 Order of pole (three term test) = 32.01 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 = 0.1196 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y2[1] (closed_form) = 0.9938683634116393 y2[1] (numeric) = 0.9938683634116448 absolute error = 5.440092820663267e-15 relative error = 5.473655285685048e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1105697798201192 y1[1] (numeric) = 0.110569779820071 absolute error = 4.819755705653961e-14 relative error = 4.359017186698747e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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 = 0.1099 Order of pole (three term test) = 32.01 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 = 0.1099 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y2[1] (closed_form) = 0.9949243497775757 y2[1] (numeric) = 0.9949243497775808 absolute error = 5.10702591327572e-15 relative error = 5.133079630041663e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.1006257333869825 y1[1] (numeric) = 0.1006257333869332 absolute error = 4.934941344458821e-14 relative error = 4.904253791105517e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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 = 0.1001 Order of pole (three term test) = 32.01 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 = 0.1001 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y2[1] (closed_form) = 0.9958808445376354 y2[1] (numeric) = 0.9958808445376399 absolute error = 4.551914400963142e-15 relative error = 4.570741997830565e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.09067162446436164 y1[1] (numeric) = 0.09067162446431115 absolute error = 5.048739204482899e-14 relative error = 5.568157882146801e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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 = 0.0903 Order of pole (three term test) = 32.01 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 = 0.0903 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y2[1] (closed_form) = 0.9967377520431391 y2[1] (numeric) = 0.9967377520431431 absolute error = 3.996802888650564e-15 relative error = 4.009884124944413e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.08070844845485374 y1[1] (numeric) = 0.08070844845480209 absolute error = 5.165312622068541e-14 relative error = 6.399965209290185e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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 = 0.08045 Order of pole (three term test) = 32.01 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 = 0.08045 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y2[1] (closed_form) = 0.9974949866040506 y2[1] (numeric) = 0.9974949866040542 absolute error = 3.663735981263017e-15 relative error = 3.672936736991655e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.07073720166775717 y1[1] (numeric) = 0.07073720166770441 absolute error = 5.276334924531056e-14 relative error = 7.459066516814264e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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 = 0.07056 Order of pole (three term test) = 32.01 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 = 0.07056 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y2[1] (closed_form) = 0.9981524724975448 y2[1] (numeric) = 0.998152472497548 absolute error = 3.219646771412954e-15 relative error = 3.225606167519536e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.06075888121944131 y1[1] (numeric) = 0.06075888121938738 absolute error = 5.392214452726307e-14 relative error = 8.874775743897231e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 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 = 0.06065 Order of pole (three term test) = 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 = 0.06065 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y2[1] (closed_form) = 0.9987101439755801 y2[1] (numeric) = 0.9987101439755828 absolute error = 2.664535259100376e-15 relative error = 2.667976564745424e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.05077448493363573 y1[1] (numeric) = 0.05077448493358068 absolute error = 5.504624533969604e-14 relative error = 1.08413202835329e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 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 = 0.05071 Order of pole (three term test) = 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 = 0.05071 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y2[1] (closed_form) = 0.9991679452714737 y2[1] (numeric) = 0.9991679452714759 absolute error = 2.220446049250313e-15 relative error = 2.222295120413434e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.04078501124164872 y1[1] (numeric) = 0.04078501124159254 absolute error = 5.617728504603292e-14 relative error = 1.377400258962439e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 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 = 0.04075 Order of pole (three term test) = 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 = 0.04075 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y2[1] (closed_form) = 0.9995258306054773 y2[1] (numeric) = 0.9995258306054788 absolute error = 1.554312234475219e-15 relative error = 1.555049591398425e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y1[1] (closed_form) = 0.03079145908252493 y1[1] (numeric) = 0.03079145908246765 absolute error = 5.728750807065808e-14 relative error = 1.860499949584086e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 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 = 0.03078 Order of pole (three term test) = 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 = 0.03078 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y2[1] (closed_form) = 0.9997837641893558 y2[1] (numeric) = 0.9997837641893567 absolute error = 8.881784197001252e-16 relative error = 8.883705172190686e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.02079482780315237 y1[1] (numeric) = 0.02079482780309397 absolute error = 5.840120054223519e-14 relative error = 2.808448384140114e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 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 = 0.02079 Order of pole (three term test) = 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 = 0.02079 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y2[1] (closed_form) = 0.9999417202299656 y2[1] (numeric) = 0.9999417202299661 absolute error = 4.440892098500626e-16 relative error = 4.441150927755383e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y1[1] (closed_form) = 0.01079611705832845 y1[1] (numeric) = 0.01079611705826894 absolute error = 5.950968884338437e-14 relative error = 5.512138162440245e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 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 = 0.0108 Order of pole (three term test) = 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 = 0.0108 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 2 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.569989504568902 y2[1] (closed_form) = 0.9999996745189654 y2[1] (numeric) = 0.9999996745189652 absolute error = 2.220446049250313e-16 relative error = 2.220446771963626e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001613636266322163 y1[1] (closed_form) = 0.0008068221384592121 y1[1] (numeric) = 0.000806822138399817 absolute error = 5.939508867375265e-14 relative error = 7.36160869199492e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.5799940494201 y2[1] (closed_form) = 0.9999577012474556 y2[1] (numeric) = 0.9999577012474549 absolute error = 7.771561172376096e-16 relative error = 7.771889913624355e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0001613636266322163 y1[1] (closed_form) = -0.009197592940772936 y1[1] (numeric) = -0.009197592940832344 absolute error = 5.940734015830174e-14 relative error = 6.459009497468512e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.589998594271297 y2[1] (closed_form) = 0.9998156421267984 y2[1] (numeric) = 0.9998156421267969 absolute error = 1.554312234475219e-15 relative error = 1.554598837010492e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613636266322163 y1[1] (closed_form) = -0.01920108743216578 y1[1] (numeric) = -0.01920108743222518 absolute error = 5.940387071134978e-14 relative error = 3.093776377052274e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.600003139122494 y2[1] (closed_form) = 0.9995735113757029 y2[1] (numeric) = 0.9995735113757003 absolute error = 2.664535259100376e-15 relative error = 2.665672137943314e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613636266322163 y1[1] (closed_form) = -0.02920266008512705 y1[1] (numeric) = -0.02920266008518646 absolute error = 5.941080960525369e-14 relative error = 2.034431433029339e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.610007683973692 y2[1] (closed_form) = 0.9992313332290561 y2[1] (numeric) = 0.9992313332290528 absolute error = 3.33066907387547e-15 relative error = 3.333231217952583e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613636266322163 y1[1] (closed_form) = -0.03920130984142145 y1[1] (numeric) = -0.03920130984148084 absolute error = 5.938999292354197e-14 relative error = 1.515000217181224e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.620012228824889 y2[1] (closed_form) = 0.9987891419354968 y2[1] (numeric) = 0.9987891419354932 absolute error = 3.663735981263017e-15 relative error = 3.668177623720729e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613636266322163 y1[1] (closed_form) = -0.04919603593536666 y1[1] (numeric) = -0.04919603593542604 absolute error = 5.938305402963806e-14 relative error = 1.207069897006641e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.630016773676087 y2[1] (closed_form) = 0.9982469817539885 y2[1] (numeric) = 0.9982469817539841 absolute error = 4.440892098500626e-15 relative error = 4.448690734529118e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613636266322163 y1[1] (closed_form) = -0.05918583799400004 y1[1] (numeric) = -0.05918583799405942 absolute error = 5.937611513573415e-14 relative error = 1.003214909988322e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.640021318527284 y2[1] (closed_form) = 0.9976049069493886 y2[1] (numeric) = 0.9976049069493835 absolute error = 5.10702591327572e-15 relative error = 5.119287082190359e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613636266322163 y1[1] (closed_form) = -0.06916971613720606 y1[1] (numeric) = -0.0691697161372654 absolute error = 5.934142066621462e-14 relative error = 8.579104264141277e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.650025863378481 y2[1] (closed_form) = 0.9968629817870174 y2[1] (numeric) = 0.9968629817870118 absolute error = 5.551115123125783e-15 relative error = 5.568583872153249e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613636266322163 y1[1] (closed_form) = -0.07914667107779436 y1[1] (numeric) = -0.07914667107785375 absolute error = 5.939693181744587e-14 relative error = 7.504665832257659e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.660030408229679 y2[1] (closed_form) = 0.996021280526226 y2[1] (numeric) = 0.9960212805262197 absolute error = 6.217248937900877e-15 relative error = 6.242084440822519e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613636266322163 y1[1] (closed_form) = -0.08911570422151852 y1[1] (numeric) = -0.08911570422157793 absolute error = 5.941080960525369e-14 relative error = 6.666704833255184e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.670034953080876 y2[1] (closed_form) = 0.995079887412963 y2[1] (numeric) = 0.9950798874129559 absolute error = 7.105427357601002e-15 relative error = 7.14055971533491e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613636266322163 y1[1] (closed_form) = -0.09907581776702541 y1[1] (numeric) = -0.09907581776708477 absolute error = 5.935529845402243e-14 relative error = 5.990896647817241e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.680039497932074 y2[1] (closed_form) = 0.9940388966713434 y2[1] (numeric) = 0.9940388966713354 absolute error = 7.993605777301127e-15 relative error = 8.041542241524612e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1090260148057253 y1[1] (numeric) = -0.1090260148057846 absolute error = 5.929978730279117e-14 relative error = 5.439049332258743e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.690044042783271 y2[1] (closed_form) = 0.9928984124942167 y2[1] (numeric) = 0.9928984124942083 absolute error = 8.43769498715119e-15 relative error = 8.498044594466844e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1189652994215722 y1[1] (numeric) = -0.1189652994216315 absolute error = 5.925815393936773e-14 relative error = 4.981129306401958e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.700048587634468 y2[1] (closed_form) = 0.9916585490327385 y2[1] (numeric) = 0.9916585490327294 absolute error = 9.103828801926284e-15 relative error = 9.180406714393917e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1288926767907458 y1[1] (numeric) = -0.128892676790805 absolute error = 5.914713163690521e-14 relative error = 4.588866730801871e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.710053132485666 y2[1] (closed_form) = 0.9903194303849456 y2[1] (numeric) = 0.9903194303849356 absolute error = 9.992007221626409e-15 relative error = 1.008968108173181e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1388071532812229 y1[1] (numeric) = -0.1388071532812821 absolute error = 5.920264278813647e-14 relative error = 4.265100276798567e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.720057677336863 y2[1] (closed_form) = 0.9888811905833342 y2[1] (numeric) = 0.9888811905833236 absolute error = 1.06581410364015e-14 relative error = 1.077797933451878e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1487077365522302 y1[1] (numeric) = -0.1487077365522893 absolute error = 5.909162048567396e-14 relative error = 3.973674931493519e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.730062222188061 y2[1] (closed_form) = 0.9873439735814452 y2[1] (numeric) = 0.9873439735814336 absolute error = 1.165734175856414e-14 relative error = 1.180676853303601e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.158593435653568 y1[1] (numeric) = -0.1585934356536272 absolute error = 5.911937606128959e-14 relative error = 3.727731593533929e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.740066767039258 y2[1] (closed_form) = 0.9857079332394557 y2[1] (numeric) = 0.9857079332394434 absolute error = 1.232347557333924e-14 relative error = 1.250215723925347e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1684632611247946 y1[1] (numeric) = -0.1684632611248535 absolute error = 5.895284260759581e-14 relative error = 3.49944802290896e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.750071311890455 y2[1] (closed_form) = 0.9839732333087791 y2[1] (numeric) = 0.9839732333087664 absolute error = 1.265654248072678e-14 relative error = 1.286268980932234e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1783162250942608 y1[1] (numeric) = -0.1783162250943195 absolute error = 5.873079800267078e-14 relative error = 3.293631747286303e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.760075856741653 y2[1] (closed_form) = 0.982140047415675 y2[1] (numeric) = 0.982140047415662 absolute error = 1.298960938811433e-14 relative error = 1.322582194086694e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1881513413779868 y1[1] (numeric) = -0.1881513413780452 absolute error = 5.839773109528323e-14 relative error = 3.103763739742097e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.77008040159285 y2[1] (closed_form) = 0.9802085590438714 y2[1] (numeric) = 0.9802085590438576 absolute error = 1.376676550535194e-14 relative error = 1.404473096907102e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1979676255783692 y1[1] (numeric) = -0.1979676255784275 absolute error = 5.831446436843635e-14 relative error = 2.945656604107295e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.780084946444048 y2[1] (closed_form) = 0.9781789615161993 y2[1] (numeric) = 0.9781789615161856 absolute error = 1.376676550535194e-14 relative error = 1.407387200805581e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2077640951827091 y1[1] (numeric) = -0.2077640951827673 absolute error = 5.820344206597383e-14 relative error = 2.801419658906383e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.790089491295245 y2[1] (closed_form) = 0.9760514579752436 y2[1] (numeric) = 0.9760514579752291 absolute error = 1.454392162258955e-14 relative error = 1.490077342106531e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2175397696615525 y1[1] (numeric) = -0.2175397696616106 absolute error = 5.814793091474257e-14 relative error = 2.672979336385659e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.800094036146442 y2[1] (closed_form) = 0.9738262613630098 y2[1] (numeric) = 0.9738262613629941 absolute error = 1.565414464721471e-14 relative error = 1.607488447200477e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2272936705668309 y1[1] (numeric) = -0.2272936705668889 absolute error = 5.795364188543317e-14 relative error = 2.549725284514384e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.81009858099764 y2[1] (closed_form) = 0.971503594399611 y2[1] (numeric) = 0.9715035943995949 absolute error = 1.609823385706477e-14 relative error = 1.657043159682129e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2370248216297949 y1[1] (numeric) = -0.2370248216298526 absolute error = 5.773159728050814e-14 relative error = 2.435677279853759e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.820103125848837 y2[1] (closed_form) = 0.9690836895609762 y2[1] (numeric) = 0.9690836895609595 absolute error = 1.676436767183986e-14 relative error = 1.729919495336323e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2467322488587285 y1[1] (numeric) = -0.246732248858786 absolute error = 5.753730825119874e-14 relative error = 2.331973567190355e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.830107670700035 y2[1] (closed_form) = 0.966566789055581 y2[1] (numeric) = 0.9665667890555639 absolute error = 1.709743457922741e-14 relative error = 1.768882892814171e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2564149806364361 y1[1] (numeric) = -0.2564149806364935 absolute error = 5.734301922188934e-14 relative error = 2.236336546311015e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.840112215551232 