##############ECHO OF PROBLEM################# ##############temp/mtest1postode.ode################# diff ( y1 , x , 1 ) = neg ( y2 ) + 1.0 ; diff ( y2 , x , 1 ) = y1 - 1.0 ; ! // 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(10.0); array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_look_poles=true; glob_type_given_pole=3; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=true; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y1 (double x) { return(c(1.0) + cos(c(x))); } double exact_soln_y2 (double x) { return(c(1.0) + sin(c(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y1[1] (closed_form) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 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) = 32.01 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 = 0.09933 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.11 y1[1] (closed_form) = 1.993956097956697 y1[1] (numeric) = 1.993956097956697 absolute error = 2.220446049250313e-16 relative error = 1.113588233725763e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.109778300837175 y2[1] (numeric) = 1.109778300837175 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 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) = 32.01 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 = 0.1091 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.12 y1[1] (closed_form) = 1.992808635853866 y1[1] (numeric) = 1.992808635853866 absolute error = 2.220446049250313e-16 relative error = 1.114229439445855e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.119712207288919 y2[1] (numeric) = 1.119712207288919 absolute error = 2.220446049250313e-16 relative error = 1.983050675696859e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 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) = 32.01 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 = 0.1189 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.13 y1[1] (closed_form) = 1.991561893714788 y1[1] (numeric) = 1.991561893714788 absolute error = 2.220446049250313e-16 relative error = 1.114926960722569e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.129634142619695 y2[1] (numeric) = 1.129634142619694 absolute error = 6.661338147750939e-16 relative error = 5.896898735995057e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 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) = 32.02 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 = 0.1285 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.14 y1[1] (closed_form) = 1.990215996212637 y1[1] (numeric) = 1.990215996212637 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.139543114644237 y2[1] (numeric) = 1.139543114644236 absolute error = 6.661338147750939e-16 relative error = 5.845621865593561e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 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) = 32.02 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 = 0.1382 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.15 y1[1] (closed_form) = 1.988771077936042 y1[1] (numeric) = 1.988771077936042 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.149438132473599 y2[1] (numeric) = 1.149438132473598 absolute error = 6.661338147750939e-16 relative error = 5.79529942461165e-14 % Desired digits = 8 Estimated correct digits = 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 = 0.1478 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 = 0.1478 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y1[1] (closed_form) = 1.987227283375627 y1[1] (numeric) = 1.987227283375627 absolute error = 2.220446049250313e-16 relative error = 1.117358878788402e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.159318206614246 y2[1] (numeric) = 1.159318206614245 absolute error = 8.881784197001252e-16 relative error = 7.66121341520223e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.03 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 = 0.1573 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y1[1] (closed_form) = 1.985584766909561 y1[1] (numeric) = 1.985584766909561 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.169182349066996 y2[1] (numeric) = 1.169182349066995 absolute error = 1.110223024625157e-15 relative error = 9.49572173674287e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.03 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 = 0.1667 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y1[1] (closed_form) = 1.983843692788121 y1[1] (numeric) = 1.983843692788121 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.179029573425824 y2[1] (numeric) = 1.179029573425823 absolute error = 8.881784197001252e-16 relative error = 7.533130972443778e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.03 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 = 0.1761 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y1[1] (closed_form) = 1.98200423511727 y1[1] (numeric) = 1.98200423511727 absolute error = 4.440892098500626e-16 relative error = 2.240606765523823e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.188858894976501 y2[1] (numeric) = 1.1888588949765 absolute error = 1.110223024625157e-15 relative error = 9.338560104284719e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.04 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 = 0.1855 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y1[1] (closed_form) = 1.980066577841242 y1[1] (numeric) = 1.980066577841241 absolute error = 6.661338147750939e-16 relative error = 3.364199074060142e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.198669330795061 y2[1] (numeric) = 1.19866933079506 absolute error = 1.110223024625157e-15 relative error = 9.262129230325435e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.04 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 = 0.1947 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y1[1] (closed_form) = 1.978030914724148 y1[1] (numeric) = 1.978030914724147 absolute error = 8.881784197001252e-16 relative error = 4.49021505725045e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.2084598998461 y2[1] (numeric) = 1.208459899846098 absolute error = 1.110223024625157e-15 relative error = 9.187090318566187e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.04 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 = 0.2039 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y1[1] (closed_form) = 1.975897449330605 y1[1] (numeric) = 1.975897449330604 absolute error = 1.110223024625157e-15 relative error = 5.61882918064031e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.218229623080869 y2[1] (numeric) = 1.218229623080868 absolute error = 1.110223024625157e-15 relative error = 9.113413461556065e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.05 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 = 0.213 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y1[1] (closed_form) = 1.973666395005375 y1[1] (numeric) = 1.973666395005373 absolute error = 1.332267629550188e-15 relative error = 6.750216920760612e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.227977523535189 y2[1] (numeric) = 1.227977523535187 absolute error = 1.332267629550188e-15 relative error = 1.084928350899096e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 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) = 32.05 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 = 0.222 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y1[1] (closed_form) = 1.971337974852029 y1[1] (numeric) = 1.971337974852028 absolute error = 1.554312234475219e-15 relative error = 7.884554826738359e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.237702626427135 y2[1] (numeric) = 1.237702626427134 absolute error = 8.881784197001252e-16 relative error = 7.176024359453951e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.06 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 = 0.2309 Order of pole (three term test) = 32.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y1[1] (closed_form) = 1.968912421710645 y1[1] (numeric) = 1.968912421710643 absolute error = 1.332267629550188e-15 relative error = 6.766515436947051e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.247403959254523 y2[1] (numeric) = 1.247403959254522 absolute error = 8.881784197001252e-16 relative error = 7.120214851898666e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.06 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 = 0.2397 Order of pole (three term test) = 32.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y1[1] (closed_form) = 1.966389978134513 y1[1] (numeric) = 1.966389978134512 absolute error = 1.332267629550188e-15 relative error = 6.775195380186445e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.257080551892155 y2[1] (numeric) = 1.257080551892154 absolute error = 8.881784197001252e-16 relative error = 7.065405779790649e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.07 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 = 0.2484 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y1[1] (closed_form) = 1.963770896365891 y1[1] (numeric) = 1.96377089636589 absolute error = 1.110223024625157e-15 relative error = 5.653526216727775e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.266731436688831 y2[1] (numeric) = 1.26673143668883 absolute error = 1.110223024625157e-15 relative error = 8.764470451031203e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.07 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 = 0.2571 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y1[1] (closed_form) = 1.961055438310771 y1[1] (numeric) = 1.96105543831077 absolute error = 1.110223024625157e-15 relative error = 5.661354610053702e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.276355648564114 y2[1] (numeric) = 1.276355648564113 absolute error = 1.110223024625157e-15 relative error = 8.698382977143912e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.08 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 = 0.2656 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y1[1] (closed_form) = 1.958243875512697 y1[1] (numeric) = 1.958243875512696 absolute error = 1.332267629550188e-15 relative error = 6.80337952902511e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.285952225104836 y2[1] (numeric) = 1.285952225104835 absolute error = 8.881784197001252e-16 relative error = 6.906776180022688e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.08 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 = 0.274 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y1[1] (closed_form) = 1.955336489125606 y1[1] (numeric) = 1.955336489125604 absolute error = 1.554312234475219e-15 relative error = 7.94907803909639e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.29552020666134 y2[1] (numeric) = 1.295520206661339 absolute error = 1.110223024625157e-15 relative error = 8.569708283333465e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.09 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 = 0.2823 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y1[1] (closed_form) = 1.952333569885713 y1[1] (numeric) = 1.952333569885712 absolute error = 1.332267629550188e-15 relative error = 6.823975421516604e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.305058636443444 y2[1] (numeric) = 1.305058636443443 absolute error = 8.881784197001252e-16 relative error = 6.805659109084909e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.09 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 = 0.2905 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y1[1] (closed_form) = 1.949235418082441 y1[1] (numeric) = 1.94923541808244 absolute error = 1.110223024625157e-15 relative error = 5.695684648072616e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.314566560616118 y2[1] (numeric) = 1.314566560616117 absolute error = 6.661338147750939e-16 relative error = 5.067326636263187e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.1 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 = 0.2986 Order of pole (three term test) = 32.9 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y1[1] (closed_form) = 1.946042343528387 y1[1] (numeric) = 1.946042343528386 absolute error = 8.881784197001252e-16 relative error = 4.564024121334179e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.324043028394869 y2[1] (numeric) = 1.324043028394868 absolute error = 8.881784197001252e-16 relative error = 6.708078216890428e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.11 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 = 0.3066 Order of pole (three term test) = 32.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y1[1] (closed_form) = 1.942754665528346 y1[1] (numeric) = 1.942754665528345 absolute error = 1.110223024625157e-15 relative error = 5.714684639932255e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.333487092140815 y2[1] (numeric) = 1.333487092140814 absolute error = 1.110223024625157e-15 relative error = 8.325712570961417e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.11 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 = 0.3144 Order of pole (three term test) = 32.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y1[1] (closed_form) = 1.939372712847379 y1[1] (numeric) = 1.939372712847378 absolute error = 1.110223024625157e-15 relative error = 5.724650126664573e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.342897807455452 y2[1] (numeric) = 1.342897807455451 absolute error = 1.110223024625157e-15 relative error = 8.267367914829114e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.12 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 = 0.3221 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y1[1] (closed_form) = 1.935896823677935 y1[1] (numeric) = 1.935896823677934 absolute error = 8.881784197001252e-16 relative error = 4.587942956653598e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.35227423327509 y2[1] (numeric) = 1.352274233275089 absolute error = 8.881784197001252e-16 relative error = 6.568034780556565e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.12 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 = 0.3297 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y1[1] (closed_form) = 1.932327345606034 y1[1] (numeric) = 1.932327345606034 absolute error = 4.440892098500626e-16 relative error = 2.298209000974332e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.361615431964962 y2[1] (numeric) = 1.361615431964961 absolute error = 1.110223024625157e-15 relative error = 8.153719461176946e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.13 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 = 0.3371 Order of pole (three term test) = 32.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y1[1] (closed_form) = 1.92866463557651 y1[1] (numeric) = 1.92866463557651 absolute error = 4.440892098500626e-16 relative error = 2.302573509454727e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.370920469412983 y2[1] (numeric) = 1.370920469412982 absolute error = 8.881784197001252e-16 relative error = 6.478701277838795e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.14 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 = 0.3445 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y1[1] (closed_form) = 1.924909059857313 y1[1] (numeric) = 1.924909059857312 absolute error = 6.661338147750939e-16 relative error = 3.460598885770075e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.380188415123162 y2[1] (numeric) = 1.380188415123161 absolute error = 8.881784197001252e-16 relative error = 6.435196890280146e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.14 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 = 0.3516 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y1[1] (closed_form) = 1.921060994002885 y1[1] (numeric) = 1.921060994002885 absolute error = 4.440892098500626e-16 relative error = 2.311687193880923e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.389418342308651 y2[1] (numeric) = 1.389418342308649 absolute error = 1.332267629550188e-15 relative error = 9.588671669156882e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.15 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 = 0.3587 Order of pole (three term test) = 32.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y1[1] (closed_form) = 1.917120822816605 y1[1] (numeric) = 1.917120822816605 absolute error = 2.220446049250313e-16 relative error = 1.158219149687221e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.398609327984423 y2[1] (numeric) = 1.398609327984422 absolute error = 1.332267629550188e-15 relative error = 9.525659545472629e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.16 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 = 0.3656 Order of pole (three term test) = 32.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y1[1] (closed_form) = 1.913088940312308 y1[1] (numeric) = 1.913088940312308 absolute error = 2.220446049250313e-16 relative error = 1.16066012534045e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.40776045305957 y2[1] (numeric) = 1.407760453059569 absolute error = 1.110223024625157e-15 relative error = 7.886448452307651e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.17 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 = 0.3723 Order of pole (three term test) = 32.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y1[1] (closed_form) = 1.908965749674885 y1[1] (numeric) = 1.908965749674885 absolute error = 2.220446049250313e-16 relative error = 1.163167044578184e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.416870802429211 y2[1] (numeric) = 1.41687080242921 absolute error = 1.110223024625157e-15 relative error = 7.835739311740281e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.17 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 = 0.3789 Order of pole (three term test) = 32.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y1[1] (closed_form) = 1.904751663219963 y1[1] (numeric) = 1.904751663219963 absolute error = 2.220446049250313e-16 relative error = 1.16574044382073e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.425939465066 y2[1] (numeric) = 1.425939465065999 absolute error = 1.110223024625157e-15 relative error = 7.785905726185717e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.18 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 = 0.3854 Order of pole (three term test) = 32.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y1[1] (closed_form) = 1.900447102352677 y1[1] (numeric) = 1.900447102352677 absolute error = 2.220446049250313e-16 relative error = 1.168380875480033e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.43496553411123 y2[1] (numeric) = 1.434965534111229 absolute error = 1.332267629550188e-15 relative error = 9.284317970573069e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.19 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 = 0.3917 Order of pole (three term test) = 32.81 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y1[1] (closed_form) = 1.896052497525525 y1[1] (numeric) = 1.896052497525524 absolute error = 6.661338147750939e-16 relative error = 3.513266724652629e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.44394810696552 y2[1] (numeric) = 1.443948106965519 absolute error = 1.110223024625157e-15 relative error = 7.688801413773159e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.2 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 = 0.3978 Order of pole (three term test) = 32.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y1[1] (closed_form) = 1.891568288195329 y1[1] (numeric) = 1.891568288195328 absolute error = 6.661338147750939e-16 relative error = 3.521595381632381e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.452886285379068 y2[1] (numeric) = 1.452886285379067 absolute error = 1.110223024625157e-15 relative error = 7.641499791124336e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.21 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 = 0.4038 Order of pole (three term test) = 32.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y1[1] (closed_form) = 1.886994922779284 y1[1] (numeric) = 1.886994922779283 absolute error = 6.661338147750939e-16 relative error = 3.530130403286779e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.461779175541483 y2[1] (numeric) = 1.461779175541482 absolute error = 6.661338147750939e-16 relative error = 4.557007145271034e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.21 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 = 0.4096 Order of pole (three term test) = 32.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y1[1] (closed_form) = 1.882332858610121 y1[1] (numeric) = 1.882332858610121 absolute error = 6.661338147750939e-16 relative error = 3.538873646752118e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.470625888171158 y2[1] (numeric) = 1.470625888171158 absolute error = 6.661338147750939e-16 relative error = 4.529593964944307e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.22 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 = 0.4152 Order of pole (three term test) = 32.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y1[1] (closed_form) = 1.877582561890373 y1[1] (numeric) = 1.877582561890372 absolute error = 6.661338147750939e-16 relative error = 3.547827021275818e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.479425538604203 y2[1] (numeric) = 1.479425538604202 absolute error = 1.332267629550188e-15 relative error = 9.005303712731262e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.23 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 = 0.4207 Order of pole (three term test) = 32.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y1[1] (closed_form) = 1.872744507645751 y1[1] (numeric) = 1.87274450764575 absolute error = 8.881784197001252e-16 relative error = 4.74265665217016e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.488177246882908 y2[1] (numeric) = 1.488177246882906 absolute error = 1.332267629550188e-15 relative error = 8.952345107686039e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.24 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 = 0.4261 Order of pole (three term test) = 32.76 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y1[1] (closed_form) = 1.86781917967765 y1[1] (numeric) = 1.867819179677649 absolute error = 6.661338147750939e-16 relative error = 3.566372066540488e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.496880137843737 y2[1] (numeric) = 1.496880137843736 absolute error = 1.332267629550188e-15 relative error = 8.900295994770334e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.25 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 = 0.4312 Order of pole (three term test) = 32.75 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y1[1] (closed_form) = 1.862807070514761 y1[1] (numeric) = 1.86280707051476 absolute error = 1.110223024625157e-15 relative error = 5.959946374470019e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.505533341204847 y2[1] (numeric) = 1.505533341204846 absolute error = 1.332267629550188e-15 relative error = 8.849140653929334e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.26 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 = 0.4362 Order of pole (three term test) = 32.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y1[1] (closed_form) = 1.857708681363824 y1[1] (numeric) = 1.857708681363823 absolute error = 8.881784197001252e-16 relative error = 4.781042520876175e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.514135991653113 y2[1] (numeric) = 1.514135991653112 absolute error = 1.332267629550188e-15 relative error = 8.798863753946143e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.26 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 = 0.441 Order of pole (three term test) = 32.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y1[1] (closed_form) = 1.852524522059506 y1[1] (numeric) = 1.852524522059505 absolute error = 8.881784197001252e-16 relative error = 4.794421931390745e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.522687228930659 y2[1] (numeric) = 1.522687228930658 absolute error = 1.554312234475219e-15 relative error = 1.020769206534141e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 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) = 32.27 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 = 0.4456 Order of pole (three term test) = 32.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y1[1] (closed_form) = 1.847255111013416 y1[1] (numeric) = 1.847255111013415 absolute error = 4.440892098500626e-16 relative error = 2.40404916030484e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.531186197920884 y2[1] (numeric) = 1.531186197920882 absolute error = 1.554312234475219e-15 relative error = 1.015103347055856e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 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) = 32.28 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 = 0.4501 Order of pole (three term test) = 32.72 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y1[1] (closed_form) = 1.841900975162269 y1[1] (numeric) = 1.841900975162268 absolute error = 6.661338147750939e-16 relative error = 3.616556067659438e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.539632048733969 y2[1] (numeric) = 1.539632048733968 absolute error = 1.554312234475219e-15 relative error = 1.009534866303492e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 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) = 32.29 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 = 0.4543 Order of pole (three term test) = 32.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y1[1] (closed_form) = 1.836462649915187 y1[1] (numeric) = 1.836462649915186 absolute error = 4.440892098500626e-16 relative error = 2.418177194458989e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.548023936791874 y2[1] (numeric) = 1.548023936791872 absolute error = 1.998401444325282e-15 relative error = 1.290937043561982e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 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) = 32.3 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 = 0.4584 Order of pole (three term test) = 32.7 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y1[1] (closed_form) = 1.830940679100163 y1[1] (numeric) = 1.830940679100163 absolute error = 6.661338147750939e-16 relative error = 3.638205335535355e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.556361022912784 y2[1] (numeric) = 1.556361022912782 absolute error = 1.77635683940025e-15 relative error = 1.141352689542261e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 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) = 32.31 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 = 0.4623 Order of pole (three term test) = 32.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y1[1] (closed_form) = 1.825335614909678 y1[1] (numeric) = 1.825335614909677 absolute error = 8.881784197001252e-16 relative error = 4.865836246470622e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.564642473395036 y2[1] (numeric) = 1.564642473395034 absolute error = 1.998401444325282e-15 relative error = 1.277225614353326e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 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) = 32.32 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 = 0.466 Order of pole (three term test) = 32.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y1[1] (closed_form) = 1.819648017845479 y1[1] (numeric) = 1.819648017845479 absolute error = 6.661338147750939e-16 relative error = 3.660783889204118e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.572867460100482 y2[1] (numeric) = 1.57286746010048 absolute error = 1.998401444325282e-15 relative error = 1.270546625840689e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 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) = 32.33 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 = 0.4695 Order of pole (three term test) = 32.67 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y1[1] (closed_form) = 1.813878456662534 y1[1] (numeric) = 1.813878456662533 absolute error = 6.661338147750939e-16 relative error = 3.672428063348602e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.581035160537305 y2[1] (numeric) = 1.581035160537304 absolute error = 1.77635683940025e-15 relative error = 1.123540376418046e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 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) = 32.34 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 = 0.4729 Order of pole (three term test) = 32.66 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y1[1] (closed_form) = 1.808027508312152 y1[1] (numeric) = 1.808027508312151 absolute error = 4.440892098500626e-16 relative error = 2.456208259047084e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.58914475794227 y2[1] (numeric) = 1.589144757942268 absolute error = 2.220446049250313e-15 relative error = 1.397258517924757e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 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) = 32.35 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 = 0.476 Order of pole (three term test) = 32.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y1[1] (closed_form) = 1.802095757884292 y1[1] (numeric) = 1.802095757884292 absolute error = 2.220446049250313e-16 relative error = 1.232146538015924e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.597195441362393 y2[1] (numeric) = 1.597195441362391 absolute error = 1.77635683940025e-15 relative error = 1.112172495236422e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 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) = 32.36 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 = 0.479 Order of pole (three term test) = 32.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y1[1] (closed_form) = 1.796083798549056 y1[1] (numeric) = 1.796083798549055 absolute error = 2.220446049250313e-16 relative error = 1.236270852754239e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.60518640573604 y2[1] (numeric) = 1.605186405736039 absolute error = 1.332267629550188e-15 relative error = 8.299768953869826e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.37 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 = 0.4818 Order of pole (three term test) = 32.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y1[1] (closed_form) = 1.789992231497365 y1[1] (numeric) = 1.789992231497365 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.613116851973434 y2[1] (numeric) = 1.613116851973433 absolute error = 1.332267629550188e-15 relative error = 8.258965417913373e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.38 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 = 0.4844 Order of pole (three term test) = 32.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y1[1] (closed_form) = 1.783821665880849 y1[1] (numeric) = 1.783821665880849 absolute error = 2.220446049250313e-16 relative error = 1.244769077380759e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.62098598703656 y2[1] (numeric) = 1.620985987036559 absolute error = 1.110223024625157e-15 relative error = 6.849059976482797e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.39 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 = 0.4867 Order of pole (three term test) = 32.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y1[1] (closed_form) = 1.777572718750928 y1[1] (numeric) = 1.777572718750928 absolute error = 2.220446049250313e-16 relative error = 1.249144986209389e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.628793024018469 y2[1] (numeric) = 1.628793024018468 absolute error = 8.881784197001252e-16 relative error = 5.452985165106246e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.4 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 = 0.4889 Order of pole (three term test) = 32.6 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y1[1] (closed_form) = 1.771246014997106 y1[1] (numeric) = 1.771246014997107 absolute error = 4.440892098500626e-16 relative error = 2.507213600425733e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.636537182221968 y2[1] (numeric) = 1.636537182221968 absolute error = 4.440892098500626e-16 relative error = 2.713590712599095e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 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) = 32.41 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 = 0.4909 Order of pole (three term test) = 32.59 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y1[1] (closed_form) = 1.764842187284488 y1[1] (numeric) = 1.764842187284489 absolute error = 4.440892098500626e-16 relative error = 2.516311163965147e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.644217687237691 y2[1] (numeric) = 1.644217687237691 absolute error = 4.440892098500626e-16 relative error = 2.70091492931291e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4927 Order of pole (three term test) = 32.42 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 = 0.4927 Order of pole (three term test) = 32.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y1[1] (closed_form) = 1.758361875990508 y1[1] (numeric) = 1.758361875990508 absolute error = 4.440892098500626e-16 relative error = 2.525584840719442e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.651833771021537 y2[1] (numeric) = 1.651833771021537 absolute error = 6.661338147750939e-16 relative error = 4.032692795493213e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4943 Order of pole (three term test) = 32.42 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 = 0.4943 Order of pole (three term test) = 32.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y1[1] (closed_form) = 1.751805729140895 y1[1] (numeric) = 1.751805729140895 absolute error = 6.661338147750939e-16 relative error = 3.802555293056231e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.659384671971474 y2[1] (numeric) = 1.659384671971473 absolute error = 4.440892098500626e-16 relative error = 2.676228226951448e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4957 Order of pole (three term test) = 32.43 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 = 0.4957 Order of pole (three term test) = 32.57 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y1[1] (closed_form) = 1.74517440234487 y1[1] (numeric) = 1.745174402344871 absolute error = 6.661338147750939e-16 relative error = 3.817004271206683e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.666869635003698 y2[1] (numeric) = 1.666869635003698 absolute error = 4.440892098500626e-16 relative error = 2.664210808837953e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4969 Order of pole (three term test) = 32.44 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 = 0.4969 Order of pole (three term test) = 32.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y1[1] (closed_form) = 1.738468558729588 y1[1] (numeric) = 1.738468558729588 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.674287911628145 y2[1] (numeric) = 1.674287911628145 absolute error = 4.440892098500626e-16 relative error = 2.652406475408475e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4979 Order of pole (three term test) = 32.45 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 = 0.4979 Order of pole (three term test) = 32.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y1[1] (closed_form) = 1.731688868873821 y1[1] (numeric) = 1.731688868873821 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.681638760023334 y2[1] (numeric) = 1.681638760023334 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 = 0.4987 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 = 0.4987 Order of pole (three term test) = 32.54 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y1[1] (closed_form) = 1.724836010740905 y1[1] (numeric) = 1.724836010740905 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.688921445110552 y2[1] (numeric) = 1.688921445110552 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 = 0.4994 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 = 0.4994 Order of pole (three term test) = 32.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y1[1] (closed_form) = 1.717910669610943 y1[1] (numeric) = 1.717910669610943 absolute error = 2.220446049250313e-16 relative error = 1.292527072873457e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.696135238627357 y2[1] (numeric) = 1.696135238627357 absolute error = 2.220446049250313e-16 relative error = 1.309120875908025e-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 = 0.4998 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 = 0.4998 Order of pole (three term test) = 32.52 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y1[1] (closed_form) = 1.710913538012277 y1[1] (numeric) = 1.710913538012277 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.703279419200411 y2[1] (numeric) = 1.70327941920041 absolute error = 4.440892098500626e-16 relative error = 2.607259882577201e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 32.49 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 = 0.5 Order of pole (three term test) = 32.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y1[1] (closed_form) = 1.703845315652236 y1[1] (numeric) = 1.703845315652236 absolute error = 2.220446049250313e-16 relative error = 1.303196967971427e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.710353272417608 y2[1] (numeric) = 1.710353272417608 absolute error = 2.220446049250313e-16 relative error = 1.298238255838036e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 32.5 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 y1[1] (closed_form) = 1.696706709347165 y1[1] (numeric) = 1.696706709347165 absolute error = 2.220446049250313e-16 relative error = 1.308679948642783e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.717356090899523 y2[1] (numeric) = 1.717356090899523 absolute error = 2.220446049250313e-16 relative error = 1.292944463304218e-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 = 0.4998 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 = 0.4998 Order of pole (three term test) = 32.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y1[1] (closed_form) = 1.689498432951747 y1[1] (numeric) = 1.689498432951747 absolute error = 2.220446049250313e-16 relative error = 1.314263455912735e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.724287174370143 y2[1] (numeric) = 1.724287174370143 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 = 0.4994 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 = 0.4994 Order of pole (three term test) = 32.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y1[1] (closed_form) = 1.682221207287613 y1[1] (numeric) = 1.682221207287614 absolute error = 6.661338147750939e-16 relative error = 3.959846730556664e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.731145829726896 y2[1] (numeric) = 1.731145829726896 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 = 0.4988 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 = 0.4988 Order of pole (three term test) = 32.47 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y1[1] (closed_form) = 1.674875760071266 y1[1] (numeric) = 1.674875760071268 absolute error = 1.110223024625157e-15 relative error = 6.62868883228638e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.737931371109963 y2[1] (numeric) = 1.737931371109963 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 = 0.498 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 = 0.498 Order of pole (three term test) = 32.46 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y1[1] (closed_form) = 1.667462825841308 y1[1] (numeric) = 1.667462825841309 absolute error = 8.881784197001252e-16 relative error = 5.326526060645463e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.74464311997086 y2[1] (numeric) = 1.744643119970859 absolute error = 4.440892098500626e-16 relative error = 2.545444422223613e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.497 Order of pole (three term test) = 32.55 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 = 0.497 Order of pole (three term test) = 32.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y1[1] (closed_form) = 1.659983145884982 y1[1] (numeric) = 1.659983145884983 absolute error = 1.554312234475219e-15 relative error = 9.363421781289071e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.751280405140293 y2[1] (numeric) = 1.751280405140293 absolute error = 4.440892098500626e-16 relative error = 2.53579728606903e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4958 Order of pole (three term test) = 32.56 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 = 0.4958 Order of pole (three term test) = 32.44 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y1[1] (closed_form) = 1.652437468164051 y1[1] (numeric) = 1.652437468164053 absolute error = 1.554312234475219e-15 relative error = 9.406178838356559e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.757842562895277 y2[1] (numeric) = 1.757842562895277 absolute error = 2.220446049250313e-16 relative error = 1.263165482574901e-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 = 0.4944 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 = 0.4944 Order of pole (three term test) = 32.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y1[1] (closed_form) = 1.644826547240001 y1[1] (numeric) = 1.644826547240002 absolute error = 1.77635683940025e-15 relative error = 1.079966056226996e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.764328937025506 y2[1] (numeric) = 1.764328937025505 absolute error = 4.440892098500626e-16 relative error = 2.517043168825172e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4929 Order of pole (three term test) = 32.58 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 = 0.4929 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y1[1] (closed_form) = 1.63715114419858 y1[1] (numeric) = 1.637151144198582 absolute error = 2.220446049250313e-15 relative error = 1.356286532931734e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.77073887889897 y2[1] (numeric) = 1.770738878898969 absolute error = 4.440892098500626e-16 relative error = 2.507931661421437e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4911 Order of pole (three term test) = 32.59 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 = 0.4911 Order of pole (three term test) = 32.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y1[1] (closed_form) = 1.629412026573696 y1[1] (numeric) = 1.629412026573699 absolute error = 2.220446049250313e-15 relative error = 1.362728403275281e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.777071747526824 y2[1] (numeric) = 1.777071747526824 absolute error = 4.440892098500626e-16 relative error = 2.498994261025802e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4891 Order of pole (three term test) = 32.6 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 = 0.4891 Order of pole (three term test) = 32.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y1[1] (closed_form) = 1.621609968270664 y1[1] (numeric) = 1.621609968270666 absolute error = 2.220446049250313e-15 relative error = 1.369284903704845e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.783326909627484 y2[1] (numeric) = 1.783326909627483 absolute error = 4.440892098500626e-16 relative error = 2.490228838316737e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4869 Order of pole (three term test) = 32.61 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 = 0.4869 Order of pole (three term test) = 32.39 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y1[1] (closed_form) = 1.613745749488811 y1[1] (numeric) = 1.613745749488813 absolute error = 2.220446049250313e-15 relative error = 1.375957798775729e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.789503739689951 y2[1] (numeric) = 1.78950373968995 absolute error = 6.661338147750939e-16 relative error = 3.722449973144555e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4846 Order of pole (three term test) = 32.62 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 = 0.4846 Order of pole (three term test) = 32.38 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y1[1] (closed_form) = 1.605820156643462 y1[1] (numeric) = 1.605820156643465 absolute error = 2.664535259100376e-15 relative error = 1.659298675556467e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.795601620036366 y2[1] (numeric) = 1.795601620036366 absolute error = 4.440892098500626e-16 relative error = 2.473205664857155e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.482 Order of pole (three term test) = 32.63 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 = 0.482 Order of pole (three term test) = 32.37 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y1[1] (closed_form) = 1.597833982287298 y1[1] (numeric) = 1.5978339822873 absolute error = 2.220446049250313e-15 relative error = 1.38966004845619e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.801619940883778 y2[1] (numeric) = 1.801619940883777 absolute error = 6.661338147750939e-16 relative error = 3.697415862572683e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4792 Order of pole (three term test) = 32.64 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 = 0.4792 Order of pole (three term test) = 32.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y1[1] (closed_form) = 1.589788025031098 y1[1] (numeric) = 1.5897880250311 absolute error = 2.664535259100376e-15 relative error = 1.676031783575836e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.807558100405115 y2[1] (numeric) = 1.807558100405114 absolute error = 8.881784197001252e-16 relative error = 4.913692232084072e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = 32.65 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 = 0.4763 Order of pole (three term test) = 32.35 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y1[1] (closed_form) = 1.581683089463883 y1[1] (numeric) = 1.581683089463885 absolute error = 2.442490654175344e-15 relative error = 1.544235169766679e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.813415504789374 y2[1] (numeric) = 1.813415504789373 absolute error = 1.332267629550188e-15 relative error = 7.346731215386454e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4732 Order of pole (three term test) = 32.66 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 = 0.4732 Order of pole (three term test) = 32.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y1[1] (closed_form) = 1.573519986072456 y1[1] (numeric) = 1.573519986072458 absolute error = 2.220446049250313e-15 relative error = 1.411133044959029e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.819191568300999 y2[1] (numeric) = 1.819191568300997 absolute error = 1.332267629550188e-15 relative error = 7.323404817637954e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4698 Order of pole (three term test) = 32.67 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 = 0.4698 Order of pole (three term test) = 32.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y1[1] (closed_form) = 1.565299531160354 y1[1] (numeric) = 1.565299531160356 absolute error = 2.664535259100376e-15 relative error = 1.702252639867055e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.824885713338451 y2[1] (numeric) = 1.82488571333845 absolute error = 1.110223024625157e-15 relative error = 6.083794818000474e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4663 Order of pole (three term test) = 32.68 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 = 0.4663 Order of pole (three term test) = 32.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y1[1] (closed_form) = 1.557022546766217 y1[1] (numeric) = 1.557022546766219 absolute error = 2.664535259100376e-15 relative error = 1.71130165368148e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.830497370491971 y2[1] (numeric) = 1.83049737049197 absolute error = 6.661338147750939e-16 relative error = 3.639086433629027e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4626 Order of pole (three term test) = 32.69 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 = 0.4626 Order of pole (three term test) = 32.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y1[1] (closed_form) = 1.548689860581587 y1[1] (numeric) = 1.54868986058159 absolute error = 2.886579864025407e-15 relative error = 1.863885040831478e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.836025978600521 y2[1] (numeric) = 1.83602597860052 absolute error = 4.440892098500626e-16 relative error = 2.41875232173219e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4587 Order of pole (three term test) = 32.7 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 = 0.4587 Order of pole (three term test) = 32.3 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y1[1] (closed_form) = 1.540302305868139 y1[1] (numeric) = 1.540302305868142 absolute error = 2.442490654175344e-15 relative error = 1.585721611186394e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.841470984807897 y2[1] (numeric) = 1.841470984807897 absolute error = 2.220446049250313e-16 relative error = 1.205800182337356e-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 = 0.4546 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 = 0.4546 Order of pole (three term test) = 32.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.01 y1[1] (closed_form) = 1.531860721374356 y1[1] (numeric) = 1.531860721374357 absolute error = 1.554312234475219e-15 relative error = 1.014656367114577e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.846831844618015 y2[1] (numeric) = 1.846831844618015 absolute error = 4.440892098500626e-16 relative error = 2.404600132622874e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4504 Order of pole (three term test) = 32.72 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 = 0.4504 Order of pole (three term test) = 32.28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.019999999999998 y1[1] (closed_form) = 1.523365951251651 y1[1] (numeric) = 1.523365951251652 absolute error = 8.881784197001252e-16 relative error = 5.830368067307575e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.852108021949362 y2[1] (numeric) = 1.852108021949363 absolute error = 8.881784197001252e-16 relative error = 4.795500095967991e-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) = 32.73 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 = 0.446 Order of pole (three term test) = 32.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.029999999999997 y1[1] (closed_form) = 1.514818844969958 y1[1] (numeric) = 1.514818844969958 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.857298989188602 y2[1] (numeric) = 1.857298989188604 absolute error = 1.554312234475219e-15 relative error = 8.368670006945146e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4414 Order of pole (three term test) = 32.73 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 = 0.4414 Order of pole (three term test) = 32.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.039999999999996 y1[1] (closed_form) = 1.506220257232782 y1[1] (numeric) = 1.506220257232781 absolute error = 8.881784197001252e-16 relative error = 5.896736652127365e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.001 y2[1] (closed_form) = 1.862404227243337 y2[1] (numeric) = 1.862404227243339 absolute error = 1.998401444325282e-15 relative error = 1.073022394973428e-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) = 32.74 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 = 0.4366 Order of pole (three term test) = 32.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.049999999999995 y1[1] (closed_form) = 1.497571047891731 y1[1] (numeric) = 1.497571047891729 absolute error = 1.77635683940025e-15 relative error = 1.1861586412885e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.867423225594015 y2[1] (numeric) = 1.867423225594017 absolute error = 2.442490654175344e-15 relative error = 1.307947025987323e-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) = 32.75 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 = 0.4316 Order of pole (three term test) = 32.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.059999999999994 y1[1] (closed_form) = 1.488872081860533 y1[1] (numeric) = 1.48887208186053 absolute error = 2.664535259100376e-15 relative error = 1.789633435647946e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.872355482344983 y2[1] (numeric) = 1.872355482344986 absolute error = 3.108624468950438e-15 relative error = 1.660274717201203e-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) = 32.76 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 = 0.4265 Order of pole (three term test) = 32.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.069999999999993 y1[1] (closed_form) = 1.48012422902854 y1[1] (numeric) = 1.480124229028537 absolute error = 3.552713678800501e-15 relative error = 2.40028073936218e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.877200504274678 y2[1] (numeric) = 1.877200504274682 absolute error = 3.774758283725532e-15 relative error = 2.010844486313433e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4212 Order of pole (three term test) = 32.77 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 = 0.4212 Order of pole (three term test) = 32.23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.079999999999992 y1[1] (closed_form) = 1.471328364173747 y1[1] (numeric) = 1.471328364173743 absolute error = 4.440892098500626e-15 relative error = 3.01828756016302e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.881957806884944 y2[1] (numeric) = 1.881957806884948 absolute error = 3.996802888650564e-15 relative error = 2.123747341214921e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4157 Order of pole (three term test) = 32.78 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 = 0.4157 Order of pole (three term test) = 32.22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.089999999999991 y1[1] (closed_form) = 1.462485366875309 y1[1] (numeric) = 1.462485366875304 absolute error = 5.551115123125783e-15 relative error = 3.795672250031523e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.886626914449483 y2[1] (numeric) = 1.886626914449487 absolute error = 4.440892098500626e-15 relative error = 2.353879330612898e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4101 Order of pole (three term test) = 32.79 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 = 0.4101 Order of pole (three term test) = 32.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.09999999999999 y1[1] (closed_form) = 1.453596121425587 y1[1] (numeric) = 1.45359612142558 absolute error = 6.661338147750939e-15 relative error = 4.582660925937227e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.891207360061431 y2[1] (numeric) = 1.891207360061435 absolute error = 4.884981308350689e-15 relative error = 2.582996138610635e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4042 Order of pole (three term test) = 32.79 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 = 0.4042 Order of pole (three term test) = 32.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.109999999999989 y1[1] (closed_form) = 1.444661516741717 y1[1] (numeric) = 1.44466151674171 absolute error = 7.549516567451064e-15 relative error = 5.225803054876279e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.895698685680042 y2[1] (numeric) = 1.895698685680048 absolute error = 5.773159728050814e-15 relative error = 3.045399446473643e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3983 Order of pole (three term test) = 32.8 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 = 0.3983 Order of pole (three term test) = 32.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.119999999999987 y1[1] (closed_form) = 1.435682446276723 y1[1] (numeric) = 1.435682446276715 absolute error = 8.43769498715119e-15 relative error = 5.8771318191104e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.9001004421765 y2[1] (numeric) = 1.900100442176506 absolute error = 6.217248937900877e-15 relative error = 3.272063307758211e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3922 Order of pole (three term test) = 32.81 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 = 0.3922 Order of pole (three term test) = 32.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.129999999999986 y1[1] (closed_form) = 1.42665980793017 y1[1] (numeric) = 1.42665980793016 absolute error = 9.547918011776346e-15 relative error = 6.692498070460596e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.90441218937882 y2[1] (numeric) = 1.904412189378826 absolute error = 6.439293542825908e-15 relative error = 3.381249909414974e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3859 Order of pole (three term test) = 32.82 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 = 0.3859 Order of pole (three term test) = 32.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.139999999999985 y1[1] (closed_form) = 1.417594503958371 y1[1] (numeric) = 1.417594503958361 absolute error = 1.043609643147647e-14 relative error = 7.361834715312168e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.908633496115877 y2[1] (numeric) = 1.908633496115884 absolute error = 6.883382752675971e-15 relative error = 3.606445536392319e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3794 Order of pole (three term test) = 32.83 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 = 0.3794 Order of pole (three term test) = 32.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.149999999999984 y1[1] (closed_form) = 1.408487440884172 y1[1] (numeric) = 1.40848744088416 absolute error = 1.154631945610163e-14 relative error = 8.197672993699877e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.912763940260515 y2[1] (numeric) = 1.912763940260522 absolute error = 7.105427357601002e-15 relative error = 3.714743470453159e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3729 Order of pole (three term test) = 32.83 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 = 0.3729 Order of pole (three term test) = 32.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.159999999999983 y1[1] (closed_form) = 1.399339529406289 y1[1] (numeric) = 1.399339529406276 absolute error = 1.243449787580175e-14 relative error = 8.885976287025535e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.91680310877176 y2[1] (numeric) = 1.916803108771767 absolute error = 7.105427357601002e-15 relative error = 3.706915606034249e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3661 Order of pole (three term test) = 32.84 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 = 0.3661 Order of pole (three term test) = 32.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.169999999999982 y1[1] (closed_form) = 1.390151684308247 y1[1] (numeric) = 1.390151684308234 absolute error = 1.332267629550188e-14 relative error = 9.583613389736943e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 y2[1] (closed_form) = 1.920750597736129 y2[1] (numeric) = 1.920750597736136 absolute error = 7.327471962526033e-15 relative error = 3.814900264075136e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3592 Order of pole (three term test) = 32.85 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 = 0.3592 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.179999999999981 y1[1] (closed_form) = 1.380924824366899 y1[1] (numeric) = 1.380924824366885 absolute error = 1.4210854715202e-14 relative error = 1.029082428271729e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.924606012408013 y2[1] (numeric) = 1.924606012408021 absolute error = 7.771561172376096e-15 relative error = 4.038001088156498e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3522 Order of pole (three term test) = 32.85 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 = 0.3522 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.18999999999998 y1[1] (closed_form) = 1.371659872260552 y1[1] (numeric) = 1.371659872260536 absolute error = 1.554312234475219e-14 relative error = 1.133161555505483e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.928368967249159 y2[1] (numeric) = 1.928368967249167 absolute error = 7.771561172376096e-15 relative error = 4.030121467606024e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.345 Order of pole (three term test) = 32.86 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 = 0.345 Order of pole (three term test) = 32.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.199999999999979 y1[1] (closed_form) = 1.362357754476693 y1[1] (numeric) = 1.362357754476677 absolute error = 1.620925615952729e-14 relative error = 1.189794391837521e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.932039085967219 y2[1] (numeric) = 1.932039085967227 absolute error = 8.215650382226158e-15 relative error = 4.25232100214641e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3377 Order of pole (three term test) = 32.87 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 = 0.3377 Order of pole (three term test) = 32.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.209999999999978 y1[1] (closed_form) = 1.353019401219351 y1[1] (numeric) = 1.353019401219334 absolute error = 1.731947918415244e-14 relative error = 1.280061406994164e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.935616001553378 y2[1] (numeric) = 1.935616001553386 absolute error = 8.43769498715119e-15 relative error = 4.359178153300933e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3303 Order of pole (three term test) = 32.88 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 = 0.3303 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.219999999999976 y1[1] (closed_form) = 1.343645746316069 y1[1] (numeric) = 1.34364574631605 absolute error = 1.865174681370263e-14 relative error = 1.388144670188621e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.939099356319059 y2[1] (numeric) = 1.939099356319068 absolute error = 8.43769498715119e-15 relative error = 4.351347423047079e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3227 Order of pole (three term test) = 32.88 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 = 0.3227 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.229999999999975 y1[1] (closed_form) = 1.334237727124526 y1[1] (numeric) = 1.334237727124506 absolute error = 1.998401444325282e-14 relative error = 1.49778514255636e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.942488801931689 y2[1] (numeric) = 1.942488801931698 absolute error = 8.881784197001252e-15 relative error = 4.572373435650619e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.315 Order of pole (three term test) = 32.89 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 = 0.315 Order of pole (three term test) = 32.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.239999999999974 y1[1] (closed_form) = 1.324796284438801 y1[1] (numeric) = 1.32479628443878 absolute error = 2.109423746787797e-14 relative error = 1.592262728666524e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.945783999449531 y2[1] (numeric) = 1.94578399944954 absolute error = 9.325873406851315e-15 relative error = 4.792861596913963e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3072 Order of pole (three term test) = 32.89 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 = 0.3072 Order of pole (three term test) = 32.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.249999999999973 y1[1] (closed_form) = 1.315322362395294 y1[1] (numeric) = 1.315322362395272 absolute error = 2.220446049250313e-14 relative error = 1.688138294255657e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.948984619355578 y2[1] (numeric) = 1.948984619355587 absolute error = 9.547918011776346e-15 relative error = 4.898919117654874e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2992 Order of pole (three term test) = 32.9 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 = 0.2992 Order of pole (three term test) = 32.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.259999999999972 y1[1] (closed_form) = 1.305816908378316 y1[1] (numeric) = 1.305816908378293 absolute error = 2.331468351712829e-14 relative error = 1.785448125808281e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.952090341590507 y2[1] (numeric) = 1.952090341590517 absolute error = 9.992007221626409e-15 relative error = 5.118619260973961e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2912 Order of pole (three term test) = 32.91 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 = 0.2912 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.269999999999971 y1[1] (closed_form) = 1.296280872925347 y1[1] (numeric) = 1.296280872925322 absolute error = 2.442490654175344e-14 relative error = 1.884229494695328e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.955100855584684 y2[1] (numeric) = 1.955100855584694 absolute error = 9.992007221626409e-15 relative error = 5.110737480925629e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.283 Order of pole (three term test) = 32.91 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 = 0.283 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.27999999999997 y1[1] (closed_form) = 1.286715209631984 y1[1] (numeric) = 1.286715209631959 absolute error = 2.531308496145357e-14 relative error = 1.967263989107069e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.958015860289216 y2[1] (numeric) = 1.958015860289226 absolute error = 9.992007221626409e-15 relative error = 5.103128848073019e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2747 Order of pole (three term test) = 32.92 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 = 0.2747 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.289999999999969 y1[1] (closed_form) = 1.277120875056588 y1[1] (numeric) = 1.277120875056561 absolute error = 2.620126338115369e-14 relative error = 2.051588372948077e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.960835064206064 y2[1] (numeric) = 1.960835064206074 absolute error = 1.021405182655144e-14 relative error = 5.209031607503958e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2663 Order of pole (three term test) = 32.92 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 = 0.2663 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.299999999999968 y1[1] (closed_form) = 1.267498828624618 y1[1] (numeric) = 1.267498828624591 absolute error = 2.708944180085382e-14 relative error = 2.13723604228092e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.963558185417184 y2[1] (numeric) = 1.963558185417194 absolute error = 1.021405182655144e-14 relative error = 5.201807566696237e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2578 Order of pole (three term test) = 32.93 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 = 0.2578 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.309999999999967 y1[1] (closed_form) = 1.257850032532702 y1[1] (numeric) = 1.257850032532674 absolute error = 2.819966482547898e-14 relative error = 2.241894033162163e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.966184951612725 y2[1] (numeric) = 1.966184951612736 absolute error = 1.021405182655144e-14 relative error = 5.194858102323263e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2491 Order of pole (three term test) = 32.93 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 = 0.2491 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.319999999999965 y1[1] (closed_form) = 1.248175451652406 y1[1] (numeric) = 1.248175451652377 absolute error = 2.953193245502916e-14 relative error = 2.366008113357228e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.968715100118257 y2[1] (numeric) = 1.968715100118267 absolute error = 1.021405182655144e-14 relative error = 5.1881817871656e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2404 Order of pole (three term test) = 32.94 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 = 0.2404 Order of pole (three term test) = 32.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.329999999999964 y1[1] (closed_form) = 1.238476053433758 y1[1] (numeric) = 1.238476053433727 absolute error = 3.086420008457935e-14 relative error = 2.492111171548799e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.971148377921036 y2[1] (numeric) = 1.971148377921046 absolute error = 9.992007221626409e-15 relative error = 5.069129921190888e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2316 Order of pole (three term test) = 32.94 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 = 0.2316 Order of pole (three term test) = 32.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.339999999999963 y1[1] (closed_form) = 1.228752807808495 y1[1] (numeric) = 1.228752807808463 absolute error = 3.241851231905457e-14 relative error = 2.638326611588675e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.973484541695311 y2[1] (numeric) = 1.973484541695321 absolute error = 1.043609643147647e-14 relative error = 5.288157171229424e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2227 Order of pole (three term test) = 32.95 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 = 0.2227 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.349999999999962 y1[1] (closed_form) = 1.219006687093078 y1[1] (numeric) = 1.219006687093045 absolute error = 3.352873534367973e-14 relative error = 2.75049642456306e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.975723357826651 y2[1] (numeric) = 1.975723357826661 absolute error = 1.021405182655144e-14 relative error = 5.169778342746919e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2137 Order of pole (three term test) = 32.95 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 = 0.2137 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.359999999999961 y1[1] (closed_form) = 1.209238665891458 y1[1] (numeric) = 1.209238665891423 absolute error = 3.463895836830488e-14 relative error = 2.864526196966159e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.977864602435308 y2[1] (numeric) = 1.977864602435318 absolute error = 9.992007221626409e-15 relative error = 5.051916703157251e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2046 Order of pole (three term test) = 32.96 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 = 0.2046 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.36999999999996 y1[1] (closed_form) = 1.199449720997612 y1[1] (numeric) = 1.199449720997577 absolute error = 3.552713678800501e-14 relative error = 2.961952982777486e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.979908061398606 y2[1] (numeric) = 1.979908061398616 absolute error = 9.769962616701378e-15 relative error = 4.934553683164399e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1954 Order of pole (three term test) = 32.96 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 = 0.1954 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.379999999999959 y1[1] (closed_form) = 1.189640831297875 y1[1] (numeric) = 1.189640831297838 absolute error = 3.641531520770513e-14 relative error = 3.061034410526809e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.981853530372352 y2[1] (numeric) = 1.981853530372361 absolute error = 9.547918011776346e-15 relative error = 4.81767086490114e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1862 Order of pole (three term test) = 32.96 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 = 0.1862 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.389999999999958 y1[1] (closed_form) = 1.179812977673041 y1[1] (numeric) = 1.179812977673004 absolute error = 3.752553823233029e-14 relative error = 3.180634468553003e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.983700814811269 y2[1] (numeric) = 1.983700814811278 absolute error = 9.103828801926284e-15 relative error = 4.58931545218548e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1769 Order of pole (three term test) = 32.97 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 = 0.1769 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.399999999999957 y1[1] (closed_form) = 1.169967142900284 y1[1] (numeric) = 1.169967142900245 absolute error = 3.885780586188048e-14 relative error = 3.321273259482666e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.985449729988453 y2[1] (numeric) = 1.985449729988461 absolute error = 8.659739592076221e-15 relative error = 4.36160103239007e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1675 Order of pole (three term test) = 32.97 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 = 0.1675 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.409999999999956 y1[1] (closed_form) = 1.160104311554875 y1[1] (numeric) = 1.160104311554835 absolute error = 3.97459842815806e-14 relative error = 3.42606987024378e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.987100101013843 y2[1] (numeric) = 1.987100101013852 absolute error = 8.215650382226158e-15 relative error = 4.134492458650891e-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 = 0.158 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 = 0.158 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.419999999999954 y1[1] (closed_form) = 1.150225469911731 y1[1] (numeric) = 1.15022546991169 absolute error = 4.107825191113079e-14 relative error = 3.571321709150047e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.988651762851713 y2[1] (numeric) = 1.988651762851721 absolute error = 8.215650382226158e-15 relative error = 4.131266487021827e-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 = 0.1485 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 = 0.1485 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.429999999999953 y1[1] (closed_form) = 1.140331605846783 y1[1] (numeric) = 1.140331605846741 absolute error = 4.196643033083092e-14 relative error = 3.680195314736335e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.990104560337171 y2[1] (numeric) = 1.990104560337179 absolute error = 7.771561172376096e-15 relative error = 3.905101936482879e-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 = 0.1389 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 = 0.1389 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.439999999999952 y1[1] (closed_form) = 1.130423708738193 y1[1] (numeric) = 1.13042370873815 absolute error = 4.329869796038111e-14 relative error = 3.830306957088876e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.99145834819168 y2[1] (numeric) = 1.991458348191688 absolute error = 7.549516567451064e-15 relative error = 3.790948765916351e-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 = 0.1293 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 = 0.1293 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.449999999999951 y1[1] (closed_form) = 1.120502769367415 y1[1] (numeric) = 1.120502769367371 absolute error = 4.440892098500626e-14 relative error = 3.963303099204076e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.992712991037583 y2[1] (numeric) = 1.99271299103759 absolute error = 7.105427357601002e-15 relative error = 3.565705342193452e-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 = 0.1196 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 = 0.1196 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.45999999999995 y1[1] (closed_form) = 1.110569779820119 y1[1] (numeric) = 1.110569779820074 absolute error = 4.551914400963142e-14 relative error = 4.098719849643687e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.993868363411639 y2[1] (numeric) = 1.993868363411647 absolute error = 7.105427357601002e-15 relative error = 3.563639148897046e-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 = 0.1099 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 = 0.1099 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.469999999999949 y1[1] (closed_form) = 1.100625733386982 y1[1] (numeric) = 1.100625733386936 absolute error = 4.640732242933154e-14 relative error = 4.216448972760355e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.994924349777576 y2[1] (numeric) = 1.994924349777582 absolute error = 6.661338147750939e-15 relative error = 3.339143235428274e-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 = 0.1001 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 = 0.1001 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.479999999999948 y1[1] (closed_form) = 1.090671624464362 y1[1] (numeric) = 1.090671624464314 absolute error = 4.796163466380676e-14 relative error = 4.39744040167554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.995880844537635 y2[1] (numeric) = 1.995880844537642 absolute error = 6.217248937900877e-15 relative error = 3.115040136246791e-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 = 0.0903 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 = 0.0903 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.489999999999947 y1[1] (closed_form) = 1.080708448454854 y1[1] (numeric) = 1.080708448454805 absolute error = 4.907185768843192e-14 relative error = 4.540711952293199e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.996737752043139 y2[1] (numeric) = 1.996737752043145 absolute error = 5.773159728050814e-15 relative error = 2.891295926139271e-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 = 0.08045 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 = 0.08045 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.499999999999946 y1[1] (closed_form) = 1.070737201667757 y1[1] (numeric) = 1.070737201667707 absolute error = 4.996003610813204e-14 relative error = 4.665947538790599e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.997494986604051 y2[1] (numeric) = 1.997494986604056 absolute error = 5.329070518200751e-15 relative error = 2.667876792652544e-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 = 0.07056 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 = 0.07056 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.509999999999944 y1[1] (closed_form) = 1.060758881219441 y1[1] (numeric) = 1.06075888121939 absolute error = 5.129230373768223e-14 relative error = 4.835434767109086e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.998152472497545 y2[1] (numeric) = 1.998152472497549 absolute error = 4.662936703425657e-15 relative error = 2.333624069036797e-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 = 0.06065 Order of pole (three term test) = 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 = 0.06065 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.519999999999943 y1[1] (closed_form) = 1.050774484933636 y1[1] (numeric) = 1.050774484933583 absolute error = 5.284661597215745e-14 relative error = 5.029301408617198e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.99871014397558 y2[1] (numeric) = 1.998710143975585 absolute error = 4.440892098500626e-15 relative error = 2.221879001257965e-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 = 0.05071 Order of pole (three term test) = 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 = 0.05071 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.529999999999942 y1[1] (closed_form) = 1.040785011241649 y1[1] (numeric) = 1.040785011241595 absolute error = 5.395683899678261e-14 relative error = 5.184244432230293e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999167945271474 y2[1] (numeric) = 1.999167945271477 absolute error = 3.774758283725532e-15 relative error = 1.888164670033735e-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 = 0.04075 Order of pole (three term test) = 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 = 0.04075 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.539999999999941 y1[1] (closed_form) = 1.030791459082525 y1[1] (numeric) = 1.03079145908247 absolute error = 5.506706202140776e-14 relative error = 5.342211708896117e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999525830605477 y2[1] (numeric) = 1.999525830605481 absolute error = 3.33066907387547e-15 relative error = 1.665729455901507e-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 = 0.03078 Order of pole (three term test) = 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 = 0.03078 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.54999999999994 y1[1] (closed_form) = 1.020794827803152 y1[1] (numeric) = 1.020794827803096 absolute error = 5.617728504603292e-14 relative error = 5.503288566511625e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999783764189356 y2[1] (numeric) = 1.999783764189359 absolute error = 3.108624468950438e-15 relative error = 1.554480301629296e-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 = 0.02079 Order of pole (three term test) = 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 = 0.02079 Order of pole (three term test) = 32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.559999999999939 