y2[1] (closed_form) = 0.9639531448002056 y2[1] (numeric) = 0.963953144800188 absolute error = 1.754152378907747e-14 relative error = 1.819748592937391e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2660720478174923 y1[1] (numeric) = -0.2660720478175495 absolute error = 5.717648576819556e-14 relative error = 2.148909900051389e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.850116760402429 y2[1] (closed_form) = 0.9612430183947198 y2[1] (numeric) = 0.9612430183947014 absolute error = 1.84297022087776e-14 relative error = 1.91727813425946e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2757024838252428 y1[1] (numeric) = -0.2757024838252998 absolute error = 5.700995231450179e-14 relative error = 2.067806989749073e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.860121305253627 y2[1] (closed_form) = 0.9584366810959003 y2[1] (numeric) = 0.9584366810958813 absolute error = 1.898481372109018e-14 relative error = 1.980810427599919e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.28530532474855 y1[1] (numeric) = -0.2853053247486068 absolute error = 5.684341886080801e-14 relative error = 1.992371467686634e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.870125850104824 y2[1] (closed_form) = 0.9555344137902795 y2[1] (numeric) = 0.9555344137902597 absolute error = 1.976196983832779e-14 relative error = 2.068158880844363e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2948796094382704 y1[1] (numeric) = -0.294879609438327 absolute error = 5.662137425588298e-14 relative error = 1.920152239883376e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.880130394956022 y2[1] (closed_form) = 0.9525365069660326 y2[1] (numeric) = 0.9525365069660122 absolute error = 2.042810365310288e-14 relative error = 2.144600600996319e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3044243796034563 y1[1] (numeric) = -0.3044243796035128 absolute error = 5.651035195342047e-14 relative error = 1.856301785915798e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.890134939807219 y2[1] (closed_form) = 0.9494432606839021 y2[1] (numeric) = 0.949443260683881 absolute error = 2.109423746787797e-14 relative error = 2.221748085576319e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3139386799072712 y1[1] (numeric) = -0.3139386799073276 absolute error = 5.639932965095795e-14 relative error = 1.796507829733397e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.900139484658416 y2[1] (closed_form) = 0.9462549845471642 y2[1] (numeric) = 0.9462549845471426 absolute error = 2.153832667772804e-14 relative error = 2.276165201712024e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3234215580626097 y1[1] (numeric) = -0.3234215580626659 absolute error = 5.617728504603292e-14 relative error = 1.736967856519874e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.910144029509614 y2[1] (closed_form) = 0.9429719976706418 y2[1] (numeric) = 0.9429719976706196 absolute error = 2.220446049250313e-14 relative error = 2.3547316937675e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3328720649274118 y1[1] (numeric) = -0.3328720649274677 absolute error = 5.589972928987663e-14 relative error = 1.679315724558217e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.919987210734179 y2[1] (closed_form) = 0.9396498494513172 y2[1] (numeric) = 0.9396498494512945 absolute error = 2.275957200481571e-14 relative error = 2.422133310414037e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3421376337471761 y1[1] (numeric) = -0.3421376337472319 absolute error = 5.578870698741412e-14 relative error = 1.630592530158182e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.929991755585376 y2[1] (closed_form) = 0.936179950434015 y2[1] (numeric) = 0.9361799504339915 absolute error = 2.353672812205332e-14 relative error = 2.514124353030808e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3515211236972327 y1[1] (numeric) = -0.3515211236972882 absolute error = 5.551115123125783e-14 relative error = 1.579169713825503e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.939996300436574 y2[1] (closed_form) = 0.9326163490879271 y2[1] (numeric) = 0.9326163490879027 absolute error = 2.442490654175344e-14 relative error = 2.618966155337114e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3608694298689009 y1[1] (numeric) = -0.3608694298689562 absolute error = 5.52891066263328e-14 relative error = 1.532108348618463e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.950000845287771 y2[1] (closed_form) = 0.9289594020942076 y2[1] (numeric) = 0.9289594020941824 absolute error = 2.520206265899105e-14 relative error = 2.712934774348219e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3701816165894416 y1[1] (numeric) = -0.3701816165894967 absolute error = 5.512257317263902e-14 relative error = 1.489068357324021e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.960005390138968 y2[1] (closed_form) = 0.9252094754769838 y2[1] (numeric) = 0.9252094754769579 absolute error = 2.597921877622866e-14 relative error = 2.807928308649811e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3794567518013146 y1[1] (numeric) = -0.3794567518013691 absolute error = 5.456746166032644e-14 relative error = 1.438041658273042e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.970009934990166 y2[1] (closed_form) = 0.9213669445667216 y2[1] (numeric) = 0.921366944566695 absolute error = 2.664535259100376e-14 relative error = 2.89193711019597e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3886939071554681 y1[1] (numeric) = -0.3886939071555225 absolute error = 5.440092820663267e-14 relative error = 1.39958273605955e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.980014479841363 y2[1] (closed_form) = 0.9174321939626581 y2[1] (numeric) = 0.917432193962631 absolute error = 2.708944180085382e-14 relative error = 2.952745933609174e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3978921581042578 y1[1] (numeric) = -0.397892158104312 absolute error = 5.417888360170764e-14 relative error = 1.361647433813244e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.990019024692561 y2[1] (closed_form) = 0.913405617494307 y2[1] (numeric) = 0.9134056174942793 absolute error = 2.775557561562891e-14 relative error = 3.038691144879225e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4070505839939842 y1[1] (numeric) = -0.4070505839940382 absolute error = 5.395683899678261e-14 relative error = 1.325556113133596e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.000023569543758 y2[1] (closed_form) = 0.9092876181820408 y2[1] (numeric) = 0.9092876181820121 absolute error = 2.875477633779155e-14 relative error = 3.162341129782634e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4161682681570414 y1[1] (numeric) = -0.4161682681570952 absolute error = 5.379030554308883e-14 relative error = 1.292513381217018e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.010028114394955 y2[1] (closed_form) = 0.9050786081967517 y2[1] (numeric) = 0.9050786081967217 absolute error = 2.997602166487923e-14 relative error = 3.311979909082422e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4252442980036663 y1[1] (numeric) = -0.4252442980037198 absolute error = 5.351274978693255e-14 relative error = 1.258400172280998e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.020032659246153 y2[1] (closed_form) = 0.9007790088185976 y2[1] (numeric) = 0.9007790088185669 absolute error = 3.075317778211684e-14 relative error = 3.414064657484712e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4342777651132796 y1[1] (numeric) = -0.434277765113333 absolute error = 5.345723863570129e-14 relative error = 1.230945789309687e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.03003720409735 y2[1] (closed_form) = 0.8963892503948366 y2[1] (numeric) = 0.8963892503948057 absolute error = 3.097522238704187e-14 relative error = 3.455554868981089e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4432677653254102 y1[1] (numeric) = -0.4432677653254634 absolute error = 5.3179682879545e-14 relative error = 1.199719154865793e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.040041748948548 y2[1] (closed_form) = 0.8919097722967529 y2[1] (numeric) = 0.8919097722967213 absolute error = 3.164135620181696e-14 relative error = 3.547596089270044e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4522133988301921 y1[1] (numeric) = -0.4522133988302451 absolute error = 5.295763827461997e-14 relative error = 1.171076275307485e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.050046293799745 y2[1] (closed_form) = 0.8873410228756804 y2[1] (numeric) = 0.8873410228756476 absolute error = 3.275157922644212e-14 relative error = 3.690979948194137e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4611137702584269 y1[1] (numeric) = -0.4611137702584797 absolute error = 5.279110482092619e-14 relative error = 1.144860731253806e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.060050838650942 y2[1] (closed_form) = 0.882683459418127 y2[1] (numeric) = 0.8826834594180935 absolute error = 3.352873534367973e-14 relative error = 3.798500468761721e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4699679887712011 y1[1] (numeric) = -0.4699679887712536 absolute error = 5.25135490647699e-14 relative error = 1.117385658586538e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.07005538350214 y2[1] (closed_form) = 0.8779375481000051 y2[1] (numeric) = 0.8779375480999707 absolute error = 3.441691376337985e-14 relative error = 3.920200683734676e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4787751681490502 y1[1] (numeric) = -0.4787751681491025 absolute error = 5.229150445984487e-14 relative error = 1.092193328697568e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.080059928353337 y2[1] (closed_form) = 0.8731037639399716 y2[1] (numeric) = 0.8731037639399364 absolute error = 3.519406988061746e-14 relative error = 4.030914919184469e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4875344268806608 y1[1] (numeric) = -0.487534426880713 absolute error = 5.218048215738236e-14 relative error = 1.070293281466155e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.090064473204535 y2[1] (closed_form) = 0.8681825907518834 y2[1] (numeric) = 0.8681825907518481 absolute error = 3.530509218307998e-14 relative error = 4.066551501856798e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.496244888251101 y1[1] (numeric) = -0.4962448882511529 absolute error = 5.184741524999481e-14 relative error = 1.04479494857305e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.100069018055732 y2[1] (closed_form) = 0.8631745210963726 y2[1] (numeric) = 0.8631745210963364 absolute error = 3.61932706027801e-14 relative error = 4.193042046330184e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5049056804295707 y1[1] (numeric) = -0.5049056804296221 absolute error = 5.140332604014475e-14 relative error = 1.018077792200933e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.110073562906929 y2[1] (closed_form) = 0.8580800562315459 y2[1] (numeric) = 0.8580800562315087 absolute error = 3.719247132494274e-14 relative error = 4.334382445419132e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5135159365566633 y1[1] (numeric) = -0.5135159365567143 absolute error = 5.10702591327572e-14 relative error = 9.945214061944097e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.120078107758127 y2[1] (closed_form) = 0.8528997060628135 y2[1] (numeric) = 0.8528997060627757 absolute error = 3.785860513971784e-14 relative error = 4.438810902454417e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5220747948311297 y1[1] (numeric) = -0.52207479483118 absolute error = 5.029310301551959e-14 relative error = 9.633313753786447e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.130082652609324 y2[1] (closed_form) = 0.8476339890918531 y2[1] (numeric) = 0.8476339890918144 absolute error = 3.863576125695545e-14 relative error = 4.558071261199593e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5305813985961365 y1[1] (numeric) = -0.5305813985961864 absolute error = 4.984901380566953e-14 relative error = 9.395168005807377e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.140087197460522 y2[1] (closed_form) = 0.8422834323647123 y2[1] (numeric) = 0.8422834323646727 absolute error = 3.952393967665557e-14 relative error = 4.692475021821579e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5390348964250081 y1[1] (numeric) = -0.5390348964250578 absolute error = 4.96269692007445e-14 relative error = 9.20663384316691e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.150091742311719 y2[1] (closed_form) = 0.8368485714190571 y2[1] (numeric) = 0.8368485714190165 absolute error = 4.063416270128073e-14 relative error = 4.855617143777488e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5474344422064467 y1[1] (numeric) = -0.547434442206496 absolute error = 4.929390229335695e-14 relative error = 9.004530678536919e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.160096287162916 y2[1] (closed_form) = 0.8313299502305698 y2[1] (numeric) = 0.8313299502305284 absolute error = 4.141131881851834e-14 relative error = 4.981333681895244e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5557791952292189 y1[1] (numeric) = -0.555779195229268 absolute error = 4.907185768843192e-14 relative error = 8.829380104484355e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.170100832014114 y2[1] (closed_form) = 0.8257281211585024 y2[1] (numeric) = 0.8257281211584608 absolute error = 4.152234112098085e-14 relative error = 5.02857297178213e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5640683202663039 y1[1] (numeric) = -0.5640683202663526 absolute error = 4.862776847858186e-14 relative error = 8.620900470996857e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.180105376865311 y2[1] (closed_form) = 0.8200436448903906 y2[1] (numeric) = 0.8200436448903482 absolute error = 4.241051954068098e-14 relative error = 5.171739309844867e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5723009876584899 y1[1] (numeric) = -0.5723009876585382 absolute error = 4.829470157119431e-14 relative error = 8.438689188496262e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.190109921716509 y2[1] (closed_form) = 0.8142770903859349 y2[1] (numeric) = 0.8142770903858918 absolute error = 4.307665335545607e-14 relative error = 5.290171351258263e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5804763733974158 y1[1] (numeric) = -0.5804763733974634 absolute error = 4.762856775641922e-14 relative error = 8.205082917958993e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.200114466567706 y2[1] (closed_form) = 0.8084290348200535 y2[1] (numeric) = 0.8084290348200094 absolute error = 4.407585407761871e-14 relative error = 5.452037492373028e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5885936592080455 y1[1] (numeric) = -0.5885936592080929 absolute error = 4.740652315149418e-14 relative error = 8.05420214945567e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.210119011418903 y2[1] (closed_form) = 0.8025000635251122 y2[1] (numeric) = 0.8025000635250672 absolute error = 4.496403249731884e-14 relative error = 5.602994260188218e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5966520326305701 y1[1] (numeric) = -0.5966520326306172 absolute error = 4.707345624410664e-14 relative error = 7.889599577255303e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.220123556270101 y2[1] (closed_form) = 0.7964907699323391 y2[1] (numeric) = 0.7964907699322933 absolute error = 4.585221091701897e-14 relative error = 5.756778690720302e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6046506871017262 y1[1] (numeric) = -0.6046506871017729 absolute error = 4.674038933671909e-14 relative error = 7.730147394814009e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.230128101121298 y2[1] (closed_form) = 0.7904017555124278 y2[1] (numeric) = 0.7904017555123815 absolute error = 4.629630012686903e-14 relative error = 5.857312411566512e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6125888220355252 y1[1] (numeric) = -0.6125888220355712 absolute error = 4.596323321948148e-14 relative error = 7.503113273721469e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.240132645972496 y2[1] (closed_form) = 0.7842336297153357 y2[1] (numeric) = 0.7842336297152885 absolute error = 4.718447854656915e-14 relative error = 6.016635446212166e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.620465642903384 y1[1] (numeric) = -0.6204656429034299 absolute error = 4.585221091701897e-14 relative error = 7.389967751068346e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.250137190823693 y2[1] (closed_form) = 0.7779870099092849 y2[1] (numeric) = 0.777987009909237 absolute error = 4.796163466380676e-14 relative error = 6.164837465525189e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6282803613136496 y1[1] (numeric) = -0.628280361313695 absolute error = 4.54081217071689e-14 relative error = 7.227366077817017e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.26014173567489 y2[1] (closed_form) = 0.7716625213189694 y2[1] (numeric) = 0.7716625213189204 absolute error = 4.89608353859694e-14 relative error = 6.344850764850257e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6360321950905089 y1[1] (numeric) = -0.6360321950905535 absolute error = 4.463096558993129e-14 relative error = 7.017092206091895e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.269984916899455 y2[1] (closed_form) = 0.7653646600526848 y2[1] (numeric) = 0.7653646600526351 absolute error = 4.96269692007445e-14 relative error = 6.484094679434031e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6435968747146292 y1[1] (numeric) = -0.6435968747146735 absolute error = 4.429789868254375e-14 relative error = 6.882864169001043e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.279989461750653 y2[1] (closed_form) = 0.758887570959328 y2[1] (numeric) = 0.7588875709592778 absolute error = 5.018208071305708e-14 relative error = 6.612584344953852e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6512216632172573 y1[1] (numeric) = -0.6512216632173007 absolute error = 4.340972026284362e-14 relative error = 6.665890082400636e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.28999400660185 y2[1] (closed_form) = 0.7523345247461329 y2[1] (numeric) = 0.7523345247460821 absolute error = 5.084821452783217e-14 relative error = 