y1[1] (closed_form) = 1.010796117058328 y1[1] (numeric) = 1.010796117058271 absolute error = 5.706546346573305e-14 relative error = 5.645595833095198e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.001 y2[1] (closed_form) = 1.999941720229966 y2[1] (numeric) = 1.999941720229968 absolute error = 2.220446049250313e-15 relative error = 1.110255377339192e-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 = 0.0108 Order of pole (three term test) = 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 = 0.0108 Order of pole (three term test) = 32 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] = 1.569989504570034 y1[1] (closed_form) = 1.000806822137327 y1[1] (numeric) = 1.00080682213727 absolute error = 5.684341886080801e-14 relative error = 5.679759330518249e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999999674518966 y2[1] (numeric) = 1.999999674518967 absolute error = 1.110223024625157e-15 relative error = 5.551116026517274e-14 % Desired digits = 8 Estimated correct digits = 12 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] = 1.579994049421232 y1[1] (closed_form) = 0.9908024070580951 y1[1] (numeric) = 0.9908024070580383 absolute error = 5.67323965583455e-14 relative error = 5.725904191815214e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999957701247445 y2[1] (numeric) = 1.999957701247445 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 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] = 1.589998594272429 y1[1] (closed_form) = 0.9807989125667025 y1[1] (numeric) = 0.9807989125666452 absolute error = 5.728750807065808e-14 relative error = 5.840902486396471e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999815642126777 y2[1] (numeric) = 1.999815642126776 absolute error = 1.110223024625157e-15 relative error = 5.551626866186773e-14 % Desired digits = 8 Estimated correct digits = 12 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] = 1.600003139123626 y1[1] (closed_form) = 0.9707973399137415 y1[1] (numeric) = 0.9707973399136842 absolute error = 5.728750807065808e-14 relative error = 5.901077981502118e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.99957351137567 y2[1] (numeric) = 1.999573511375667 absolute error = 2.664535259100376e-15 relative error = 1.332551788639781e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.610007683974824 y1[1] (closed_form) = 0.9607986901574475 y1[1] (numeric) = 0.9607986901573899 absolute error = 5.750955267558311e-14 relative error = 5.985598571763138e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999231333229012 y2[1] (numeric) = 1.999231333229007 absolute error = 4.218847493575595e-15 relative error = 2.110234780465161e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.620012228826021 y1[1] (closed_form) = 0.9508039640635028 y1[1] (numeric) = 0.9508039640634454 absolute error = 5.739853037312059e-14 relative error = 6.036841719486882e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.998789141935441 y2[1] (numeric) = 1.998789141935436 absolute error = 4.662936703425657e-15 relative error = 2.332880745444967e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.630016773677219 y1[1] (closed_form) = 0.94081416200487 y1[1] (numeric) = 0.9408141620048129 absolute error = 5.706546346573305e-14 relative error = 6.065540440433725e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.998246981753922 y2[1] (numeric) = 1.998246981753917 absolute error = 4.218847493575595e-15 relative error = 2.111274297971207e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.640021318528416 y1[1] (closed_form) = 0.9308302838616647 y1[1] (numeric) = 0.9308302838616077 absolute error = 5.695444116327053e-14 relative error = 6.118670841583278e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.99760490694931 y2[1] (numeric) = 1.997604906949306 absolute error = 4.218847493575595e-15 relative error = 2.11195290865525e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.650025863379613 y1[1] (closed_form) = 0.9208533289210772 y1[1] (numeric) = 0.9208533289210201 absolute error = 5.706546346573305e-14 relative error = 6.197019837306133e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.996862981786928 y2[1] (numeric) = 1.996862981786923 absolute error = 4.884981308350689e-15 relative error = 2.446327741515483e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.660030408230811 y1[1] (closed_form) = 0.910884295777354 y1[1] (numeric) = 0.9108842957772968 absolute error = 5.717648576819556e-14 relative error = 6.277030577127341e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.996021280526125 y2[1] (numeric) = 1.996021280526119 absolute error = 6.217248937900877e-15 relative error = 3.114820968372688e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.670034953082008 y1[1] (closed_form) = 0.9009241822318481 y1[1] (numeric) = 0.9009241822317913 absolute error = 5.684341886080801e-14 relative error = 6.309456442826358e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.995079887412851 y2[1] (numeric) = 1.995079887412845 absolute error = 6.217248937900877e-15 relative error = 3.11629071954767e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.680039497933206 y1[1] (closed_form) = 0.8909739851931495 y1[1] (numeric) = 0.8909739851930928 absolute error = 5.67323965583455e-14 relative error = 6.367458253682545e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.99403889667122 y2[1] (numeric) = 1.994038896671213 absolute error = 7.105427357601002e-15 relative error = 3.56333438102063e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.690044042784403 y1[1] (closed_form) = 0.8810347005773038 y1[1] (numeric) = 0.8810347005772474 absolute error = 5.639932965095795e-14 relative error = 6.401487888502225e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.992898412494082 y2[1] (numeric) = 1.992898412494075 absolute error = 7.105427357601002e-15 relative error = 3.565373585053273e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.7000485876356 y1[1] (closed_form) = 0.8711073232081317 y1[1] (numeric) = 0.8711073232080753 absolute error = 5.639932965095795e-14 relative error = 6.474440995771837e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.991658549032593 y2[1] (numeric) = 1.991658549032584 absolute error = 8.659739592076221e-15 relative error = 4.348004127656577e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.710053132486798 y1[1] (closed_form) = 0.8611928467176561 y1[1] (numeric) = 0.8611928467176 absolute error = 5.606626274357041e-14 relative error = 6.510302884802276e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.990319430384788 y2[1] (numeric) = 1.990319430384779 absolute error = 9.325873406851315e-15 relative error = 4.68561642140445e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.720057677337995 y1[1] (closed_form) = 0.8512922634466504 y1[1] (numeric) = 0.8512922634465945 absolute error = 5.595524044110789e-14 relative error = 6.572976502166291e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.988881190583166 y2[1] (numeric) = 1.988881190583156 absolute error = 9.992007221626409e-15 relative error = 5.023933691432128e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.730062222189193 y1[1] (closed_form) = 0.8414065643453144 y1[1] (numeric) = 0.8414065643452585 absolute error = 5.584421813864537e-14 relative error = 6.637007661343468e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.987343973581266 y2[1] (numeric) = 1.987343973581256 absolute error = 9.992007221626409e-15 relative error = 5.027819720418328e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.74006676704039 y1[1] (closed_form) = 0.8315367388740896 y1[1] (numeric) = 0.8315367388740339 absolute error = 5.573319583618286e-14 relative error = 6.702433365920338e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.985707933239265 y2[1] (numeric) = 1.985707933239255 absolute error = 9.992007221626409e-15 relative error = 5.031962180523975e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.750071311891587 y1[1] (closed_form) = 0.8216837749046254 y1[1] (numeric) = 0.8216837749045697 absolute error = 5.573319583618286e-14 relative error = 6.782803499150501e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.983973233308577 y2[1] (numeric) = 1.983973233308568 absolute error = 9.547918011776346e-15 relative error = 4.812523602374282e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.760075856742785 y1[1] (closed_form) = 0.8118486586209015 y1[1] (numeric) = 0.8118486586208459 absolute error = 5.562217353372034e-14 relative error = 6.851298323040466e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.982140047415462 y2[1] (numeric) = 1.982140047415452 absolute error = 9.547918011776346e-15 relative error = 4.816974473739129e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.770080401593982 y1[1] (closed_form) = 0.8020323744205213 y1[1] (numeric) = 0.8020323744204657 absolute error = 5.562217353372034e-14 relative error = 6.935153156867025e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.980208559043647 y2[1] (numeric) = 1.980208559043636 absolute error = 1.06581410364015e-14 relative error = 5.38233257690236e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.78008494644518 y1[1] (closed_form) = 0.7922359048161836 y1[1] (numeric) = 0.792235904816128 absolute error = 5.551115123125783e-14 relative error = 7.006896669766268e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.978178961515964 y2[1] (numeric) = 1.978178961515953 absolute error = 1.154631945610163e-14 relative error = 5.836842712781246e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.790089491296377 y1[1] (closed_form) = 0.7824602303373427 y1[1] (numeric) = 0.7824602303372868 absolute error = 5.584421813864537e-14 relative error = 7.137004025695876e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.976051457974997 y2[1] (numeric) = 1.976051457974985 absolute error = 1.243449787580175e-14 relative error = 6.292598214291585e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.800094036147574 y1[1] (closed_form) = 0.7727063294320667 y1[1] (numeric) = 0.7727063294320112 absolute error = 5.551115123125783e-14 relative error = 7.183990750025058e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.973826261362752 y2[1] (numeric) = 1.973826261362739 absolute error = 1.354472090042691e-14 relative error = 6.862164702923488e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.810098580998772 y1[1] (closed_form) = 0.7629751783691053 y1[1] (numeric) = 0.7629751783690503 absolute error = 5.506706202140776e-14 relative error = 7.217411992237566e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.971503594399343 y2[1] (numeric) = 1.971503594399328 absolute error = 1.465494392505207e-14 relative error = 7.433384329951974e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.820103125849969 y1[1] (closed_form) = 0.7532677511401745 y1[1] (numeric) = 0.753267751140119 absolute error = 5.551115123125783e-14 relative error = 7.36937843777781e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.969083689560697 y2[1] (numeric) = 1.969083689560682 absolute error = 1.48769885299771e-14 relative error = 7.555285033769264e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.830107670701167 y1[1] (closed_form) = 0.7435850193624698 y1[1] (numeric) = 0.7435850193624141 absolute error = 5.573319583618286e-14 relative error = 7.495201541844809e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.966566789055291 y2[1] (numeric) = 1.966566789055276 absolute error = 1.48769885299771e-14 relative error = 7.564954626902746e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.840112215552364 y1[1] (closed_form) = 0.7339279521814166 y1[1] (numeric) = 0.7339279521813612 absolute error = 5.540012892879531e-14 relative error = 7.548442427370744e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.963953144799904 y2[1] (numeric) = 1.963953144799889 absolute error = 1.576516694967722e-14 relative error = 8.027262254916699e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.850116760403561 y1[1] (closed_form) = 0.7242975161736691 y1[1] (numeric) = 0.7242975161736135 absolute error = 5.562217353372034e-14 relative error = 7.679464901048132e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.961243018394408 y2[1] (numeric) = 1.961243018394391 absolute error = 1.643130076445232e-14 relative error = 8.378003444929519e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.860121305254759 y1[1] (closed_form) = 0.7146946752503651 y1[1] (numeric) = 0.7146946752503095 absolute error = 5.562217353372034e-14 relative error = 7.782648375578748e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.958436681095577 y2[1] (numeric) = 1.958436681095561 absolute error = 1.643130076445232e-14 relative error = 8.390008685529936e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.870125850105956 y1[1] (closed_form) = 0.705120390560648 y1[1] (numeric) = 0.7051203905605928 absolute error = 5.517808432387028e-14 relative error = 7.825342319202775e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.955534413789946 y2[1] (numeric) = 1.955534413789928 absolute error = 1.798561299892754e-14 relative error = 9.197287898437089e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.880130394957154 y1[1] (closed_form) = 0.6955756203954655 y1[1] (numeric) = 0.6955756203954107 absolute error = 5.484501741648273e-14 relative error = 7.884838946094878e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.952536506965688 y2[1] (numeric) = 1.952536506965669 absolute error = 1.887379141862766e-14 relative error = 9.66629374216322e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.890134939808351 y1[1] (closed_form) = 0.6860613200916541 y1[1] (numeric) = 0.6860613200915991 absolute error = 5.495603971894525e-14 relative error = 8.01036847720892e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.949443260683547 y2[1] (numeric) = 1.949443260683528 absolute error = 1.887379141862766e-14 relative error = 9.681631571061891e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.900139484659548 y1[1] (closed_form) = 0.6765784419363191 y1[1] (numeric) = 0.6765784419362644 absolute error = 5.473399511402022e-14 relative error = 8.089822513022353e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.946254984546798 y2[1] (numeric) = 1.946254984546779 absolute error = 1.909583602355269e-14 relative error = 9.81157976481654e-13 % Desired digits = 8 Estimated correct digits = 12 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] = 1.910144029510746 y1[1] (closed_form) = 0.6671279350715207 y1[1] (numeric) = 0.6671279350714661 absolute error = 5.46229728115577e-14 relative error = 8.187780774867679e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.942971997670265 y2[1] (numeric) = 1.942971997670245 absolute error = 2.020605904817785e-14 relative error = 1.039956266606316e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 1.919987210735311 y1[1] (closed_form) = 0.6578623662517602 y1[1] (numeric) = 0.657862366251706 absolute error = 5.417888360170764e-14 relative error = 8.235595525914867e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.93964984945093 y2[1] (numeric) = 1.93964984945091 absolute error = 2.020605904817785e-14 relative error = 1.041737458639647e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 1.929991755586508 y1[1] (closed_form) = 0.6484788763017075 y1[1] (numeric) = 0.6484788763016535 absolute error = 5.406786129924512e-14 relative error = 8.337644181657172e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.936179950433617 y2[1] (numeric) = 1.936179950433597 absolute error = 2.020605904817785e-14 relative error = 1.043604394501276e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 1.939996300437706 y1[1] (closed_form) = 0.6391305701300434 y1[1] (numeric) = 0.6391305701299894 absolute error = 5.395683899678261e-14 relative error = 8.442224721906832e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.932616349087519 y2[1] (numeric) = 1.932616349087498 absolute error = 2.109423746787797e-14 relative error = 1.091486030211717e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 1.950000845288903 y1[1] (closed_form) = 0.6298183834095068 y1[1] (numeric) = 0.6298183834094527 absolute error = 5.406786129924512e-14 relative error = 8.584674998933827e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.928959402093789 y2[1] (numeric) = 1.928959402093767 absolute error = 2.19824158875781e-14 relative error = 1.139599717014121e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 1.9600053901401 y1[1] (closed_form) = 0.6205432481976381 y1[1] (numeric) = 0.6205432481975844 absolute error = 5.362377208939506e-14 relative error = 8.64142382422898e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.925209475476554 y2[1] (numeric) = 1.925209475476532 absolute error = 2.220446049250313e-14 relative error = 1.153352961085275e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 1.970009934991298 y1[1] (closed_form) = 0.6113060928434889 y1[1] (numeric) = 0.6113060928434351 absolute error = 5.384581669432009e-14 relative error = 8.808323248318432e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.921366944566282 y2[1] (numeric) = 1.921366944566259 absolute error = 2.287059430727822e-14 relative error = 1.190329331518759e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 1.980014479842495 y1[1] (closed_form) = 0.6021078418947037 y1[1] (numeric) = 0.6021078418946502 absolute error = 5.351274978693255e-14 relative error = 8.887568980755915e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.917432193962208 y2[1] (numeric) = 1.917432193962184 absolute error = 2.375877272697835e-14 relative error = 1.239093241565059e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 1.990019024693693 y1[1] (closed_form) = 0.5929494160049817 y1[1] (numeric) = 0.5929494160049285 absolute error = 5.329070518200751e-14 relative error = 8.987394833956593e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.913405617493846 y2[1] (numeric) = 1.913405617493822 absolute error = 2.442490654175344e-14 relative error = 1.276514833992432e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.00002356954489 y1[1] (closed_form) = 0.5838317318419293 y1[1] (numeric) = 0.5838317318418761 absolute error = 5.3179682879545e-14 relative error = 9.108734585523221e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.90928761818157 y2[1] (numeric) = 1.909287618181545 absolute error = 2.464695114667848e-14 relative error = 1.290897762703377e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.010028114396087 y1[1] (closed_form) = 0.5747557019953092 y1[1] (numeric) = 0.5747557019952563 absolute error = 5.295763827461997e-14 relative error = 9.213938737932203e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.90507860819627 y2[1] (numeric) = 1.905078608196246 absolute error = 2.420286193682841e-14 relative error = 1.270439016673632e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.020032659247285 y1[1] (closed_form) = 0.5657222348857007 y1[1] (numeric) = 0.5657222348856481 absolute error = 5.262457136723242e-14 relative error = 9.302192511111881e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.900779008818106 y2[1] (numeric) = 1.900779008818081 absolute error = 2.486899575160351e-14 relative error = 1.308358080357112e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.030037204098482 y1[1] (closed_form) = 0.5567322346735751 y1[1] (numeric) = 0.556732234673523 absolute error = 5.218048215738236e-14 relative error = 9.372635336622276e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.896389250394335 y2[1] (numeric) = 1.896389250394309 absolute error = 2.55351295663786e-14 relative error = 1.346513093821262e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.04004174894968 y1[1] (closed_form) = 0.5477866011687983 y1[1] (numeric) = 0.5477866011687463 absolute error = 5.195843755245733e-14 relative error = 9.485160360183132e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.891909772296241 y2[1] (numeric) = 1.891909772296215 absolute error = 2.597921877622866e-14 relative error = 1.373174300204458e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.050046293800877 y1[1] (closed_form) = 0.5388862297405687 y1[1] (numeric) = 0.5388862297405168 absolute error = 5.184741524999481e-14 relative error = 9.621217316121672e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.887341022875158 y2[1] (numeric) = 1.887341022875131 absolute error = 2.708944180085382e-14 relative error = 1.435323106556864e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.060050838652074 y1[1] (closed_form) = 0.5300320112277999 y1[1] (numeric) = 0.5300320112277482 absolute error = 5.162537064506978e-14 relative error = 9.740047686078712e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.882683459417595 y2[1] (numeric) = 1.882683459417567 absolute error = 2.797762022055394e-14 relative error = 1.486050141918641e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.070055383503272 y1[1] (closed_form) = 0.5212248318499559 y1[1] (numeric) = 0.5212248318499045 absolute error = 5.140332604014475e-14 relative error = 9.862025540437438e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.877937548099463 y2[1] (numeric) = 1.877937548099434 absolute error = 2.930988785010413e-14 relative error = 1.560748805505632e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.080059928354469 y1[1] (closed_form) = 0.5124655731183508 y1[1] (numeric) = 0.5124655731182993 absolute error = 5.151434834260726e-14 relative error = 1.005225541866992e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.87310376393942 y2[1] (numeric) = 1.873103763939389 absolute error = 3.042011087472929e-14 relative error = 1.624048355481984e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.090064473205667 y1[1] (closed_form) = 0.5037551117479162 y1[1] (numeric) = 0.5037551117478651 absolute error = 5.10702591327572e-14 relative error = 1.013791382792225e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.868182590751322 y2[1] (numeric) = 1.868182590751291 absolute error = 3.064215547965432e-14 relative error = 1.640212023779274e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.100069018056864 y1[1] (closed_form) = 0.4950943195694522 y1[1] (numeric) = 0.4950943195694017 absolute error = 5.045963646921336e-14 relative error = 1.019192393746195e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.863174521095801 y2[1] (numeric) = 1.86317452109577 absolute error = 3.064215547965432e-14 relative error = 1.644620787409252e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.110073562908061 y1[1] (closed_form) = 0.4864840634423654 y1[1] (numeric) = 0.4864840634423153 absolute error = 5.012656956182582e-14 relative error = 1.030384617476054e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.858080056230965 y2[1] (numeric) = 1.858080056230933 absolute error = 3.197442310920451e-14 relative error = 1.720831295830345e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.120078107759259 y1[1] (closed_form) = 0.4779252051679048 y1[1] (numeric) = 0.4779252051678549 absolute error = 4.996003610813204e-14 relative error = 1.045352610992343e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.852899706062223 y2[1] (numeric) = 1.85289970606219 absolute error = 3.286260152890463e-14 relative error = 1.773576919537871e-12 % Desired digits = 8 Estimated correct digits = 12 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] = 2.130082652610456 y1[1] (closed_form) = 0.4694186014029039 y1[1] (numeric) = 0.4694186014028541 absolute error = 4.979350265443827e-14 relative error = 1.060748391853784e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.847633989091253 y2[1] (numeric) = 1.847633989091219 absolute error = 3.308464613382966e-14 relative error = 1.790649356375076e-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] = 2.140087197461654 y1[1] (closed_form) = 0.4609651035740384 y1[1] (numeric) = 0.4609651035739888 absolute error = 4.957145804951324e-14 relative error = 1.075384181257254e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.842283432364102 y2[1] (numeric) = 1.842283432364068 absolute error = 3.352873534367973e-14 relative error = 1.819955320374028e-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] = 2.150091742312851 y1[1] (closed_form) = 0.4525655577926061 y1[1] (numeric) = 0.4525655577925568 absolute error = 4.929390229335695e-14 relative error = 1.089210202689496e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.836848571418437 y2[1] (numeric) = 1.836848571418403 absolute error = 3.463895836830488e-14 relative error = 1.88578192602759e-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] = 2.160096287164048 y1[1] (closed_form) = 0.4442208047698399 y1[1] (numeric) = 0.4442208047697911 absolute error = 4.884981308350689e-14 relative error = 1.099674138603594e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.831329950229941 y2[1] (numeric) = 1.831329950229905 absolute error = 3.574918139293004e-14 relative error = 1.952088502044178e-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] = 2.170100832015246 y1[1] (closed_form) = 0.4359316797327614 y1[1] (numeric) = 0.4359316797327126 absolute error = 4.873879078104437e-14 relative error = 1.118037367940835e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.825728121157864 y2[1] (numeric) = 1.825728121157828 absolute error = 3.641531520770513e-14 relative error = 1.994563965231077e-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] = 2.180105376866443 y1[1] (closed_form) = 0.4276990123405818 y1[1] (numeric) = 0.4276990123405333 absolute error = 4.851674617611934e-14 relative error = 1.13436657032738e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.820043644889743 y2[1] (numeric) = 1.820043644889707 absolute error = 3.597122599785507e-14 relative error = 1.976393593574191e-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] = 2.190109921717641 y1[1] (closed_form) = 0.4195236266016625 y1[1] (numeric) = 0.4195236266016143 absolute error = 4.823919041996305e-14 relative error = 1.149856345653832e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.814277090385278 y2[1] (numeric) = 1.814277090385241 absolute error = 3.663735981263017e-14 relative error = 2.019391635753384e-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] = 2.200114466568838 y1[1] (closed_form) = 0.4114063407910393 y1[1] (numeric) = 0.4114063407909914 absolute error = 4.79061235125755e-14 relative error = 1.164447864864287e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.808429034819387 y2[1] (numeric) = 1.80842903481935 absolute error = 3.730349362740526e-14 relative error = 2.062756840836216e-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] = 2.210119011420035 y1[1] (closed_form) = 0.4033479673685214 y1[1] (numeric) = 0.4033479673684738 absolute error = 4.762856775641922e-14 relative error = 1.180830736972652e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.802500063524437 y2[1] (numeric) = 1.802500063524399 absolute error = 3.796962744218035e-14 relative error = 2.106497980806623e-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] = 2.220123556271233 y1[1] (closed_form) = 0.3953493128973722 y1[1] (numeric) = 0.3953493128973248 absolute error = 4.735101200026293e-14 relative error = 1.197700627155375e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.796490769931655 y2[1] (numeric) = 1.796490769931615 absolute error = 3.930189507173054e-14 relative error = 2.187703701546195e-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] = 2.23012810112243 y1[1] (closed_form) = 0.38741117796358 y1[1] (numeric) = 0.3874111779635332 absolute error = 4.685141163918161e-14 relative error = 1.209345891500994e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.790401755511734 y2[1] (numeric) = 1.790401755511695 absolute error = 3.907985046680551e-14 relative error = 2.182741965399585e-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] = 2.240132645973627 y1[1] (closed_form) = 0.3795343570957281 y1[1] (numeric) = 0.3795343570956817 absolute error = 4.640732242933154e-14 relative error = 1.222743647886045e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.784233629714633 y2[1] (numeric) = 1.784233629714594 absolute error = 3.952393967665557e-14 relative error = 2.215177374667966e-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] = 2.250137190824825 y1[1] (closed_form) = 0.3717196386854698 y1[1] (numeric) = 0.3717196386854236 absolute error = 4.612976667317525e-14 relative error = 1.240982769603086e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.777987009908574 y2[1] (numeric) = 1.777987009908533 absolute error = 4.04121180963557e-14 relative error = 2.272914136669296e-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] = 2.260141735676022 y1[1] (closed_form) = 0.3639678049086176 y1[1] (numeric) = 0.363967804908572 absolute error = 4.557465516086268e-14 relative error = 1.252161717224006e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.77166252131825 y2[1] (numeric) = 1.771662521318208 absolute error = 4.196643033083092e-14 relative error = 2.368759841440047e-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] = 2.269984916900587 y1[1] (closed_form) = 0.3564031252845044 y1[1] (numeric) = 0.3564031252844592 absolute error = 4.518607710224387e-14 relative error = 1.267836163506518e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.765364660051956 y2[1] (numeric) = 1.765364660051914 absolute error = 4.174438572590589e-14 relative error = 2.364632456428425e-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] = 2.279989461751785 y1[1] (closed_form) = 0.3487783367818837 y1[1] (numeric) = 0.3487783367818389 absolute error = 4.479749904362507e-14 relative error = 1.28441174004566e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.758887570958591 y2[1] (numeric) = 1.758887570958548 absolute error = 4.285460875053104e-14 relative error = 2.436460946004374e-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] = 2.289994006602982 y1[1] (closed_form) = 0.3412187291094773 y1[1] (numeric) = 0.3412187291094326 absolute error = 4.463096558993129e-14 relative error = 1.30798698261407e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.752334524745387 y2[1] (numeric) = 1.752334524745344 absolute error = 4.329869796038111e-14 relative error = 2.470915076370613e-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] = 2.29999855145418 y1[1] (closed_form) = 0.3337250589090431 y1[1] (numeric) = 0.333725058908999 absolute error = 4.418687638008123e-14 relative error = 1.324050298306319e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.745706177307284 y2[1] (numeric) = 1.74570617730724 absolute error = 4.374278717023117e-14 relative error = 2.505735944504907e-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] = 2.310003096305377 y1[1] (closed_form) = 0.3262980762226524 y1[1] (numeric) = 0.3262980762226087 absolute error = 4.368727601899991e-14 relative error = 1.338876297547936e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.739003192076124 y2[1] (numeric) = 1.73900319207608 absolute error = 4.440892098500626e-14 relative error = 2.553699796950245e-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] = 2.320007641156574 y1[1] (closed_form) = 0.3189385244176174 y1[1] (numeric) = 0.3189385244175739 absolute error = 4.352074256530614e-14 relative error = 1.364549567813268e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.732226239954256 y2[1] (numeric) = 1.732226239954211 absolute error = 4.485301019485632e-14 relative error = 2.589327488541034e-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] = 2.330012186007772 y1[1] (closed_form) = 0.3116471401120878 y1[1] (numeric) = 0.3116471401120448 absolute error = 4.302114220422482e-14 relative error = 1.380443991520401e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.725375999247378 y2[1] (numeric) = 1.725375999247333 absolute error = 4.551914400963142e-14 relative error = 2.638215903634176e-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] = 2.340016730858969 y1[1] (closed_form) = 0.3044246531013228 y1[1] (numeric) = 0.3044246531012803 absolute error = 4.257705299437475e-14 relative error = 1.398607259977846e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.71845315559665 y2[1] (numeric) = 1.718453155596604 absolute error = 4.662936703425657e-14 relative error = 2.713449993233406e-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] = 2.350021275710167 y1[1] (closed_form) = 0.2972717862846456 y1[1] (numeric) = 0.2972717862846034 absolute error = 4.213296378452469e-14 relative error = 1.417321310949478e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.711458401910068 y2[1] (numeric) = 1.71145840191002 absolute error = 4.729550084903167e-14 relative error = 2.763461898708591e-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] = 2.360025820561364 y1[1] (closed_form) = 0.2901892555930883 y1[1] (numeric) = 0.2901892555930465 absolute error = 4.174438572590589e-14 relative error = 1.438522788880959e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.704392438293105 y2[1] (numeric) = 1.704392438293057 absolute error = 4.773959005888173e-14 relative error = 2.800974058925737e-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] = 2.370030365412561 y1[1] (closed_form) = 0.2831777699177345 y1[1] (numeric) = 0.2831777699176931 absolute error = 4.135580766728708e-14 relative error = 1.46041858014848e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.697255971978647 y2[1] (numeric) = 1.697255971978598 absolute error = 4.862776847858186e-14 relative error = 2.865081595317176e-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] = 2.380034910263759 y1[1] (closed_form) = 0.2762380310387662 y1[1] (numeric) = 0.2762380310387251 absolute error = 4.107825191113079e-14 relative error = 1.487059973482291e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.690049717256197 y2[1] (numeric) = 1.690049717256149 absolute error = 4.862776847858186e-14 relative error = 2.877298104432646e-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] = 2.390039455114956 y1[1] (closed_form) = 0.2693707335552227 y1[1] (numeric) = 0.2693707335551821 absolute error = 4.057865155004947e-14 relative error = 1.506423916751543e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.682774395400389 y2[1] (numeric) = 1.68277439540034 absolute error = 4.884981308350689e-14 relative error = 2.902932990722376e-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] = 2.400043999966154 y1[1] (closed_form) = 0.2625765648154779 y1[1] (numeric) = 0.2625765648154378 absolute error = 4.002354003773689e-14 relative error = 1.524261697378168e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.675430734598788 y2[1] (numeric) = 1.67543073459874 absolute error = 4.884981308350689e-14 relative error = 2.915656975530226e-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] = 2.410048544817351 y1[1] (closed_form) = 0.2558562048484437 y1[1] (numeric) = 0.2558562048484042 absolute error = 3.952393967665557e-14 relative error = 1.544771591529998e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.668019469879014 y2[1] (numeric) = 1.668019469878964 absolute error = 4.951594689828198e-14 relative error = 2.968547297704715e-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] = 2.420053089668548 y1[1] (closed_form) = 0.2492103262955061 y1[1] (numeric) = 0.2492103262954669 absolute error = 3.919087276926803e-14 relative error = 1.572602281447867e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.660541343035165 y2[1] (numeric) = 1.660541343035115 absolute error = 4.951594689828198e-14 relative error = 2.981915933979452e-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] = 2.430057634519746 y1[1] (closed_form) = 0.2426395943431998 y1[1] (numeric) = 0.2426395943431611 absolute error = 3.869127240818671e-14 relative error = 1.594598462502378e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.652997102553577 y2[1] (numeric) = 1.652997102553527 absolute error = 5.040412531798211e-14 relative error = 3.04925672526086e-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] = 2.440062179370943 y1[1] (closed_form) = 0.2361446666566301 y1[1] (numeric) = 0.236144666656592 absolute error = 3.816391647148976e-14 relative error = 1.616124429648145e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.645387503537905 y2[1] (numeric) = 1.645387503537855 absolute error = 5.040412531798211e-14 relative error = 3.063358947944079e-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] = 2.450066724222141 y1[1] (closed_form) = 0.2297261933136473 y1[1] (numeric) = 0.2297261933136097 absolute error = 3.758104938356155e-14 relative error = 1.635906155997274e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.637713307633544 y2[1] (numeric) = 1.637713307633493 absolute error = 5.129230373768223e-14 relative error = 3.131946446218866e-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] = 2.460071269073338 y1[1] (closed_form) = 0.2233848167397798 y1[1] (numeric) = 0.2233848167397427 absolute error = 3.710920459809586e-14 relative error = 1.661223226345067e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.629975282951399 y2[1] (numeric) = 1.629975282951347 absolute error = 5.218048215738236e-14 relative error = 3.201305118130324e-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] = 2.470075813924535 y1[1] (closed_form) = 0.2171211716439344 y1[1] (numeric) = 0.2171211716438978 absolute error = 3.663735981263017e-14 relative error = 1.687415351309601e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.622174203990999 y2[1] (numeric) = 1.622174203990947 absolute error = 5.240252676230739e-14 relative error = 3.230388366020284e-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] = 2.480080358775733 y1[1] (closed_form) = 0.2109358849548674 y1[1] (numeric) = 0.2109358849548312 absolute error = 3.616551502716447e-14 relative error = 1.714526432280718e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.614310851562986 y2[1] (numeric) = 1.614310851562933 absolute error = 5.373479439185758e-14 relative error = 3.328652244382251e-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] = 2.49008490362693 y1[1] (closed_form) = 0.2048295757584357 y1[1] (numeric) = 0.2048295757584002 absolute error = 3.549938121238938e-14 relative error = 1.733117938703115e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.606386012710955 y2[1] (numeric) = 1.6063860127109 absolute error = 5.484501741648273e-14 relative error = 3.414186688785073e-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] = 2.500089448478128 y1[1] (closed_form) = 0.198802855235633 y1[1] (numeric) = 0.198802855235598 absolute error = 3.505529200253932e-14 relative error = 1.7633193427222e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.598400480632683 y2[1] (numeric) = 1.598400480632628 absolute error = 5.484501741648273e-14 relative error = 3.431243801601826e-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] = 2.510093993329325 y1[1] (closed_form) = 0.1928563266014153 y1[1] (numeric) = 0.1928563266013808 absolute error = 3.444466933899548e-14 relative error = 1.786027450900473e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.590355054600737 y2[1] (numeric) = 1.590355054600682 absolute error = 5.440092820663267e-14 relative error = 3.420678171786626e-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] = 2.520098538180522 y1[1] (closed_form) = 0.1869905850443263 y1[1] (numeric) = 0.1869905850442923 absolute error = 3.397282455352979e-14 relative error = 1.816820057837484e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.582250539882474 y2[1] (numeric) = 1.58225053988242 absolute error = 5.484501741648273e-14 relative error = 3.466266310805398e-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] = 2.53010308303172 y1[1] (closed_form) = 0.1812062176669242 y1[1] (numeric) = 0.1812062176668909 absolute error = 3.338995746560158e-14 relative error = 1.842649656038612e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.574087747659446 y2[1] (numeric) = 1.574087747659392 absolute error = 5.395683899678261e-14 relative error = 3.427816465569502e-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] = 2.540107627882917 y1[1] (closed_form) = 0.1755038034270191 y1[1] (numeric) = 0.1755038034269862 absolute error = 3.286260152890463e-14 relative error = 1.872472327505432e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.565867494946201 