6.75872405895374e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6587812708896711 y1[1] (numeric) = -0.6587812708897141 absolute error = 4.296563105299356e-14 relative error = 6.521987335032965e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.299998551453048 y2[1] (closed_form) = 0.7457061773080379 y2[1] (numeric) = 0.7457061773079859 absolute error = 5.195843755245733e-14 relative error = 6.967682330328105e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6662749410901128 y1[1] (numeric) = -0.6662749410901551 absolute error = 4.229949723821846e-14 relative error = 6.348654981532244e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.310003096304245 y2[1] (closed_form) = 0.7390031920768868 y2[1] (numeric) = 0.7390031920768341 absolute error = 5.273559366969494e-14 relative error = 7.136044097656382e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6737019237765111 y1[1] (numeric) = -0.673701923776553 absolute error = 4.196643033083092e-14 relative error = 6.229228216476424e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.320007641155442 y2[1] (closed_form) = 0.7322262399550269 y2[1] (numeric) = 0.7322262399549732 absolute error = 5.373479439185758e-14 relative error = 7.338550772935692e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6810614755815537 y1[1] (numeric) = -0.6810614755815955 absolute error = 4.174438572590589e-14 relative error = 6.12931243692218e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.33001218600664 y2[1] (closed_form) = 0.7253759992481573 y2[1] (numeric) = 0.725375999248103 absolute error = 5.428990590417015e-14 relative error = 7.484381336085137e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6883528598870911 y1[1] (numeric) = -0.6883528598871324 absolute error = 4.130029651605582e-14 relative error = 5.999872873751148e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.340016730857837 y2[1] (closed_form) = 0.7184531555974379 y2[1] (numeric) = 0.7184531555973832 absolute error = 5.473399511402022e-14 relative error = 7.618310906924131e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6955753468978638 y1[1] (numeric) = -0.6955753468979046 absolute error = 4.074518500374325e-14 relative error = 5.857767269277033e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.350021275709035 y2[1] (closed_form) = 0.7114584019108631 y2[1] (numeric) = 0.7114584019108069 absolute error = 5.617728504603292e-14 relative error = 7.896074443024322e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7027282137145491 y1[1] (numeric) = -0.702728213714589 absolute error = 3.996802888650564e-14 relative error = 5.687551475304904e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.360025820560232 y2[1] (closed_form) = 0.7043924382939085 y2[1] (numeric) = 0.7043924382938516 absolute error = 5.695444116327053e-14 relative error = 8.08561223360354e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7098107444061144 y1[1] (numeric) = -0.7098107444061541 absolute error = 3.97459842815806e-14 relative error = 5.599518546994571e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.370030365411429 y2[1] (closed_form) = 0.6972559719794583 y2[1] (numeric) = 0.6972559719794005 absolute error = 5.784261958297066e-14 relative error = 8.295751045166342e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7168222300814763 y1[1] (numeric) = -0.7168222300815155 absolute error = 3.919087276926803e-14 relative error = 5.467307112505909e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.380034910262627 y2[1] (closed_form) = 0.6900497172570167 y2[1] (numeric) = 0.690049717256958 absolute error = 5.873079800267078e-14 relative error = 8.511096596942136e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7237619689604528 y1[1] (numeric) = -0.7237619689604914 absolute error = 3.863576125695545e-14 relative error = 5.338186159801739e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.390039455113824 y2[1] (closed_form) = 0.6827743954012159 y2[1] (numeric) = 0.6827743954011565 absolute error = 5.939693181744587e-14 relative error = 8.699349626686382e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7306292664440045 y1[1] (numeric) = -0.7306292664440426 absolute error = 3.808064974464287e-14 relative error = 5.212034542495483e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.400043999965022 y2[1] (closed_form) = 0.6754307345996231 y2[1] (numeric) = 0.675430734599563 absolute error = 6.006306563222097e-14 relative error = 8.892557379377281e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7374234351837575 y1[1] (numeric) = -0.7374234351837952 absolute error = 3.763656053479281e-14 relative error = 5.103792304270097e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.410048544816219 y2[1] (closed_form) = 0.6680194698798562 y2[1] (numeric) = 0.6680194698797961 absolute error = 6.006306563222097e-14 relative error = 8.991214828367706e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7441437951508001 y1[1] (numeric) = -0.7441437951508367 absolute error = 3.663735981263017e-14 relative error = 4.923424753572747e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.420053089667416 y2[1] (closed_form) = 0.660541343036015 y2[1] (numeric) = 0.6605413430359541 absolute error = 6.084022174945858e-14 relative error = 9.210660678682358e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7507896737037462 y1[1] (numeric) = -0.7507896737037828 absolute error = 3.663735981263017e-14 relative error = 4.879843329742824e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.430057634518614 y2[1] (closed_form) = 0.6529971025544345 y2[1] (numeric) = 0.6529971025543728 absolute error = 6.17284001691587e-14 relative error = 9.453089443687533e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7573604056560611 y1[1] (numeric) = -0.7573604056560973 absolute error = 3.61932706027801e-14 relative error = 4.778870182872551e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.440062179369811 y2[1] (closed_form) = 0.6453875035387696 y2[1] (numeric) = 0.6453875035387067 absolute error = 6.294964549624638e-14 relative error = 9.753775081030039e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7638553333426393 y1[1] (numeric) = -0.763855333342675 absolute error = 3.563815909046752e-14 relative error = 4.665563953650039e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.450066724221009 y2[1] (closed_form) = 0.6377133076344161 y2[1] (numeric) = 0.6377133076343525 absolute error = 6.361577931102147e-14 relative error = 9.975607933759895e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7702738066856308 y1[1] (numeric) = -0.7702738066856654 absolute error = 3.452793606584237e-14 relative error = 4.482553575904488e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.460071269072206 y2[1] (closed_form) = 0.6299752829522777 y2[1] (numeric) = 0.6299752829522136 absolute error = 6.405986852087153e-14 relative error = 1.016863204865202e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.776615183259507 y1[1] (numeric) = -0.7766151832595407 absolute error = 3.375077994860476e-14 relative error = 4.345882063102402e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.470075813923403 y2[1] (closed_form) = 0.6221742039918858 y2[1] (numeric) = 0.622174203991821 absolute error = 6.483702463810914e-14 relative error = 1.042104031670119e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7828788283553613 y1[1] (numeric) = -0.7828788283553944 absolute error = 3.308464613382966e-14 relative error = 4.226023866724368e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.480080358774601 y2[1] (closed_form) = 0.6143108515638798 y2[1] (numeric) = 0.614310851563814 absolute error = 6.572520305780927e-14 relative error = 1.069901384461784e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7890641150444373 y1[1] (numeric) = -0.7890641150444698 absolute error = 3.252953462151709e-14 relative error = 4.122546444744245e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.490084903625798 y2[1] (closed_form) = 0.6063860127118554 y2[1] (numeric) = 0.6063860127117889 absolute error = 6.650235917504688e-14 relative error = 1.096700085109775e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7951704242408778 y1[1] (numeric) = -0.7951704242409099 absolute error = 3.208544541166702e-14 relative error = 4.035040091222949e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.500089448476996 y2[1] (closed_form) = 0.5984004806335899 y2[1] (numeric) = 0.5984004806335225 absolute error = 6.7390537594747e-14 relative error = 1.126177865422058e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8011971447636896 y1[1] (numeric) = -0.8011971447637207 absolute error = 3.108624468950438e-14 relative error = 3.879974472284617e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.510093993328193 y2[1] (closed_form) = 0.5903550546016504 y2[1] (numeric) = 0.5903550546015822 absolute error = 6.816769371198461e-14 relative error = 1.154689761367109e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8071436733979164 y1[1] (numeric) = -0.8071436733979468 absolute error = 3.042011087472929e-14 relative error = 3.7688594828064e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.52009853817939 y2[1] (closed_form) = 0.5822505398833949 y2[1] (numeric) = 0.5822505398833258 absolute error = 6.916689443414725e-14 relative error = 1.187923234008491e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8130094149550147 y1[1] (numeric) = -0.8130094149550441 absolute error = 2.942091015256665e-14 relative error = 3.618766229686843e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.530103083030588 y2[1] (closed_form) = 0.5740877476603728 y2[1] (numeric) = 0.5740877476603028 absolute error = 7.005507285384738e-14 relative error = 1.220285106925702e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8187937823324259 y1[1] (numeric) = -0.8187937823324547 absolute error = 2.875477633779155e-14 relative error = 3.51184595660709e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.540107627881785 y2[1] (closed_form) = 0.5658674949471341 y2[1] (numeric) = 0.5658674949470629 absolute error = 7.116529587847253e-14 relative error = 1.257631804511428e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8244961965723403 y1[1] (numeric) = -0.8244961965723685 absolute error = 2.819966482547898e-14 relative error = 3.420229825524098e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.550112172732983 y2[1] (closed_form) = 0.5575906045094534 y2[1] (numeric) = 0.5575906045093815 absolute error = 7.194245199571014e-14 relative error = 1.290237880873232e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8301160869196442 y1[1] (numeric) = -0.8301160869196721 absolute error = 2.786659791809143e-14 relative error = 3.356951920001634e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.56011671758418 y2[1] (closed_form) = 0.5492579047819804 y2[1] (numeric) = 0.5492579047819076 absolute error = 7.283063041541027e-14 relative error = 1.325982380614427e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8356528908790473 y1[1] (numeric) = -0.8356528908790741 absolute error = 2.686739719592879e-14 relative error = 3.215138425197836e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.570121262435377 y2[1] (closed_form) = 0.5408702297853212 y2[1] (numeric) = 0.5408702297852477 absolute error = 7.349676423018536e-14 relative error = 1.358861334619161e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8411060542713825 y1[1] (numeric) = -0.8411060542714086 absolute error = 2.609024107869118e-14 relative error = 3.101896716376883e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.580125807286575 y2[1] (closed_form) = 0.5324284190425607 y2[1] (numeric) = 0.5324284190424867 absolute error = 7.394085344003543e-14 relative error = 1.388747309412964e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8464750312890743 y1[1] (numeric) = -0.8464750312890993 absolute error = 2.498001805406602e-14 relative error = 2.951063779876013e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.590130352137772 y2[1] (closed_form) = 0.5239333174952356 y2[1] (numeric) = 0.5239333174951609 absolute error = 7.471800955727304e-14 relative error = 1.426097693394971e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8517592845507683 y1[1] (numeric) = -0.8517592845507924 absolute error = 2.40918396343659e-14 relative error = 2.828479838299893e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.600134896988969 y2[1] (closed_form) = 0.5153857754187634 y2[1] (numeric) = 0.5153857754186878 absolute error = 7.560618797697316e-14 relative error = 1.466982434964203e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8569582851551177 y1[1] (numeric) = -0.8569582851551414 absolute error = 2.364775042451583e-14 relative error = 2.759498429988965e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.610139441840167 y2[1] (closed_form) = 0.5067866483373384 y2[1] (numeric) = 0.5067866483372622 absolute error = 7.627232179174825e-14 relative error = 1.505018374931184e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8620715127337214 y1[1] (numeric) = -0.8620715127337445 absolute error = 2.309263891220326e-14 relative error = 2.678738198757318e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.620143986691364 y2[1] (closed_form) = 0.4981367969383028 y2[1] (numeric) = 0.4981367969382258 absolute error = 7.699396675775461e-14 relative error = 1.545639013840826e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8670984555032076 y1[1] (numeric) = -0.8670984555032302 absolute error = 2.253752739989068e-14 relative error = 2.599188968317486e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.629987167915929 y2[1] (closed_form) = 0.4895777959260774 y2[1] (numeric) = 0.4895777959259998 absolute error = 7.760458942129844e-14 relative error = 1.58513294653208e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8719596216202699 y1[1] (numeric) = -0.8719596216202917 absolute error = 2.187139358511558e-14 relative error = 2.508303485942881e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.639991712767127 y2[1] (closed_form) = 0.4808298813661823 y2[1] (numeric) = 0.4808298813661039 absolute error = 7.832623438730479e-14 relative error = 1.628980174126375e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8768139056751912 y1[1] (numeric) = -0.876813905675212 absolute error = 2.076117056049043e-14 relative error = 2.367796681383979e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.649996257618324 y2[1] (closed_form) = 0.4720338405036326 y2[1] (numeric) = 0.4720338405035536 absolute error = 7.904787935331115e-14 relative error = 1.674623142886782e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8815804293536643 y1[1] (numeric) = -0.8815804293536846 absolute error = 2.031708135064036e-14 relative error = 2.304620279006868e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.660000802469522 y2[1] (closed_form) = 0.4631905537348869 y2[1] (numeric) = 0.4631905537348071 absolute error = 7.97695243193175e-14 relative error = 1.722175110785498e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8862587155739394 y1[1] (numeric) = -0.8862587155739589 absolute error = 1.942890293094024e-14 relative error = 2.192238292219007e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.670005347320719 y2[1] (closed_form) = 0.4543009061852503 y2[1] (numeric) = 0.4543009061851697 absolute error = 8.065770273901762e-14 relative error = 1.775424650069437e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8908482960859612 y1[1] (numeric) = -0.8908482960859798 absolute error = 1.865174681370263e-14 relative error = 2.093706290470679e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.680009892171916 y2[1] (closed_form) = 0.4453657876202826 y2[1] (numeric) = 0.445365787620201 absolute error = 8.160139230994901e-14 relative error = 1.832233067249478e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.895348711518236 y1[1] (numeric) = -0.8953487115182539 absolute error = 1.787459069646502e-14 relative error = 1.996383137264498e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.690014437023114 y2[1] (closed_form) = 0.4363860923567409 y2[1] (numeric) = 0.4363860923566584 absolute error = 8.248957072964913e-14 relative error = 1.890288718509728e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8997595114238104 y1[1] (numeric) = -0.8997595114238276 absolute error = 1.720845688168993e-14 relative error = 1.912561819375343e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.700018981874311 y2[1] (closed_form) = 0.427362719173068 y2[1] (numeric) = 0.4273627191729846 absolute error = 8.3322237998118e-14 relative error = 1.949684290649958e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9040802543253565 y1[1] (numeric) = -0.9040802543253726 absolute error = 1.609823385706477e-14 relative error = 1.780620003594438e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.710023526725509 y2[1] (closed_form) = 0.4182965712194333 y2[1] (numeric) = 0.4182965712193492 absolute error = 8.409939411535561e-14 relative error = 2.010520762103931e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9083105077593596 y1[1] (numeric) = -0.9083105077593747 absolute error = 1.509903313490213e-14 relative error = 1.662320649812668e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.720028071576706 y2[1] (closed_form) = 0.4091885559273364 y2[1] (numeric) = 0.4091885559272516 absolute error = 8.47655279301307e-14 relative error = 2.071551774903093e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9124498483194028 y1[1] (numeric) = -0.9124498483194174 absolute error = 1.465494392505207e-14 relative error = 1.606109525037929e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.730032616427903 y2[1] (closed_form) = 0.4000395849187824 y2[1] (numeric) = 0.4000395849186968 absolute error = 8.565370634983083e-14 relative error = 2.141130767526933e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9164978616985466 y1[1] (numeric) = -0.9164978616985601 absolute error = 1.343369859796439e-14 relative error = 1.465764314285219e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.740037161279101 y2[1] (closed_form) = 0.3908505739150374 y2[1] (numeric) = 0.390850573914951 absolute error = 8.637535131583718e-14 relative error = 2.209932825494925e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9204541427307967 y1[1] (numeric) = -0.9204541427308091 absolute error = 1.232347557333924e-14 relative error = 1.338847314737271e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.750041706130298 y2[1] (closed_form) = 0.3816224426449739 y2[1] (numeric) = 0.3816224426448865 absolute error = 8.737455203799982e-14 relative error = 2.289554865600108e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9243182954316568 y1[1] (numeric) = -0.9243182954316685 absolute error = 1.176836406102666e-14 relative error = 1.273193889939269e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.760046250981496 y2[1] (closed_form) = 0.3723561147530151 y2[1] (numeric) = 0.372356114752927 absolute error = 8.804068585277491e-14 relative error = 2.364421648108896e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.928089933037763 y1[1] (numeric) = -0.928089933037774 absolute error = 1.099120794378905e-14 relative error = 1.184282638193623e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.770050795832693 y2[1] (closed_form) = 0.3630525177066872 y2[1] (numeric) = 0.3630525177065984 absolute error = 8.881784197001252e-14 relative error = 2.446418565860742e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9317686780455949 y1[1] (numeric) = -0.9317686780456045 absolute error = 9.547918011776346e-15 relative error = 1.024709054591029e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.78005534068389 y2[1] (closed_form) = 0.3537125827037893 y2[1] (numeric) = 0.3537125827036997 absolute error = 8.959499808725013e-14 relative error = 2.532988716499237e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.93535416224926 y1[1] (numeric) = -0.9353541622492685 absolute error = 8.43769498715119e-15 relative error = 9.020855765329508e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.790059885535088 y2[1] (closed_form) = 0.3443372445791895 y2[1] (numeric) = 0.3443372445790991 absolute error = 9.037215420448774e-14 relative error = 2.624524521444972e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9388460267773473 y1[1] (numeric) = -0.9388460267773547 absolute error = 7.438494264988549e-15 relative error = 7.92301831485796e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.800064430386285 y2[1] (closed_form) = 0.3349274417112572 y2[1] (numeric) = 0.334927441711166 absolute error = 9.126033262418787e-14 relative error = 2.724779198679811e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9422439221288469 y1[1] (numeric) = -0.9422439221288536 absolute error = 6.661338147750939e-15 relative error = 7.069653612305324e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.810068975237483 y2[1] (closed_form) = 0.325484115927941 y2[1] (numeric) = 0.3254841159278489 absolute error = 9.209299989265674e-14 relative error = 2.829416103151566e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9455475082081316 y1[1] (numeric) = -0.9455475082081373 absolute error = 5.662137425588298e-15 relative error = 5.988210403428997e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.82007352008868 y2[1] (closed_form) = 0.3160082124125007 y2[1] (numeric) = 0.3160082124124078 absolute error = 9.29256671611256e-14 relative error = 2.94060924719973e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9487564543589971 y1[1] (numeric) = -0.948756454359002 absolute error = 4.884981308350689e-15 relative error = 5.148825376530483e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.830078064939877 y2[1] (closed_form) = 0.3065006796089041 y2[1] (numeric) = 0.3065006796088104 absolute error = 9.364731212713195e-14 relative error = 3.055370456164281e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9518704393977575 y1[1] (numeric) = -0.9518704393977613 absolute error = 3.774758283725532e-15 relative error = 3.965621924464635e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.840082609791075 y2[1] (closed_form) = 0.296962469126897 y2[1] (numeric) = 0.2969624691268029 absolute error = 9.414691248821327e-14 relative error = 3.170330337197686e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9548891516453921 y1[1] (numeric) = -0.9548891516453951 absolute error = 2.997602166487923e-15 relative error = 3.139214809721823e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.850087154642272 y2[1] (closed_form) = 0.2873945356467567 y2[1] (numeric) = 0.2873945356466618 absolute error = 9.492406860545088e-14 relative error = 3.302918352008065e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9578122889587422 y1[1] (numeric) = -0.9578122889587444 absolute error = 2.220446049250313e-15 relative error = 2.318247609522954e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.86009169949347 y2[1] (closed_form) = 0.2777978368237378 y2[1] (numeric) = 0.2777978368236419 absolute error = 9.586775817638227e-14 relative error = 3.450990089502036e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9606395587607518 y1[1] (numeric) = -0.9606395587607534 absolute error = 1.554312234475219e-15 relative error = 1.61799732303375e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.870096244344667 y2[1] (closed_form) = 0.2681733331922203 y2[1] (numeric) = 0.2681733331921236 absolute error = 9.670042544485113e-14 relative error = 3.605892662546673e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9633706780697523 y1[1] (numeric) = -0.963370678069753 absolute error = 6.661338147750939e-16 relative error = 6.914615837278606e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.880100789195864 y2[1] (closed_form) = 0.25852198806957 y2[1] (numeric) = 0.2585219880694727 absolute error = 9.731104810839497e-14 relative error = 3.764130426004921e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9660053735277859 y1[1] (numeric) = -0.9660053735277855 absolute error = 4.440892098500626e-16 relative error = 4.597171216846124e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.890105334047062 y2[1] (closed_form) = 0.2488447674597196 y2[1] (numeric) = 0.2488447674596215 absolute error = 9.808820422563258e-14 relative error = 3.941742686693626e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9685433814279658 y1[1] (numeric) = -0.9685433814279646 absolute error = 1.221245327087672e-15 relative error = 1.260909269017085e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.900109878898259 y2[1] (closed_form) = 0.2391426399564816 y2[1] (numeric) = 0.2391426399563827 absolute error = 9.886536034287019e-14 relative error = 4.134158607635234e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9709844477408712 y1[1] (numeric) = -0.9709844477408689 absolute error = 2.331468351712829e-15 relative error = 2.401138717656405e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.910114423749457 y2[1] (closed_form) = 0.2294165766466014 y2[1] (numeric) = 0.2294165766465018 absolute error = 9.961476088449217e-14 relative error = 4.342090808805898e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9733283281399725 y1[1] (numeric) = -0.9733283281399693 absolute error = 3.219646771412954e-15 relative error = 3.307873282148984e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.920118968600654 y2[1] (closed_form) = 0.2196675510125614 y2[1] (numeric) = 0.219667551012461 absolute error = 1.004196725773454e-13 relative error = 4.571438617786705e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9755747880260865 y1[1] (numeric) = -0.9755747880260823 absolute error = 4.218847493575595e-15 relative error = 4.32447367988233e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.930123513451851 y2[1] (closed_form) = 0.2098965388351448 y2[1] (numeric) = 0.2098965388350437 absolute error = 1.010302952408892e-13 relative error = 4.813337837849705e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9777236025508572 y1[1] (numeric) = -0.9777236025508521 absolute error = 5.10702591327572e-15 relative error = 5.223384093369141e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.940128058303049 y2[1] (closed_form) = 0.2001045180957698 y2[1] (numeric) = 0.200104518095668 absolute error = 1.018352069337425e-13 relative error = 5.089100831046917e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9797745566392606 y1[1] (numeric) = -0.9797745566392542 absolute error = 6.439293542825908e-15 relative error = 6.572219598060829e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.950132603154246 y2[1] (closed_form) = 0.1902924688786033 y2[1] (numeric) = 0.1902924688785006 absolute error = 1.027233853534426e-13 relative error = 5.39818448721556e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9817274450111323 y1[1] (numeric) = -0.9817274450111244 absolute error = 7.882583474838611e-15 relative error = 8.029299287593235e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.960137148005443 y2[1] (closed_form) = 0.1804613732724643 y2[1] (numeric) = 0.1804613732723608 absolute error = 1.035005414706802e-13 relative error = 5.735329372364522e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9835820722017132 y1[1] (numeric) = -0.9835820722017047 absolute error = 8.548717289613705e-15 relative error = 8.691412268706472e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.970141692856641 y2[1] (closed_form) = 0.1706122152725262 y2[1] (numeric) = 0.1706122152724218 absolute error = 1.043887198903803e-13 relative error = 6.118478663654637e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9853382525812144 y1[1] (numeric) = -0.985338252581205 absolute error = 9.436895709313831e-15 relative error = 9.577315895929874e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.979984874081206 y2[1] (closed_form) = 0.160905243811801 y2[1] (numeric) = 0.1609052438116959 absolute error = 1.051936315832336e-13 relative error = 6.537613634660086e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9869698589692923 y1[1] (numeric) = -0.986969858969282 absolute error = 1.032507412901396e-14 relative error = 1.046138748329821e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.989989418932403 y2[1] (closed_form) = 0.1510231717999078 y2[1] (numeric) = 0.1510231717998017 absolute error = 1.060262988517024e-13 relative error = 7.020531855348518e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.988530222896344 y1[1] (numeric) = -0.9885302228963326 absolute error = 1.13242748511766e-14 relative error = 1.145566881910503e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.999993963783601 y2[1] (closed_form) = 0.1411259838662393 y2[1] (numeric) = 0.1411259838661325 absolute error = 1.068312105445557e-13 relative error = 7.56991785763644e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9899916447515029 y1[1] (numeric) = -0.9899916447514904 absolute error = 1.254552017826427e-14 relative error = 1.267234955443822e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.009998508634798 y2[1] (closed_form) = 0.1312146706211558 y2[1] (numeric) = 0.131214670621048 absolute error = 1.077749001154871e-13 relative error = 8.213631875558776e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9913539782609346 y1[1] (numeric) = -0.9913539782609211 absolute error = 1.354472090042691e-14 relative error = 1.366285020027609e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.020003053485996 y2[1] (closed_form) = 0.1212902240888208 y2[1] (numeric) = 0.1212902240887123 absolute error = 1.085659340205325e-13 relative error = 8.950922041419403e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9926170870685652 y1[1] (numeric) = -0.9926170870685508 absolute error = 1.443289932012704e-14 relative error = 1.454024871035701e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.030007598337193 y2[1] (closed_form) = 0.11135363760791 y2[1] (numeric) = 0.1113536376078006 absolute error = 1.093708457133857e-13 relative error = 9.821937393594099e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9937808447497296 y1[1] (numeric) = -0.9937808447497142 absolute error = 1.543210004228968e-14 relative error = 1.552867528471636e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.04001214318839 y2[1] (closed_form) = 0.1014059057321872 y2[1] (numeric) = 0.101405905732077 absolute error = 1.102312685574702e-13 relative error = 1.087030067544495e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9948451348238251 y1[1] (numeric) = -0.9948451348238084 absolute error = 1.665334536937735e-14 relative error = 1.673963593572426e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.050016688039588 y2[1] (closed_form) = 0.09144802413096 y2[1] (numeric) = 0.09144802413084885 absolute error = 1.11147202552786e-13 relative error = 1.215413931673531e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.99580985076597 y1[1] (numeric) = -0.9958098507659516 absolute error = 1.831867990631508e-14 relative error = 1.839576088971653e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.060021232890785 y2[1] (closed_form) = 0.08148098948942253 y2[1] (numeric) = 0.08148098948931053 absolute error = 1.120076253968705e-13 relative error = 1.374647339198191e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9966748960176657 y1[1] (numeric) = -0.9966748960176463 absolute error = 1.942890293094024e-14 relative error = 1.949372158220374e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.070025777741983 y2[1] (closed_form) = 0.07150579940889777 y2[1] (numeric) = 0.07150579940878495 absolute error = 1.128264148775315e-13 relative error = 1.577863834964581e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9974401839964613 y1[1] (numeric) = -0.9974401839964404 absolute error = 2.087219286295294e-14 relative error = 2.092575895561371e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.08003032259318 y2[1] (closed_form) = 0.06152345230698712 y2[1] (numeric) = 0.06152345230687344 absolute error = 1.136729599338082e-13 relative error = 1.847636237423864e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9981056381046196 y1[1] (numeric) = -0.9981056381045972 absolute error = 2.242650509742816e-14 relative error = 2.246906964679169e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.090034867444377 y2[1] (closed_form) = 0.05153494731763889 y2[1] (numeric) = 0.05153494731752434 absolute error = 1.145472605657005e-13 relative error = 2.222710345654984e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9986711917367839 y1[1] (numeric) = -0.9986711917367601 absolute error = 2.375877272697835e-14 relative error = 2.379038558793269e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.100039412295575 y2[1] (closed_form) = 0.04154128419114483 y2[1] (numeric) = 0.04154128419102943 absolute error = 1.153938056219772e-13 relative error = 2.777810264386945e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9991367882866442 y1[1] (numeric) = -0.9991367882866196 absolute error = 2.464695114667848e-14 relative error = 2.466824506476631e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.110043957146772 y2[1] (closed_form) = 0.03154346319407508 y2[1] (numeric) = 0.03154346319395883 absolute error = 1.162542284660617e-13 relative error = 3.685525199018037e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9995023811526034 y1[1] (numeric) = -0.9995023811525776 absolute error = 2.575717417130363e-14 relative error = 2.576999780791022e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.12004850199797 y2[1] (closed_form) = 0.0215424850091614 y2[1] (numeric) = 0.02154248500904427 absolute error = 1.17131998544906e-13 relative error = 5.437255659924706e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9997679337424411 y1[1] (numeric) = -0.999767933742414 absolute error = 2.708944180085382e-14 relative error = 2.70957298054656e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.130053046849167 y2[1] (closed_form) = 0.01153935063513873 y2[1] (numeric) = 0.01153935063502072 absolute error = 1.180097686237502e-13 relative error = 1.022672525994627e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9999334194769767 y1[1] (numeric) = -0.999933419476948 absolute error = 2.864375403532904e-14 relative error = 2.864566127843931e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.140057591700364 y2[1] (closed_form) = 0.001535061286555139 y2[1] (numeric) = 0.001535061286436251 absolute error = 1.188879723834635e-13 relative error = 7.744835559644807e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9999988217927291 y1[1] (numeric) = -0.9999988217926993 absolute error = 2.986499936241671e-14 relative error = 2.986503454961756e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.150062136551562 y2[1] (closed_form) = -0.008469381706439775 y2[1] (numeric) = -0.008469381706559542 absolute error = 1.197670435049147e-13 relative error = 1.414117909148536e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9999641341435754 y1[1] (numeric) = -0.9999641341435447 absolute error = 3.075317778211684e-14 relative error = 3.075428081073684e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.160066681402759 y2[1] (closed_form) = -0.01847297699831815 y2[1] (numeric) = -0.01847297699843879 absolute error = 1.20646548307235e-13 relative error = 6.530974856852749e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9998293600014052 y1[1] (numeric) = -0.9998293600013736 absolute error = 3.164135620181696e-14 relative error = 3.164675640428532e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.170071226253957 y2[1] (closed_form) = -0.02847472332839858 y2[1] (numeric) = -0.02847472332852012 absolute error = 1.215381961738871e-13 relative error = 4.268283655373531e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9995945128557735 y1[1] (numeric) = -0.9995945128557407 absolute error = 3.275157922644212e-14 relative error = 3.276486495796489e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.180075771105154 y2[1] (closed_form) = -0.03847361962106242 y2[1] (numeric) = -0.03847361962118487 absolute error = 1.22443721828347e-13 relative error = 3.182537100338618e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9992596162125505 y1[1] (numeric) = -0.9992596162125166 absolute error = 3.397282455352979e-14 relative error = 3.399799611866182e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.190080315956351 y2[1] (closed_form) = -0.04846866508595151 y2[1] (numeric) = -0.04846866508607485 absolute error = 1.23338839141951e-13 relative error = 2.544712938209234e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9988247035915691 y1[1] (numeric) = -0.9988247035915337 absolute error = 3.530509218307998e-14 relative error = 3.534663495619411e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.200084860807549 