y2[1] (numeric) = 1.565867494946147 absolute error = 5.417888360170764e-14 relative error = 3.459991587830303e-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] = 2.550112172734115 y1[1] (closed_form) = 0.1698839130797246 y1[1] (numeric) = 0.1698839130796922 absolute error = 3.24462678946702e-14 relative error = 1.909908201810935e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.557590604508514 y2[1] (numeric) = 1.557590604508459 absolute error = 5.440092820663267e-14 relative error = 3.492633304872719e-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] = 2.560116717585312 y1[1] (closed_form) = 0.164347109120331 y1[1] (numeric) = 0.1643471091202991 absolute error = 3.191891195797325e-14 relative error = 1.942164491290382e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.549257904781034 y2[1] (numeric) = 1.549257904780979 absolute error = 5.506706202140776e-14 relative error = 3.554415430217909e-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] = 2.570121262436509 y1[1] (closed_form) = 0.1588939457280052 y1[1] (numeric) = 0.1588939457279739 absolute error = 3.130828929442941e-14 relative error = 1.970389063660297e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.540870229784369 y2[1] (numeric) = 1.540870229784313 absolute error = 5.595524044110789e-14 relative error = 3.631405121568111e-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] = 2.580125807287707 y1[1] (closed_form) = 0.153524968710323 y1[1] (numeric) = 0.1535249687102922 absolute error = 3.078093335773247e-14 relative error = 2.004946401637844e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.532428419041603 y2[1] (numeric) = 1.532428419041546 absolute error = 5.662137425588298e-14 relative error = 3.694878896287672e-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] = 2.590130352138904 y1[1] (closed_form) = 0.1482407154486386 y1[1] (numeric) = 0.1482407154486085 absolute error = 3.0142555118573e-14 relative error = 2.03335197265805e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.523933317494271 y2[1] (numeric) = 1.523933317494215 absolute error = 5.639932965095795e-14 relative error = 3.700905348253203e-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] = 2.600134896990101 y1[1] (closed_form) = 0.1430417148442988 y1[1] (numeric) = 0.1430417148442692 absolute error = 2.964295475749168e-14 relative error = 2.072329375368443e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.515385775417793 y2[1] (numeric) = 1.515385775417737 absolute error = 5.639932965095795e-14 relative error = 3.72178032589811e-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] = 2.610139441841299 y1[1] (closed_form) = 0.1379284872657048 y1[1] (numeric) = 0.1379284872656757 absolute error = 2.914335439641036e-14 relative error = 2.112932213942775e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.506786648336363 y2[1] (numeric) = 1.506786648336306 absolute error = 5.662137425588298e-14 relative error = 3.757756568814731e-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] = 2.620143986692496 y1[1] (closed_form) = 0.1329015444962285 y1[1] (numeric) = 0.1329015444961999 absolute error = 2.858824288409778e-14 relative error = 2.151084322794237e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.498136796937321 y2[1] (numeric) = 1.498136796937264 absolute error = 5.706546346573305e-14 relative error = 3.809095643494867e-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] = 2.629987167917061 y1[1] (closed_form) = 0.128040378379176 y1[1] (numeric) = 0.1280403783791479 absolute error = 2.814415367424772e-14 relative error = 2.198068611676718e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.48957779592509 y2[1] (numeric) = 1.489577795925033 absolute error = 5.750955267558311e-14 relative error = 3.860795510842538e-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] = 2.639991712768259 y1[1] (closed_form) = 0.1231860943242645 y1[1] (numeric) = 0.123186094324237 absolute error = 2.750577543508825e-14 relative error = 2.23286366744321e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.48082988136519 y2[1] (numeric) = 1.480829881365132 absolute error = 5.728750807065808e-14 relative error = 3.868608325072711e-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] = 2.649996257619456 y1[1] (closed_form) = 0.1184195706458013 y1[1] (numeric) = 0.1184195706457744 absolute error = 2.695066392277568e-14 relative error = 2.275862323752753e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.472033840502635 y2[1] (numeric) = 1.472033840502578 absolute error = 5.662137425588298e-14 relative error = 3.846472322711636e-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] = 2.660000802470654 y1[1] (closed_form) = 0.1137412844255362 y1[1] (numeric) = 0.1137412844255099 absolute error = 2.632616347142402e-14 relative error = 2.314565340490695e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.463190553733884 y2[1] (numeric) = 1.463190553733827 absolute error = 5.706546346573305e-14 relative error = 3.900070521922722e-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] = 2.670005347321851 y1[1] (closed_form) = 0.1091517039135246 y1[1] (numeric) = 0.1091517039134988 absolute error = 2.577105195911145e-14 relative error = 2.361030660550069e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.454300906184242 y2[1] (numeric) = 1.454300906184184 absolute error = 5.750955267558311e-14 relative error = 3.954446595682542e-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] = 2.680009892173048 y1[1] (closed_form) = 0.1046512884812598 y1[1] (numeric) = 0.1046512884812346 absolute error = 2.518818487118324e-14 relative error = 2.406868108049501e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.445365787619269 y2[1] (numeric) = 1.445365787619211 absolute error = 5.795364188543317e-14 relative error = 4.009617660930758e-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] = 2.690014437024246 y1[1] (closed_form) = 0.1002404885756956 y1[1] (numeric) = 0.100240488575671 absolute error = 2.460531778325503e-14 relative error = 2.454628676782095e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.436386092355722 y2[1] (numeric) = 1.436386092355664 absolute error = 5.795364188543317e-14 relative error = 4.034684141948717e-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] = 2.700018981875443 y1[1] (closed_form) = 0.09591974567415962 y1[1] (numeric) = 0.09591974567413561 absolute error = 2.400857290751901e-14 relative error = 2.502985463397326e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.427362719172045 y2[1] (numeric) = 1.427362719171987 absolute error = 5.750955267558311e-14 relative error = 4.02907767613141e-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] = 2.710023526726641 y1[1] (closed_form) = 0.09168949224016698 y1[1] (numeric) = 0.0916894922401435 absolute error = 2.348121697082206e-14 relative error = 2.560949613431876e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.418296571218405 y2[1] (numeric) = 1.418296571218347 absolute error = 5.795364188543317e-14 relative error = 4.086144115517912e-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] = 2.720028071577838 y1[1] (closed_form) = 0.08755015168013403 y1[1] (numeric) = 0.08755015168011122 absolute error = 2.280120536823915e-14 relative error = 2.604359322133872e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.409188555926304 y2[1] (numeric) = 1.409188555926245 absolute error = 5.88418203051333e-14 relative error = 4.175581759990574e-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] = 2.730032616429035 y1[1] (closed_form) = 0.08350213830100051 y1[1] (numeric) = 0.0835021383009783 absolute error = 2.220446049250313e-14 relative error = 2.65914872891789e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.400039584917745 y2[1] (numeric) = 1.400039584917686 absolute error = 5.928590951498336e-14 relative error = 4.234588089769371e-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] = 2.740037161280233 y1[1] (closed_form) = 0.07954585726876084 y1[1] (numeric) = 0.07954585726873921 absolute error = 2.163547119238274e-14 relative error = 2.719874036844329e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.390850573913995 y2[1] (numeric) = 1.390850573913935 absolute error = 5.995204332975845e-14 relative error = 4.310458970516674e-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] = 2.75004170613143 y1[1] (closed_form) = 0.07568170456791123 y1[1] (numeric) = 0.07568170456789013 absolute error = 2.110811525568579e-14 relative error = 2.78906446098144e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.381622442643928 y2[1] (numeric) = 1.381622442643868 absolute error = 5.995204332975845e-14 relative error = 4.339249383864367e-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] = 2.760046250982628 y1[1] (closed_form) = 0.07191006696181546 y1[1] (numeric) = 0.07191006696179497 absolute error = 2.048361480433414e-14 relative error = 2.848504482023501e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.372356114751965 y2[1] (numeric) = 1.372356114751904 absolute error = 6.039613253960852e-14 relative error = 4.400908181949867e-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] = 2.770050795833825 y1[1] (closed_form) = 0.06823132195399406 y1[1] (numeric) = 0.06823132195397417 absolute error = 1.988686992859812e-14 relative error = 2.914624744044549e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.363052517705633 y2[1] (numeric) = 1.363052517705572 absolute error = 6.084022174945858e-14 relative error = 4.463527337293526e-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] = 2.780055340685022 y1[1] (closed_form) = 0.06464583775033961 y1[1] (numeric) = 0.06464583775032026 absolute error = 1.934563620409335e-14 relative error = 2.992557120043158e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.353712582702731 y2[1] (numeric) = 1.35371258270267 absolute error = 6.061817714453355e-14 relative error = 4.477920787550591e-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] = 2.79005988553622 y1[1] (closed_form) = 0.06115397322226301 y1[1] (numeric) = 0.06115397322224426 absolute error = 1.875583022226124e-14 relative error = 3.066984732797902e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.344337244578127 y2[1] (numeric) = 1.344337244578065 absolute error = 6.128431095930864e-14 relative error = 4.55870066878498e-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] = 2.800064430387417 y1[1] (closed_form) = 0.05775607787077397 y1[1] (numeric) = 0.05775607787075595 absolute error = 1.802030746844707e-14 relative error = 3.1200711912548e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.334927441710191 y2[1] (numeric) = 1.334927441710129 absolute error = 6.128431095930864e-14 relative error = 4.590834606021479e-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] = 2.810068975238615 y1[1] (closed_form) = 0.05445249179150002 y1[1] (numeric) = 0.05445249179148252 absolute error = 1.749989042565403e-14 relative error = 3.213790563095176e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.325484115926871 y2[1] (numeric) = 1.325484115926809 absolute error = 6.17284001691587e-14 relative error = 4.657045635435164e-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] = 2.820073520089812 y1[1] (closed_form) = 0.05124354564064515 y1[1] (numeric) = 0.05124354564062831 absolute error = 1.684069550478284e-14 relative error = 3.286403252202988e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.316008212411427 y2[1] (numeric) = 1.316008212411364 absolute error = 6.283862319378386e-14 relative error = 4.774941569600059e-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] = 2.830078064941009 y1[1] (closed_form) = 0.04812956060189555 y1[1] (numeric) = 0.04812956060187935 absolute error = 1.620231726562338e-14 relative error = 3.36639625689524e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.306500679607827 y2[1] (numeric) = 1.306500679607763 absolute error = 6.394884621840902e-14 relative error = 4.894666127353611e-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] = 2.840082609792207 y1[1] (closed_form) = 0.0451108483542717 y1[1] (numeric) = 0.04511084835425614 absolute error = 1.556393902646391e-14 relative error = 3.450154362922796e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.296962469125816 y2[1] (numeric) = 1.296962469125752 absolute error = 6.394884621840902e-14 relative error = 4.930662817214138e-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] = 2.850087154643404 y1[1] (closed_form) = 0.04218771104093244 y1[1] (numeric) = 0.04218771104091756 absolute error = 1.48769885299771e-14 relative error = 3.526379640635816e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.287394535645673 y2[1] (numeric) = 1.287394535645609 absolute error = 6.394884621840902e-14 relative error = 4.967307569496283e-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] = 2.860091699494602 y1[1] (closed_form) = 0.03936044123893367 y1[1] (numeric) = 0.03936044123891944 absolute error = 1.423861029081763e-14 relative error = 3.617492549024934e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.27779783682265 y2[1] (numeric) = 1.277797836822587 absolute error = 6.350475700855895e-14 relative error = 4.969859486260266e-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] = 2.870096244345799 y1[1] (closed_form) = 0.03662932192994406 y1[1] (numeric) = 0.03662932192993042 absolute error = 1.36349265211777e-14 relative error = 3.722407569338952e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.26817333319113 y2[1] (numeric) = 1.268173333191067 absolute error = 6.261657858885883e-14 relative error = 4.937541024561326e-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] = 2.880100789196996 y1[1] (closed_form) = 0.03399462647192153 y1[1] (numeric) = 0.03399462647190845 absolute error = 1.307981500886513e-14 relative error = 3.8476125100738e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.258521988068476 y2[1] (numeric) = 1.258521988068414 absolute error = 6.261657858885883e-14 relative error = 4.975406006609386e-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] = 2.890105334048194 y1[1] (closed_form) = 0.03145661857175253 y1[1] (numeric) = 0.03145661857174007 absolute error = 1.245531455751347e-14 relative error = 3.959521119252824e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.248844767458623 y2[1] (numeric) = 1.248844767458561 absolute error = 6.217248937900877e-14 relative error = 4.978400118177111e-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] = 2.900109878899391 y1[1] (closed_form) = 0.0290155522588581 y1[1] (numeric) = 0.02901555225884629 absolute error = 1.181346687140206e-14 relative error = 4.071425822265901e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.239142639955382 y2[1] (numeric) = 1.23914263995532 absolute error = 6.23945339839338e-14 relative error = 5.035298759970073e-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] = 2.910114423750588 y1[1] (closed_form) = 0.02667167185976771 y1[1] (numeric) = 0.02667167185975657 absolute error = 1.114386360967501e-14 relative error = 4.178164634098068e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.2294165766455 y2[1] (numeric) = 1.229416576645437 absolute error = 6.217248937900877e-14 relative error = 5.057072644054327e-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] = 2.920118968601786 y1[1] (closed_form) = 0.02442521197366476 y1[1] (numeric) = 0.02442521197365418 absolute error = 1.058181320345852e-14 relative error = 4.332332188096391e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.219667551011457 y2[1] (numeric) = 1.219667551011394 absolute error = 6.261657858885883e-14 relative error = 5.133905426682179e-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] = 2.930123513452983 y1[1] (closed_form) = 0.02227639744890519 y1[1] (numeric) = 0.02227639744889525 absolute error = 9.939965517347105e-15 relative error = 4.462106379699029e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.209896538834038 y2[1] (numeric) = 1.209896538833975 absolute error = 6.328271240363392e-14 relative error = 5.230423459564458e-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] = 2.940128058304181 y1[1] (closed_form) = 0.0202254433605128 y1[1] (numeric) = 0.02022544336050353 absolute error = 9.270362255620057e-15 relative error = 4.583514976843018e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.200104518094661 y2[1] (numeric) = 1.200104518094597 absolute error = 6.417089082333405e-14 relative error = 5.347108510616609e-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] = 2.950132603155378 y1[1] (closed_form) = 0.01827255498865232 y1[1] (numeric) = 0.0182725549886436 absolute error = 8.722189637211386e-15 relative error = 4.773382618154969e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.190292468877492 y2[1] (numeric) = 1.190292468877428 absolute error = 6.394884621840902e-14 relative error = 5.372532204519122e-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] = 2.960137148006575 y1[1] (closed_form) = 0.01641792779808249 y1[1] (numeric) = 0.0164179277980744 absolute error = 8.090750291955828e-15 relative error = 4.927997242685388e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.180461373271351 y2[1] (numeric) = 1.180461373271287 absolute error = 6.417089082333405e-14 relative error = 5.436085608248291e-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] = 2.970141692857773 y1[1] (closed_form) = 0.01466174741859239 y1[1] (numeric) = 0.01466174741858502 absolute error = 7.365635878997523e-15 relative error = 5.023709431562877e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.170612215271411 y2[1] (numeric) = 1.170612215271346 absolute error = 6.505906924303417e-14 relative error = 5.557696083664221e-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] = 2.979984874082338 y1[1] (closed_form) = 0.01303014103052547 y1[1] (numeric) = 0.01303014103051874 absolute error = 6.725522916362081e-15 relative error = 5.161511990243487e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.160905243810684 y2[1] (numeric) = 1.160905243810618 absolute error = 6.52811138479592e-14 relative error = 5.623293907577957e-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] = 2.989989418933535 y1[1] (closed_form) = 0.01146977710348507 y1[1] (numeric) = 0.01146977710347894 absolute error = 6.127043317150083e-15 relative error = 5.341902690757951e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.151023171798789 y2[1] (numeric) = 1.151023171798724 absolute error = 6.52811138479592e-14 relative error = 5.671572514560206e-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] = 2.999993963784733 y1[1] (closed_form) = 0.01000835524833732 y1[1] (numeric) = 0.01000835524833188 absolute error = 5.443562267615221e-15 relative error = 5.439017833144518e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.141125983865119 y2[1] (numeric) = 1.141125983865053 absolute error = 6.59472476627343e-14 relative error = 5.779138201670226e-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] = 3.00999850863593 y1[1] (closed_form) = 0.00864602173891682 y1[1] (numeric) = 0.008646021738912072 absolute error = 4.747938153748521e-15 relative error = 5.491471450247991e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.131214670620034 y2[1] (numeric) = 1.131214670619967 absolute error = 6.705747068735946e-14 relative error = 5.927917346634514e-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] = 3.020003053487128 y1[1] (closed_form) = 0.007382912931297447 y1[1] (numeric) = 0.007382912931293333 absolute error = 4.113896723278998e-15 relative error = 5.572186427716731e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.121290224087697 y2[1] (numeric) = 1.121290224087631 absolute error = 6.639133687258436e-14 relative error = 5.920977053608186e-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] = 3.030007598338325 y1[1] (closed_form) = 0.00621915525014427 y1[1] (numeric) = 0.006219155250140843 absolute error = 3.427813588530171e-15 relative error = 5.511702877091954e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.111353637606785 y2[1] (numeric) = 1.111353637606719 absolute error = 6.639133687258436e-14 relative error = 5.97391636883045e-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] = 3.040012143189522 y1[1] (closed_form) = 0.005154865176060119 y1[1] (numeric) = 0.005154865176057302 absolute error = 2.817190924986335e-15 relative error = 5.465110781305677e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.101405905731061 y2[1] (numeric) = 1.101405905730995 absolute error = 6.616929226765933e-14 relative error = 6.007711773048764e-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] = 3.05001668804072 y1[1] (closed_form) = 0.004190149233926577 y1[1] (numeric) = 0.004190149233924388 absolute error = 2.188353664944742e-15 relative error = 5.222615097396048e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.091448024129833 y2[1] (numeric) = 1.091448024129766 absolute error = 6.661338147750939e-14 relative error = 6.103211513953451e-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] = 3.060021232891917 y1[1] (closed_form) = 0.003325103982242172 y1[1] (numeric) = 0.003325103982240658 absolute error = 1.514413594527753e-15 relative error = 4.554484920217618e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.081480989488294 y2[1] (numeric) = 1.081480989488228 absolute error = 6.683542608243442e-14 relative error = 6.17999083960392e-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] = 3.070025777743115 y1[1] (closed_form) = 0.002559816003457782 y1[1] (numeric) = 0.002559816003457002 absolute error = 7.797582024515748e-16 relative error = 3.046149416201331e-11 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.071505799407769 y2[1] (numeric) = 1.071505799407703 absolute error = 6.59472476627343e-14 relative error = 6.154632825989739e-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] = 3.080030322594312 y1[1] (closed_form) = 0.001894361895310781 y1[1] (numeric) = 0.001894361895310605 absolute error = 1.758575923771488e-16 relative error = 9.283209972310933e-12 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.061523452305857 y2[1] (numeric) = 1.061523452305791 absolute error = 6.572520305780927e-14 relative error = 6.191592179620713e-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] = 3.090034867445509 y1[1] (closed_form) = 0.001328808263157732 y1[1] (numeric) = 0.001328808263158278 absolute error = 5.457873736292029e-16 relative error = 4.107344819878026e-11 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.051534947316508 y2[1] (numeric) = 1.051534947316442 absolute error = 6.59472476627343e-14 relative error = 6.271522200097113e-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] = 3.100039412296707 y1[1] (closed_form) = 0.0008632117133087203 y1[1] (numeric) = 0.0008632117133099119 absolute error = 1.191646607778818e-15 relative error = 1.380480117920545e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.041541284190014 y2[1] (numeric) = 1.041541284189949 absolute error = 6.52811138479592e-14 relative error = 6.2677413597414e-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] = 3.110043957147904 y1[1] (closed_form) = 0.0004976188473608811 y1[1] (numeric) = 0.0004976188473627391 absolute error = 1.857997262988409e-15 relative error = 3.733775906684981e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.031543463192944 y2[1] (numeric) = 1.031543463192878 absolute error = 6.52811138479592e-14 relative error = 6.32848892725219e-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] = 3.120048501999102 y1[1] (closed_form) = 0.00023206625753458 y1[1] (numeric) = 0.0002320662575370009 absolute error = 2.420887925888571e-15 relative error = 1.043188247876939e-09 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.02154248500803 y2[1] (numeric) = 1.021542485007966 absolute error = 6.417089082333405e-14 relative error = 6.281764269728795e-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] = 3.130053046850299 y1[1] (closed_form) = 6.658052301034001e-05 y1[1] (numeric) = 6.658052301340447e-05 absolute error = 3.06445678294881e-15 relative error = 4.602632488292255e-09 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.011539350634007 y2[1] (numeric) = 1.011539350633943 absolute error = 6.417089082333405e-14 relative error = 6.343884771572493e-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] = 3.140057591701496 y1[1] (closed_form) = 1.178207269081355e-06 y1[1] (numeric) = 1.178207272832223e-06 absolute error = 3.750868142964698e-15 relative error = 3.183538449808785e-07 % Desired digits = 8 Estimated correct digits = 5 Correct digits = 9 h = 0.0001613636266322163 y2[1] (closed_form) = 1.001535061285423 y2[1] (numeric) = 1.00153506128536 absolute error = 6.372680161348399e-14 relative error = 6.362912700399488e-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] = 3.150062136552694 y1[1] (closed_form) = 3.586585643411411e-05 y1[1] (numeric) = 3.586585643848712e-05 absolute error = 4.373014266239456e-15 relative error = 1.219269439243064e-08 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9915306182924283 y2[1] (numeric) = 0.9915306182923644 absolute error = 6.38378239159465e-14 relative error = 6.438310904194293e-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] = 3.160066681403891 y1[1] (closed_form) = 0.0001706399986156626 y1[1] (numeric) = 0.0001706399986206882 absolute error = 5.025575225067747e-15 relative error = 2.945133184387205e-09 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9815270230005501 y2[1] (numeric) = 0.9815270230004864 absolute error = 6.361577931102147e-14 relative error = 6.481306965604126e-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] = 3.170071226255089 y1[1] (closed_form) = 0.0004054871442586983 y1[1] (numeric) = 0.0004054871442643804 absolute error = 5.682140955670656e-15 relative error = 1.401312232983023e-09 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9715252766704698 y2[1] (numeric) = 0.9715252766704063 absolute error = 6.350475700855895e-14 relative error = 6.536603682221954e-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] = 3.180075771106286 y1[1] (closed_form) = 0.0007403837874929708 y1[1] (numeric) = 0.0007403837874993058 absolute error = 6.334993293832802e-15 relative error = 8.556364146335317e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9615263803778065 y2[1] (numeric) = 0.9615263803777427 absolute error = 6.372680161348399e-14 relative error = 6.627670640554263e-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] = 3.190080315957483 y1[1] (closed_form) = 0.001175296408485793 y1[1] (numeric) = 0.001175296408492704 absolute error = 6.911138328291599e-15 relative error = 5.880336465245943e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9515313349129179 y2[1] (numeric) = 0.951531334912854 absolute error = 6.38378239159465e-14 relative error = 6.7089565601945e-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] = 3.200084860808681 y1[1] (closed_form) = 0.001710181476796691 y1[1] (numeric) = 0.001710181476804312 absolute error = 7.621507591704102e-15 relative error = 4.456549024247303e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9415411406807326 y2[1] (numeric) = 0.9415411406806687 absolute error = 6.38378239159465e-14 relative error = 6.78014174397009e-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] = 3.210089405659878 y1[1] (closed_form) = 0.002344985455735138 y1[1] (numeric) = 0.002344985455743337 absolute error = 8.199170509204379e-15 relative error = 3.49646966430075e-10 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9315567976006189 y2[1] (numeric) = 0.931556797600555 absolute error = 6.394884621840902e-14 relative error = 6.864728633092476e-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] = 3.220093950511075 y1[1] (closed_form) = 0.003079644807718052 y1[1] (numeric) = 0.003079644807726945 absolute error = 8.893059899595102e-15 relative error = 2.887690124948098e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9215793050063029 y2[1] (numeric) = 0.9215793050062393 absolute error = 6.361577931102147e-14 relative error = 6.902908839797177e-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] = 3.230098495362273 y1[1] (closed_form) = 0.003914086000630257 y1[1] (numeric) = 0.003914086000639739 absolute error = 9.481998519689228e-15 relative error = 2.422531982731706e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9116096615458446 y2[1] (numeric) = 0.9116096615457807 absolute error = 6.38378239159465e-14 relative error = 7.002758593814675e-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] = 3.24010304021347 y1[1] (closed_form) = 0.004848225515183491 y1[1] (numeric) = 0.004848225515193606 absolute error = 1.011517258842076e-14 relative error = 2.086365940846284e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9016488650816836 y2[1] (numeric) = 0.9016488650816196 absolute error = 6.405986852087153e-14 relative error = 7.104746759157526e-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] = 3.250107585064668 y1[1] (closed_form) = 0.005881969853276381 y1[1] (numeric) = 0.005881969853287159 absolute error = 1.07778369562439e-14 relative error = 1.832351614355932e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8916979125907636 y2[1] (numeric) = 0.8916979125906991 absolute error = 6.450395773072159e-14 relative error = 7.233835228268061e-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] = 3.260112129915865 y1[1] (closed_form) = 0.007015215547352516 y1[1] (numeric) = 0.007015215547363962 absolute error = 1.144657285623296e-14 relative error = 1.631677997485452e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8817578000647432 y2[1] (numeric) = 0.881757800064679 absolute error = 6.428191312579656e-14 relative error = 7.290200678811875e-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] = 3.270116674767062 y1[1] (closed_form) = 0.008247849170756605 y1[1] (numeric) = 0.008247849170768626 absolute error = 1.202163368851927e-14 relative error = 1.457547712092374e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8718295224103088 y2[1] (numeric) = 0.8718295224102446 absolute error = 6.417089082333405e-14 relative error = 7.360486101218917e-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] = 3.28012121961826 y1[1] (closed_form) = 0.009579747349086953 y1[1] (numeric) = 0.009579747349099684 absolute error = 1.273113559019379e-14 relative error = 1.328963606895874e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8619140733495929 y2[1] (numeric) = 0.8619140733495292 absolute error = 6.372680161348399e-14 relative error = 7.393637438338514e-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] = 3.290125764469457 y1[1] (closed_form) = 0.01101077677254481 y1[1] (numeric) = 0.01101077677255813 absolute error = 1.332441101897786e-14 relative error = 1.210124525655816e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8520124453207137 y2[1] (numeric) = 0.8520124453206501 absolute error = 6.361577931102147e-14 relative error = 7.466531699202502e-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] = 3.300130309320655 y1[1] (closed_form) = 0.01254079420927645 y1[1] (numeric) = 0.01254079420929044 absolute error = 1.399227955722893e-14 relative error = 1.11574110249563e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8421256293784406 y2[1] (numeric) = 0.8421256293783772 absolute error = 6.339373470609644e-14 relative error = 7.527823936778451e-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] = 3.310134854171852 y1[1] (closed_form) = 0.01416964651970998 y1[1] (numeric) = 0.01416964651972466 absolute error = 1.467923005371574e-14 relative error = 1.035963037842683e-10 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8322546150950003 y2[1] (numeric) = 0.8322546150949369 absolute error = 6.339373470609644e-14 relative error = 7.617108221005198e-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] = 3.320139399023049 y1[1] (closed_form) = 0.01589717067188279 y1[1] (numeric) = 0.01589717067189808 absolute error = 1.529332216421153e-14 relative error = 9.620153472504841e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8224003904610299 y2[1] (numeric) = 0.8224003904609666 absolute error = 6.328271240363392e-14 relative error = 7.69487869140702e-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] = 3.330143943874247 y1[1] (closed_form) = 0.01772319375775933 y1[1] (numeric) = 0.01772319375777525 absolute error = 1.592129206251514e-14 relative error = 8.98330869713857e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8125639417866894 y2[1] (numeric) = 0.8125639417866264 absolute error = 6.306066779870889e-14 relative error = 7.760702211329885e-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] = 3.339987125098812 y1[1] (closed_form) = 0.01961571619410696 y1[1] (numeric) = 0.01961571619412348 absolute error = 1.651803693825116e-14 relative error = 8.420817662122162e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8029044493997743 y2[1] (numeric) = 0.8029044493997116 absolute error = 6.272760089132134e-14 relative error = 7.812586035388706e-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] = 3.349991669950009 y1[1] (closed_form) = 0.02163659794824291 y1[1] (numeric) = 0.02163659794826003 absolute error = 1.712519015484304e-14 relative error = 7.914918138151088e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7931061781354701 y2[1] (numeric) = 0.7931061781354077 absolute error = 6.23945339839338e-14 relative error = 7.867109815058863e-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] = 3.359996214801207 y1[1] (closed_form) = 0.02375540417633104 y1[1] (numeric) = 0.02375540417634881 absolute error = 1.776703784095446e-14 relative error = 7.479156199184707e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.783328614890934 y2[1] (numeric) = 0.7833286148908717 absolute error = 6.228351168147128e-14 relative error = 7.951134491639026e-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] = 3.370000759652404 y1[1] (closed_form) = 0.02597192280688054 y1[1] (numeric) = 0.02597192280689893 absolute error = 1.839153829230611e-14 relative error = 7.081315630367491e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.773572738303281 y2[1] (numeric) = 0.7735727383032185 absolute error = 6.250555628639631e-14 relative error = 8.080113632687359e-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] = 3.380005304503602 y1[1] (closed_form) = 0.02828593198835805 y1[1] (numeric) = 0.02828593198837707 absolute error = 1.901950819060971e-14 relative error = 6.7240168004497e-11 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.763839524839007 y2[1] (numeric) = 0.7638395248389447 absolute error = 6.228351168147128e-14 relative error = 8.154004821182652e-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] = 3.390009849354799 y1[1] (closed_form) = 0.03069720011139287 y1[1] (numeric) = 0.03069720011141257 absolute error = 1.969605034624067e-14 relative error = 6.416236749530368e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7541299486962536 y2[1] (numeric) = 0.7541299486961917 absolute error = 6.195044477408373e-14 relative error = 8.214823570020552e-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] = 3.400014394205996 y1[1] (closed_form) = 0.03320548583195893 y1[1] (numeric) = 0.03320548583197925 absolute error = 2.032402024454427e-14 relative error = 6.120681488413348e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7444449817073014 y2[1] (numeric) = 0.7444449817072395 absolute error = 6.195044477408373e-14 relative error = 8.321695531079718e-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] = 3.410018939057194 y1[1] (closed_form) = 0.0358105380955307 y1[1] (numeric) = 0.03581053809555158 absolute error = 2.087913175685685e-14 relative error = 5.830443458056458e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7347855932412986 y2[1] (numeric) = 0.7347855932412367 absolute error = 6.183942247162122e-14 relative error = 8.415981891919535e-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] = 3.420023483908391 y1[1] (closed_form) = 0.03851209616221118 y1[1] (numeric) = 0.03851209616223273 absolute error = 2.154526557163194e-14 relative error = 5.594415188642101e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7251527501072368 y2[1] (numeric) = 0.7251527501071751 absolute error = 6.17284001691587e-14 relative error = 8.512468601964236e-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] = 3.430028028759589 y1[1] (closed_form) = 0.04130988963282989 y1[1] (numeric) = 0.04130988963285203 absolute error = 2.214201044736797e-14 relative error = 5.359978117630026e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7155474164571831 y2[1] (numeric) = 0.7155474164571217 absolute error = 6.139533326177116e-14 relative error = 8.580190753221023e-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] = 3.440032573610786 y1[1] (closed_form) = 0.0442036384760065 y1[1] (numeric) = 0.04420363847602923 absolute error = 2.272487753529617e-14 relative error = 5.140951812740735e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7059705536897785 y2[1] (numeric) = 0.7059705536897173 absolute error = 6.117328865684613e-14 relative error = 8.665133175473383e-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] = 3.450037118461983 y1[1] (closed_form) = 0.0471930530561796 y1[1] (numeric) = 0.04719305305620293 absolute error = 2.33285613049361e-14 relative error = 4.943219349925357e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6964231203540102 y2[1] (numeric) = 0.6964231203539492 absolute error = 6.106226635438361e-14 relative error = 8.767983797456932e-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] = 3.460041663313181 y1[1] (closed_form) = 0.05027783416259624 y1[1] (numeric) = 0.05027783416262018 absolute error = 2.394612286238385e-14 relative error = 4.762759426936166e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.686906072053272 y2[1] (numeric) = 0.6869060720532115 absolute error = 6.050715484207103e-14 relative error = 8.808650455105961e-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] = 3.470046208164378 y1[1] (closed_form) = 0.05345767303925997 y1[1] (numeric) = 0.05345767303928455 absolute error = 2.45775622076394e-14 relative error = 4.597574269570121e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6774203613497165 y2[1] (numeric) = 0.6774203613496563 absolute error = 6.017408793468348e-14 relative error = 8.882828354138999e-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] = 3.480050753015576 y1[1] (closed_form) = 0.05673225141583416 y1[1] (numeric) = 0.05673225141585939 absolute error = 2.523675712851059e-14 relative error = 4.448396899240091e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6679669376689139 y2[1] (numeric) = 0.6679669376688535 absolute error = 6.039613253960852e-14 relative error = 9.041784725211147e-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] = 3.490055297866773 y1[1] (closed_form) = 0.06010124153949803 y1[1] (numeric) = 0.06010124153952381 absolute error = 2.577799085301535e-14 relative error = 4.289094566553051e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6585467472048232 y2[1] (numeric) = 0.658546747204763 absolute error = 6.017408793468348e-14 relative error = 9.137405687612933e-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] = 3.50005984271797 y1[1] (closed_form) = 0.06356430620775089 y1[1] (numeric) = 0.06356430620777728 absolute error = 2.63955524104631e-14 relative error = 4.152574610693144e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6491607328250885 y2[1] (numeric) = 0.6491607328250285 absolute error = 5.995204332975845e-14 relative error = 9.235315738962308e-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] = 3.510064387569168 y1[1] (closed_form) = 0.06712109880216321 y1[1] (numeric) = 0.06712109880219023 absolute error = 2.702005286181475e-14 relative error = 4.025567719243584e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6398098339766664 y2[1] (numeric) = 0.6398098339766073 absolute error = 5.906386491005833e-14 relative error = 9.231471880160624e-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] = 3.520068932420365 y1[1] (closed_form) = 0.07077126332306971 y1[1] (numeric) = 0.07077126332309731 absolute error = 2.760291994974295e-14 relative