y2[1] (closed_form) = -0.05845885931813733 y2[1] (numeric) = -0.05845885931826159 absolute error = 1.242547731372667e-13 relative error = 2.125507999755235e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9982898185232695 y1[1] (numeric) = -0.9982898185232331 absolute error = 3.641531520770513e-14 relative error = 3.64776986923225e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.210089405658746 y2[1] (closed_form) = -0.06844320239825168 y2[1] (numeric) = -0.0684432023983768 absolute error = 1.251221348752551e-13 relative error = 1.828116313833546e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9976550145443424 y1[1] (numeric) = -0.9976550145443045 absolute error = 3.785860513971784e-14 relative error = 3.794759169030884e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.220093950509944 y2[1] (closed_form) = -0.07842069499256862 y2[1] (numeric) = -0.07842069499269458 absolute error = 1.25954802143724e-13 relative error = 1.606142385701374e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9969203551923707 y1[1] (numeric) = -0.9969203551923316 absolute error = 3.907985046680551e-14 relative error = 3.920057431194137e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.230098495361141 y2[1] (closed_form) = -0.08839033845302792 y2[1] (numeric) = -0.08839033845315475 absolute error = 1.268291027756163e-13 relative error = 1.434875179746205e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9960859139994698 y1[1] (numeric) = -0.9960859139994295 absolute error = 4.030109579389318e-14 relative error = 4.045945759043696e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.240103040212338 y2[1] (closed_form) = -0.09835113491718982 y2[1] (numeric) = -0.09835113491731755 absolute error = 1.277311589831243e-13 relative error = 1.298725826505937e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9951517744849279 y1[1] (numeric) = -0.9951517744848866 absolute error = 4.130029651605582e-14 relative error = 4.150150517234629e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.250107585063536 y2[1] (closed_form) = -0.1083020874081111 y2[1] (numeric) = -0.1083020874082397 absolute error = 1.285777040394009e-13 relative error = 1.187213534997584e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9941180301468462 y1[1] (numeric) = -0.9941180301468036 absolute error = 4.263256414560601e-14 relative error = 4.288481131290672e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.260112129914733 y2[1] (closed_form) = -0.1182421999341328 y2[1] (numeric) = -0.1182421999342622 absolute error = 1.294658824591011e-13 relative error = 1.094921124025268e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9929847844527813 y1[1] (numeric) = -0.9929847844527373 absolute error = 4.39648317751562e-14 relative error = 4.427543348449649e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.27011667476593 y2[1] (closed_form) = -0.1281704775885686 y2[1] (numeric) = -0.128170477588699 absolute error = 1.303401830909934e-13 relative error = 1.016928278206075e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9917521508293885 y1[1] (numeric) = -0.991752150829343 absolute error = 4.551914400963142e-14 relative error = 4.589770132745807e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.280121219617128 y2[1] (closed_form) = -0.1380859266492859 y2[1] (numeric) = -0.138085926649417 absolute error = 1.31117339208231e-13 relative error = 9.495344123028997e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9904202526510694 y1[1] (numeric) = -0.9904202526510224 absolute error = 4.696243394164412e-14 relative error = 4.741667369577634e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.290125764468325 y2[1] (closed_form) = -0.1479875546781667 y2[1] (numeric) = -0.1479875546782988 absolute error = 1.320610287791624e-13 relative error = 8.923792886932939e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9889892232276227 y1[1] (numeric) = -0.9889892232275747 absolute error = 4.807265696626928e-14 relative error = 4.860786734296398e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.300130309319523 y2[1] (closed_form) = -0.1578743706204416 y2[1] (numeric) = -0.1578743706205746 absolute error = 1.33060229501325e-13 relative error = 8.428234993330601e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9874592057909023 y1[1] (numeric) = -0.9874592057908528 absolute error = 4.951594689828198e-14 relative error = 5.014480254768838e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.31013485417072 y2[1] (closed_form) = -0.1677453849038838 y2[1] (numeric) = -0.1677453849040177 absolute error = 1.338928967697939e-13 relative error = 7.981912399349346e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9858303534804799 y1[1] (numeric) = -0.9858303534804287 absolute error = 5.118128143521972e-14 relative error = 5.191692592394208e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.320139399021917 y2[1] (closed_form) = -0.1775996095378561 y2[1] (numeric) = -0.1775996095379909 absolute error = 1.34781075189494e-13 relative error = 7.589041188785093e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9841028293283183 y1[1] (numeric) = -0.9841028293282661 absolute error = 5.218048215738236e-14 relative error = 5.30234042645698e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.330143943873115 y2[1] (closed_form) = -0.1874360582121987 y2[1] (numeric) = -0.1874360582123345 absolute error = 1.357802759116566e-13 relative error = 7.244085113971939e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9822768062424528 y1[1] (numeric) = -0.9822768062423989 absolute error = 5.395683899678261e-14 relative error = 5.493038077849573e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.33998712509768 y2[1] (closed_form) = -0.1970955505991159 y2[1] (numeric) = -0.1970955505992524 absolute error = 1.365574320288943e-13 relative error = 6.928488827565995e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9803842838061162 y1[1] (numeric) = -0.9803842838060602 absolute error = 5.595524044110789e-14 relative error = 5.707480359015401e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.349991669948877 y2[1] (closed_form) = -0.2068938218634224 y2[1] (numeric) = -0.2068938218635599 absolute error = 1.375011215998256e-13 relative error = 6.645975233160649e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9783634020519913 y1[1] (numeric) = -0.9783634020519342 absolute error = 5.717648576819556e-14 relative error = 5.844094908729746e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.359996214800075 y2[1] (closed_form) = -0.2166713851079609 y2[1] (numeric) = -0.2166713851080992 absolute error = 1.383337888682945e-13 relative error = 6.384497371416484e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9762445958239142 y1[1] (numeric) = -0.9762445958238557 absolute error = 5.850875339774575e-14 relative error = 5.993247352971674e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.370000759651272 y2[1] (closed_form) = -0.2264272616956164 y2[1] (numeric) = -0.2264272616957557 absolute error = 1.392774784392259e-13 relative error = 6.151091409940515e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9740280771933758 y1[1] (numeric) = -0.9740280771933157 absolute error = 6.006306563222097e-14 relative error = 6.166461423298019e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.38000530450247 y2[1] (closed_form) = -0.2361604751598931 y2[1] (numeric) = -0.2361604751600333 absolute error = 1.402211680101573e-13 relative error = 5.937537511949032e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9717140680119093 y1[1] (numeric) = -0.9717140680118473 absolute error = 6.195044477408373e-14 relative error = 6.375377985504731e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.390009849353667 y2[1] (closed_form) = -0.2458700513026492 y2[1] (numeric) = -0.2458700513027902 absolute error = 1.410538352786261e-13 relative error = 5.736926255609657e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9693027998888855 y1[1] (numeric) = -0.969302799888822 absolute error = 6.350475700855895e-14 relative error = 6.551591207189201e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.400014394204864 y2[1] (closed_form) = -0.2555550182916042 y2[1] (numeric) = -0.2555550182917461 absolute error = 1.419420136983263e-13 relative error = 5.554264386871151e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9667945141683303 y1[1] (numeric) = -0.9667945141682657 absolute error = 6.461498003318411e-14 relative error = 6.683424356081305e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.410018939056062 y2[1] (closed_form) = -0.26521440675761 y2[1] (numeric) = -0.2652144067577528 absolute error = 1.427746809667951e-13 relative error = 5.38336822317811e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9641894619047695 y1[1] (numeric) = -0.964189461904703 absolute error = 6.650235917504688e-14 relative error = 6.897229414193197e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.420023483907259 y2[1] (closed_form) = -0.2748472498916749 y2[1] (numeric) = -0.2748472498918185 absolute error = 1.43607348235264e-13 relative error = 5.224987635563527e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9614879038380999 y1[1] (numeric) = -0.9614879038380321 absolute error = 6.783462680459706e-14 relative error = 7.055172148688768e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.430028028758457 y2[1] (closed_form) = -0.2844525835417316 y2[1] (numeric) = -0.2844525835418762 absolute error = 1.445510378061954e-13 relative error = 5.081727014266633e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9586901103674921 y1[1] (numeric) = -0.9586901103674228 absolute error = 6.927791673660977e-14 relative error = 7.226309731103167e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.440032573609654 y2[1] (closed_form) = -0.2940294463091396 y2[1] (numeric) = -0.2940294463092851 absolute error = 1.454947273771268e-13 relative error = 4.948304641030921e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9557963615243263 y1[1] (numeric) = -0.9557963615242556 absolute error = 7.072120666862247e-14 relative error = 7.399191869263307e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.450037118460851 y2[1] (closed_form) = -0.3035768796449112 y2[1] (numeric) = -0.3035768796450575 absolute error = 1.462718834943644e-13 relative error = 4.818281407512198e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9528069469441641 y1[1] (numeric) = -0.9528069469440915 absolute error = 7.260858581048524e-14 relative error = 7.620492907126148e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.460041663312049 y2[1] (closed_form) = -0.3130939279456529 y2[1] (numeric) = -0.3130939279458 absolute error = 1.471045507628332e-13 relative error = 4.698415958688531e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9497221658377583 y1[1] (numeric) = -0.9497221658376842 absolute error = 7.405187574249794e-14 relative error = 7.797214638786085e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.470046208163246 y2[1] (closed_form) = -0.322579638649212 y2[1] (numeric) = -0.3225796386493601 absolute error = 1.481592626362271e-13 relative error = 4.592951472592552e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9465423269611052 y1[1] (numeric) = -0.9465423269610298 absolute error = 7.538414337204813e-14 relative error = 7.964159787134989e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.480050753014444 y2[1] (closed_form) = -0.3320330623300183 y2[1] (numeric) = -0.3320330623301675 absolute error = 1.491584633583898e-13 relative error = 4.49227743501448e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9432677485845417 y1[1] (numeric) = -0.9432677485844645 absolute error = 7.716050021144838e-14 relative error = 8.180127045288538e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.490055297865641 y2[1] (closed_form) = -0.3414532527941128 y2[1] (numeric) = -0.341453252794263 absolute error = 1.501576640805524e-13 relative error = 4.397605319375695e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9398987584608886 y1[1] (numeric) = -0.9398987584608103 absolute error = 7.827072323607354e-14 relative error = 8.327569595287487e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.500059842716838 y2[1] (closed_form) = -0.3508392671738515 y2[1] (numeric) = -0.3508392671740024 absolute error = 1.508793090465588e-13 relative error = 4.300525145373579e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9364356937926464 y1[1] (numeric) = -0.9364356937925662 absolute error = 8.01581023779363e-14 relative error = 8.559915316052188e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.510064387568036 y2[1] (closed_form) = -0.3601901660222777 y2[1] (numeric) = -0.3601901660224294 absolute error = 1.517119763150276e-13 relative error = 4.211996623629205e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9328789011982446 y1[1] (numeric) = -0.9328789011981626 absolute error = 8.193445921733655e-14 relative error = 8.782968412308941e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.520068932419233 y2[1] (closed_form) = -0.369505013407151 y2[1] (numeric) = -0.3695050134073036 absolute error = 1.52655665885959e-13 relative error = 4.131355742059999e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9292287366773485 y1[1] (numeric) = -0.9292287366772649 absolute error = 8.359979375427429e-14 relative error = 8.996686225310124e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.530073477270431 y2[1] (closed_form) = -0.3787828770046251 y2[1] (numeric) = -0.3787828770047786 absolute error = 1.534883331544279e-13 relative error = 4.05214550267418e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9254855655752277 y1[1] (numeric) = -0.9254855655751427 absolute error = 8.493206138382448e-14 relative error = 9.177027124246469e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.540078022121628 y2[1] (closed_form) = -0.3880228281925641 y2[1] (numeric) = -0.3880228281927184 absolute error = 1.543210004228968e-13 relative error = 3.977111376197482e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9216497625461876 y1[1] (numeric) = -0.9216497625461008 absolute error = 8.681944052568724e-14 relative error = 9.420003569016963e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.550082566972825 y2[1] (closed_form) = -0.3972239421434882 y2[1] (numeric) = -0.3972239421436434 absolute error = 1.552091788425969e-13 relative error = 3.907347024579175e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9177217115160711 y1[1] (numeric) = -0.9177217115159827 absolute error = 8.837375276016246e-14 relative error = 9.629689659860996e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.560087111824023 y2[1] (closed_form) = -0.4063852979171398 y2[1] (numeric) = -0.4063852979172958 absolute error = 1.559308238086032e-13 relative error = 3.83701931658947e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9137018056438312 y1[1] (numeric) = -0.9137018056437415 absolute error = 8.970602038971265e-14 relative error = 9.817866161105172e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.57009165667522 y2[1] (closed_form) = -0.4155059785526608 y2[1] (numeric) = -0.4155059785528178 absolute error = 1.569855356819971e-13 relative error = 3.778177542205953e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9095904472821797 y1[1] (numeric) = -0.9095904472820885 absolute error = 9.126033262418787e-14 relative error = 1.003312346747595e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.580096201526417 y2[1] (closed_form) = -0.4245850711603708 y2[1] (numeric) = -0.4245850711605287 absolute error = 1.579292252529285e-13 relative error = 3.7196132407886e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9053880479373155 y1[1] (numeric) = -0.9053880479372228 absolute error = 9.270362255620057e-14 relative error = 1.023910385910229e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.590100746377615 y2[1] (closed_form) = -0.4336216670131386 y2[1] (numeric) = -0.4336216670132977 absolute error = 1.590394482775537e-13 relative error = 3.667700679558866e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.9010950282277373 y1[1] (numeric) = -0.901095028227643 absolute error = 9.436895709313831e-14 relative error = 1.047269756650883e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.600105291228812 y2[1] (closed_form) = -0.4426148616373369 y2[1] (numeric) = -0.4426148616374967 absolute error = 1.598166043947913e-13 relative error = 3.610737420871769e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8967118178421433 y1[1] (numeric) = -0.8967118178420471 absolute error = 9.614531393253856e-14 relative error = 1.072198581746181e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.61010983608001 y2[1] (closed_form) = -0.4515637549033708 y2[1] (numeric) = -0.4515637549035314 absolute error = 1.605937605120289e-13 relative error = 3.556391733574676e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8922388554964239 y1[1] (numeric) = -0.8922388554963265 absolute error = 9.736655925962623e-14 relative error = 1.09126114223588e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.620114380931207 y2[1] (closed_form) = -0.460467451115772 y2[1] (numeric) = -0.4604674511159336 absolute error = 1.615929612341915e-13 relative error = 3.509324293012046e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8876765888897511 y1[1] (numeric) = -0.8876765888896518 absolute error = 9.925393840148899e-14 relative error = 1.118131757035853e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.630118925782404 y2[1] (closed_form) = -0.469325059102849 y2[1] (numeric) = -0.4693250591030115 absolute error = 1.625366508051229e-13 relative error = 3.463199921943743e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8830254746597672 y1[1] (numeric) = -0.8830254746596662 absolute error = 1.010302952408892e-13 relative error = 1.144137945508498e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.640123470633602 y2[1] (closed_form) = -0.4781356923058848 y2[1] (numeric) = -0.478135692306048 absolute error = 1.632582957711293e-13 relative error = 3.414476233384511e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.878285978336881 y1[1] (numeric) = -0.8782859783367785 absolute error = 1.025846074753645e-13 relative error = 1.168009167920662e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.650128015484799 y2[1] (closed_form) = -0.4868984688678722 y2[1] (numeric) = -0.4868984688680362 absolute error = 1.639799407371356e-13 relative error = 3.367846711829242e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8734585742976719 y1[1] (numeric) = -0.8734585742975675 absolute error = 1.044719866172272e-13 relative error = 1.196072597961853e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.660132560335997 y2[1] (closed_form) = -0.4956125117217794 y2[1] (numeric) = -0.4956125117219443 absolute error = 1.648681191568357e-13 relative error = 3.326552806023334e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8685437457174101 y1[1] (numeric) = -0.868543745717304 absolute error = 1.06137321154165e-13 relative error = 1.222014684666187e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.670137105187194 y2[1] (closed_form) = -0.5042769486783352 y2[1] (numeric) = -0.5042769486785011 absolute error = 1.659783421814609e-13 relative error = 3.291412439463579e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8635419845216952 y1[1] (numeric) = -0.8635419845215873 absolute error = 1.079136779935652e-13 relative error = 1.249663362382284e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.680141650038391 y2[1] (closed_form) = -0.512890912513327 y2[1] (numeric) = -0.5128909125134939 absolute error = 1.669775429036235e-13 relative error = 3.255615157721961e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8584537913372198 y1[1] (numeric) = -0.8584537913371103 absolute error = 1.094679902280404e-13 relative error = 1.275176268457285e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.689984831262957 y2[1] (closed_form) = -0.5213158459631766 y2[1] (numeric) = -0.5213158459633446 absolute error = 1.679767436257862e-13 relative error = 3.222168382690046e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8533638079668586 y1[1] (numeric) = -0.8533638079667474 absolute error = 1.112443470674407e-13 relative error = 1.303598137498714e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.699989376114154 y2[1] (closed_form) = -0.52982713076067 y2[1] (numeric) = -0.5298271307608391 absolute error = 1.690869666504113e-13 relative error = 3.191361046529536e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8481056605812249 y1[1] (numeric) = -0.8481056605811119 absolute error = 1.130207039068409e-13 relative error = 1.332625274890695e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.709993920965351 y2[1] (closed_form) = -0.5382853851167584 y2[1] (numeric) = -0.5382853851169288 absolute error = 1.704192342799615e-13 relative error = 3.16596435630509e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8427626262297724 y1[1] (numeric) = -0.8427626262296574 absolute error = 1.150191053511662e-13 relative error = 1.364786498254221e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.719998465816549 y2[1] (closed_form) = -0.5466897624440625 y2[1] (numeric) = -0.5466897624442342 absolute error = 1.716404796070492e-13 relative error = 3.139632226506373e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.837335239697252 y1[1] (numeric) = -0.8373352396971352 absolute error = 1.167954621905665e-13 relative error = 1.3948470893545e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.730003010667746 y2[1] (closed_form) = -0.5550394215477598 y2[1] (numeric) = -0.5550394215479321 absolute error = 1.723066134218243e-13 relative error = 3.104403160073518e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8318240442112312 y1[1] (numeric) = -0.8318240442111131 absolute error = 1.181277298201167e-13 relative error = 1.420104776270685e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.740007555518944 y2[1] (closed_form) = -0.5633335267097785 y2[1] (numeric) = -0.5633335267099515 absolute error = 1.729727472365994e-13 relative error = 3.070521086271375e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8262295913877227 y1[1] (numeric) = -0.826229591387603 absolute error = 1.196820420545919e-13 relative error = 1.448532506002063e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.750012100370141 y2[1] (closed_form) = -0.5715712477724463 y2[1] (numeric) = -0.57157124777262 absolute error = 1.73749903353837e-13 relative error = 3.039864304423693e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8205524411759731 y1[1] (numeric) = -0.820552441175851 absolute error = 1.221245327087672e-13 relative error = 1.488320874821171e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.760016645221338 y2[1] (closed_form) = -0.5797517602215795 y2[1] (numeric) = -0.5797517602217548 absolute error = 1.753042155883122e-13 relative error = 3.023780652624693e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8147931618024173 y1[1] (numeric) = -0.8147931618022937 absolute error = 1.236788449432424e-13 relative error = 1.517917070752661e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.770021190072536 y2[1] (closed_form) = -0.5878742452690096 y2[1] (numeric) = -0.5878742452691859 absolute error = 1.763034163104749e-13 relative error = 2.998998811893842e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8089523297138048 y1[1] (numeric) = -0.8089523297136794 absolute error = 1.254552017826427e-13 relative error = 1.550835533498332e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.780025734923733 y2[1] (closed_form) = -0.5959378899345351 y2[1] (numeric) = -0.5959378899347128 absolute error = 1.77635683940025e-13 relative error = 2.980775126742464e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.8030305295195034 y1[1] (numeric) = -0.8030305295193763 absolute error = 1.271205363195804e-13 relative error = 1.583010005804431e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.790030279774931 y2[1] (closed_form) = -0.6039418871272938 y2[1] (numeric) = -0.6039418871274722 absolute error = 1.784128400572627e-13 relative error = 2.954139195509357e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7970283539329848 y1[1] (numeric) = -0.797028353932856 absolute error = 1.287858708565182e-13 relative error = 1.615825462432001e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.800034824626128 y2[1] (closed_form) = -0.6118854357265435 y2[1] (numeric) = -0.611885435726723 absolute error = 1.795230630818878e-13 relative error = 2.933932605680095e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7909464037125006 y1[1] (numeric) = -0.79094640371237 absolute error = 1.305622276959184e-13 relative error = 1.650708911287701e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.810039369477325 y2[1] (closed_form) = -0.619767740661847 y2[1] (numeric) = -0.6197677406620274 absolute error = 1.804112415015879e-13 relative error = 2.910949209923827e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7847852876009525 y1[1] (numeric) = -0.7847852876008197 absolute error = 1.327826737451687e-13 relative error = 1.691961812269422e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.820043914328523 y2[1] (closed_form) = -0.6275880129926503 y2[1] (numeric) = -0.627588012992832 absolute error = 1.816324868286756e-13 relative error = 2.894135692021299e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.778545622264962 y1[1] (numeric) = -0.7785456222648275 absolute error = 1.34559030584569e-13 relative error = 1.728338413786297e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.83004845917972 y2[1] (closed_form) = -0.6353454699872483 y2[1] (numeric) = -0.6353454699874308 absolute error = 1.825206652483757e-13 relative error = 2.872778257977333e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7722280322331498 y1[1] (numeric) = -0.7722280322330138 absolute error = 1.360023205165817e-13 relative error = 1.761167878395796e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.840053004030918 y2[1] (closed_form) = -0.6430393352011274 y2[1] (numeric) = -0.6430393352013114 absolute error = 1.839639551803884e-13 relative error = 2.860850730427694e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7658331498336254 y1[1] (numeric) = -0.7658331498334873 absolute error = 1.381117442633695e-13 relative error = 1.803418202690414e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.850057548882115 y2[1] (closed_form) = -0.6506688385546815 y2[1] (numeric) = -0.6506688385548662 absolute error = 1.84741111297626e-13 relative error = 2.839249405396269e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7593616151306977 y1[1] (numeric) = -0.7593616151305576 absolute error = 1.401101457076948e-13 relative error = 1.845104399747407e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.860062093733312 y2[1] (closed_form) = -0.6582332164102876 y2[1] (numeric) = -0.6582332164104736 absolute error = 1.859623566247137e-13 relative error = 2.825174299754577e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7528140758608114 y1[1] (numeric) = -0.7528140758606694 absolute error = 1.419975248495575e-13 relative error = 1.886223031725188e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.87006663858451 y2[1] (closed_form) = -0.6657317116487398 y2[1] (numeric) = -0.6657317116489266 absolute error = 1.868505350444138e-13 relative error = 2.806694224940299e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7461911873677142 y1[1] (numeric) = -0.7461911873675702 absolute error = 1.439959262938828e-13 relative error = 1.929745737172896e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.880071183435707 y2[1] (closed_form) = -0.6731635737450284 y2[1] (numeric) = -0.6731635737452162 absolute error = 1.87738713464114e-13 relative error = 2.788901847728663e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7394936125368641 y1[1] (numeric) = -0.7394936125367185 absolute error = 1.45550238528358e-13 relative error = 1.968241997777936e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.890075728286905 y2[1] (closed_form) = -0.6805280588434608 y2[1] (numeric) = -0.6805280588436496 absolute error = 1.888489364887391e-13 relative error = 2.775035269077411e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7327220217290805 y1[1] (numeric) = -0.7327220217289333 absolute error = 1.472155730652958e-13 relative error = 2.009159936504922e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.900080273138102 y2[1] (closed_form) = -0.6878244298321131 y2[1] (numeric) = -0.6878244298323026 absolute error = 1.895150703035142e-13 relative error = 2.7552826285884e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7258770927134486 y1[1] (numeric) = -0.7258770927132989 absolute error = 1.496580637194711e-13 relative error = 2.06175487863964e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.910084817989299 y2[1] (closed_form) = -0.695051956416609 y2[1] (numeric) = -0.6950519564167997 absolute error = 1.907363156306019e-13 relative error = 2.74420226962538e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7189595105994803 y1[1] (numeric) = -0.7189595105993284 absolute error = 1.518785097687214e-13 relative error = 2.112476537685448e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.920089362840497 y2[1] (closed_form) = -0.7022099151932139 y2[1] (numeric) = -0.7022099151934058 absolute error = 1.919575609576896e-13 relative error = 2.733620770718856e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.7119699677685425 y1[1] (numeric) = -0.7119699677683887 absolute error = 1.537658889105842e-13 relative error = 2.159724368606691e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.930093907691694 y2[1] (closed_form) = -0.7092975897212408 y2[1] (numeric) = -0.7092975897214339 absolute error = 1.930677839823147e-13 relative error = 2.721957423515168e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.704909163804556 y1[1] (numeric) = -0.7049091638044005 absolute error = 1.555422457499844e-13 relative error = 2.206557294708546e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.940098452542891 y2[1] (closed_form) = -0.7163142705947593 y2[1] (numeric) = -0.7163142705949537 absolute error = 1.944000516118649e-13 relative error = 2.713893322974755e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6977778054239745 y1[1] (numeric) = -0.6977778054238171 absolute error = 1.574296248918472e-13 relative error = 2.256156955238665e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.950102997394089 y2[1] (closed_form) = -0.7232592555135993 y2[1] (numeric) = -0.7232592555137946 absolute error = 1.95288230031565e-13 relative error = 2.700113804874677e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.690576606405049 y1[1] (numeric) = -0.6905766064048897 absolute error = 1.5931700403371e-13 relative error = 2.30701420459448e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.960107542245286 y2[1] (closed_form) = -0.7301318493536453 y2[1] (numeric) = -0.7301318493538411 absolute error = 1.958433415438776e-13 relative error = 2.682301035316421e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.683306287516386 y1[1] (numeric) = -0.6833062875162244 absolute error = 1.616484723854228e-13 relative error = 2.365681032629842e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.970112087096484 y2[1] (closed_form) = -0.7369313642364103 y2[1] (numeric) = -0.7369313642366072 absolute error = 1.969535645685028e-13 relative error = 2.672617480090308e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.675967576444805 y1[1] (numeric) = -0.6759675764446413 absolute error = 1.636468738297481e-13 relative error = 2.420927860037831e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.980116631947681 y2[1] (closed_form) = -0.7436571195978866 y2[1] (numeric) = -0.7436571195980844 absolute error = 1.978417429882029e-13 relative error = 2.660389281221172e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6685612077225052 y1[1] (numeric) = -0.6685612077223397 absolute error = 1.654232306691483e-13 relative error = 2.474316917559018e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.990121176798878 y2[1] (closed_form) = -0.7503084422566629 y2[1] (numeric) = -0.7503084422568619 absolute error = 1.989519660128281e-13 relative error = 2.651602391870346e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6610879226535453 y1[1] (numeric) = -0.661087922653378 absolute error = 1.673106098110111e-13 relative error = 2.530837488899236e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.000125721650076 y2[1] (closed_form) = -0.7568846664813037 y2[1] (numeric) = -0.7568846664815033 absolute error = 1.996180998276031e-13 relative error = 2.63736482806042e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6535484692396468 y1[1] (numeric) = -0.6535484692394782 absolute error = 1.686428774405613e-13 relative error = 2.580418827034577e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.010130266501274 y2[1] (closed_form) = -0.7633851340569811 y2[1] (numeric) = -0.7633851340571819 absolute error = 2.008393451546908e-13 relative error = 2.630904587928479e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6459436021053271 y1[1] (numeric) = -0.6459436021051569 absolute error = 1.701971896750365e-13 relative error = 2.634861451066501e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.020134811352471 y2[1] (closed_form) = -0.769809194351357 y2[1] (numeric) = -0.7698091943515588 absolute error = 2.018385458768535e-13 relative error = 2.621929529523521e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6382740824223671 y1[1] (numeric) = -0.6382740824221946 absolute error = 1.724176357242868e-13 relative error = 2.701310306536814e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.030139356203668 y2[1] (closed_form) = -0.7761562043797047 y2[1] (numeric) = -0.7761562043799072 absolute error = 2.025046796916286e-13 relative error = 2.609071196608781e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6305406778336272 y1[1] (numeric) = -0.6305406778334529 absolute error = 1.743050148661496e-13 relative error = 2.764373830170894e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.040143901054866 y2[1] (closed_form) = -0.7824255288692645 y2[1] (numeric) = -0.7824255288694675 absolute error = 2.029487689014786e-13 relative error = 2.593841348642771e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6227441623762133 y1[1] (numeric) = -0.6227441623760371 absolute error = 1.761923940080123e-13 relative error = 2.829290174888395e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.049987082279431 y2[1] (closed_form) = -0.7885173099315566 y2[1] (numeric) = -0.7885173099317606 absolute error = 2.040589919261038e-13 relative error = 2.587882210776275e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6150125624231603 y1[1] (numeric) = -0.6150125624229823 absolute error = 1.779687508474126e-13 relative error = 2.893741717180745e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.059991627130628 y2[1] (closed_form) = -0.7946306666735351 y2[1] (numeric) = -0.7946306666737404 absolute error = 2.052802372531914e-13 relative error = 2.583341492627398e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.6070931588990056 y1[1] (numeric) = -0.6070931588988261 absolute error = 1.795230630818878e-13 relative error = 2.95709250632081e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.069996171981826 y2[1] (closed_form) = -0.8006644887662645 y2[1] (numeric) = -0.8006644887664707 absolute error = 2.061684156728916e-13 relative error = 2.574966400602758e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5991129913702893 y1[1] (numeric) = -0.5991129913701078 absolute error = 1.815214645262131e-13 relative error = 3.029836894557032e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.080000716833023 y2[1] (closed_form) = -0.8066181722839919 y2[1] (numeric) = -0.8066181722841994 absolute error = 2.075006833024418e-13 relative error = 2.572477169896756e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5910728585726402 y1[1] (numeric) = -0.5910728585724566 absolute error = 1.836308882730009e-13 relative error = 3.106738629759523e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.090005261684221 y2[1] (closed_form) = -0.8124911213220406 y2[1] (numeric) = -0.8124911213222491 absolute error = 2.084998840246044e-13 relative error = 2.566180460967314e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5829735652436164 y1[1] (numeric) = -0.5829735652434306 absolute error = 1.858513343222512e-13 relative error = 3.18798905134895e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.100009806535418 y2[1] (closed_form) = -0.8182827480564552 y2[1] (numeric) = -0.8182827480566647 absolute error = 2.09499084746767e-13 relative