error = 3.900300581570242e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6304949865917971 y2[1] (numeric) = 0.6304949865917383 absolute error = 5.88418203051333e-14 relative error = 9.332638887932886e-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] = 3.530073477271563 y1[1] (closed_form) = 0.07451443442520111 y1[1] (numeric) = 0.07451443442522931 absolute error = 2.819966482547898e-14 relative error = 3.784456668430637e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6212171229943273 y2[1] (numeric) = 0.6212171229942687 absolute error = 5.861977570020827e-14 relative error = 9.436278159503268e-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] = 3.54007802212276 y1[1] (closed_form) = 0.07835023745425174 y1[1] (numeric) = 0.07835023745428044 absolute error = 2.86992651865603e-14 relative error = 3.662945527550907e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6119771718063927 y2[1] (numeric) = 0.6119771718063345 absolute error = 5.81756864903582e-14 relative error = 9.506185715823217e-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] = 3.550082566973957 y1[1] (closed_form) = 0.08227828848437857 y1[1] (numeric) = 0.08227828848440792 absolute error = 2.935152121352758e-14 relative error = 3.56734707955189e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6027760578554729 y2[1] (numeric) = 0.6027760578554148 absolute error = 5.81756864903582e-14 relative error = 9.651293499833555e-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] = 3.560087111825155 y1[1] (closed_form) = 0.08629819435662878 y1[1] (numeric) = 0.08629819435665873 absolute error = 2.99482660892636e-14 relative error = 3.470323604396851e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5936147020818259 y2[1] (numeric) = 0.5936147020817681 absolute error = 5.773159728050814e-14 relative error = 9.72543252012485e-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] = 3.570091656676352 y1[1] (closed_form) = 0.09040955271829065 y1[1] (numeric) = 0.09040955271832114 absolute error = 3.048949981376836e-14 relative error = 3.372375915714498e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5844940214463096 y2[1] (numeric) = 0.584494021446252 absolute error = 5.762057497804562e-14 relative error = 9.858197494555302e-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] = 3.580096201527549 y1[1] (closed_form) = 0.09461195206316508 y1[1] (numeric) = 0.09461195206319616 absolute error = 3.107236690169657e-14 relative error = 3.284190445722117e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5754149288386043 y2[1] (numeric) = 0.5754149288385465 absolute error = 5.784261958297066e-14 relative error = 1.005233209706915e-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] = 3.590100746378747 y1[1] (closed_form) = 0.09890497177275359 y1[1] (numeric) = 0.09890497177278537 absolute error = 3.178013407989511e-14 relative error = 3.213198842310364e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5663783329858414 y2[1] (numeric) = 0.5663783329857839 absolute error = 5.750955267558311e-14 relative error = 1.015391114494148e-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] = 3.600105291229944 y1[1] (closed_form) = 0.1032881821583578 y1[1] (numeric) = 0.1032881821583903 absolute error = 3.247402347028583e-14 relative error = 3.144021202783665e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5573851383616479 y2[1] (numeric) = 0.5573851383615906 absolute error = 5.728750807065808e-14 relative error = 1.027790375592832e-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] = 3.610109836081142 y1[1] (closed_form) = 0.1077611445040872 y1[1] (numeric) = 0.1077611445041203 absolute error = 3.302913498259841e-14 relative error = 3.065031940278405e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5484362450956192 y2[1] (numeric) = 0.5484362450955621 absolute error = 5.706546346573305e-14 relative error = 1.040512256001311e-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] = 3.620114380932339 y1[1] (closed_form) = 0.1123234111107702 y1[1] (numeric) = 0.1123234111108038 absolute error = 3.363975764614224e-14 relative error = 2.994901714030717e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5395325488832232 y2[1] (numeric) = 0.5395325488831664 absolute error = 5.684341886080801e-14 relative error = 1.053567926132872e-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] = 3.630118925783536 y1[1] (closed_form) = 0.116974525340764 y1[1] (numeric) = 0.1169745253407982 absolute error = 3.422262473407045e-14 relative error = 2.925647668530811e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5306749408961514 y2[1] (numeric) = 0.5306749408960953 absolute error = 5.606626274357041e-14 relative error = 1.056508578469736e-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] = 3.640123470634734 y1[1] (closed_form) = 0.1217140216636602 y1[1] (numeric) = 0.121714021663695 absolute error = 3.483324739761429e-14 relative error = 2.861892731954181e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5218643076931211 y2[1] (numeric) = 0.5218643076930655 absolute error = 5.562217353372034e-14 relative error = 1.065835940756243e-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] = 3.650128015485931 y1[1] (closed_form) = 0.1265414257028792 y1[1] (numeric) = 0.1265414257029146 absolute error = 3.541611448554249e-14 relative error = 2.798776312881124e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5131015311311391 y2[1] (numeric) = 0.5131015311310833 absolute error = 5.584421813864537e-14 relative error = 1.088365844778051e-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] = 3.660132560337129 y1[1] (closed_form) = 0.131456254283151 y1[1] (numeric) = 0.1314562542831869 absolute error = 3.588795927100819e-14 relative error = 2.730030569234621e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5043874882772375 y2[1] (numeric) = 0.5043874882771822 absolute error = 5.52891066263328e-14 relative error = 1.096163325049471e-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] = 3.670137105188326 y1[1] (closed_form) = 0.1364580154788756 y1[1] (numeric) = 0.1364580154789121 absolute error = 3.647082635893639e-14 relative error = 2.672677470132362e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4957230513206873 y2[1] (numeric) = 0.4957230513206327 absolute error = 5.456746166032644e-14 relative error = 1.100765064584949e-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] = 3.680141650039523 y1[1] (closed_form) = 0.1415462086633609 y1[1] (numeric) = 0.1415462086633979 absolute error = 3.702593787124897e-14 relative error = 2.615819824556919e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4871090874857013 y2[1] (numeric) = 0.4871090874856471 absolute error = 5.417888360170764e-14 relative error = 1.112253599729815e-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] = 3.689984831264089 y1[1] (closed_form) = 0.1466361920337316 y1[1] (numeric) = 0.1466361920337692 absolute error = 3.760880495917718e-14 relative error = 2.564769613665759e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4786841540358574 y2[1] (numeric) = 0.4786841540358038 absolute error = 5.362377208939506e-14 relative error = 1.120232864139852e-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] = 3.699989376115286 y1[1] (closed_form) = 0.1518943394193748 y1[1] (numeric) = 0.151894339419413 absolute error = 3.821942762272101e-14 relative error = 2.516185117155587e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.47017286923837 y2[1] (numeric) = 0.4701728692383169 absolute error = 5.312417172831374e-14 relative error = 1.129885946298204e-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] = 3.709993920966483 y1[1] (closed_form) = 0.1572373737708369 y1[1] (numeric) = 0.1572373737708757 absolute error = 3.877453913503359e-14 relative error = 2.465987456108554e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4617146148822876 y2[1] (numeric) = 0.4617146148822348 absolute error = 5.279110482092619e-14 relative error = 1.143370885809735e-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] = 3.719998465817681 y1[1] (closed_form) = 0.1626647603033669 y1[1] (numeric) = 0.1626647603034063 absolute error = 3.941291737419306e-14 relative error = 2.422953644089148e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4533102375549896 y2[1] (numeric) = 0.453310237554937 absolute error = 5.256906021600116e-14 relative error = 1.159670703656327e-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] = 3.730003010668878 y1[1] (closed_form) = 0.1681759557893971 y1[1] (numeric) = 0.1681759557894371 absolute error = 3.996802888650564e-14 relative error = 2.376560234125065e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4449605784512987 y2[1] (numeric) = 0.4449605784512466 absolute error = 5.206945985491984e-14 relative error = 1.170203887188152e-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] = 3.740007555520076 y1[1] (closed_form) = 0.1737704086129149 y1[1] (numeric) = 0.1737704086129556 absolute error = 4.063416270128073e-14 relative error = 2.338382180581506e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4366664732892862 y2[1] (numeric) = 0.4366664732892347 absolute error = 5.151434834260726e-14 relative error = 1.179718423412819e-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] = 3.750012100371273 y1[1] (closed_form) = 0.1794475588246739 y1[1] (numeric) = 0.1794475588247151 absolute error = 4.116151863797768e-14 relative error = 2.293790949711042e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4284287522266249 y2[1] (numeric) = 0.4284287522265738 absolute error = 5.10702591327572e-14 relative error = 1.192036222296833e-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] = 3.76001664522247 y1[1] (closed_form) = 0.1852068381982389 y1[1] (numeric) = 0.1852068381982807 absolute error = 4.182765245275277e-14 relative error = 2.258429162749483e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4202482397774981 y2[1] (numeric) = 0.4202482397774476 absolute error = 5.051514762044462e-14 relative error = 1.202031152996382e-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] = 3.770021190073668 y1[1] (closed_form) = 0.1910476702868606 y1[1] (numeric) = 0.1910476702869029 absolute error = 4.224398608698721e-14 relative error = 2.211175149299507e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4121257547300747 y2[1] (numeric) = 0.4121257547300246 absolute error = 5.018208071305708e-14 relative error = 1.217640007621563e-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] = 3.780025734924865 y1[1] (closed_form) = 0.1969694704811712 y1[1] (numeric) = 0.196969470481214 absolute error = 4.279909759929978e-14 relative error = 2.172879761251684e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4040621100645558 y2[1] (numeric) = 0.4040621100645062 absolute error = 4.968248035197576e-14 relative error = 1.229575332961513e-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] = 3.790030279776063 y1[1] (closed_form) = 0.2029716460676989 y1[1] (numeric) = 0.2029716460677422 absolute error = 4.324318680914985e-14 relative error = 2.13050382390487e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.396058112871804 y2[1] (numeric) = 0.3960581128717547 absolute error = 4.929390229335695e-14 relative error = 1.24461286592335e-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] = 3.80003482462726 y1[1] (closed_form) = 0.209053596288192 y1[1] (numeric) = 0.2090535962882358 absolute error = 4.382605389707805e-14 relative error = 2.096402773031535e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3881145642725612 y2[1] (numeric) = 0.3881145642725122 absolute error = 4.89608353859694e-14 relative error = 1.261504717756113e-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] = 3.810039369478457 y1[1] (closed_form) = 0.2152147123997492 y1[1] (numeric) = 0.2152147123997935 absolute error = 4.427014310692812e-14 relative error = 2.057022153053311e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3802322593372647 y2[1] (numeric) = 0.3802322593372162 absolute error = 4.851674617611934e-14 relative error = 1.275976590221009e-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] = 3.820043914329655 y1[1] (closed_form) = 0.2214543777357484 y1[1] (numeric) = 0.2214543777357932 absolute error = 4.48252546192407e-14 relative error = 2.02413043614467e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3724119870064684 y2[1] (numeric) = 0.3724119870064202 absolute error = 4.818367926873179e-14 relative error = 1.293827292081629e-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] = 3.830048459180852 y1[1] (closed_form) = 0.2277719677675694 y1[1] (numeric) = 0.2277719677676146 absolute error = 4.52138326778595e-14 relative error = 1.985048165540638e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3646545300118776 y2[1] (numeric) = 0.3646545300118296 absolute error = 4.807265696626928e-14 relative error = 1.318306863340034e-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] = 3.84005300403205 y1[1] (closed_form) = 0.2341668501671026 y1[1] (numeric) = 0.2341668501671482 absolute error = 4.563016631209393e-14 relative error = 1.948617674941266e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3569606647980056 y2[1] (numeric) = 0.3569606647979578 absolute error = 4.779510121011299e-14 relative error = 1.338945881814708e-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] = 3.850057548883247 y1[1] (closed_form) = 0.2406383848700389 y1[1] (numeric) = 0.240638384870085 absolute error = 4.612976667317525e-14 relative error = 1.916974579848866e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.349331161444459 y2[1] (numeric) = 0.3493311614444114 absolute error = 4.757305660518796e-14 relative error = 1.361832606300475e-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] = 3.860062093734444 y1[1] (closed_form) = 0.2471859241399338 y1[1] (numeric) = 0.2471859241399804 absolute error = 4.657385588302532e-14 relative error = 1.884162945162667e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3417667835888601 y2[1] (numeric) = 0.3417667835888131 absolute error = 4.707345624410664e-14 relative error = 1.377356094989478e-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] = 3.870066638585642 y1[1] (closed_form) = 0.2538088126330394 y1[1] (numeric) = 0.2538088126330864 absolute error = 4.696243394164412e-14 relative error = 1.850307459951878e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3342682883504154 y2[1] (numeric) = 0.3342682883503688 absolute error = 4.662936703425657e-14 relative error = 1.394968313158523e-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] = 3.880071183436839 y1[1] (closed_form) = 0.260506387463898 y1[1] (numeric) = 0.2605063874639457 absolute error = 4.768407890765047e-14 relative error = 1.830437993166625e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3268364262541344 y2[1] (numeric) = 0.3268364262540884 absolute error = 4.6074255521944e-14 relative error = 1.409703809639583e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 3.890075728288036 y1[1] (closed_form) = 0.2672779782716898 y1[1] (numeric) = 0.2672779782717378 absolute error = 4.807265696626928e-14 relative error = 1.798601488873996e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3194719411557099 y2[1] (numeric) = 0.3194719411556642 absolute error = 4.568567746332519e-14 relative error = 1.430037245150681e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 3.900080273139234 y1[1] (closed_form) = 0.27412290728733 y1[1] (numeric) = 0.2741229072873784 absolute error = 4.835021272242557e-14 relative error = 1.763815114938419e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3121755701670652 y2[1] (numeric) = 0.3121755701670201 absolute error = 4.513056595101261e-14 relative error = 1.445678978879108e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 3.910084817990431 y1[1] (closed_form) = 0.2810404894013064 y1[1] (numeric) = 0.2810404894013552 absolute error = 4.873879078104437e-14 relative error = 1.734226654845051e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3049480435825771 y2[1] (numeric) = 0.3049480435825325 absolute error = 4.463096558993129e-14 relative error = 1.463559663003565e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 3.920089362841629 y1[1] (closed_form) = 0.2880300322322524 y1[1] (numeric) = 0.2880300322323015 absolute error = 4.907185768843192e-14 relative error = 1.703706287435434e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2977900848059802 y2[1] (numeric) = 0.2977900848059361 absolute error = 4.418687638008123e-14 relative error = 1.483826313722648e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 3.930093907692826 y1[1] (closed_form) = 0.2950908361962469 y1[1] (numeric) = 0.2950908361962964 absolute error = 4.951594689828198e-14 relative error = 1.677989988999589e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2907024102779613 y2[1] (numeric) = 0.2907024102779178 absolute error = 4.352074256530614e-14 relative error = 1.49708915463387e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 3.940098452544023 y1[1] (closed_form) = 0.3022221945768363 y1[1] (numeric) = 0.3022221945768861 absolute error = 4.979350265443827e-14 relative error = 1.647579282658504e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2836857294044509 y2[1] (numeric) = 0.2836857294044078 absolute error = 4.313216450668733e-14 relative error = 1.520420663994479e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 3.950102997395221 y1[1] (closed_form) = 0.3094233935957696 y1[1] (numeric) = 0.3094233935958196 absolute error = 4.990452495690079e-14 relative error = 1.612823270308256e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.276740744485619 y2[1] (numeric) = 0.2767407444855764 absolute error = 4.263256414560601e-14 relative error = 1.540523576492056e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 3.960107542246418 y1[1] (closed_form) = 0.3166937124844406 y1[1] (numeric) = 0.3166937124844909 absolute error = 5.034861416675085e-14 relative error = 1.589820453704919e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2698681506455813 y2[1] (numeric) = 0.2698681506455394 absolute error = 4.191091917959966e-14 relative error = 1.553014651019023e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 3.970112087097616 y1[1] (closed_form) = 0.3240324235560292 y1[1] (numeric) = 0.3240324235560801 absolute error = 5.084821452783217e-14 relative error = 1.569232299959633e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2630686357628246 y2[1] (numeric) = 0.2630686357627834 absolute error = 4.118927421359331e-14 relative error = 1.565723488630869e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 3.980116631948813 y1[1] (closed_form) = 0.3314387922783367 y1[1] (numeric) = 0.3314387922783882 absolute error = 5.145883719137601e-14 relative error = 1.552589449099903e-11 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2563428804013567 y2[1] (numeric) = 0.2563428804013158 absolute error = 4.085620730620576e-14 relative error = 1.593810884945862e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 3.99012117680001 y1[1] (closed_form) = 0.338912077347304 y1[1] (numeric) = 0.3389120773473561 absolute error = 5.21249710061511e-14 relative error = 1.53800866036224e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2496915577425888 y2[1] (numeric) = 0.2496915577425485 absolute error = 4.030109579389318e-14 relative error = 1.614035178371559e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.000125721651208 y1[1] (closed_form) = 0.3464515307612096 y1[1] (numeric) = 0.3464515307612619 absolute error = 5.234701561107613e-14 relative error = 1.510947736211797e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2431153335179568 y2[1] (numeric) = 0.2431153335179171 absolute error = 3.971822870596498e-14 relative error = 1.633719606708038e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.010130266502405 y1[1] (closed_form) = 0.3540563978955367 y1[1] (numeric) = 0.3540563978955895 absolute error = 5.284661597215745e-14 relative error = 1.492604463194863e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2366148659422881 y2[1] (numeric) = 0.236614865942249 absolute error = 3.913536161803677e-14 relative error = 1.65396884351223e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.020134811353603 y1[1] (closed_form) = 0.3617259175785039 y1[1] (numeric) = 0.361725917578557 absolute error = 5.312417172831374e-14 relative error = 1.468630505769176e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2301908056479208 y2[1] (numeric) = 0.2301908056478822 absolute error = 3.863576125695545e-14 relative error = 1.678423304015419e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.0301393562048 y1[1] (closed_form) = 0.369459322167251 y1[1] (numeric) = 0.3694593221673044 absolute error = 5.345723863570129e-14 relative error = 1.446904582678297e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2238437956195818 y2[1] (numeric) = 0.2238437956195438 absolute error = 3.796962744218035e-14 relative error = 1.696255522163724e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.040143901055997 y1[1] (closed_form) = 0.377255837624672 y1[1] (numeric) = 0.3772558376247258 absolute error = 5.384581669432009e-14 relative error = 1.427302411895101e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2175744711300308 y2[1] (numeric) = 0.2175744711299932 absolute error = 3.763656053479281e-14 relative error = 1.729824291393992e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.049987082280563 y1[1] (closed_form) = 0.3849874375777319 y1[1] (numeric) = 0.3849874375777862 absolute error = 5.428990590417015e-14 relative error = 1.41017343957382e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2114826900677476 y2[1] (numeric) = 0.2114826900677104 absolute error = 3.719247132494274e-14 relative error = 1.758653217103882e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.05999162713176 y1[1] (closed_form) = 0.3929068411018936 y1[1] (numeric) = 0.3929068411019481 absolute error = 5.451195050909519e-14 relative error = 1.387401409357453e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.205369333325778 y2[1] (numeric) = 0.2053693333257412 absolute error = 3.680389326632394e-14 relative error = 1.792083202994179e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.069996171982957 y1[1] (closed_form) = 0.4008870086306168 y1[1] (numeric) = 0.4008870086306715 absolute error = 5.473399511402022e-14 relative error = 1.365322246310379e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1993355112330576 y2[1] (numeric) = 0.1993355112330212 absolute error = 3.635980405647388e-14 relative error = 1.824050508188829e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.080000716834155 y1[1] (closed_form) = 0.4089271414282725 y1[1] (numeric) = 0.4089271414283275 absolute error = 5.501155087017651e-14 relative error = 1.345265336950635e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1933818277153393 y2[1] (numeric) = 0.1933818277153034 absolute error = 3.588795927100819e-14 relative error = 1.855808257425085e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.090005261685352 y1[1] (closed_form) = 0.4170264347573029 y1[1] (numeric) = 0.4170264347573583 absolute error = 5.540012892879531e-14 relative error = 1.32845604766126e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1875088786772997 y2[1] (numeric) = 0.1875088786772644 absolute error = 3.533284775869561e-14 relative error = 1.88432931858672e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.10000980653655 y1[1] (closed_form) = 0.4251840779587681 y1[1] (numeric) = 0.425184077958824 absolute error = 5.584421813864537e-14 relative error = 1.313412731886466e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1817172519428945 y2[1] (numeric) = 0.1817172519428597 absolute error = 3.477773624638303e-14 relative error = 1.913837892359945e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.110014351387747 y1[1] (closed_form) = 0.4333992545334843 y1[1] (numeric) = 0.4333992545335404 absolute error = 5.612177389480166e-14 relative error = 1.294920868177583e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1760075271965231 y2[1] (numeric) = 0.176007527196489 absolute error = 3.413935800722356e-14 relative error = 1.939653295003963e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.120018896238944 y1[1] (closed_form) = 0.4416711422237474 y1[1] (numeric) = 0.4416711422238038 absolute error = 5.645484080218921e-14 relative error = 1.278209858084629e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1703802759250085 y2[1] (numeric) = 0.170380275924975 absolute error = 3.35009797680641e-14 relative error = 1.966247535765777e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.130023441090142 y1[1] (closed_form) = 0.4499989130956333 y1[1] (numeric) = 0.4499989130956904 absolute error = 5.706546346573305e-14 relative error = 1.26812447330524e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1648360613603965 y2[1] (numeric) = 0.1648360613603637 absolute error = 3.286260152890463e-14 relative error = 1.993653649431361e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.140027985941339 y1[1] (closed_form) = 0.458381733621866 y1[1] (numeric) = 0.4583817336219232 absolute error = 5.723199691942682e-14 relative error = 1.248566265222064e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1593754384235823 y2[1] (numeric) = 0.1593754384235499 absolute error = 3.236300116782331e-14 relative error = 2.030614095116093e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.150032530792537 y1[1] (closed_form) = 0.4668187647652442 y1[1] (numeric) = 0.4668187647653019 absolute error = 5.767608612927688e-14 relative error = 1.235513447242878e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1539989536687676 y2[1] (numeric) = 0.1539989536687359 absolute error = 3.172462292866385e-14 relative error = 2.06005444666199e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.160037075643734 y1[1] (closed_form) = 0.4753091620626222 y1[1] (numeric) = 0.4753091620626801 absolute error = 5.795364188543317e-14 relative error = 1.21928307954219e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1487071452287572 y2[1] (numeric) = 0.1487071452287259 absolute error = 3.122502256758253e-14 relative error = 2.099766122169104e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.170041620494931 y1[1] (closed_form) = 0.483852075709431 y1[1] (numeric) = 0.4838520757094895 absolute error = 5.850875339774575e-14 relative error = 1.209228116092286e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.143500542761096 y2[1] (numeric) = 0.1435005427610654 absolute error = 3.066991105526995e-14 relative error = 2.13726794792199e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.180046165346129 y1[1] (closed_form) = 0.4924466506447364 y1[1] (numeric) = 0.4924466506447951 absolute error = 5.873079800267078e-14 relative error = 1.192632702969498e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1383796673950564 y2[1] (numeric) = 0.1383796673950264 absolute error = 2.992051051364797e-14 relative error = 2.162204251310181e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.190050710197326 y1[1] (closed_form) = 0.5010920266368207 y1[1] (numeric) = 0.5010920266368799 absolute error = 5.917488721252084e-14 relative error = 1.180918555213998e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1333450316794779 y2[1] (numeric) = 0.1333450316794486 absolute error = 2.92821322744885e-14 relative error = 2.195967251698894e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.200055255048524 y1[1] (closed_form) = 0.5097873383692852 y1[1] (numeric) = 0.5097873383693448 absolute error = 5.950795411990839e-14 relative error = 1.167309378657054e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1283971395314663 y2[1] (numeric) = 0.1283971395314376 absolute error = 2.861599845971341e-14 relative error = 2.228709966914839e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.210059799899721 y1[1] (closed_form) = 0.5185317155276581 y1[1] (numeric) = 0.5185317155277183 absolute error = 6.017408793468348e-14 relative error = 1.160470731736251e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1235364861859565 y2[1] (numeric) = 0.1235364861859285 absolute error = 2.797762022055394e-14 relative error = 2.264725271401998e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.220064344750918 y1[1] (closed_form) = 0.5273242828865053 y1[1] (numeric) = 0.5273242828865661 absolute error = 6.072919944699606e-14 relative error = 1.151648073450595e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1187635581461446 y2[1] (numeric) = 0.1187635581461172 absolute error = 2.743638649604918e-14 relative error = 2.310168786142911e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.230068889602116 y1[1] (closed_form) = 0.5361641603970316 y1[1] (numeric) = 0.5361641603970924 absolute error = 6.072919944699606e-14 relative error = 1.132660553104218e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1140788331347933 y2[1] (numeric) = 0.1140788331347665 absolute error = 2.674249710565846e-14 relative error = 2.344212012938461e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.240073434453313 y1[1] (closed_form) = 0.5450504632751647 y1[1] (numeric) = 0.5450504632752255 absolute error = 6.084022174945858e-14 relative error = 1.11623098866616e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1094827800464172 y2[1] (numeric) = 0.109482780046391 absolute error = 2.615963001773025e-14 relative error = 2.3893830615773e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.25007797930451 y1[1] (closed_form) = 0.5539823020901136 y1[1] (numeric) = 0.5539823020901748 absolute error = 6.128431095930864e-14 relative error = 1.106250339191158e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1049758589003505 y2[1] (numeric) = 0.104975858900325 absolute error = 2.552125177857079e-14 relative error = 2.43115436690993e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.260082524155708 y1[1] (closed_form) = 0.5629587828533912 y1[1] (numeric) = 0.5629587828534527 absolute error = 6.150635556423367e-14 relative error = 1.09255521785245e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1005585207947041 y2[1] (numeric) = 0.1005585207946792 absolute error = 2.482736238818006e-14 relative error = 2.468946658321132e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.270087069006905 y1[1] (closed_form) = 0.5719790071082944 y1[1] (numeric) = 0.5719790071083566 absolute error = 6.217248937900877e-14 relative error = 1.086971525289519e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.09623120786121486 y2[1] (numeric) = 0.09623120786119065 absolute error = 2.421673972463623e-14 relative error = 2.516516238636611e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.280091613858103 y1[1] (closed_form) = 0.5810420720198306 y1[1] (numeric) = 0.5810420720198931 absolute error = 6.250555628639631e-14 relative error = 1.075749232221915e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.09199435322099281 y2[1] (numeric) = 0.09199435322096913 absolute error = 2.367550600013146e-14 relative error = 2.573582526664125e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.2900961587093 y1[1] (closed_form) = 0.5901470704650819 y1[1] (numeric) = 0.590147070465144 absolute error = 6.217248937900877e-14 relative error = 1.053508396305552e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.08784838094116976 y2[1] (numeric) = 0.08784838094114669 absolute error = 2.306488333658763e-14 relative error = 2.625533116203212e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.300100703560497 y1[1] (closed_form) = 0.5992930911239996 y1[1] (numeric) = 0.599293091124062 absolute error = 6.23945339839338e-14 relative error = 1.041135546330264e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.08379370599245461 y2[1] (numeric) = 0.08379370599243217 absolute error = 2.244038288523598e-14 relative error = 2.678051127999598e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.310105248411695 y1[1] (closed_form) = 0.6084792185706186 y1[1] (numeric) = 0.6084792185706814 absolute error = 6.283862319378386e-14 relative error = 1.032716011919e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.0798307342075989 y2[1] (numeric) = 0.07983073420757712 absolute error = 2.177424907046088e-14 relative error = 2.72755214975691e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.320109793262892 y1[1] (closed_form) = 0.6177045333646817 y1[1] (numeric) = 0.6177045333647448 absolute error = 6.317169010117141e-14 relative error = 1.022684579584848e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.07595986224077678 y2[1] (numeric) = 0.07595986224075565 absolute error = 2.11219930434936e-14 relative error = 2.780678166126912e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.33011433811409 y1[1] (closed_form) = 0.626968112143667 y1[1] (numeric) = 0.6269681121437303 absolute error = 6.328271240363392e-14 relative error = 1.009344991841195e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.07218147752788406 y2[1] (numeric) = 0.07218147752786364 absolute error = 2.042810365310288e-14 relative error = 2.830103283104922e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.340118882965287 y1[1] (closed_form) = 0.6362690277152073 y1[1] (numeric) = 0.6362690277152711 absolute error = 6.372680161348399e-14 relative error = 1.001570072368947e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 0.06849595824775978 y2[1] (numeric) = 0.06849595824773988 absolute error = 1.990074771640593e-14 relative error = 2.905390073443757e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.350123427816484 y1[1] (closed_form) = 0.6456063491498926 y1[1] (numeric) = 0.6456063491499562 absolute error = 6.361577931102147e-14 relative error = 9.853648340786621e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.06490367328433366 y2[1] (numeric) = 0.06490367328431448 absolute error = 1.917910275039958e-14 relative error = 2.955010368423785e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.360127972667682 y1[1] (closed_form) = 0.6549791418744468 y1[1] (numeric) = 0.6549791418745111 absolute error = 6.428191312579656e-14 relative error = 9.814345070872315e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.06140498218970558 y2[1] (numeric) = 0.06140498218968703 absolute error = 1.855460229904793e-14 relative error = 3.021677010136577e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.370132517518879 y1[1] (closed_form) = 0.6643864677652701 y1[1] (numeric) = 0.6643864677653349 absolute error = 6.483702463810914e-14 relative error = 9.758932155285299e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.05800023514815678 y2[1] (numeric) = 0.05800023514813887 absolute error = 1.790234627208065e-14 relative error = 3.086598912288992e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.380137062370077 y1[1] (closed_form) = 0.6738273852423347 y1[1] (numeric) = 0.6738273852423995 absolute error = 6.483702463810914e-14 relative error = 9.622200886773282e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.05468977294110078 y2[1] (numeric) = 0.05468977294108351 absolute error = 1.727090692682509e-14 relative error = 3.157977442222211e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.390141607221274 y1[1] (closed_form) = 0.6833009493634281 y1[1] (numeric) = 0.6833009493634932 absolute error = 6.505906924303417e-14 relative error = 9.521290626574429e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.05147392691297403 y2[1] (numeric) = 0.05147392691295744 absolute error = 1.659089532424218e-14 relative error = 3.223164875742254e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.399984788445839 y1[1] (closed_form) = 0.6926526547106515 y1[1] (numeric) = 0.6926526547107164 absolute error = 6.483702463810914e-14 relative error = 9.360683770885731e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.04840260123117723 y2[1] (numeric) = 0.04840260123116125 absolute error = 1.598027266069835e-14 relative error = 3.301531788420719e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.409989333297037 y1[1] (closed_form) = 0.7021881759624278 y1[1] (numeric) = 0.7021881759624929 absolute error = 6.517009154549669e-14 relative error = 9.281000987544935e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.04537540495574166 y2[1] (numeric) = 0.04537540495572641 absolute error = 1.525168880078809e-14 relative error = 3.361223732474521e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.419993878148234 y1[1] (closed_form) = 0.7117535052243407 y1[1] (numeric) = 0.7117535052244061 absolute error = 6.539213615042172e-14 relative error = 9.18746949195712e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.04244375713509874 y2[1] (numeric) = 0.04244375713508405 absolute error = 1.46826995006677e-14 relative error = 3.4593307689356e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.429998422999431 y1[1] (closed_form) = 0.7213476851017921 y1[1] (numeric) = 0.7213476851018576 absolute error = 6.550315845288424e-14 relative error = 9.08066384709349e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.03960795119812144 y2[1] (numeric) = 0.0396079511981074 absolute error = 1.403738236760432e-14 relative error = 3.544081918650238e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.440002967850629 y1[1] (closed_form) = 0.7309697553125233 y1[1] (numeric) = 0.7309697553125893 absolute error = 6.605826996519681e-14 relative error = 9.037072941130629e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.03686827098086087 y2[1] (numeric) = 0.03686827098084754 absolute error = 1.332961518940579e-14 relative error = 3.615470656686201e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 4.450007512701826 y1[1] (closed_form) = 0.7406187527827298 y1[1] (numeric) = 0.740618752782796 absolute error = 6.616929226765933e-14 relative error = 8.934325794349816e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.03422499069813711 y2[1] (numeric) = 0.03422499069812437 absolute error = 1.273980920757367e-14 relative error = 3.722370393008494e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.460012057553024 y1[1] (closed_form) = 0.7502937117434557 y1[1] (numeric) = 0.7502937117435221 absolute error = 6.639133687258436e-14 relative error = 8.84871295513206e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.03167837491609249 y2[1] (numeric) = 0.03167837491608039 absolute error = 1.210143096841421e-14 relative error = 3.820092097674723e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.470016602404221 y1[1] (closed_form) = 0.7599936638272571 y1[1] (numeric) = 0.7599936638273235 absolute error = 6.639133687258436e-14 relative error = 8.73577505083974e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.02922867852571154 y2[1] (numeric) = 0.02922867852570013 absolute error = 1.141101102497544e-14 relative error = 3.904046163064654e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.480021147255418 y1[1] (closed_form) = 0.7697176381651265 y1[1] (numeric) = 0.7697176381651936 absolute error = 6.705747068735946e-14 relative error = 8.711957133685133e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.02687614671730898 y2[1] (numeric) = 0.0268761467172982 absolute error = 1.077610223276793e-14 relative error = 4.009541377383469e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.490025692106616 y1[1] (closed_form) = 0.779464661483667 y1[1] (numeric) = 0.7794646614837339 absolute error = 6.694644838489694e-14 relative error = 8.588772742752462e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.02462101495598834 y2[1] (numeric) = 0.02462101495597821 absolute error = 1.013425454665651e-14 relative error = 4.116099423509609e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.500030236957813 y1[1] (closed_form) = 0.7892337582025072 y1[1] (numeric) = 0.7892337582025739 absolute error = 6.672440377997191e-14 relative error = 8.454327135212491e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.02246350895807436 y2[1] (numeric) = 0.02246350895806493 absolute error = 9.436895709313831e-15 relative error = 4.200989136170464e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.510034781809011 y1[1] (closed_form) = 0.7990239505319473 y1[1] (numeric) = 0.7990239505320144 absolute error = 6.705747068735946e-14 relative error = 8.392423111061462e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.02040384466852119 