error = 2.560228542571121e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5748159220421577 y1[1] (numeric) = -0.5748159220419697 absolute error = 1.87960758069039e-13 relative error = 3.269929569822419e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.110014351386615 y2[1] (closed_form) = -0.8239924728028357 y2[1] (numeric) = -0.8239924728030462 absolute error = 2.104982854689297e-13 relative error = 2.554614179337261e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5666007454674481 y1[1] (numeric) = -0.566600745467258 absolute error = 1.900701818158268e-13 relative error = 3.354569921347669e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.120018896237813 y2[1] (closed_form) = -0.8296197240743597 y2[1] (numeric) = -0.8296197240745712 absolute error = 2.114974861910923e-13 relative error = 2.549330495090008e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5583288577771914 y1[1] (numeric) = -0.558328857776999 absolute error = 1.924016501675396e-13 relative error = 3.446027327577613e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.13002344108901 y2[1] (closed_form) = -0.8351639386389811 y2[1] (numeric) = -0.8351639386391937 absolute error = 2.126077092157175e-13 relative error = 2.545700303609757e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5500010869053117 y1[1] (numeric) = -0.5500010869051171 absolute error = 1.946220962167899e-13 relative error = 3.538576574673136e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.140027985940208 y2[1] (closed_form) = -0.8406245615758049 y2[1] (numeric) = -0.8406245615760183 absolute error = 2.133848653329551e-13 relative error = 2.538408643841567e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5416182663790853 y1[1] (numeric) = -0.5416182663788884 absolute error = 1.968425422660403e-13 relative error = 3.634340909179524e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.150032530791405 y2[1] (closed_form) = -0.8460010463306291 y2[1] (numeric) = -0.8460010463308432 absolute error = 2.140509991477302e-13 relative error = 2.530150524944812e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.533181235235713 y1[1] (numeric) = -0.5331812352355142 absolute error = 1.988409437103655e-13 relative error = 3.729331239919956e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.160037075642602 y2[1] (closed_form) = -0.8512928547706491 y2[1] (numeric) = -0.8512928547708642 absolute error = 2.151612221723553e-13 relative error = 2.527464208898158e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5246908379383411 y1[1] (numeric) = -0.5246908379381399 absolute error = 2.012834343645409e-13 relative error = 3.836229257507916e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.1700416204938 y2[1] (closed_form) = -0.85649945723832 y2[1] (numeric) = -0.856499457238536 absolute error = 2.160494005920555e-13 relative error = 2.522469789866311e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5161479242915381 y1[1] (numeric) = -0.5161479242913343 absolute error = 2.038369473211787e-13 relative error = 3.94919630067222e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.180046165344997 y2[1] (closed_form) = -0.8616203326043693 y2[1] (numeric) = -0.8616203326045866 absolute error = 2.172706459191431e-13 relative error = 2.521651796011033e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.5075533493562386 y1[1] (numeric) = -0.5075533493560325 absolute error = 2.061684156728916e-13 relative error = 4.062004830317596e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.190050710196195 y2[1] (closed_form) = -0.8666549683199576 y2[1] (numeric) = -0.8666549683201757 absolute error = 2.181588243388433e-13 relative error = 2.517251181998669e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4989079733641599 y1[1] (numeric) = -0.4989079733639517 absolute error = 2.082778394196794e-13 relative error = 4.174674499893279e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.200055255047392 y2[1] (closed_form) = -0.8716028604679791 y2[1] (numeric) = -0.871602860468198 absolute error = 2.189359804560809e-13 relative error = 2.511877718466071e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4902126616317011 y1[1] (numeric) = -0.4902126616314906 absolute error = 2.104427743176984e-13 relative error = 4.292887368866147e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.210059799898589 y2[1] (closed_form) = -0.8764635138134987 y2[1] (numeric) = -0.8764635138137189 absolute error = 2.201572257831685e-13 relative error = 2.51188123993049e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4814682844733337 y1[1] (numeric) = -0.481468284473121 absolute error = 2.126632203669487e-13 relative error = 4.416972565484263e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.220064344749787 y2[1] (closed_form) = -0.8812364418533206 y2[1] (numeric) = -0.8812364418535413 absolute error = 2.207123372954811e-13 relative error = 2.504575694024897e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4726757171144919 y1[1] (numeric) = -0.4726757171142771 absolute error = 2.147726441137365e-13 relative error = 4.54376301420439e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.230068889600984 y2[1] (closed_form) = -0.8859211668646818 y2[1] (numeric) = -0.8859211668649039 absolute error = 2.220446049250313e-13 relative error = 2.506369790337644e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4638358396039708 y1[1] (numeric) = -0.4638358396037539 absolute error = 2.169375790117556e-13 relative error = 4.677033564223492e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.240073434452182 y2[1] (closed_form) = -0.890517219953068 y2[1] (numeric) = -0.8905172199532909 absolute error = 2.229327833447314e-13 relative error = 2.503407888692825e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4549495367258429 y1[1] (numeric) = -0.4549495367256238 absolute error = 2.190470027585434e-13 relative error = 4.814753836985294e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.250077979303379 y2[1] (closed_form) = -0.8950241410991449 y2[1] (numeric) = -0.8950241410993686 absolute error = 2.23709939461969e-13 relative error = 2.499484976877154e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4460176979108992 y1[1] (numeric) = -0.4460176979106778 absolute error = 2.213784711102562e-13 relative error = 4.96344589345154e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.260082524154576 y2[1] (closed_form) = -0.8994414792048013 y2[1] (numeric) = -0.8994414792050259 absolute error = 2.245981178816692e-13 relative error = 2.49708428034959e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4370412171476266 y1[1] (numeric) = -0.437041217147403 absolute error = 2.235434060082753e-13 relative error = 5.114927316632595e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.270087069005774 y2[1] (closed_form) = -0.9037687921383007 y2[1] (numeric) = -0.9037687921385262 absolute error = 2.254862963013693e-13 relative error = 2.494955549061091e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4280209928927282 y1[1] (numeric) = -0.4280209928925023 absolute error = 2.258193632087568e-13 relative error = 5.275894569623419e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.280091613856971 y2[1] (closed_form) = -0.9080056467785331 y2[1] (numeric) = -0.9080056467787599 absolute error = 2.268185639309195e-13 relative error = 2.497986270632099e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4189579279811969 y1[1] (numeric) = -0.4189579279809687 absolute error = 2.281508315604697e-13 relative error = 5.445674047984819e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.290096158708169 y2[1] (closed_form) = -0.9121516190583665 y2[1] (numeric) = -0.912151619058595 absolute error = 2.284838984678572e-13 relative error = 2.504889468964885e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4098529295359503 y1[1] (numeric) = -0.4098529295357198 absolute error = 2.305378110634138e-13 relative error = 5.624891136545898e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.300100703559366 y2[1] (closed_form) = -0.916206294007092 y2[1] (numeric) = -0.9162062940073215 absolute error = 2.294830991900199e-13 relative error = 2.504709918400141e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.4007069088770371 y1[1] (numeric) = -0.4007069088768044 absolute error = 2.326472348102016e-13 relative error = 5.805920228882124e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.310105248410563 y2[1] (closed_form) = -0.9201692657919581 y2[1] (numeric) = -0.9201692657921886 absolute error = 2.304822999121825e-13 relative error = 2.504781549227405e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3915207814304226 y1[1] (numeric) = -0.3915207814301875 absolute error = 2.351452366156082e-13 relative error = 6.005945221004723e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.320109793261761 y2[1] (closed_form) = -0.9240401377587907 y2[1] (numeric) = -0.9240401377590219 absolute error = 2.312594560294201e-13 relative error = 2.502699250601034e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3822954666363639 y1[1] (numeric) = -0.3822954666361265 absolute error = 2.374211938160897e-13 relative error = 6.210410913449902e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.330114338112958 y2[1] (closed_form) = -0.9278185224716938 y2[1] (numeric) = -0.9278185224719259 absolute error = 2.320366121466577e-13 relative error = 2.500883594439523e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3730318878573828 y1[1] (numeric) = -0.373031887857143 absolute error = 2.398636844702651e-13 relative error = 6.430112070257369e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.340118882964155 y2[1] (closed_form) = -0.9315040417518287 y2[1] (numeric) = -0.9315040417520616 absolute error = 2.329247905663578e-13 relative error = 2.500523670603822e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3637309722858467 y1[1] (numeric) = -0.3637309722856044 absolute error = 2.423061751244404e-13 relative error = 6.661686619692598e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.350123427815353 y2[1] (closed_form) = -0.9350963267152653 y2[1] (numeric) = -0.9350963267154989 absolute error = 2.335909243811329e-13 relative error = 2.498041300212067e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3543936508511655 y1[1] (numeric) = -0.3543936508509212 absolute error = 2.44360087719997e-13 relative error = 6.895159863420372e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.36012797266655 y2[1] (closed_form) = -0.9385950178099041 y2[1] (numeric) = -0.9385950178101387 absolute error = 2.345901251032956e-13 relative error = 2.499375349878617e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3450208581266152 y1[1] (numeric) = -0.3450208581263684 absolute error = 2.468025783741723e-13 relative error = 7.153265449348603e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.370132517517748 y2[1] (closed_form) = -0.9419997648514634 y2[1] (numeric) = -0.9419997648516991 absolute error = 2.357003481279207e-13 relative error = 2.50212746247433e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3356135322357958 y1[1] (numeric) = -0.3356135322355465 absolute error = 2.493005801795789e-13 relative error = 7.428204057172075e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.380137062368945 y2[1] (closed_form) = -0.9453102270585302 y2[1] (numeric) = -0.9453102270587667 absolute error = 2.364775042451583e-13 relative error = 2.501586225095569e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.326172614758735 y1[1] (numeric) = -0.3261726147584835 absolute error = 2.515210262288292e-13 relative error = 7.711285829893339e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.390141607220142 y2[1] (closed_form) = -0.9485260730866676 y2[1] (numeric) = -0.948526073086905 absolute error = 2.373656826648585e-13 relative error = 2.50246871857122e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3166990506376451 y1[1] (numeric) = -0.316699050637391 absolute error = 2.540745391854671e-13 relative error = 8.022586069453344e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.399984788444708 y2[1] (closed_form) = -0.951597398768475 y2[1] (numeric) = -0.9515973987687135 absolute error = 2.384759056894836e-13 relative error = 2.506058822755411e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.3073473452904253 y1[1] (numeric) = -0.3073473452901688 absolute error = 2.565725409908737e-13 relative error = 8.347966719817526e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.409989333295905 y2[1] (closed_form) = -0.9546245950439213 y2[1] (numeric) = -0.9546245950441603 absolute error = 2.390310172017962e-13 relative error = 2.503926867616465e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2978118240386524 y1[1] (numeric) = -0.2978118240383933 absolute error = 2.590705427962803e-13 relative error = 8.699135557581354e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.419993878147102 y2[1] (closed_form) = -0.9575562428645751 y2[1] (numeric) = -0.9575562428648154 absolute error = 2.403632848313464e-13 relative error = 2.51017406677114e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2882464947767428 y1[1] (numeric) = -0.2882464947764815 absolute error = 2.613464999967618e-13 relative error = 9.066771139721371e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.4299984229983 y2[1] (closed_form) = -0.9603920488015633 y2[1] (numeric) = -0.9603920488018048 absolute error = 2.415845301584341e-13 relative error = 2.515478240994375e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2786523148992946 y1[1] (numeric) = -0.2786523148990309 absolute error = 2.636779683484747e-13 relative error = 9.462615390213727e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.440002967849497 y2[1] (closed_form) = -0.9631317290188347 y2[1] (numeric) = -0.9631317290190771 absolute error = 2.423616862756717e-13 relative error = 2.516391880501863e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2690302446885665 y1[1] (numeric) = -0.2690302446883004 absolute error = 2.660649478514188e-13 relative error = 9.889778309476676e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.450007512700695 y2[1] (closed_form) = -0.9657750093015695 y2[1] (numeric) = -0.9657750093018128 absolute error = 2.433608869978343e-13 relative error = 2.519850738049521e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.259381247218363 y1[1] (numeric) = -0.2593812472180944 absolute error = 2.686184608080566e-13 relative error = 1.035612495848311e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.460012057551892 y2[1] (closed_form) = -0.968321625083625 y2[1] (numeric) = -0.9683216250838694 absolute error = 2.444711100224595e-13 relative error = 2.524689149654659e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.24970628825764 y1[1] (numeric) = -0.2497062882573687 absolute error = 2.71282996067157e-13 relative error = 1.086408347823643e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.470016602403089 y2[1] (closed_form) = -0.9707713214740169 y2[1] (numeric) = -0.9707713214742625 absolute error = 2.455813330470846e-13 relative error = 2.529754717869029e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2400063361738413 y1[1] (numeric) = -0.2400063361735676 absolute error = 2.736977311457167e-13 relative error = 1.140377106325527e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.480021147254287 y2[1] (closed_form) = -0.9731238532824305 y2[1] (numeric) = -0.9731238532826769 absolute error = 2.464695114667848e-13 relative error = 2.532766108192928e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2302823618359746 y1[1] (numeric) = -0.2302823618356984 absolute error = 2.761957329511233e-13 relative error = 1.199378583531516e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.490025692105484 y2[1] (closed_form) = -0.9753789850437622 y2[1] (numeric) = -0.9753789850440095 absolute error = 2.473576898864849e-13 relative error = 2.536016191443644e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2205353385174367 y1[1] (numeric) = -0.220535338517158 absolute error = 2.787214903321455e-13 relative error = 1.263840490172093e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.500030236956682 y2[1] (closed_form) = -0.9775364910416872 y2[1] (numeric) = -0.9775364910419354 absolute error = 2.48245868306185e-13 relative error = 2.539504873538256e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2107662417985989 y1[1] (numeric) = -0.2107662417983177 absolute error = 2.812194921375522e-13 relative error = 1.334271986527501e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.510034781807879 y2[1] (closed_form) = -0.9795961553312514 y2[1] (numeric) = -0.9795961553315007 absolute error = 2.492450690283476e-13 relative error = 2.544365529324328e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.2009760494691611 y1[1] (numeric) = -0.2009760494688773 absolute error = 2.8377300509419e-13 relative error = 1.411974241924452e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.520039326659076 y2[1] (closed_form) = -0.9815577717604856 y2[1] (numeric) = -0.9815577717607357 absolute error = 2.500222251455853e-13 relative error = 2.547198263197027e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1911657414302845 y1[1] (numeric) = -0.1911657414299982 absolute error = 2.863265180508279e-13 relative error = 1.49779199928062e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.530043871510274 y2[1] (closed_form) = -0.9834211439910389 y2[1] (numeric) = -0.9834211439912899 absolute error = 2.510214258677479e-13 relative error = 2.552532324544318e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1813362995965133 y1[1] (numeric) = -0.1813362995962245 absolute error = 2.887690087050032e-13 relative error = 1.592450101538058e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.540048416361471 y2[1] (closed_form) = -0.9851860855178302 y2[1] (numeric) = -0.9851860855180821 absolute error = 2.51909604287448e-13 relative error = 2.556974849629957e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1714887077974948 y1[1] (numeric) = -0.1714887077972034 absolute error = 2.913502772372567e-13 relative error = 1.698947300840953e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.550052961212669 y2[1] (closed_form) = -0.9868524196877161 y2[1] (numeric) = -0.9868524196879688 absolute error = 2.526867604046856e-13 relative error = 2.560532409543536e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1616239516795079 