y2[1] (numeric) = 0.02040384466851239 absolute error = 8.795048023202412e-15 relative error = 4.310485678599244e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.520039326660208 y1[1] (closed_form) = 0.8088342585708261 y1[1] (numeric) = 0.8088342585708931 absolute error = 6.694644838489694e-14 relative error = 8.276905642348571e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.01844222823929809 y2[1] (numeric) = 0.01844222823928998 absolute error = 8.108097526715596e-15 relative error = 4.396484753094126e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.530043871511405 y1[1] (closed_form) = 0.8186637004045996 y1[1] (numeric) = 0.8186637004046664 absolute error = 6.683542608243442e-14 relative error = 8.163965991090487e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.01657885600875597 y2[1] (numeric) = 0.01657885600874856 absolute error = 7.41073868937292e-15 relative error = 4.469994000466019e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.540048416362603 y1[1] (closed_form) = 0.82851129220362 y1[1] (numeric) = 0.8285112922036871 absolute error = 6.716849298982197e-14 relative error = 8.10713065976103e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.01481391448197578 y2[1] (numeric) = 0.01481391448196901 absolute error = 6.765421556309548e-15 relative error = 4.566937094541147e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.5500529612138 y1[1] (closed_form) = 0.8383760483216087 y1[1] (numeric) = 0.8383760483216762 absolute error = 6.750155989720952e-14 relative error = 8.051465691600399e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.01314758031210106 y2[1] (numeric) = 0.01314758031209498 absolute error = 6.076736336346755e-15 relative error = 4.621942739344756e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.560057506064997 y1[1] (closed_form) = 0.8482569813943088 y1[1] (numeric) = 0.8482569813943761 absolute error = 6.727951529228449e-14 relative error = 7.931501510508626e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.01158002028265692 y2[1] (numeric) = 0.01158002028265154 absolute error = 5.382846945956032e-15 relative error = 4.648391638845205e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.570062050916195 y1[1] (closed_form) = 0.8581531024383104 y1[1] (numeric) = 0.8581531024383774 absolute error = 6.694644838489694e-14 relative error = 7.801224303061874e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.01011139129085659 y2[1] (numeric) = 0.01011139129085189 absolute error = 4.695896449469217e-15 relative error = 4.644164501590961e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.580066595767392 y1[1] (closed_form) = 0.8680634209500387 y1[1] (numeric) = 0.8680634209501052 absolute error = 6.650235917504688e-14 relative error = 7.661002361125227e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.00874184033189751 y2[1] (numeric) = 0.008741840331893468 absolute error = 4.041905699025961e-15 relative error = 4.623632491064523e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.59007114061859 y1[1] (closed_form) = 0.8779869450048927 y1[1] (numeric) = 0.877986945004959 absolute error = 6.628031457012185e-14 relative error = 7.549123019107362e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.007471504484248603 y2[1] (numeric) = 0.007471504484245202 absolute error = 3.401792736390519e-15 relative error = 4.553022411432885e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.600075685469787 y1[1] (closed_form) = 0.887922681356528 y1[1] (numeric) = 0.8879226813565942 absolute error = 6.628031457012185e-14 relative error = 7.464649339609367e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.006300510895930089 y2[1] (numeric) = 0.006300510895927301 absolute error = 2.788567987632717e-15 relative error = 4.425939473311657e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.610080230320984 y1[1] (closed_form) = 0.89786963553627 y1[1] (numeric) = 0.8978696355363356 absolute error = 6.561418075534675e-14 relative error = 7.307762525698669e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.00522897677178713 y2[1] (numeric) = 0.005228976771785025 absolute error = 2.105954299835844e-15 relative error = 4.027469219596633e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.620084775172182 y1[1] (closed_form) = 0.9078268119526508 y1[1] (numeric) = 0.9078268119527161 absolute error = 6.52811138479592e-14 relative error = 7.190921548962144e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.004257009361759101 y2[1] (numeric) = 0.004257009361757607 absolute error = 1.493596912816031e-15 relative error = 3.508559145378153e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.630089320023379 y1[1] (closed_form) = 0.9177932139910584 y1[1] (numeric) = 0.9177932139911239 absolute error = 6.550315845288424e-14 relative error = 7.137027976927535e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.003384705950144395 y2[1] (numeric) = 0.003384705950143641 absolute error = 7.546047120499111e-16 relative error = 2.229454266234616e-11 % Desired digits = 8 Estimated correct digits = 8 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] = 4.640093864874577 y1[1] (closed_form) = 0.927767844113487 y1[1] (numeric) = 0.9277678441135525 absolute error = 6.550315845288424e-14 relative error = 7.060296265761903e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.002612153845863996 y2[1] (numeric) = 0.002612153845863851 absolute error = 1.448494102440634e-16 relative error = 5.545209769072886e-12 % Desired digits = 8 Estimated correct digits = 8 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] = 4.650098409725774 y1[1] (closed_form) = 0.9377497039583815 y1[1] (numeric) = 0.9377497039584469 absolute error = 6.539213615042172e-14 relative error = 6.973303843700696e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.001939430373721795 y2[1] (numeric) = 0.001939430373722345 absolute error = 5.496905014501507e-16 relative error = 2.83428840188414e-11 % Desired digits = 8 Estimated correct digits = 8 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] = 4.660102954576971 y1[1] (closed_form) = 0.9477377944405633 y1[1] (numeric) = 0.9477377944406284 absolute error = 6.517009154549669e-14 relative error = 6.876384156861203e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.001366602866666011 y2[1] (numeric) = 0.001366602866667171 absolute error = 1.159879484124993e-15 relative error = 8.487319267481527e-11 % Desired digits = 8 Estimated correct digits = 8 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] = 4.670107499428169 y1[1] (closed_form) = 0.9577311158512285 y1[1] (numeric) = 0.9577311158512936 absolute error = 6.505906924303417e-14 relative error = 6.793041195618863e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.0008937286590491311 y2[1] (numeric) = 0.0008937286590509592 absolute error = 1.828073283027809e-15 relative error = 2.045445521432377e-10 % Desired digits = 8 Estimated correct digits = 8 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] = 4.680112044279366 y1[1] (closed_form) = 0.9677286679580094 y1[1] (numeric) = 0.9677286679580747 absolute error = 6.52811138479592e-14 relative error = 6.745807581138209e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.0005208550808898371 y2[1] (numeric) = 0.0005208550808923229 absolute error = 2.485750320857516e-15 relative error = 4.772441341285988e-10 % Desired digits = 8 Estimated correct digits = 8 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] = 4.690116589130564 y1[1] (closed_form) = 0.9777294501050875 y1[1] (numeric) = 0.9777294501051531 absolute error = 6.561418075534675e-14 relative error = 6.710872905413094e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.0002480194531354618 y2[1] (numeric) = 0.0002480194531385878 absolute error = 3.125971703710206e-15 relative error = 1.260373597389912e-09 % Desired digits = 8 Estimated correct digits = 7 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] = 4.700121133981761 y1[1] (closed_form) = 0.9877324613133494 y1[1] (numeric) = 0.9877324613134147 absolute error = 6.539213615042172e-14 relative error = 6.620429996142108e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 7.524908392653185e-05 y2[1] (numeric) = 7.524908393033413e-05 absolute error = 3.802283466379508e-15 relative error = 5.052929906883388e-09 % Desired digits = 8 Estimated correct digits = 7 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] = 4.710125678832958 y1[1] (closed_form) = 0.9977367003805745 y1[1] (numeric) = 0.9977367003806399 absolute error = 6.539213615042172e-14 relative error = 6.554047388001132e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 2.561265863731954e-06 y2[1] (numeric) = 2.561265868124675e-06 absolute error = 4.392721334790274e-15 relative error = 1.715058712565572e-07 % Desired digits = 8 Estimated correct digits = 5 Correct digits = 9 h = 0.0001613636266322163 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.720130223684156 y1[1] (closed_form) = 1.007741165981646 y1[1] (numeric) = 1.007741165981711 absolute error = 6.483702463810914e-14 relative error = 6.433896602303733e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 2.996327427662315e-05 y2[1] (numeric) = 2.996327428168808e-05 absolute error = 5.064924987665392e-15 relative error = 1.690377673983702e-08 % Desired digits = 8 Estimated correct digits = 6 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] = 4.730134768535353 y1[1] (closed_form) = 1.017744856768773 y1[1] (numeric) = 1.017744856768838 absolute error = 6.505906924303417e-14 relative error = 6.392473399432299e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.0001574523664960026 y2[1] (numeric) = 0.0001574523665017358 absolute error = 5.733179772940411e-15 relative error = 3.641215372324026e-09 % Desired digits = 8 Estimated correct digits = 7 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] = 4.740139313386551 y1[1] (closed_form) = 1.027746771471717 y1[1] (numeric) = 1.027746771471782 absolute error = 6.505906924303417e-14 relative error = 6.3302625752714e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.0003850157821281286 y2[1] (numeric) = 0.0003850157821344667 absolute error = 6.338083270024386e-15 relative error = 1.646187913386664e-09 % Desired digits = 8 Estimated correct digits = 8 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] = 4.750143858237748 y1[1] (closed_form) = 1.037745908998005 y1[1] (numeric) = 1.03774590899807 absolute error = 6.52811138479592e-14 relative error = 6.29066453376736e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.0007126307443316993 y2[1] (numeric) = 0.0007126307443387621 absolute error = 7.062818212222322e-15 relative error = 9.910908655569988e-10 % Desired digits = 8 Estimated correct digits = 8 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] = 4.759987039462313 y1[1] (closed_form) = 1.047580088282863 y1[1] (numeric) = 1.047580088282929 absolute error = 6.639133687258436e-14 relative error = 6.33759056850818e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.001132573762165912 y2[1] (numeric) = 0.001132573762173559 absolute error = 7.647745284278251e-15 relative error = 6.75253616122349e-10 % Desired digits = 8 Estimated correct digits = 8 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] = 4.769991584313511 y1[1] (closed_form) = 1.057570754397412 y1[1] (numeric) = 1.057570754397479 absolute error = 6.661338147750939e-14 relative error = 6.298716298699532e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.001658571310339307 y2[1] (numeric) = 0.001658571310347654 absolute error = 8.347055685531402e-15 relative error = 5.032678205330693e-10 % Desired digits = 8 Estimated correct digits = 8 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] = 4.779996129164708 y1[1] (closed_form) = 1.067555658250385 y1[1] (numeric) = 1.067555658250451 absolute error = 6.59472476627343e-14 relative error = 6.177406035280177e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.002284492934806037 y2[1] (numeric) = 0.002284492934814999 absolute error = 8.96201515776518e-15 relative error = 3.922977839511721e-10 % Desired digits = 8 Estimated correct digits = 8 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] = 4.790000674015905 y1[1] (closed_form) = 1.077533800451928 y1[1] (numeric) = 1.077533800451993 absolute error = 6.550315845288424e-14 relative error = 6.078988744985225e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.00301027598701864 y2[1] (numeric) = 0.003010275987028352 absolute error = 9.711849380256155e-15 relative error = 3.226232219948282e-10 % Desired digits = 8 Estimated correct digits = 8 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] = 4.800005218867103 y1[1] (closed_form) = 1.087504182288961 y1[1] (numeric) = 1.087504182289026 absolute error = 6.550315845288424e-14 relative error = 6.023255774061877e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.003835847823291605 y2[1] (numeric) = 0.003835847823301904 absolute error = 1.02990532768743e-14 relative error = 2.684948348142892e-10 % Desired digits = 8 Estimated correct digits = 8 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] = 4.8100097637183 y1[1] (closed_form) = 1.097465805825141 y1[1] (numeric) = 1.097465805825206 absolute error = 6.505906924303417e-14 relative error = 5.928118115180716e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.004761125812071221 y2[1] (numeric) = 0.004761125812082169 absolute error = 1.094783985688963e-14 relative error = 2.299422508250631e-10 % Desired digits = 8 Estimated correct digits = 9 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] = 4.820014308569498 y1[1] (closed_form) = 1.107417674000742 y1[1] (numeric) = 1.107417674000806 absolute error = 6.439293542825908e-14 relative error = 5.814692770400551e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.005786017342206962 y2[1] (numeric) = 0.005786017342218611 absolute error = 1.164953550292225e-14 relative error = 2.013394501593174e-10 % Desired digits = 8 Estimated correct digits = 9 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] = 4.830018853420695 y1[1] (closed_form) = 1.117358790732455 y1[1] (numeric) = 1.117358790732519 absolute error = 6.417089082333405e-14 relative error = 5.743087301552309e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.006910419832220849 y2[1] (numeric) = 0.006910419832233084 absolute error = 1.223500467606442e-14 relative error = 1.770515391701227e-10 % Desired digits = 8 Estimated correct digits = 9 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] = 4.840023398271892 y1[1] (closed_form) = 1.127288161013082 y1[1] (numeric) = 1.127288161013146 absolute error = 6.394884621840902e-14 relative error = 5.672803851762168e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.008134220740574349 y2[1] (numeric) = 0.008134220740587226 absolute error = 1.287685236217584e-14 relative error = 1.583046830527323e-10 % Desired digits = 8 Estimated correct digits = 9 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] = 4.85002794312309 y1[1] (closed_form) = 1.137204791011129 y1[1] (numeric) = 1.137204791011194 absolute error = 6.439293542825908e-14 relative error = 5.66238692777622e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.009457297576933144 y2[1] (numeric) = 0.009457297576946751 absolute error = 1.360717094556207e-14 relative error = 1.438801183411072e-10 % Desired digits = 8 Estimated correct digits = 9 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] = 4.860032487974287 y1[1] (closed_form) = 1.14710768817028 y1[1] (numeric) = 1.147107688170344 absolute error = 6.417089082333405e-14 relative error = 5.594147043482141e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.01087951791442732 y2[1] (numeric) = 0.01087951791444151 absolute error = 1.419350748044224e-14 relative error = 1.304608126213041e-10 % Desired digits = 8 Estimated correct digits = 9 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] = 4.870037032825485 y1[1] (closed_form) = 1.156995861308736 y1[1] (numeric) = 1.156995861308799 absolute error = 6.350475700855895e-14 relative error = 5.488762676879895e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.01240073940290531 y2[1] (numeric) = 0.01240073940292011 absolute error = 1.479719125008216e-14 relative error = 1.193250722341234e-10 % Desired digits = 8 Estimated correct digits = 9 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] = 4.880041577676682 y1[1] (closed_form) = 1.166868320718429 y1[1] (numeric) = 1.166868320718493 absolute error = 6.417089082333405e-14 relative error = 5.499411517473085e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.01402080978318232 y2[1] (numeric) = 0.01402080978319778 absolute error = 1.545812089442933e-14 relative error = 1.102512703151499e-10 % Desired digits = 8 Estimated correct digits = 9 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] = 4.890046122527879 y1[1] (closed_form) = 1.176724078264079 y1[1] (numeric) = 1.176724078264143 absolute error = 6.439293542825908e-14 relative error = 5.472220431084618e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.01573956690227984 y2[1] (numeric) = 0.01573956690229596 absolute error = 1.611211164487258e-14 relative error = 1.023669313450981e-10 % Desired digits = 8 Estimated correct digits = 9 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] = 4.900050667379077 y1[1] (closed_form) = 1.186562147482097 y1[1] (numeric) = 1.186562147482162 absolute error = 6.461498003318411e-14 relative error = 5.445562221102206e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.01755683872965541 y2[1] (numeric) = 0.01755683872967222 absolute error = 1.680947048221526e-14 relative error = 9.574315023935508e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.910055212230274 y1[1] (closed_form) = 1.19638154367932 y1[1] (numeric) = 1.196381543679385 absolute error = 6.439293542825908e-14 relative error = 5.382307656654979e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.01947244337442144 y2[1] (numeric) = 0.01947244337443884 absolute error = 1.739580701709542e-14 relative error = 8.933551215224565e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.920059757081471 y1[1] (closed_form) = 1.20618128403157 y1[1] (numeric) = 1.206181284031634 absolute error = 6.439293542825908e-14 relative error = 5.338578560349616e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.02148618910355016 y2[1] (numeric) = 0.02148618910356823 absolute error = 1.807581861967833e-14 relative error = 8.41276158027096e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.930064301932669 y1[1] (closed_form) = 1.215960387682022 y1[1] (numeric) = 1.215960387682086 absolute error = 6.417089082333405e-14 relative error = 5.277383332006617e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.02359787436106486 y2[1] (numeric) = 0.02359787436108358 absolute error = 1.871419685883779e-14 relative error = 7.930458723737908e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.940068846783866 y1[1] (closed_form) = 1.225717875839382 y1[1] (numeric) = 1.225717875839446 absolute error = 6.417089082333405e-14 relative error = 5.235372028770428e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.02580728778821317 y2[1] (numeric) = 0.02580728778823252 absolute error = 1.934563620409335e-14 relative error = 7.496191139050645e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.950073391635064 y1[1] (closed_form) = 1.235452771875853 y1[1] (numeric) = 1.235452771875917 absolute error = 6.417089082333405e-14 relative error = 5.194119296515077e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.02811420824462207 y2[1] (numeric) = 0.02811420824464212 absolute error = 2.004993393533994e-14 relative error = 7.131601843767113e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.960077936486261 y1[1] (closed_form) = 1.245164101424883 y1[1] (numeric) = 1.245164101424947 absolute error = 6.417089082333405e-14 relative error = 5.153609130708247e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.03051840483043211 y2[1] (numeric) = 0.03051840483045284 absolute error = 2.072994553792284e-14 relative error = 6.79260454571712e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.970082481337458 y1[1] (closed_form) = 1.254850892478694 y1[1] (numeric) = 1.254850892478758 absolute error = 6.439293542825908e-14 relative error = 5.131520869468754e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.0330196369094079 y2[1] (numeric) = 0.03301963690942921 absolute error = 2.13093431788991e-14 relative error = 6.453536493257948e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.980087026188656 y1[1] (closed_form) = 1.264512175485566 y1[1] (numeric) = 1.264512175485631 absolute error = 6.439293542825908e-14 relative error = 5.092314386259865e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.03561765413302331 y2[1] (numeric) = 0.03561765413304534 absolute error = 2.202404925100154e-14 relative error = 6.183464292383505e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 4.990091571039853 y1[1] (closed_form) = 1.274146983446884 y1[1] (numeric) = 1.274146983446948 absolute error = 6.417089082333405e-14 relative error = 5.036380547692845e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.03831219646551942 y2[1] (numeric) = 0.03831219646554204 absolute error = 2.262079412673756e-14 relative error = 5.904332357215814e-11 % Desired digits = 8 Estimated correct digits = 9 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] = 5.000096115891051 y1[1] (closed_form) = 1.283754352013921 y1[1] (numeric) = 1.283754352013984 absolute error = 6.372680161348399e-14 relative error = 4.964096247347557e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.0411029942099308 y2[1] (numeric) = 0.04110299420995406 absolute error = 2.326611125980094e-14 relative error = 5.660441947603823e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.010100660742248 y1[1] (closed_form) = 1.293333319584359 y1[1] (numeric) = 1.293333319584423 absolute error = 6.394884621840902e-14 relative error = 4.944498471512383e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.04398976803508003 y2[1] (numeric) = 0.04398976803510401 absolute error = 2.397387843799947e-14 relative error = 5.449876075473117e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.020105205593445 y1[1] (closed_form) = 1.302882927398544 y1[1] (numeric) = 1.302882927398608 absolute error = 6.417089082333405e-14 relative error = 4.925299846507589e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.04697222900353604 y2[1] (numeric) = 0.04697222900356062 absolute error = 2.458450110154331e-14 relative error = 5.233837444608517e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.030109750444643 y1[1] (closed_form) = 1.312402219635436 y1[1] (numeric) = 1.3124022196355 absolute error = 6.417089082333405e-14 relative error = 4.889574999435744e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.05005007860053323 y2[1] (numeric) = 0.0500500786005585 absolute error = 2.526451270412622e-14 relative error = 5.047846758797508e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.04011429529584 y1[1] (closed_form) = 1.321890243508287 y1[1] (numeric) = 1.321890243508351 absolute error = 6.394884621840902e-14 relative error = 4.837681988535542e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.05322300876385067 y2[1] (numeric) = 0.05322300876387649 absolute error = 2.58265631103427e-14 relative error = 4.852518433321687e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.050118840147038 y1[1] (closed_form) = 1.331346049360003 y1[1] (numeric) = 1.331346049360067 absolute error = 6.394884621840902e-14 relative error = 4.80332264095801e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.05649070191464534 y2[1] (numeric) = 0.05649070191467181 absolute error = 2.647881913730998e-14 relative error = 4.687288038537417e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.060123384998235 y1[1] (closed_form) = 1.340768690758191 y1[1] (numeric) = 1.340768690758255 absolute error = 6.372680161348399e-14 relative error = 4.753004903287763e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.0598528309892391 y2[1] (numeric) = 0.05985283098926628 absolute error = 2.717964742160461e-14 relative error = 4.541079673656744e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.070127929849432 y1[1] (closed_form) = 1.350157224589895 y1[1] (numeric) = 1.350157224589958 absolute error = 6.306066779870889e-14 relative error = 4.670616625249946e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.0633090594718545 y2[1] (numeric) = 0.06330905947188233 absolute error = 2.782496455466799e-14 relative error = 4.395099972546301e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.08013247470063 y1[1] (closed_form) = 1.359510711155985 y1[1] (numeric) = 1.359510711156049 absolute error = 6.350475700855895e-14 relative error = 4.671147971652329e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.06685904142829646 y2[1] (numeric) = 0.06685904142832487 absolute error = 2.840783164259619e-14 relative error = 4.2489139891517e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.090137019551827 y1[1] (closed_form) = 1.368828214265216 y1[1] (numeric) = 1.368828214265279 absolute error = 6.23945339839338e-14 relative error = 4.558244294915198e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.07050242154057673 y2[1] (numeric) = 0.07050242154060575 absolute error = 2.901845430614003e-14 relative error = 4.115951434297734e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.100141564403025 y1[1] (closed_form) = 1.37810880132793 y1[1] (numeric) = 1.378108801327992 absolute error = 6.195044477408373e-14 relative error = 4.495323207745933e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.07423883514247809 y2[1] (numeric) = 0.07423883514250777 absolute error = 2.968458812091512e-14 relative error = 3.998525578148538e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.10998474562759 y1[1] (closed_form) = 1.38720277210124 y1[1] (numeric) = 1.387202772101302 absolute error = 6.17284001691587e-14 relative error = 4.44984694455712e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.07800541580922771 y2[1] (numeric) = 0.07800541580925804 absolute error = 3.03368441478824e-14 relative error = 3.889068961836581e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.119989290478787 y1[1] (closed_form) = 1.396407376817966 y1[1] (numeric) = 1.396407376818027 absolute error = 6.128431095930864e-14 relative error = 4.388712919789853e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.08192527994487331 y2[1] (numeric) = 0.08192527994490423 absolute error = 3.091971123581061e-14 relative error = 3.774135560673844e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.129993835329985 y1[1] (closed_form) = 1.40557230508751 y1[1] (numeric) = 1.405572305087571 absolute error = 6.084022174945858e-14 relative error = 4.32850174475163e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.0859370342552962 y2[1] (numeric) = 0.0859370342553277 absolute error = 3.150257832373882e-14 relative error = 3.665774435519032e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.139998380181182 y1[1] (closed_form) = 1.414696639591444 y1[1] (numeric) = 1.414696639591505 absolute error = 6.106226635438361e-14 relative error = 4.316279875522858e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.09004027720367513 y2[1] (numeric) = 0.09004027720370726 absolute error = 3.212707877509047e-14 relative error = 3.568078616908029e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.150002925032379 y1[1] (closed_form) = 1.42377946707437 y1[1] (numeric) = 1.42377946707443 absolute error = 6.084022174945858e-14 relative error = 4.27314925916688e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.09423459809608348 y2[1] (numeric) = 0.09423459809611621 absolute error = 3.27377014386343e-14 relative error = 3.474063889491447e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.160007469883577 y1[1] (closed_form) = 1.432819878435333 y1[1] (numeric) = 1.432819878435393 absolute error = 6.039613253960852e-14 relative error = 4.215193650548892e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.09851957712259574 y2[1] (numeric) = 0.09851957712262915 absolute error = 3.341771304121721e-14 relative error = 3.39198705650481e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.170012014734774 y1[1] (closed_form) = 1.441816968818812 y1[1] (numeric) = 1.441816968818872 absolute error = 5.995204332975845e-14 relative error = 4.158089731658056e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1028947853993063 y2[1] (numeric) = 0.1028947853993403 absolute error = 3.397282455352979e-14 relative error = 3.301705175990272e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.180016559585972 y1[1] (closed_form) = 1.450769837705285 y1[1] (numeric) = 1.450769837705345 absolute error = 6.017408793468348e-14 relative error = 4.147734972892887e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1073597850112561 y2[1] (numeric) = 0.1073597850112907 absolute error = 3.46528361561127e-14 relative error = 3.227729652446634e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.190021104437169 y1[1] (closed_form) = 1.459677589001364 y1[1] (numeric) = 1.459677589001424 absolute error = 6.017408793468348e-14 relative error = 4.122423224696593e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1119141290562643 y2[1] (numeric) = 0.1119141290562996 absolute error = 3.530509218307998e-14 relative error = 3.154659065910302e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.200025649288366 y1[1] (closed_form) = 1.468539331129482 y1[1] (numeric) = 1.468539331129543 absolute error = 6.039613253960852e-14 relative error = 4.112667005871519e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1165573616896582 y2[1] (numeric) = 0.116557361689694 absolute error = 3.579081475635348e-14 relative error = 3.070661023681105e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.210030194139564 y1[1] (closed_form) = 1.477354177117138 y1[1] (numeric) = 1.477354177117198 absolute error = 5.972999872483342e-14 relative error = 4.043038538083579e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1212890181698989 y2[1] (numeric) = 0.1212890181699353 absolute error = 3.640143741989732e-14 relative error = 3.0012146168837e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.220034738990761 y1[1] (closed_form) = 1.486121244685665 y1[1] (numeric) = 1.486121244685723 absolute error = 5.861977570020827e-14 relative error = 3.944481374573658e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1261086249050972 y2[1] (numeric) = 0.1261086249051342 absolute error = 3.702593787124897e-14 relative error = 2.936035334546924e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.230039283841958 y1[1] (closed_form) = 1.494839656338544 y1[1] (numeric) = 1.494839656338603 absolute error = 5.861977570020827e-14 relative error = 3.921475821948111e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.131015699500416 y2[1] (numeric) = 0.1310156995004536 absolute error = 3.755329380794592e-14 relative error = 2.866320139581949e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.240043828693156 y1[1] (closed_form) = 1.503508539449232 y1[1] (numeric) = 1.50350853944929 absolute error = 5.839773109528323e-14 relative error = 3.88409706782747e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1360097508063525 y2[1] (numeric) = 0.1360097508063907 absolute error = 3.821942762272101e-14 relative error = 2.810050558590976e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.250048373544353 y1[1] (closed_form) = 1.512127026348499 y1[1] (numeric) = 1.512127026348556 absolute error = 5.750955267558311e-14 relative error = 3.803222326794714e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1410902789678976 y2[1] (numeric) = 0.1410902789679364 absolute error = 3.874678355941796e-14 relative error = 2.746240481120181e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.260052918395551 y1[1] (closed_form) = 1.520694254411278 y1[1] (numeric) = 1.520694254411336 absolute error = 5.839773109528323e-14 relative error = 3.840201994969157e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1462567754745671 y2[1] (numeric) = 0.1462567754746063 absolute error = 3.921862834488365e-14 relative error = 2.681491385108752e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.270057463246748 y1[1] (closed_form) = 1.529209366143002 y1[1] (numeric) = 1.52920936614306 absolute error = 5.81756864903582e-14 relative error = 3.804298337322504e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1515087232112974 y2[1] (numeric) = 0.1515087232113372 absolute error = 3.980149543281186e-14 relative error = 2.627010154214278e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.280062008097945 y1[1] (closed_form) = 1.537671509265432 y1[1] (numeric) = 1.53767150926549 absolute error = 5.773159728050814e-14 relative error = 3.754481820898623e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1568455965102047 y2[1] (numeric) = 0.1568455965102451 absolute error = 4.038436252074007e-14 relative error = 2.574784591935457e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.290066552949143 y1[1] (closed_form) = 1.546079836801963 y1[1] (numeric) = 1.546079836802021 absolute error = 5.795364188543317e-14 relative error = 3.74842491997756e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1622668612031983 y2[1] (numeric) = 0.1622668612032393 absolute error = 4.099498518428391e-14 relative error = 2.526392935705339e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.30007109780034 y1[1] (closed_form) = 1.554433507162395 y1[1] (numeric) = 1.554433507162453 absolute error = 5.773159728050814e-14 relative error = 3.713995935786064e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1677719746754462 y2[1] (numeric) = 0.1677719746754878 absolute error = 4.155009669659648e-14 relative error = 2.476581489666249e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.310075642651538 y1[1] (closed_form) = 1.56273168422717 y1[1] (numeric) = 1.562731684227228 absolute error = 5.773159728050814e-14 relative error = 3.694274446675636e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1733603859196848 y2[1] (numeric) = 0.173360385919727 absolute error = 4.218847493575595e-14 relative error = 2.433570663329119e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.320080187502735 y1[1] (closed_form) = 1.570973537431058 y1[1] (numeric) = 1.570973537431116 absolute error = 5.81756864903582e-14 relative error = 3.703161453979057e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1790315355913699 y2[1] (numeric) = 0.1790315355914127 absolute error = 4.282685317491541e-14 relative error = 2.392140191025645e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.330084732353932 y1[1] (closed_form) = 1.579158241846289 y1[1] (numeric) = 1.579158241846346 absolute error = 5.728750807065808e-14 relative error = 3.627724350390611e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.184784856064661 y2[1] (numeric) = 0.1847848560647044 absolute error = 4.335420911161236e-14 relative error = 2.346199252196382e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.34008927720513 y1[1] (closed_form) = 1.58728497826512 y1[1] (numeric) = 1.587284978265177 absolute error = 5.662137425588298e-14 relative error = 3.567183904037783e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1906197714892353 y2[1] (numeric) = 0.1906197714892792 absolute error = 4.393707619954057e-14 relative error = 2.304959021631279e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.350093822056327 y1[1] (closed_form) = 1.59535293328183 y1[1] (numeric) = 1.595352933281886 absolute error = 5.595524044110789e-14 relative error = 3.507389448051557e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.1965356978479247 y2[1] (numeric) = 0.1965356978479691 absolute error = 4.440892098500626e-14 relative error = 2.259585483517044e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.360098366907525 y1[1] (closed_form) = 1.603361299374132 y1[1] (numeric) = 1.603361299374188 absolute error = 5.551115123125783e-14 relative error = 3.462173575782729e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2025320430151699 y2[1] (numeric) = 0.2025320430152149 absolute error = 4.50195436485501e-14 relative error = 2.222835605582573e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.370102911758722 y1[1] (closed_form) = 1.611309274984002 y1[1] (numeric) = 1.611309274984057 absolute error = 5.417888360170764e-14 relative error = 3.362413686984179e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2086082068162866 y2[1] (numeric) = 0.2086082068163321 absolute error = 4.554689958524705e-14 relative error = 2.1833704570098e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.380107456609919 y1[1] (closed_form) = 1.619196064597903 y1[1] (numeric) = 1.619196064597956 absolute error = 5.351274978693255e-14 relative error = 3.30489623566504e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2147635810875363 y2[1] (numeric) = 0.2147635810875824 absolute error = 4.6074255521944e-14 relative error = 2.145347702279392e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.390112001461117 y1[1] (closed_form) = 1.627020878826407 y1[1] (numeric) = 1.62702087882646 absolute error = 5.306866057708248e-14 relative error = 3.261707410624112e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2209975497369987 y2[1] (numeric) = 0.2209975497370453 absolute error = 4.660161145864095e-14 relative error = 2.108693581177704e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.400116546312314 y1[1] (closed_form) = 1.634782934483212 y1[1] (numeric) = 1.634782934483265 absolute error = 5.284661597215745e-14 relative error = 3.232638098761615e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.227309488806235 y2[1] (numeric) = 0.2273094888062822 absolute error = 4.715672297095352e-14 relative error = 2.074560249051074e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.410121091163512 y1[1] (closed_form) = 1.642481454663524 y1[1] (numeric) = 1.642481454663576 absolute error = 5.240252676230739e-14 relative error = 3.1904486113691e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.233698766532741 y2[1] (numeric) = 0.2336987665327888 absolute error = 4.782285678572862e-14 relative error = 2.046346135893219e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.420125636014709 y1[1] (closed_form) = 1.650115668821819 y1[1] (numeric) = 1.650115668821871 absolute error = 5.218048215738236e-14 relative error = 3.162231784311167e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2401647434131798 y2[1] (numeric) = 0.2401647434132283 absolute error = 4.846123502488808e-14 relative error = 2.017833023122603e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.430130180865906 y1[1] (closed_form) = 1.657684812848971 y1[1] (numeric) = 1.657684812849022 absolute error = 5.129230373768223e-14 relative error = 3.094213287116324e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.24670677226739 y2[1] (numeric) = 0.2467067722674391 absolute error = 4.904410211281629e-14 relative error = 1.987951188452194e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.440134725717104 y1[1] (closed_form) = 1.665188129148727 y1[1] (numeric) = 1.665188129148778 absolute error = 5.062616992290714e-14 relative error = 3.040267284921621e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2533241983031616 y2[1] (numeric) = 0.2533241983032111 absolute error = 4.951594689828198e-14 relative error = 1.95464733452051e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.450139270568301 y1[1] (closed_form) = 1.672624866713537 y1[1] (numeric) = 1.672624866713587 absolute error = 5.040412531798211e-14 relative error = 3.013474588418552e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2600163591817743 y2[1] (numeric) = 0.2600163591818245 absolute error = 5.012656956182582e-14 relative error = 1.927823684616049e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.460143815419499 y1[1] (closed_form) = 1.679994281199721 y1[1] (numeric) = 1.679994281199771 absolute error = 4.907185768843192e-14 relative error = 2.920953853092202e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2667825850842918 y2[1] (numeric) = 0.2667825850843424 absolute error = 5.062616992290714e-14 relative error = 1.89765647210111e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.469986996644064 