y1[1] (numeric) = -0.1616239516792139 absolute error = 2.939870569207415e-13 relative error = 1.818957239108365e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.560057506063866 y2[1] (closed_form) = -0.9884199797171713 y2[1] (numeric) = -0.9884199797174249 absolute error = 2.535749388243858e-13 relative error = 2.565457437403726e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1517430186068096 y1[1] (numeric) = -0.1517430186065131 absolute error = 2.964850587261481e-13 relative error = 1.953862928576557e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.570062050915063 y2[1] (closed_form) = -0.9898886087089829 y2[1] (numeric) = -0.9898886087092376 absolute error = 2.546851618490109e-13 relative error = 2.572866882276506e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1418468975628096 y1[1] (numeric) = -0.1418468975625106 absolute error = 2.989830605315547e-13 relative error = 2.107787097699232e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.580066595766261 y2[1] (closed_form) = -0.9912581596679532 y2[1] (numeric) = -0.9912581596682095 absolute error = 2.563504963859486e-13 relative error = 2.586112345060743e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1319365790510829 y1[1] (numeric) = -0.1319365790507814 absolute error = 3.015088179125769e-13 relative error = 2.285255689370567e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.590071140617458 y2[1] (closed_form) = -0.9925284955156133 y2[1] (numeric) = -0.9925284955158706 absolute error = 2.573496971081113e-13 relative error = 2.5928696079846e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1220130549962303 y1[1] (numeric) = -0.1220130549959262 absolute error = 3.04117842020446e-13 relative error = 2.492502478770341e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.600075685468656 y2[1] (closed_form) = -0.9936994891039431 y2[1] (numeric) = -0.9936994891042015 absolute error = 2.583488978302739e-13 relative error = 2.599869484317004e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1120773186445964 y1[1] (numeric) = -0.1120773186442897 absolute error = 3.067407439161229e-13 relative error = 2.736867259367753e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.610080230319853 y2[1] (closed_form) = -0.9947710232280973 y2[1] (numeric) = -0.9947710232283565 absolute error = 2.592370762499741e-13 relative error = 2.605997462699835e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.1021303644648557 y1[1] (numeric) = -0.1021303644645464 absolute error = 3.09280379084953e-13 relative error = 3.028290173108901e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.62008477517105 y2[1] (closed_form) = -0.9957429906381366 y2[1] (numeric) = -0.9957429906383967 absolute error = 2.600142323672117e-13 relative error = 2.611258475448345e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.09217318804847588 y1[1] (numeric) = -0.09217318804816392 absolute error = 3.119587921318612e-13 relative error = 3.384485214591854e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.630089320022248 y2[1] (closed_form) = -0.9966152940497626 y2[1] (numeric) = -0.9966152940500236 absolute error = 2.610134330893743e-13 relative error = 2.618998871959329e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.0822067860100693 y1[1] (numeric) = -0.08220678600975473 absolute error = 3.145678162397303e-13 relative error = 3.826543178578952e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.640093864873445 y2[1] (closed_form) = -0.9973878461540543 y2[1] (numeric) = -0.9973878461543167 absolute error = 2.62456723021387e-13 relative error = 2.63144095883487e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.07223215588764154 y1[1] (numeric) = -0.07223215588732432 absolute error = 3.172184737110229e-13 relative error = 4.3916517486265e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.650098409724643 y2[1] (closed_form) = -0.9980605696262077 y2[1] (numeric) = -0.9980605696264712 absolute error = 2.634559237435496e-13 relative error = 2.6396787105037e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.06225029604274777 y1[1] (numeric) = -0.06225029604242788 absolute error = 3.19896886757931e-13 relative error = 5.138881372359343e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.66010295457584 y2[1] (closed_form) = -0.9986333971332748 y2[1] (numeric) = -0.9986333971335393 absolute error = 2.644551244657123e-13 relative error = 2.648170241701008e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.0522622055605667 y1[1] (numeric) = -0.05226220556024415 absolute error = 3.225544831231275e-13 relative error = 6.171849803570171e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.670107499427037 y2[1] (closed_form) = -0.999106271340903 y2[1] (numeric) = -0.9991062713411688 absolute error = 2.657873920952625e-13 relative error = 2.660251463926341e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.04226888414990203 y1[1] (numeric) = -0.04226888414957682 absolute error = 3.252190183822279e-13 relative error = 7.694052609216599e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.680112044278235 y2[1] (closed_form) = -0.9994791449190736 y2[1] (numeric) = -0.9994791449193405 absolute error = 2.668976151198876e-13 relative error = 2.670367025432011e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.03227133204312154 y1[1] (numeric) = -0.03227133204279363 absolute error = 3.279113092169439e-13 relative error = 1.016107140476206e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.690116589129432 y2[1] (closed_form) = -0.9997519805468393 y2[1] (numeric) = -0.9997519805471073 absolute error = 2.680078381445128e-13 relative error = 2.680743257922022e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.02227054989604372 y1[1] (numeric) = -0.02227054989571312 absolute error = 3.306070694986118e-13 relative error = 1.484503395928014e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.700121133980629 y2[1] (closed_form) = -0.9999247509160596 y2[1] (numeric) = -0.9999247509163286 absolute error = 2.690070388666754e-13 relative error = 2.690272829232704e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.01226753868778206 y1[1] (numeric) = -0.01226753868744876 absolute error = 3.333080339507077e-13 relative error = 2.716991912017918e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.710125678831827 y2[1] (closed_form) = -0.9999974387341337 y2[1] (numeric) = -0.9999974387344043 absolute error = 2.705613511011506e-13 relative error = 2.705620440824789e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = -0.002263299620556989 y1[1] (numeric) = -0.002263299620220967 absolute error = 3.360224425097424e-13 relative error = 1.484657353616525e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.720130223683024 y2[1] (closed_form) = -0.9999700367257321 y2[1] (numeric) = -0.9999700367260033 absolute error = 2.711164626134632e-13 relative error = 2.711245863938061e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.007741165980514583 y1[1] (numeric) = 0.007741165980853335 absolute error = 3.38751596218323e-13 relative error = 4.375976397754553e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.730134768534222 y2[1] (closed_form) = -0.9998425476335241 y2[1] (numeric) = -0.9998425476337961 absolute error = 2.720046410331634e-13 relative error = 2.720474755519828e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.01774485676764194 y1[1] (numeric) = 0.01774485676798343 absolute error = 3.414872551399384e-13 relative error = 1.924429481801433e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.740139313385419 y2[1] (closed_form) = -0.9996149842179033 y2[1] (numeric) = -0.9996149842181761 absolute error = 2.72781797150401e-13 relative error = 2.728868628993441e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.02774677147058556 y1[1] (numeric) = 0.0277467714709298 absolute error = 3.442315876789337e-13 relative error = 1.240618527614482e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.750143858236616 y2[1] (closed_form) = -0.9992873692557109 y2[1] (numeric) = -0.9992873692559853 absolute error = 2.743361093848762e-13 relative error = 2.745317491496036e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.03774590899687435 y1[1] (numeric) = 0.03774590899722134 absolute error = 3.469932674526888e-13 relative error = 9.192870874600542e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.759987039461182 y2[1] (closed_form) = -0.9988674262378879 y2[1] (numeric) = -0.9988674262381634 absolute error = 2.754463324095013e-13 relative error = 2.757586494205105e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.04758008828173237 y1[1] (numeric) = 0.04758008828208209 absolute error = 3.497202527569243e-13 relative error = 7.35013879516474e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.769991584312379 y2[1] (closed_form) = -0.9983414286897259 y2[1] (numeric) = -0.9983414286900022 absolute error = 2.763345108292015e-13 relative error = 2.767935927409894e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.0575707543962823 y1[1] (numeric) = 0.05757075439663482 absolute error = 3.525166270001989e-13 relative error = 6.123189294579803e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.779996129163576 y2[1] (closed_form) = -0.9977155070652705 y2[1] (numeric) = -0.9977155070655482 absolute error = 2.777778007612142e-13 relative error = 2.78413835200661e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.06755565824925594 y1[1] (numeric) = 0.06755565824961128 absolute error = 3.553407568190892e-13 relative error = 5.259970312301752e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.790000674014774 y2[1] (closed_form) = -0.9969897240130691 y2[1] (numeric) = -0.9969897240133482 absolute error = 2.791100683907644e-13 relative error = 2.79952803592894e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.07753380045079958 y1[1] (numeric) = 0.07753380045115772 absolute error = 3.581440699562677e-13 relative error = 4.619199212136315e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.800005218865971 y2[1] (closed_form) = -0.9961641521768074 y2[1] (numeric) = -0.9961641521770873 absolute error = 2.79887224508002e-13 relative error = 2.809649633510655e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.08750418228783373 y1[1] (numeric) = 0.0875041822881947 absolute error = 3.609751386690618e-13 relative error = 4.125232980084091e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.810009763717169 y2[1] (closed_form) = -0.9952388741880391 y2[1] (numeric) = -0.9952388741883199 absolute error = 2.807754029277021e-13 relative error = 2.821186051004804e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.09746580582401444 y1[1] (numeric) = 0.09746580582437826 absolute error = 3.638200851696638e-13 relative error = 3.732797180444824e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.820014308568366 y2[1] (closed_form) = -0.9942139826579146 y2[1] (numeric) = -0.9942139826581966 absolute error = 2.819966482547898e-13 relative error = 2.83637781376706e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.1074176739996168 y1[1] (numeric) = 0.1074176739999834 absolute error = 3.665956427312267e-13 relative error = 3.412805631338976e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.830018853419563 y2[1] (closed_form) = -0.9930895801679119 y2[1] (numeric) = -0.9930895801681955 absolute error = 2.83550960489265e-13 relative error = 2.855240515576874e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.1173587907313309 y1[1] (numeric) = 0.1173587907317003 absolute error = 3.693989558684052e-13 relative error = 3.147603631278624e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.840023398270761 y2[1] (closed_form) = -0.9918657792595698 y2[1] (numeric) = -0.9918657792598542 absolute error = 2.844391389089651e-13 relative error = 2.867718040653642e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.1272881610119594 y1[1] (numeric) = 0.1272881610123318 absolute error = 3.723132913080462e-13 relative error = 2.92496402138346e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.850027943121958 y2[1] (closed_form) = -0.9905427024232221 y2[1] (numeric) = -0.9905427024235081 absolute error = 2.859934511434403e-13 relative error = 2.887239999283201e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.1372047910100086 y1[1] (numeric) = 0.137204791010384 absolute error = 3.753941602013811e-13 relative error = 2.736013498056328e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.860032487973156 y2[1] (closed_form) = -0.9891204820857391 y2[1] (numeric) = -0.989120482086026 absolute error = 2.868816295631405e-13 relative error = 2.900370933156684e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.1471076881691605 y1[1] (numeric) = 0.1471076881695387 absolute error = 3.781697177629439e-13 relative error = 2.570699889784706e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.870037032824353 y2[1] (closed_form) = -0.9875992605972723 y2[1] (numeric) = -0.9875992605975602 absolute error = 2.878808302853031e-13 relative error = 2.914955911481757e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.1569958613076182 y1[1] (numeric) = 0.1569958613079993 absolute error = 3.811118087782006e-13 relative error = 2.427527742476274e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.88004157767555 y2[1] (closed_form) = -0.9859791902170065 y2[1] (numeric) = -0.9859791902172956 absolute error = 2.891020756123908e-13 relative error = 2.932131615767282e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.1668683207173131 y1[1] (numeric) = 0.1668683207176972 absolute error = 3.840538997934573e-13 relative error = 2.30153871113782e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.890046122526748 y2[1] (closed_form) = -0.9842604330979201 y2[1] (numeric) = -0.9842604330982104 absolute error = 2.903233209394784e-13 relative error = 2.949659573591691e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.1767240782629652 y1[1] (numeric) = 0.1767240782633522 absolute error = 3.869959908087139e-13 relative error = 2.189831711742552e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.900050667377945 y2[1] (closed_form) = -0.9824431612705556 y2[1] (numeric) = -0.982443161270847 absolute error = 2.913225216616411e-13 relative error = 2.965286269435526e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.1865621474809854 y1[1] (numeric) = 0.1865621474813754 absolute error = 3.899380818239706e-13 relative error = 2.09012432097842e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.910055212229143 y2[1] (closed_form) = -0.9805275566258008 y2[1] (numeric) = -0.9805275566260931 absolute error = 2.923217223838037e-13 relative error = 2.981269831821387e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.1963815436782107 y1[1] (numeric) = 0.1963815436786036 absolute error = 3.929079284148429e-13 relative error = 2.00073754924067e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.92005975708034 y2[1] (closed_form) = -0.9785138108966832 y2[1] (numeric) = -0.978513810896976 absolute error = 2.927658115936538e-13 relative error = 2.991943581515433e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.2061812840304624 y1[1] (numeric) = 0.2061812840308583 absolute error = 3.959610417325621e-13 relative error = 1.920450944878492e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.930064301931537 y2[1] (closed_form) = -0.9764021256391795 y2[1] (numeric) = -0.9764021256394729 absolute error = 2.934319454084289e-13 relative error = 3.005236650999099e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.2159603876809168 y1[1] (numeric) = 0.2159603876813157 absolute error = 3.989308883234344e-13 relative error = 1.847241026964899e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.940068846782735 y2[1] (closed_form) = -0.9741927122120423 y2[1] (numeric) = -0.9741927122123365 absolute error = 2.942091015256665e-13 relative error = 3.02002979325952e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.2257178758382795 y1[1] (numeric) = 0.2257178758386814 absolute error = 4.019284904899223e-13 relative error = 1.780667521334875e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.950073391633932 y2[1] (closed_form) = -0.9718857917556444 y2[1] (numeric) = -0.9718857917559395 absolute error = 2.950972799453666e-13 relative error = 3.03633701046595e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.2354527718747527 y1[1] (numeric) = 0.2354527718751575 absolute error = 4.048150703539477e-13 relative error = 1.719304755389696e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.96007793648513 y2[1] (closed_form) = -0.9694815951698452 y2[1] (numeric) = -0.9694815951701417 absolute error = 2.964295475749168e-13 relative error = 3.05760881951539e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.2451641014237857 y1[1] (numeric) = 0.2451641014241935 absolute error = 4.078404280960513e-13 relative error = 1.663540566206577e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.970082481336327 y2[1] (closed_form) = -0.9669803630908804 y2[1] (numeric) = -0.9669803630911781 absolute error = 2.976507929020045e-13 relative error = 3.078147233006738e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.2548508924775995 y1[1] (numeric) = 0.2548508924780103 absolute error = 4.108380302625392e-13 relative error = 1.612072166075112e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.980087026187524 y2[1] (closed_form) = -0.964382345867276 y2[1] (numeric) = -0.9643823458675743 absolute error = 2.983169267167796e-13 relative error = 3.093347031861113e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.264512175484475 y1[1] (numeric) = 0.2645121754848891 absolute error = 4.140576770339521e-13 relative error = 1.565363394995231e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.990091571038722 y2[1] (closed_form) = -0.9616878035347908 y2[1] (numeric) = -0.9616878035350904 absolute error = 2.996491943463298e-13 relative error = 3.11586767810651e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y1[1] (closed_form) = 0.274146983445796 y1[1] (numeric) = 0.2741469834462131 absolute error = 4.170552792004401e-13 relative error = 1.521283487997597e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; diff ( y1 , x , 1 ) = neg ( y2 ) ; Iterations = 22740 Total Elapsed Time = 6.0 Seconds Elapsed Time(since restart) = 6.0 Seconds Time to Timeout = 2 Minutes 54.0 Seconds Percent Done = 100 %