y1[1] (closed_form) = 1.687178415098196 y1[1] (numeric) = 1.687178415098245 absolute error = 4.862776847858186e-14 relative error = 2.88219479596363e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2735113037196442 y2[1] (numeric) = 0.273511303719695 absolute error = 5.084821452783217e-14 relative error = 1.859090057204833e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.479991541495261 y1[1] (closed_form) = 1.69441209272577 y1[1] (numeric) = 1.694412092725818 absolute error = 4.818367926873179e-14 relative error = 2.843681267124315e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2804224534657737 y2[1] (numeric) = 0.2804224534658252 absolute error = 5.156985949383852e-14 relative error = 1.839006073033049e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.489996086346459 y1[1] (closed_form) = 1.701576266589463 y1[1] (numeric) = 1.701576266589511 absolute error = 4.796163466380676e-14 relative error = 2.818659122458153e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.2874056257881407 y2[1] (numeric) = 0.2874056257881926 absolute error = 5.190292640122607e-14 relative error = 1.805911984460805e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.500000631197656 y1[1] (closed_form) = 1.708670219626518 y1[1] (numeric) = 1.708670219626566 absolute error = 4.796163466380676e-14 relative error = 2.806956785042478e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.294460121740449 y2[1] (numeric) = 0.2944601217405015 absolute error = 5.25135490647699e-14 relative error = 1.783384070969645e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.510005176048853 y1[1] (closed_form) = 1.715693241802591 y1[1] (numeric) = 1.715693241802638 absolute error = 4.773959005888173e-14 relative error = 2.782524806632927e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3015852352376143 y2[1] (numeric) = 0.3015852352376672 absolute error = 5.290212712338871e-14 relative error = 1.754135181110838e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.520009720900051 y1[1] (closed_form) = 1.722644630182808 y1[1] (numeric) = 1.722644630182855 absolute error = 4.75175454539567e-14 relative error = 2.758406732380672e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3087802531264365 y2[1] (numeric) = 0.30878025312649 absolute error = 5.345723863570129e-14 relative error = 1.731238901919421e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.530014265751248 y1[1] (closed_form) = 1.729523689002131 y1[1] (numeric) = 1.729523689002178 absolute error = 4.707345624410664e-14 relative error = 2.721758397612133e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3160444552569792 y2[1] (numeric) = 0.3160444552570331 absolute error = 5.384581669432009e-14 relative error = 1.703741856522604e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.540018810602445 y1[1] (closed_form) = 1.736329729734993 y1[1] (numeric) = 1.73632972973504 absolute error = 4.685141163918161e-14 relative error = 2.698301528611866e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3233771145546495 y2[1] (numeric) = 0.3233771145547037 absolute error = 5.42343947529389e-14 relative error = 1.677125322477744e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.550023355453643 y1[1] (closed_form) = 1.743062071164214 y1[1] (numeric) = 1.743062071164259 absolute error = 4.574118861455645e-14 relative error = 2.624185872164915e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3307774970929706 y2[1] (numeric) = 0.3307774970930253 absolute error = 5.478950626525148e-14 relative error = 1.656385538519628e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.56002790030484 y1[1] (closed_form) = 1.749720039449181 y1[1] (numeric) = 1.749720039449228 absolute error = 4.618527782440651e-14 relative error = 2.639581006281772e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3382448621670415 y2[1] (numeric) = 0.3382448621670969 absolute error = 5.540012892879531e-14 relative error = 1.637870522965581e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.570032445156038 y1[1] (closed_form) = 1.756302968193299 y1[1] (numeric) = 1.756302968193345 absolute error = 4.640732242933154e-14 relative error = 2.642330125825076e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3457784623676733 y2[1] (numeric) = 0.3457784623677292 absolute error = 5.595524044110789e-14 relative error = 1.618239610933591e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.580036990007235 y1[1] (closed_form) = 1.762810198510683 y1[1] (numeric) = 1.76281019851073 absolute error = 4.662936703425657e-14 relative error = 2.645172297826027e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3533775436561979 y2[1] (numeric) = 0.3533775436562542 absolute error = 5.628830734849544e-14 relative error = 1.592865997259252e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.590041534858432 y1[1] (closed_form) = 1.769241079092112 y1[1] (numeric) = 1.769241079092159 absolute error = 4.662936703425657e-14 relative error = 2.635557561108884e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3610413454399397 y2[1] (numeric) = 0.3610413454399964 absolute error = 5.667688540711424e-14 relative error = 1.569817034058849e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.60004607970963 y1[1] (closed_form) = 1.775594966270217 y1[1] (numeric) = 1.775594966270264 absolute error = 4.685141163918161e-14 relative error = 2.638631699750583e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3687691006483433 y2[1] (numeric) = 0.3687691006484003 absolute error = 5.700995231450179e-14 relative error = 1.54595252732051e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.610050624560827 y1[1] (closed_form) = 1.781871224083902 y1[1] (numeric) = 1.781871224083949 absolute error = 4.662936703425657e-14 relative error = 2.616876371536317e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3765600358097499 y2[1] (numeric) = 0.3765600358098073 absolute error = 5.734301922188934e-14 relative error = 1.522812135349935e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.620055169412025 y1[1] (closed_form) = 1.788069224342004 y1[1] (numeric) = 1.78806922434205 absolute error = 4.574118861455645e-14 relative error = 2.558132984554267e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3844133711288137 y2[1] (numeric) = 0.3844133711288716 absolute error = 5.795364188543317e-14 relative error = 1.507586526328539e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.630059714263222 y1[1] (closed_form) = 1.794188346686164 y1[1] (numeric) = 1.794188346686209 absolute error = 4.529709940470639e-14 relative error = 2.524656872750811e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.3923283205645522 y2[1] (numeric) = 0.3923283205646107 absolute error = 5.845324224651449e-14 relative error = 1.489906264283993e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.640064259114419 y1[1] (closed_form) = 1.800227978652919 y1[1] (numeric) = 1.800227978652964 absolute error = 4.507505479978136e-14 relative error = 2.503852586132468e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4003040919090207 y2[1] (numeric) = 0.4003040919090796 absolute error = 5.889733145636455e-14 relative error = 1.471314749132029e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.650068803965617 y1[1] (closed_form) = 1.806187515735004 y1[1] (numeric) = 1.806187515735049 absolute error = 4.463096558993129e-14 relative error = 2.471003990511434e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4083398868666047 y2[1] (numeric) = 0.4083398868666641 absolute error = 5.939693181744587e-14 relative error = 1.45459539290242e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.660073348816814 y1[1] (closed_form) = 1.812066361441861 y1[1] (numeric) = 1.812066361441906 absolute error = 4.463096558993129e-14 relative error = 2.462987368432712e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4164349011339212 y2[1] (numeric) = 0.4164349011339814 absolute error = 6.017408793468348e-14 relative error = 1.444981863211607e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.670077893668012 y1[1] (closed_form) = 1.817863927359336 y1[1] (numeric) = 1.817863927359379 absolute error = 4.307665335545607e-14 relative error = 2.369630240588472e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4245883244803218 y2[1] (numeric) = 0.4245883244803825 absolute error = 6.06736882957648e-14 relative error = 1.429000393970485e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.680082438519209 y1[1] (closed_form) = 1.823579633208574 y1[1] (numeric) = 1.823579633208617 absolute error = 4.263256414560601e-14 relative error = 2.337850421733124e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4327993408289882 y2[1] (numeric) = 0.4327993408290491 absolute error = 6.089573290068984e-14 relative error = 1.407020001094492e-11 % Desired digits = 8 Estimated correct digits = 10 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] = 5.690086983370406 y1[1] (closed_form) = 1.829212906904105 y1[1] (numeric) = 1.829212906904148 absolute error = 4.241051954068098e-14 relative error = 2.318511933772634e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4410671283386141 y2[1] (numeric) = 0.4410671283386753 absolute error = 6.122879980807738e-14 relative error = 1.388196849733746e-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] = 5.700091528221604 y1[1] (closed_form) = 1.834763184611098 y1[1] (numeric) = 1.83476318461114 absolute error = 4.130029651605582e-14 relative error = 2.250987858403642e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4493908594856626 y2[1] (numeric) = 0.4493908594857243 absolute error = 6.167288901792745e-14 relative error = 1.372366342486658e-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] = 5.710096073072801 y1[1] (closed_form) = 1.840229910801797 y1[1] (numeric) = 1.840229910801838 absolute error = 4.085620730620576e-14 relative error = 2.220168635798584e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.457769701147194 y2[1] (numeric) = 0.457769701147256 absolute error = 6.200595592531499e-14 relative error = 1.354522935221028e-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] = 5.720100617923999 y1[1] (closed_form) = 1.845612538311126 y1[1] (numeric) = 1.845612538311166 absolute error = 3.996802888650564e-14 relative error = 2.165569861325248e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4662028146842521 y2[1] (numeric) = 0.4662028146843147 absolute error = 6.261657858885883e-14 relative error = 1.343118844772903e-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] = 5.730105162775196 y1[1] (closed_form) = 1.85091052839145 y1[1] (numeric) = 1.850910528391489 absolute error = 3.907985046680551e-14 relative error = 2.111385173262168e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4746893560258044 y2[1] (numeric) = 0.4746893560258676 absolute error = 6.317169010117141e-14 relative error = 1.330800644658595e-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] = 5.740109707626393 y1[1] (closed_form) = 1.856123350766503 y1[1] (numeric) = 1.856123350766542 absolute error = 3.907985046680551e-14 relative error = 2.105455461818695e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4832284757532254 y2[1] (numeric) = 0.4832284757532888 absolute error = 6.339373470609644e-14 relative error = 1.3118791190292e-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] = 5.750114252477591 y1[1] (closed_form) = 1.861250483684463 y1[1] (numeric) = 1.861250483684502 absolute error = 3.907985046680551e-14 relative error = 2.099655624504901e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4918193191853139 y2[1] (numeric) = 0.4918193191853777 absolute error = 6.389333506717776e-14 relative error = 1.299122107952478e-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] = 5.760118797328788 y1[1] (closed_form) = 1.866291413970171 y1[1] (numeric) = 1.866291413970211 absolute error = 3.930189507173054e-14 relative error = 2.105882006289865e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5004610264638394 y2[1] (numeric) = 0.5004610264639039 absolute error = 6.450395773072159e-14 relative error = 1.288890729144166e-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] = 5.770123342179986 y1[1] (closed_form) = 1.871245637076498 y1[1] (numeric) = 1.871245637076536 absolute error = 3.841371665203042e-14 relative error = 2.052842015548814e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5091527326396044 y2[1] (numeric) = 0.5091527326396698 absolute error = 6.539213615042172e-14 relative error = 1.284332420478405e-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] = 5.780127887031183 y1[1] (closed_form) = 1.876112657134841 y1[1] (numeric) = 1.87611265713488 absolute error = 3.930189507173054e-14 relative error = 2.094857945884314e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.517893567759018 y2[1] (numeric) = 0.5178935677590836 absolute error = 6.561418075534675e-14 relative error = 1.266943342031964e-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] = 5.79013243188238 y1[1] (closed_form) = 1.88089198700476 y1[1] (numeric) = 1.880891987004799 absolute error = 3.841371665203042e-14 relative error = 2.042313802038288e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5266826569511688 y2[1] (numeric) = 0.526682656951235 absolute error = 6.616929226765933e-14 relative error = 1.25634082296722e-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] = 5.800136976733578 y1[1] (closed_form) = 1.885583148322734 y1[1] (numeric) = 1.885583148322772 absolute error = 3.841371665203042e-14 relative error = 2.037232708947375e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5355191205153917 y2[1] (numeric) = 0.535519120515459 absolute error = 6.727951529228449e-14 relative error = 1.256341981356962e-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] = 5.810141521584775 y1[1] (closed_form) = 1.890185671550036 y1[1] (numeric) = 1.890185671550073 absolute error = 3.708144902248023e-14 relative error = 1.961788705766233e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5444020740093168 y2[1] (numeric) = 0.5444020740093845 absolute error = 6.761258219967203e-14 relative error = 1.241960408080938e-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] = 5.81998470280934 y1[1] (closed_form) = 1.894627008182145 y1[1] (numeric) = 1.894627008182182 absolute error = 3.663735981263017e-14 relative error = 1.93375053002031e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5531862622623787 y2[1] (numeric) = 0.5531862622624466 absolute error = 6.794564910705958e-14 relative error = 1.228259878131837e-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] = 5.829989247660538 y1[1] (closed_form) = 1.899052330045631 y1[1] (numeric) = 1.899052330045667 absolute error = 3.552713678800501e-14 relative error = 1.870782401617724e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5621588097956962 y2[1] (numeric) = 0.5621588097957643 absolute error = 6.80566714095221e-14 relative error = 1.210630701211562e-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] = 5.839993792511735 y1[1] (closed_form) = 1.903387665686932 y1[1] (numeric) = 1.903387665686967 absolute error = 3.530509218307998e-14 relative error = 1.854855572489926e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.571175180890009 y2[1] (numeric) = 0.5711751808900771 absolute error = 6.816769371198461e-14 relative error = 1.193463861748426e-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] = 5.849998337362933 y1[1] (closed_form) = 1.907632581181943 y1[1] (numeric) = 1.907632581181978 absolute error = 3.530509218307998e-14 relative error = 1.850728097818786e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5802344730959873 y2[1] (numeric) = 0.5802344730960558 absolute error = 6.850076061937216e-14 relative error = 1.180570334848757e-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] = 5.86000288221413 y1[1] (closed_form) = 1.911786651656722 y1[1] (numeric) = 1.911786651656757 absolute error = 3.441691376337985e-14 relative error = 1.800248669670056e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5893357796683241 y2[1] (numeric) = 0.5893357796683929 absolute error = 6.883382752675971e-14 relative error = 1.16798996262367e-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] = 5.870007427065327 y1[1] (closed_form) = 1.915849461330011 y1[1] (numeric) = 1.915849461330045 absolute error = 3.419486915845482e-14 relative error = 1.784841129151987e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5984781896564902 y2[1] (numeric) = 0.5984781896565593 absolute error = 6.905587213168474e-14 relative error = 1.15385779006117e-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] = 5.880011971916525 y1[1] (closed_form) = 1.919820603554852 y1[1] (numeric) = 1.919820603554886 absolute error = 3.441691376337985e-14 relative error = 1.792715095340236e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6076607879959131 y2[1] (numeric) = 0.6076607879959827 absolute error = 6.961098364399732e-14 relative error = 1.145556616769313e-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] = 5.890016516767722 y1[1] (closed_form) = 1.923699680859292 y1[1] (numeric) = 1.923699680859325 absolute error = 3.352873534367973e-14 relative error = 1.742929817855086e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6168826555995641 y2[1] (numeric) = 0.616882655599634 absolute error = 6.983302824892235e-14 relative error = 1.132030988633484e-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] = 5.900021061618919 y1[1] (closed_form) = 1.927486304986162 y1[1] (numeric) = 1.927486304986194 absolute error = 3.26405569239796e-14 relative error = 1.693426139503178e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6261428694499509 y2[1] (numeric) = 0.6261428694500208 absolute error = 6.994405055138486e-14 relative error = 1.117062158878033e-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] = 5.910025606470117 y1[1] (closed_form) = 1.931180096931939 y1[1] (numeric) = 1.931180096931971 absolute error = 3.241851231905457e-14 relative error = 1.678689231033283e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6354405026915022 y2[1] (numeric) = 0.6354405026915724 absolute error = 7.016609515630989e-14 relative error = 1.104211879147001e-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] = 5.920030151321314 y1[1] (closed_form) = 1.934780686984682 y1[1] (numeric) = 1.934780686984714 absolute error = 3.197442310920451e-14 relative error = 1.652612274057584e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6447746247233367 y2[1] (numeric) = 0.6447746247234073 absolute error = 7.061018436615996e-14 relative error = 1.09511419430406e-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] = 5.930034696172512 y1[1] (closed_form) = 1.938287714761034 y1[1] (numeric) = 1.938287714761065 absolute error = 3.153033389935445e-14 relative error = 1.626710712720054e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6541443012924071 y2[1] (numeric) = 0.6541443012924775 absolute error = 7.038813976123492e-14 relative error = 1.07603382957197e-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] = 5.940039241023709 y1[1] (closed_form) = 1.941700829242293 y1[1] (numeric) = 1.941700829242324 absolute error = 3.064215547965432e-14 relative error = 1.578108996925739e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6635485945870094 y2[1] (numeric) = 0.6635485945870803 absolute error = 7.083222897108499e-14 relative error = 1.067476135868704e-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] = 5.950043785874906 y1[1] (closed_form) = 1.945019688809551 y1[1] (numeric) = 1.94501968880958 absolute error = 2.90878432451791e-14 relative error = 1.49550379425631e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6729865633306488 y2[1] (numeric) = 0.6729865633307202 absolute error = 7.138734048339757e-14 relative error = 1.060754320711807e-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] = 5.960048330726104 y1[1] (closed_form) = 1.948243961277876 y1[1] (numeric) = 1.948243961277905 absolute error = 2.864375403532904e-14 relative error = 1.470234457523547e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.682457262876252 y2[1] (numeric) = 0.6824572628763237 absolute error = 7.172040739078511e-14 relative error = 1.050914266609394e-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] = 5.970052875577301 y1[1] (closed_form) = 1.951373323929571 y1[1] (numeric) = 1.951373323929599 absolute error = 2.731148640577885e-14 relative error = 1.399603349644057e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6919597453007169 y2[1] (numeric) = 0.6919597453007885 absolute error = 7.16093850883226e-14 relative error = 1.034877904020299e-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] = 5.980057420428499 y1[1] (closed_form) = 1.954407463546469 y1[1] (numeric) = 1.954407463546495 absolute error = 2.620126338115369e-14 relative error = 1.340624402529085e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7014930594997906 y2[1] (numeric) = 0.7014930594998623 absolute error = 7.172040739078511e-14 relative error = 1.022396535782212e-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] = 5.990061965279696 y1[1] (closed_form) = 1.957346076441284 y1[1] (numeric) = 1.957346076441309 absolute error = 2.486899575160351e-14 relative error = 1.270546688239142e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7110562512832652 y2[1] (numeric) = 0.7110562512833372 absolute error = 7.194245199571014e-14 relative error = 1.011768785744776e-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] = 6.000066510130893 y1[1] (closed_form) = 1.960188868488008 y1[1] (numeric) = 1.960188868488031 absolute error = 2.287059430727822e-14 relative error = 1.166754626298815e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.720648363470483 y2[1] (numeric) = 0.7206483634705553 absolute error = 7.227551890309769e-14 relative error = 1.002923513973372e-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] = 6.010071054982091 y1[1] (closed_form) = 1.962935555151349 y1[1] (numeric) = 1.962935555151372 absolute error = 2.242650509742816e-14 relative error = 1.142498287250138e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7302684359861406 y2[1] (numeric) = 0.730268435986213 absolute error = 7.249756350802272e-14 relative error = 9.927522529454993e-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] = 6.020075599833288 y1[1] (closed_form) = 1.965585861515213 y1[1] (numeric) = 1.965585861515235 absolute error = 2.19824158875781e-14 relative error = 1.118364570990173e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.739915505956383 y2[1] (numeric) = 0.7399155059564556 absolute error = 7.260858581048524e-14 relative error = 9.813091525448503e-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] = 6.030080144684486 y1[1] (closed_form) = 1.968139522310215 y1[1] (numeric) = 1.968139522310236 absolute error = 2.065014825802791e-14 relative error = 1.04922176623884e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7495886078051779 y2[1] (numeric) = 0.7495886078052507 absolute error = 7.283063041541027e-14 relative error = 9.716080214807553e-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] = 6.040084689535683 y1[1] (closed_form) = 1.970596281940235 y1[1] (numeric) = 1.970596281940255 absolute error = 2.042810365310288e-14 relative error = 1.036645803116482e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7592867733509598 y2[1] (numeric) = 0.7592867733510331 absolute error = 7.327471962526033e-14 relative error = 9.650467016813299e-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] = 6.05008923438688 y1[1] (closed_form) = 1.972955894507998 y1[1] (numeric) = 1.972955894508017 absolute error = 1.909583602355269e-14 relative error = 9.678795190864963e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7690090319035362 y2[1] (numeric) = 0.7690090319036091 absolute error = 7.294165271787278e-14 relative error = 9.485149028395615e-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] = 6.060093779238078 y1[1] (closed_form) = 1.975218123839687 y1[1] (numeric) = 1.975218123839706 absolute error = 1.865174681370263e-14 relative error = 9.442879542561573e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7787544103612429 y2[1] (numeric) = 0.7787544103613164 absolute error = 7.349676423018536e-14 relative error = 9.437733289509361e-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] = 6.070098324089275 y1[1] (closed_form) = 1.97738274350858 y1[1] (numeric) = 1.977382743508598 absolute error = 1.731947918415244e-14 relative error = 8.758789486258754e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7885219333083431 y2[1] (numeric) = 0.7885219333084168 absolute error = 7.371880883511039e-14 relative error = 9.34898646709976e-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] = 6.080102868940473 y1[1] (closed_form) = 1.979449536857716 y1[1] (numeric) = 1.979449536857733 absolute error = 1.643130076445232e-14 relative error = 8.300944509318606e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7983106231126559 y2[1] (numeric) = 0.7983106231127298 absolute error = 7.394085344003543e-14 relative error = 9.262165791022055e-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] = 6.09010741379167 y1[1] (closed_form) = 1.981418297021577 y1[1] (numeric) = 1.981418297021593 absolute error = 1.554312234475219e-14 relative error = 7.844442724747348e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8081195000234078 y2[1] (numeric) = 0.808119500023482 absolute error = 7.416289804496046e-14 relative error = 9.177219216070429e-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] = 6.100111958642867 y1[1] (closed_form) = 1.983288826946796 y1[1] (numeric) = 1.983288826946811 absolute error = 1.48769885299771e-14 relative error = 7.501170947894516e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8179475822692964 y2[1] (numeric) = 0.8179475822693706 absolute error = 7.416289804496046e-14 relative error = 9.066949967527808e-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] = 6.110116503494065 y1[1] (closed_form) = 1.985060939411876 y1[1] (numeric) = 1.985060939411889 absolute error = 1.287858708565182e-14 relative error = 6.48775401800381e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8277938861567558 y2[1] (numeric) = 0.8277938861568301 absolute error = 7.438494264988549e-14 relative error = 8.985925590153432e-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] = 6.120121048345262 y1[1] (closed_form) = 1.986734457045935 y1[1] (numeric) = 1.986734457045947 absolute error = 1.176836406102666e-14 relative error = 5.92347106040783e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.837657426168414 y2[1] (numeric) = 0.8376574261684884 absolute error = 7.438494264988549e-14 relative error = 8.880114988072717e-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] = 6.13012559319646 y1[1] (closed_form) = 1.988309212346454 y1[1] (numeric) = 1.988309212346465 absolute error = 1.110223024625157e-14 relative error = 5.583754366429527e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8475372150617343 y2[1] (numeric) = 0.847537215061809 absolute error = 7.471800955727304e-14 relative error = 8.815897193591741e-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] = 6.140130138047657 y1[1] (closed_form) = 1.989785047696044 y1[1] (numeric) = 1.989785047696055 absolute error = 1.043609643147647e-14 relative error = 5.24483609099402e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.857432263967828 y2[1] (numeric) = 0.8574322639679031 absolute error = 7.505107646466058e-14 relative error = 8.753003545417856e-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] = 6.150134682898854 y1[1] (closed_form) = 1.991161815378224 y1[1] (numeric) = 1.991161815378235 absolute error = 1.088018564132653e-14 relative error = 5.464239800751617e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8673415824904307 y2[1] (numeric) = 0.8673415824905056 absolute error = 7.494005416219807e-14 relative error = 8.640200778454533e-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] = 6.160139227750052 y1[1] (closed_form) = 1.992439377592202 y1[1] (numeric) = 1.992439377592211 absolute error = 9.769962616701378e-15 relative error = 4.903518132886965e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8772641788050303 y2[1] (numeric) = 0.877264178805105 absolute error = 7.471800955727304e-14 relative error = 8.517161803990508e-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] = 6.170143772601249 y1[1] (closed_form) = 1.993617606466669 y1[1] (numeric) = 1.993617606466678 absolute error = 9.547918011776346e-15 relative error = 4.789242420816259e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8871990597581398 y2[1] (numeric) = 0.8871990597582147 absolute error = 7.482903185973555e-14 relative error = 8.434300176122229e-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] = 6.179986953825814 y1[1] (closed_form) = 1.994679774104064 y1[1] (numeric) = 1.994679774104072 absolute error = 8.215650382226158e-15 relative error = 4.118781615418106e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8969847244905441 y2[1] (numeric) = 0.8969847244906186 absolute error = 7.4495964952348e-14 relative error = 8.305154248268731e-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] = 6.189991498677012 y1[1] (closed_form) = 1.995660599065219 y1[1] (numeric) = 1.995660599065226 absolute error = 7.549516567451064e-15 relative error = 3.782966187230089e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9069410323016086 y2[1] (numeric) = 0.9069410323016835 absolute error = 7.494005416219807e-14 relative error = 8.262946706911846e-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] = 6.199996043528209 y1[1] (closed_form) = 1.996541768274539 y1[1] (numeric) = 1.996541768274547 absolute error = 7.993605777301127e-15 relative error = 4.003725794431738e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9169066543924584 y2[1] (numeric) = 0.9169066543925333 absolute error = 7.482903185973555e-14 relative error = 8.1610305150765e-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] = 6.210000588379406 y1[1] (closed_form) = 1.997323193535727 y1[1] (numeric) = 1.997323193535734 absolute error = 7.105427357601002e-15 relative error = 3.557475014858633e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.926880593303153 y2[1] (numeric) = 0.9268805933032279 absolute error = 7.494005416219807e-14 relative error = 8.085189689335482e-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] = 6.220005133230604 y1[1] (closed_form) = 1.998004796635862 y1[1] (numeric) = 1.998004796635868 absolute error = 5.995204332975845e-15 relative error = 3.000595565671445e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9368618507413206 y2[1] (numeric) = 0.9368618507413956 absolute error = 7.505107646466058e-14 relative error = 8.01090111688016e-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] = 6.230009678081801 y1[1] (closed_form) = 1.998586509353234 y1[1] (numeric) = 1.998586509353239 absolute error = 4.662936703425657e-15 relative error = 2.333117271433318e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9468494276820772 y2[1] (numeric) = 0.9468494276821523 absolute error = 7.505107646466058e-14 relative error = 7.926400362134497e-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] = 6.240014222932999 y1[1] (closed_form) = 1.999068273464169 y1[1] (numeric) = 1.999068273464173 absolute error = 3.774758283725532e-15 relative error = 1.888258812283726e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.95684232446802 y2[1] (numeric) = 0.9568423244680953 absolute error = 7.527312106958561e-14 relative error = 7.866826032328321e-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] = 6.250018767784196 y1[1] (closed_form) = 1.999450040748858 y1[1] (numeric) = 1.999450040748861 absolute error = 3.108624468950438e-15 relative error = 1.554739756231248e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9668395409092816 y2[1] (numeric) = 0.9668395409093566 absolute error = 7.505107646466058e-14 relative error = 7.762516248981444e-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] = 6.260023312635393 y1[1] (closed_form) = 1.999731772996179 y1[1] (numeric) = 1.999731772996182 absolute error = 2.442490654175344e-15 relative error = 1.221409134543971e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9768400763836403 y2[1] (numeric) = 0.9768400763837156 absolute error = 7.527312106958561e-14 relative error = 7.705777321120387e-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] = 6.270027857486591 y1[1] (closed_form) = 1.999913442007531 y1[1] (numeric) = 1.999913442007534 absolute error = 2.220446049250313e-15 relative error = 1.110271076042876e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9868429299366722 y2[1] (numeric) = 0.9868429299367475 absolute error = 7.527312106958561e-14 relative error = 7.627669894176173e-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] = 6.280032402337788 y1[1] (closed_form) = 1.999995029599647 y1[1] (numeric) = 1.999995029599648 absolute error = 1.332267629550188e-15 relative error = 6.661354702550822e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9968471003819366 y2[1] (numeric) = 0.9968471003820124 absolute error = 7.582823258189819e-14 relative error = 7.606806756306461e-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] = 6.290036947188986 y1[1] (closed_form) = 1.999976527606417 y1[1] (numeric) = 1.999976527606417 absolute error = 2.220446049250313e-16 relative error = 1.110236054573978e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.0001613636266322163 y2[1] (closed_form) = 1.006851586401185 y2[1] (numeric) = 1.006851586401261 absolute error = 7.593925488436071e-14 relative error = 7.542249116952013e-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] = 6.300041492040183 y1[1] (closed_form) = 1.999857937879708 y1[1] (numeric) = 1.999857937879708 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.0001613636266322163 y2[1] (closed_form) = 1.016855386644583 y2[1] (numeric) = 1.016855386644659 absolute error = 7.616129948928574e-14 relative error = 7.489885040645025e-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] = 6.31004603689138 y1[1] (closed_form) = 1.999639272289175 y1[1] (numeric) = 1.999639272289174 absolute error = 4.440892098500626e-16 relative error = 2.22084660970712e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.0001613636266322163 y2[1] (closed_form) = 1.026857499830935 y2[1] (numeric) = 1.02685749983101 absolute error = 7.527312106958561e-14 relative error = 7.330434951488283e-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] = 6.320050581742578 y1[1] (closed_form) = 1.999320552721076 y1[1] (numeric) = 1.999320552721074 absolute error = 1.77635683940025e-15 relative error = 8.884802574467754e-14 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 16 h = 0.0001613636266322163 y2[1] (closed_form) = 1.036856924847905 y2[1] (numeric) = 1.03685692484798 absolute error = 7.549516567451064e-14 relative error = 7.281155564022e-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] = 6.330055126593775 y1[1] (closed_form) = 1.998901811076077 y1[1] (numeric) = 1.998901811076075 absolute error = 2.664535259100376e-15 relative error = 1.332999572233098e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.046852660852214 y2[1] (numeric) = 1.046852660852289 absolute error = 7.549516567451064e-14 relative error = 7.211632400404095e-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] = 6.340059671444973 y1[1] (closed_form) = 1.998383089266067 y1[1] (numeric) = 1.998383089266064 absolute error = 2.664535259100376e-15 relative error = 1.333345579940312e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.056843707369817 y2[1] (numeric) = 1.056843707369892 absolute error = 7.505107646466058e-14 relative error = 7.101435712896598e-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] = 6.35006421629617 y1[1] (closed_form) = 1.997764439209952 y1[1] (numeric) = 1.997764439209949 absolute error = 3.33066907387547e-15 relative error = 1.667198098286621e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.066829064396041 y2[1] (numeric) = 1.066829064396115 absolute error = 7.416289804496046e-14 relative error = 6.951713308162071e-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] = 6.360068761147367 y1[1] (closed_form) = 1.997045922828469 y1[1] (numeric) = 1.997045922828466 absolute error = 3.108624468950438e-15 relative error = 1.556611409590227e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.076807732495673 y2[1] (numeric) = 1.076807732495747 absolute error = 7.349676423018536e-14 relative error = 6.825430577085931e-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] = 6.370073305998565 y1[1] (closed_form) = 1.996227612037981 y1[1] (numeric) = 1.996227612037977 absolute error = 3.996802888650564e-15 relative error = 2.002177940305195e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.086778712902998 y2[1] (numeric) = 1.086778712903072 absolute error = 7.327471962526033e-14 relative error = 6.742377151419283e-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] = 6.380077850849762 y1[1] (closed_form) = 1.995309588743285 y1[1] (numeric) = 1.99530958874328 absolute error = 4.662936703425657e-15 relative error = 2.3369489776083e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.096741007621761 y2[1] (numeric) = 1.096741007621835 absolute error = 7.371880883511039e-14 relative error = 6.721624186822984e-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] = 6.39008239570096 y1[1] (closed_form) = 1.994291944829406 y1[1] (numeric) = 1.994291944829401 absolute error = 4.884981308350689e-15 relative error = 2.449481542066077e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.106693619525057 y2[1] (numeric) = 1.10669361952513 absolute error = 7.283063041541027e-14 relative error = 6.580920783356994e-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] = 6.400086940552157 y1[1] (closed_form) = 1.993174782152409 y1[1] (numeric) = 1.993174782152404 absolute error = 5.329070518200751e-15 relative error = 2.673659413072617e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.116635552455137 y2[1] (numeric) = 1.11663555245521 absolute error = 7.283063041541027e-14 relative error = 6.522327742053185e-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] = 6.410091485403354 y1[1] (closed_form) = 1.991958212529199 y1[1] (numeric) = 1.991958212529193 absolute error = 5.551115123125783e-15 relative error = 2.786762838803484e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.126565811323111 y2[1] (numeric) = 1.126565811323184 absolute error = 7.30526750203353e-14 relative error = 6.484545712827691e-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] = 6.420096030254552 y1[1] (closed_form) = 1.990642357726329 y1[1] (numeric) = 1.990642357726323 absolute error = 5.773159728050814e-15 relative error = 2.900149143136288e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.136483402208546 y2[1] (numeric) = 1.136483402208619 absolute error = 7.371880883511039e-14 relative error = 6.486571532136017e-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] = 6.430100575105749 y1[1] (closed_form) = 1.989227349447817 y1[1] (numeric) = 1.98922734944781 absolute error = 6.883382752675971e-15 relative error = 3.460329838410228e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.146387332458948 y2[1] (numeric) = 1.146387332459021 absolute error = 7.327471962526033e-14 relative error = 6.39179425230471e-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] = 6.440105119956947 y1[1] (closed_form) = 1.987713329321958 y1[1] (numeric) = 1.987713329321951 absolute error = 7.105427357601002e-15 relative error = 3.574674100527756e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.156276610789118 y2[1] (numeric) = 1.156276610789192 absolute error = 7.349676423018536e-14 relative error = 6.356330617119928e-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] = 6.450109664808144 y1[1] (closed_form) = 1.986100448887151 y1[1] (numeric) = 1.986100448887144 absolute error = 7.327471962526033e-15 relative error = 3.689376318620617e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.16615024738037 y2[1] (numeric) = 1.166150247380444 absolute error = 7.394085344003543e-14 relative error = 6.340594070629878e-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] = 6.460114209659341 y1[1] (closed_form) = 1.984388869576734 y1[1] (numeric) = 1.984388869576726 absolute error = 7.771561172376096e-15 relative error = 3.916349910808436e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.176007253979599 y2[1] (numeric) = 1.176007253979673 absolute error = 7.394085344003543e-14 relative error = 6.287448754233459e-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] = 6.470118754510539 y1[1] (closed_form) = 1.982578762702821 y1[1] (numeric) = 1.982578762702813 absolute error = 7.771561172376096e-15 relative error = 3.919925562897304e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.185846643998198 y2[1] (numeric) = 1.185846643998272 absolute error = 7.438494264988549e-14 relative error = 6.272728689359812e-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] = 6.480123299361736 y1[1] (closed_form) = 1.980670309439159 y1[1] (numeric) = 1.98067030943915 absolute error = 8.659739592076221e-15 relative error = 4.372125714616426e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.195667432610805 y2[1] (numeric) = 1.19566743261088 absolute error = 7.482903185973555e-14 relative error = 6.258348251264342e-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] = 6.490127844212934 y1[1] (closed_form) = 1.978663700802993 y1[1] (numeric) = 1.978663700802983 absolute error = 1.021405182655144e-14 relative error = 5.162095924843778e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.205468636853874 y2[1] (numeric) = 1.205468636853949 absolute error = 7.505107646466058e-14 relative error = 6.225883790766614e-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] = 6.500132389064131 y1[1] (closed_form) = 1.976559137635948 y1[1] (numeric) = 1.976559137635936 absolute error = 1.199040866595169e-14 relative error = 6.066304031911105e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.21524927572406 y2[1] (numeric) = 1.215249275724136 absolute error = 7.549516567451064e-14 relative error = 6.212319330906797e-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] = 6.510136933915328 y1[1] (closed_form) = 1.974356830583926 y1[1] (numeric) = 1.974356830583912 absolute error = 1.398881011027697e-14 relative error = 7.085249177647239e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.22500837027641 y2[1] (numeric) = 1.225008370276486 absolute error = 7.571721027943568e-14 relative error = 6.180954523792429e-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] = 6.520141478766526 y1[1] (closed_form) = 1.972057000076022 y1[1] (numeric) = 1.972057000076007 absolute error = 1.465494392505207e-14 relative error = 7.431298347100071e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.234744943722341 y2[1] (numeric) = 1.234744943722416 absolute error = 7.505107646466058e-14 relative error = 6.07826554352244e-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] = 6.529984659991091 y1[1] (closed_form) = 1.969699310311094 y1[1] (numeric) = 1.969699310311079 absolute error = 1.554312234475219e-14 relative error = 7.891114274847012e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.244301550511223 y2[1] (numeric) = 1.244301550511298 absolute error = 7.527312106958561e-14 relative error = 6.049427571528747e-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] = 6.539989204842288 y1[1] (closed_form) = 1.967206696621904 y1[1] (numeric) = 1.967206696621887 absolute error = 1.687538997430238e-14 relative error = 8.578351224241396e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.253990562835993 y2[1] (numeric) = 1.253990562836068 absolute error = 7.505107646466058e-14 relative error = 5.984979368180172e-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] = 6.549993749693486 y1[1] (closed_form) = 1.964617275134331 y1[1] (numeric) = 1.964617275134314 absolute error = 1.731947918415244e-14 relative error = 8.815701359934451e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.26365415322429 y2[1] (numeric) = 1.263654153224365 absolute error = 7.482903185973555e-14 relative error = 5.921638580366689e-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] = 6.559998294544683 y1[1] (closed_form) = 1.961931305023789 y1[1] (numeric) = 1.961931305023771 absolute error = 1.820765760385257e-14 relative error = 9.280476618742671e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.273291354446552 y2[1] (numeric) = 1.273291354446626 absolute error = 7.460698725481052e-14 relative error = 5.859380651118861e-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] = 6.57000283939588 y1[1] (closed_form) = 1.959149055129247 y1[1] (numeric) = 1.959149055129227 absolute error = 1.909583602355269e-14 relative error = 9.747005197770889e-13 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 15 h = 0.0001613636266322163 y2[1] (closed_form) = 1.282901201914509 y2[1] (numeric) = 1.282901201914584 absolute error = 7.505107646466058e-14 relative error = 5.850105709828612e-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] = 6.580007384247078 y1[1] (closed_form) = 1.956270803926327 y1[1] (numeric) = 1.956270803926307 absolute error = 2.020605904817785e-14 relative error = 1.032886602796676e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.292482733777733 y2[1] (numeric) = 1.292482733777808 absolute error = 7.482903185973555e-14 relative error = 5.789557562677957e-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] = 6.590011929098275 y1[1] (closed_form) = 1.953296839499432 y1[1] (numeric) = 1.95329683949941 absolute error = 2.153832667772804e-14 relative error = 1.102665311394638e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.302034991019906 y2[1] (numeric) = 1.302034991019981 absolute error = 7.416289804496046e-14 relative error = 5.695922041762286e-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] = 6.600016473949473 y1[1] (closed_form) = 1.950227459512906 y1[1] (numeric) = 1.950227459512884 absolute error = 2.264854970235319e-14 relative error = 1.161328623073021e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.31155701755481 y2[1] (numeric) = 1.311557017554885 absolute error = 7.460698725481052e-14 relative error = 5.688428810659213e-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] = 6.61002101880067 y1[1] (closed_form) = 1.947062971181248 y1[1] (numeric) = 1.947062971181225 absolute error = 2.331468351712829e-14 relative error = 1.197428324723555e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.321047860322019 y2[1] (numeric) = 1.321047860322094 absolute error = 7.460698725481052e-14 relative error = 5.647561265238664e-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] = 6.620025563651867 y1[1] (closed_form) = 1.943803691238356 y1[1] (numeric) = 1.943803691238332 absolute error = 2.375877272697835e-14 relative error = 1.222282519272414e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.330506569382295 y2[1] (numeric) = 1.33050656938237 absolute error = 7.438494264988549e-14 relative error = 5.590723440352471e-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] = 6.630030108503065 y1[1] (closed_form) = 1.94044994590583 y1[1] (numeric) = 1.940449945905805 absolute error = 2.486899575160351e-14 relative error = 1.281609752628497e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.339932198012665 y2[1] (numeric) = 1.339932198012739 absolute error = 7.438494264988549e-14 relative error = 5.551396015426028e-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] = 6.640034653354262 y1[1] (closed_form) = 1.937002070860318 y1[1] (numeric) = 1.937002070860291 absolute error = 2.642330798607873e-14 relative error = 1.364134214598069e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.349323802801178 y2[1] (numeric) = 1.349323802801252 absolute error = 7.349676423018536e-14 relative error = 5.44693305473505e-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] = 6.65003919820546 y1[1] (closed_form) = 1.933460411199918 y1[1] (numeric) = 1.933460411199891 absolute error = 2.686739719592879e-14 relative error = 1.389601619991521e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.358680443741334 y2[1] (numeric) = 1.358680443741407 absolute error = 7.327471962526033e-14 relative error = 5.393079731352225e-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] = 6.660043743056657 y1[1] (closed_form) = 1.92982532140964 y1[1] (numeric) = 1.929825321409612 absolute error = 2.797762022055394e-14 relative error = 1.449748840486646e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.368001184326164 y2[1] (numeric) = 1.368001184326237 absolute error = 7.327471962526033e-14 relative error = 5.356334516724359e-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] = 6.670048287907854 y1[1] (closed_form) = 1.926097165325922 y1[1] (numeric) = 1.926097165325893 absolute error = 2.90878432451791e-14 relative error = 1.510196046639061e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.377285091641973 y2[1] (numeric) = 1.377285091642046 absolute error = 7.30526750203353e-14 relative error = 5.30410700469017e-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] = 6.680052832759052 y1[1] (closed_form) = 1.922276316100215 y1[1] (numeric) = 1.922276316100186 absolute error = 2.864375403532904e-14 relative error = 1.490095559905746e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.386531236461707 y2[1] (numeric) = 1.38653123646178 absolute error = 7.283063041541027e-14 relative error = 5.252721936598195e-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] = 6.690057377610249 y1[1] (closed_form) = 1.918363156161635 y1[1] (numeric) = 1.918363156161605 absolute error = 2.953193245502916e-14 relative error = 1.53943388456846e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.395738693337967 y2[1] (numeric) = 1.395738693338038 absolute error = 7.194245199571014e-14 relative error = 5.154435593073429e-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] = 6.700061922461447 y1[1] (closed_form) = 1.914358077178683 y1[1] (numeric) = 1.914358077178653 absolute error = 3.019806626980426e-14 relative error = 1.577451294499154e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.40490654069563 y2[1] (numeric) = 1.404906540695701 absolute error = 7.127631818093505e-14 relative error = 5.07338503425595e-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] = 6.710066467312644 y1[1] (closed_form) = 1.910261480020047 y1[1] (numeric) = 1.910261480020017 absolute error = 2.997602166487923e-14 relative error = 1.569210392315749e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.414033860924095 y2[1] (numeric) = 1.414033860924165 absolute error = 7.083222897108499e-14 relative error = 5.009231456790926e-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] = 6.720071012163841 y1[1] (closed_form) = 1.906073774714477 y1[1] (numeric) = 1.906073774714446 absolute error = 3.086420008457935e-14 relative error = 1.619255271963579e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.423119740469124 y2[1] (numeric) = 1.423119740469196 absolute error = 7.149836278586008e-14 relative error = 5.024058113500064e-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] = 6.730075557015039 y1[1] (closed_form) = 1.901795380409743 y1[1] (numeric) = 1.90179538040971 absolute error = 3.26405569239796e-14 relative error = 1.71630225103119e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.432163269924282 y2[1] (numeric) = 1.432163269924352 absolute error = 7.061018436615996e-14 relative error = 4.930316664935354e-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] = 6.740080101866236 y1[1] (closed_form) = 1.897426725330684 y1[1] (numeric) = 1.897426725330652 absolute error = 3.26405569239796e-14 relative error = 1.720253883231828e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.441163544121955 y2[1] (numeric) = 1.441163544122025 absolute error = 6.94999613415348e-14 relative error = 4.822489551932041e-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] = 6.750084646717434 y1[1] (closed_form) = 1.892968246736351 y1[1] (numeric) = 1.892968246736318 absolute error = 3.286260152890463e-14 relative error = 1.736035540245471e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.450119662223955 y2[1] (numeric) = 1.450119662224024 absolute error = 6.883382752675971e-14 relative error = 4.746768788804209e-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] = 6.760089191568631 y1[1] (closed_form) = 1.888420390876235 y1[1] (numeric) = 1.888420390876202 absolute error = 3.33066907387547e-14 relative error = 1.763732847816807e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.459030727811677 y2[1] (numeric) = 1.459030727811746 absolute error = 6.816769371198461e-14 relative error = 4.672121869168973e-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] = 6.770093736419828 y1[1] (closed_form) = 1.883783612945605 y1[1] (numeric) = 1.883783612945571 absolute error = 3.397282455352979e-14 relative error = 1.803435613308457e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.46789584897583 y2[1] (numeric) = 1.467895848975897 absolute error = 6.683542608243442e-14 relative error = 4.553144974765503e-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] = 6.780098281271026 y1[1] (closed_form) = 1.879058377039949 y1[1] (numeric) = 1.879058377039914 absolute error = 3.552713678800501e-14 relative error = 1.890688294845333e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.476714138405702 y2[1] (numeric) = 1.476714138405768 absolute error = 6.550315845288424e-14 relative error = 4.435737205279493e-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] = 6.790102826122223 y1[1] (closed_form) = 1.87424515610852 y1[1] (numeric) = 1.874245156108484 absolute error = 3.61932706027801e-14 relative error = 1.93108518833939e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.485484713477973 y2[1] (numeric) = 1.485484713478038 absolute error = 6.52811138479592e-14 relative error = 4.39460017700998e-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] = 6.800107370973421 y1[1] (closed_form) = 1.869344431906999 y1[1] (numeric) = 1.869344431906963 absolute error = 3.61932706027801e-14 relative error = 1.93614777378708e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.494206696345058 y2[1] (numeric) = 1.494206696345123 absolute error = 6.550315845288424e-14 relative error = 4.383808385620938e-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] = 6.810111915824618 y1[1] (closed_form) = 1.864356694949279 y1[1] (numeric) = 1.864356694949242 absolute error = 3.663735981263017e-14 relative error = 1.965147544559702e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.502879214022969 y2[1] (numeric) = 1.502879214023034 absolute error = 6.483702463810914e-14 relative error = 4.314187330101581e-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] = 6.820116460675815 y1[1] (closed_form) = 1.859282444458364 y1[1] (numeric) = 1.859282444458327 absolute error = 3.641531520770513e-14 relative error = 1.958568227019077e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.511501398478693 y2[1] (numeric) = 1.511501398478759 absolute error = 6.59472476627343e-14 relative error = 4.363029219100251e-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] = 6.830121005527013 y1[1] (closed_form) = 1.854122188316406 y1[1] (numeric) = 1.854122188316368 absolute error = 3.796962744218035e-14 relative error = 2.047849256184018e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.520072386717075 y2[1] (numeric) = 1.52007238671714 absolute error = 6.52811138479592e-14 relative error = 4.294605600260123e-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] = 6.84012555037821 y1[1] (closed_form) = 1.848876443013869 y1[1] (numeric) = 1.84887644301383 absolute error = 3.885780586188048e-14 relative error = 2.101698358952426e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.52859132086719 y2[1] (numeric) = 1.528591320867255 absolute error = 6.461498003318411e-14 relative error = 4.227093216552295e-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] = 6.850130095229408 y1[1] (closed_form) = 1.843545733597837 y1[1] (numeric) = 1.843545733597797 absolute error = 3.996802888650564e-14 relative error = 2.16799768826481e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.537057348268215 y2[1] (numeric) = 1.537057348268279 absolute error = 6.328271240363392e-14 relative error = 4.117134111810064e-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] = 6.860134640080605 y1[1] (closed_form) = 1.838130593619455 y1[1] (numeric) = 1.838130593619414 absolute error = 4.085620730620576e-14 relative error = 2.2227042761829e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.545469621554767 y2[1] (numeric) = 1.54546962155483 absolute error = 6.306066779870889e-14 relative error = 4.080356347300368e-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] = 6.870139184931802 y1[1] (closed_form) = 1.832631565080533 y1[1] (numeric) = 1.832631565080491 absolute error = 4.174438572590589e-14 relative error = 2.277838411239604e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.553827298741713 y2[1] (numeric) = 1.553827298741775 absolute error = 6.217248937900877e-14 relative error = 4.001248364561232e-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] = 6.880143729783 y1[1] (closed_form) = 1.827049198379292 y1[1] (numeric) = 1.82704919837925 absolute error = 4.174438572590589e-14 relative error = 2.284798119445048e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.562129543308453 y2[1] (numeric) = 1.562129543308516 absolute error = 6.261657858885883e-14 relative error = 4.008411393093712e-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] = 6.889986911007565 y1[1] (closed_form) = 1.82147607942433 y1[1] (numeric) = 1.821476079424288 absolute error = 4.241051954068098e-14 relative error = 2.328359950468559e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.570242975347905 y2[1] (numeric) = 1.570242975347967 absolute error = 6.23945339839338e-14 relative error = 3.973559185648297e-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] = 6.899991455858762 y1[1] (closed_form) = 1.815730042366626 y1[1] (numeric) = 1.815730042366584 absolute error = 4.241051954068098e-14 relative error = 2.335728249856075e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.578432794696619 y2[1] (numeric) = 1.578432794696682 absolute error = 6.217248937900877e-14 relative error = 3.938874660226414e-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] = 6.90999600070996 y1[1] (closed_form) = 1.809902358821413 y1[1] (numeric) = 1.80990235882137 absolute error = 4.285460875053104e-14 relative error = 2.367785673169544e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.586564718659 y2[1] (numeric) = 1.586564718659061 absolute error = 6.084022174945858e-14 relative error = 3.834714148999991e-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] = 6.920000545561157 y1[1] (closed_form) = 1.803993612082018 y1[1] (numeric) = 1.803993612081974 absolute error = 4.39648317751562e-14 relative error = 2.437083561754728e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.594637933310103 y2[1] (numeric) = 1.594637933310163 absolute error = 6.084022174945858e-14 relative error = 3.815300042635273e-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] = 6.930005090412354 y1[1] (closed_form) = 1.798004393555392 y1[1] (numeric) = 1.798004393555347 absolute error = 4.507505479978136e-14 relative error = 2.506949090966873e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.602651630601204 y2[1] (numeric) = 1.602651630601265 absolute error = 6.039613253960852e-14 relative error = 3.7685128437396e-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] = 6.940009635263552 y1[1] (closed_form) = 1.791935302702915 y1[1] (numeric) = 1.791935302702868 absolute error = 4.662936703425657e-14 relative error = 2.602179161486572e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.61060500844068 y2[1] (numeric) = 1.61060500844074 absolute error = 5.995204332975845e-14 relative error = 3.722330615859782e-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] = 6.950014180114749 y1[1] (closed_form) = 1.785786946980391 y1[1] (numeric) = 1.785786946980344 absolute error = 4.729550084903167e-14 relative error = 2.648440281692293e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.618497270774282 y2[1] (numeric) = 1.618497270774342 absolute error = 5.950795411990839e-14 relative error = 3.676741085355061e-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] = 6.960018724965947 y1[1] (closed_form) = 1.779559941777255 y1[1] (numeric) = 1.779559941777207 absolute error = 4.818367926873179e-14 relative error = 2.707617660836449e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.626327627664821 y2[1] (numeric) = 1.62632762766488 absolute error = 5.861977570020827e-14 relative error = 3.60442599037551e-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] = 6.970023269817144 y1[1] (closed_form) = 1.773254910354973 y1[1] (numeric) = 1.773254910354925 absolute error = 4.818367926873179e-14 relative error = 2.717244936831236e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.634095295371226 y2[1] (numeric) = 1.634095295371284 absolute error = 5.839773109528323e-14 relative error = 3.573704132231573e-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] = 6.980027814668341 y1[1] (closed_form) = 1.766872483784663 y1[1] (numeric) = 1.766872483784615 absolute error = 4.796163466380676e-14 relative error = 2.714493270112642e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.641799496426993 y2[1] (numeric) = 1.641799496427052 absolute error = 5.839773109528323e-14 relative error = 3.556934401695989e-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] = 6.990032359519539 y1[1] (closed_form) = 1.760413300883928 y1[1] (numeric) = 1.760413300883879 absolute error = 4.884981308350689e-14 relative error = 2.77490593027096e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.649439459718001 y2[1] (numeric) = 1.649439459718059 absolute error = 5.795364188543317e-14 relative error = 3.513535555608771e-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] = 7.000036904370736 y1[1] (closed_form) = 1.75387800815292 y1[1] (numeric) = 1.753878008152871 absolute error = 4.951594689828198e-14 relative error = 2.823226397053078e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.65701442055969 y2[1] (numeric) = 1.657014420559748 absolute error = 5.795364188543317e-14 relative error = 3.497473598682271e-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] = 7.010041449221934 y1[1] (closed_form) = 1.747267259709631 y1[1] (numeric) = 1.74726725970958 absolute error = 5.040412531798211e-14 relative error = 2.884740444707841e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.664523620773603 y2[1] (numeric) = 1.66452362077366 absolute error = 5.706546346573305e-14 relative error = 3.428336056847984e-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] = 7.020045994073131 y1[1] (closed_form) = 1.740581717224418 y1[1] (numeric) = 1.740581717224368 absolute error = 5.040412531798211e-14 relative error = 2.895820679902233e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.671966308763269 y2[1] (numeric) = 1.671966308763325 absolute error = 5.639932965095795e-14 relative error = 3.373233620519291e-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] = 7.030050538924328 y1[1] (closed_form) = 1.733822049853784 y1[1] (numeric) = 1.733822049853732 absolute error = 5.151434834260726e-14 relative error = 2.971143915660293e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.679341739589428 y2[1] (numeric) = 1.679341739589484 absolute error = 5.595524044110789e-14 relative error = 3.331974613742884e-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] = 7.040055083775526 y1[1] (closed_form) = 1.726988934173395 y1[1] (numeric) = 1.726988934173343 absolute error = 5.218048215738236e-14 relative error = 3.021471714429832e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.686649175044601 y2[1] (numeric) = 1.686649175044656 absolute error = 5.484501741648273e-14 relative error = 3.251714596488771e-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] = 7.050059628626723 y1[1] (closed_form) = 1.720083054110366 y1[1] (numeric) = 1.720083054110313 absolute error = 5.284661597215745e-14 relative error = 3.072329318393869e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.693887883726966 y2[1] (numeric) = 1.693887883727021 absolute error = 5.440092820663267e-14 relative error = 3.211601471930797e-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] = 7.060064173477921 y1[1] (closed_form) = 1.713105100874804 y1[1] (numeric) = 1.71310510087475 absolute error = 5.417888360170764e-14 relative error = 3.162612940329287e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.701057141113572 y2[1] (numeric) = 1.701057141113625 absolute error = 5.306866057708248e-14 relative error = 3.119745909437343e-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] = 7.070068718329118 y1[1] (closed_form) = 1.706055772890628 y1[1] (numeric) = 1.706055772890573 absolute error = 5.506706202140776e-14 relative error = 3.227741020922533e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.708156229632853 y2[1] (numeric) = 1.708156229632907 absolute error = 5.329070518200751e-14 relative error = 3.119779342048923e-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] = 7.080073263180315 y1[1] (closed_form) = 1.698935775725657 y1[1] (numeric) = 1.698935775725601 absolute error = 5.617728504603292e-14 relative error = 3.306616168114902e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.715184438736452 y2[1] (numeric) = 1.715184438736505 absolute error = 5.262457136723242e-14 relative error = 3.068158162978675e-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] = 7.090077808031513 y1[1] (closed_form) = 1.691745822021 y1[1] (numeric) = 1.691745822020942 absolute error = 5.750955267558311e-14 relative error = 3.399420405063027e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.722141064970336 y2[1] (numeric) = 1.722141064970388 absolute error = 5.173639294753229e-14 relative error = 3.004190190913509e-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] = 7.10008235288271 y1[1] (closed_form) = 1.684486631419717 y1[1] (numeric) = 1.684486631419658 absolute error = 5.88418203051333e-14 relative error = 3.493160420961033e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.729025412045211 y2[1] (numeric) = 1.729025412045262 absolute error = 5.129230373768223e-14 relative error = 2.96654423817925e-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] = 7.110086897733908 y1[1] (closed_form) = 1.677158930494796 y1[1] (numeric) = 1.677158930494738 absolute error = 5.839773109528323e-14 relative error = 3.48194378203947e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.735836790906206 y2[1] (numeric) = 1.735836790906257 absolute error = 5.084821452783217e-14 relative error = 2.929320014083035e-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] = 7.120091442585105 y1[1] (closed_form) = 1.669763452676432 y1[1] (numeric) = 1.669763452676373 absolute error = 5.88418203051333e-14 relative error = 3.523961445605775e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.742574519801848 y2[1] (numeric) = 1.742574519801898 absolute error = 5.040412531798211e-14 relative error = 2.892509028750958e-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] = 7.130095987436302 y1[1] (closed_form) = 1.66230093817861 y1[1] (numeric) = 1.66230093817855 absolute error = 6.039613253960852e-14 relative error = 3.633285114173417e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.749237924352293 y2[1] (numeric) = 1.749237924352343 absolute error = 5.040412531798211e-14 relative error = 2.881490540324623e-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] = 7.1401005322875 y1[1] (closed_form) = 1.654772133925026 y1[1] (numeric) = 1.654772133924966 absolute error = 6.061817714453355e-14 relative error = 3.663234103462369e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.755826337616828 y2[1] (numeric) = 1.755826337616877 absolute error = 4.907185768843192e-14 relative error = 2.794801321583821e-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] = 7.150105077138697 y1[1] (closed_form) = 1.647177793474321 y1[1] (numeric) = 1.647177793474259 absolute error = 6.17284001691587e-14 relative error = 3.747525034256179e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.762339100160624 y2[1] (numeric) = 1.762339100160673 absolute error = 4.884981308350689e-14 relative error = 2.771873646737714e-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] = 7.160109621989895 y1[1] (closed_form) = 1.639518676944659 y1[1] (numeric) = 1.639518676944596 absolute error = 6.23945339839338e-14 relative error = 3.805661677499749e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.768775560120737 y2[1] (numeric) = 1.768775560120785 absolute error = 4.75175454539567e-14 relative error = 2.686465514636189e-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] = 7.170114166841092 y1[1] (closed_form) = 1.631795550937648 y1[1] (numeric) = 1.631795550937585 absolute error = 6.306066779870889e-14 relative error = 3.864495632585438e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.775135073271358 y2[1] (numeric) = 1.775135073271405 absolute error = 4.640732242933154e-14 relative error = 2.614298096415192e-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] = 7.180118711692289 y1[1] (closed_form) = 1.62400918846161 y1[1] (numeric) = 1.624009188461547 absolute error = 6.350475700855895e-14 relative error = 3.910369316858095e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.781417003088289 y2[1] (numeric) = 1.781417003088335 absolute error = 4.574118861455645e-14 relative error = 2.567685642118544e-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] = 7.190123256543487 y1[1] (closed_form) = 1.616160368854211 y1[1] (numeric) = 1.616160368854147 absolute error = 6.394884621840902e-14 relative error = 3.956837913538621e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.787620720812653 y2[1] (numeric) = 1.787620720812697 absolute error = 4.418687638008123e-14 relative error = 2.471826146655643e-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] = 7.200127801394684 y1[1] (closed_form) = 1.608249877704454 y1[1] (numeric) = 1.60824987770439 absolute error = 6.417089082333405e-14 relative error = 3.990106992262221e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.79374560551383 y2[1] (numeric) = 1.793745605513875 absolute error = 4.440892098500626e-14 relative error = 2.475764726530719e-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] = 7.210132346245882 y1[1] (closed_form) = 1.600278506774055 y1[1] (numeric) = 1.600278506773991 absolute error = 6.439293542825908e-14 relative error = 4.023858044439185e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.799791044151603 y2[1] (numeric) = 1.799791044151647 absolute error = 4.418687638008123e-14 relative error = 2.45511147106026e-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] = 7.220136891097079 y1[1] (closed_form) = 1.59224705391819 y1[1] (numeric) = 1.592247053918125 absolute error = 6.505906924303417e-14 relative error = 4.085990869503403e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.805756431637517 y2[1] (numeric) = 1.805756431637561 absolute error = 4.374278717023117e-14 relative error = 2.422407939622501e-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] = 7.230141435948276 y1[1] (closed_form) = 1.58415632300564 y1[1] (numeric) = 1.584156323005575 absolute error = 6.505906924303417e-14 relative error = 4.106859171549229e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.811641170895446 y2[1] (numeric) = 1.811641170895489 absolute error = 4.374278717023117e-14 relative error = 2.414539251644976e-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] = 7.239984617172841 y1[1] (closed_form) = 1.576139022175655 y1[1] (numeric) = 1.57613902217559 absolute error = 6.483702463810914e-14 relative error = 4.113661531494225e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.817351715680881 y2[1] (numeric) = 1.817351715680925 absolute error = 4.374278717023117e-14 relative error = 2.406952203736891e-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] = 7.249989162024039 y1[1] (closed_form) = 1.567933093786121 y1[1] (numeric) = 1.567933093786055 absolute error = 6.59472476627343e-14 relative error = 4.205998835287678e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.823074723814627 y2[1] (numeric) = 1.823074723814671 absolute error = 4.374278717023117e-14 relative error = 2.399396283587495e-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] = 7.259993706875236 y1[1] (closed_form) = 1.559670320926186 y1[1] (numeric) = 1.559670320926119 absolute error = 6.705747068735946e-14 relative error = 4.29946443088937e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.828715350331089 y2[1] (numeric) = 1.828715350331132 absolute error = 4.263256414560601e-14 relative error = 2.331284862780168e-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] = 7.269998251726434 y1[1] (closed_form) = 1.55135153061747 y1[1] (numeric) = 1.551351530617402 absolute error = 6.794564910705958e-14 relative error = 4.379771300448957e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.834273030659491 y2[1] (numeric) = 1.834273030659534 absolute error = 4.241051954068098e-14 relative error = 2.312115962661936e-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] = 7.280002796577631 y1[1] (closed_form) = 1.542977555488385 y1[1] (numeric) = 1.542977555488316 absolute error = 6.861178292183467e-14 relative error = 4.446712959484209e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.839747208531149 y2[1] (numeric) = 1.839747208531192 absolute error = 4.263256414560601e-14 relative error = 2.31730554871415e-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] = 7.290007341428828 y1[1] (closed_form) = 1.534549233690794 y1[1] (numeric) = 1.534549233690726 absolute error = 6.883382752675971e-14 relative error = 4.485605675955096e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.845137336035147 y2[1] (numeric) = 1.845137336035188 absolute error = 4.152234112098085e-14 relative error = 2.250365883886159e-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] = 7.300011886280026 y1[1] (closed_form) = 1.526067408816125 y1[1] (numeric) = 1.526067408816056 absolute error = 6.883382752675971e-14 relative error = 4.510536502457569e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.850442873673175 y2[1] (numeric) = 1.850442873673216 absolute error = 4.107825191113079e-14 relative error = 2.219914621281415e-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] = 7.310016431131223 y1[1] (closed_form) = 1.517532929810932 y1[1] (numeric) = 1.517532929810862 absolute error = 6.994405055138486e-14 relative error = 4.609063116679723e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.855663290413532 y2[1] (numeric) = 1.855663290413572 absolute error = 4.019007349143067e-14 relative error = 2.165806356091377e-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] = 7.320020975982421 y1[1] (closed_form) = 1.508946650891925 y1[1] (numeric) = 1.508946650891856 absolute error = 6.94999613415348e-14 relative error = 4.605859411958268e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.860798063744275 y2[1] (numeric) = 1.860798063744315 absolute error = 3.996802888650564e-14 relative error = 2.147897166556722e-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] = 7.330025520833618 y1[1] (closed_form) = 1.500309431460473 y1[1] (numeric) = 1.500309431460403 absolute error = 7.016609515630989e-14 relative error = 4.676774916225573e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.865846679725515 y2[1] (numeric) = 1.865846679725555 absolute error = 3.97459842815806e-14 relative error = 2.130184902836049e-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] = 7.340030065684815 y1[1] (closed_form) = 1.491622136016584 y1[1] (numeric) = 1.491622136016514 absolute error = 6.994405055138486e-14 relative error = 4.689126613404404e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.87080863304086 y2[1] (numeric) = 1.870808633040899 absolute error = 3.885780586188048e-14 relative error = 2.077059362224559e-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] = 7.350034610536013 y1[1] (closed_form) = 1.482885634072378 y1[1] (numeric) = 1.482885634072307 absolute error = 7.038813976123492e-14 relative error = 4.746700496917712e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.875683427047993 y2[1] (numeric) = 1.875683427048032 absolute error = 3.885780586188048e-14 relative error = 2.071661203673163e-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] = 7.36003915538721 y1[1] (closed_form) = 1.474100800065059 y1[1] (numeric) = 1.474100800064988 absolute error = 7.083222897108499e-14 relative error = 4.80511434278842e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.880470573828377 y2[1] (numeric) = 1.880470573828415 absolute error = 3.819167204710538e-14 relative error = 2.030963556603412e-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] = 7.370043700238408 y1[1] (closed_form) = 1.46526851326939 y1[1] (numeric) = 1.465268513269319 absolute error = 7.083222897108499e-14 relative error = 4.834078418367165e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.885169594236094 y2[1] (numeric) = 1.885169594236132 absolute error = 3.819167204710538e-14 relative error = 2.025901126555214e-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] = 7.380048245089605 y1[1] (closed_form) = 1.456389657709688 y1[1] (numeric) = 1.456389657709616 absolute error = 7.172040739078511e-14 relative error = 4.924534241994845e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.889780017945803 y2[1] (numeric) = 1.88978001794584 absolute error = 3.663735981263017e-14 relative error = 1.938710297744342e-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] = 7.390052789940802 y1[1] (closed_form) = 1.447465122071342 y1[1] (numeric) = 1.44746512207127 absolute error = 7.260858581048524e-14 relative error = 5.016258057160048e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.894301383499812 y2[1] (numeric) = 1.894301383499848 absolute error = 3.552713678800501e-14 relative error = 1.875474362076795e-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] = 7.400057334792 y1[1] (closed_form) = 1.438495799611863 y1[1] (numeric) = 1.438495799611791 absolute error = 7.260858581048524e-14 relative error = 5.047535476299379e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.89873323835427 y2[1] (numeric) = 1.898733238354304 absolute error = 3.463895836830488e-14 relative error = 1.824319376129333e-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] = 7.410061879643197 y1[1] (closed_form) = 1.429482588071479 y1[1] (numeric) = 1.429482588071406 absolute error = 7.349676423018536e-14 relative error = 5.141494191219225e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.903075138924455 y2[1] (numeric) = 1.903075138924489 absolute error = 3.419486915845482e-14 relative error = 1.796821810082625e-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] = 7.420066424494395 y1[1] (closed_form) = 1.42042638958328 y1[1] (numeric) = 1.420426389583206 absolute error = 7.416289804496046e-14 relative error = 5.221171515034871e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.907326650629181 y2[1] (numeric) = 1.907326650629214 absolute error = 3.286260152890463e-14 relative error = 1.722966620220194e-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] = 7.430070969345592 y1[1] (closed_form) = 1.411328110582922 y1[1] (numeric) = 1.411328110582847 absolute error = 7.505107646466058e-14 relative error = 5.31776246089665e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.911487347934289 y2[1] (numeric) = 1.911487347934321 absolute error = 3.175237850427948e-14 relative error = 1.661134641492329e-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] = 7.440075514196789 y1[1] (closed_form) = 1.402188661717904 y1[1] (numeric) = 1.402188661717828 absolute error = 7.593925488436071e-14 relative error = 5.415765863583796e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.915556814395241 y2[1] (numeric) = 1.915556814395273 absolute error = 3.197442310920451e-14 relative error = 1.669197325233036e-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] = 7.450080059047987 y1[1] (closed_form) = 1.39300895775642 y1[1] (numeric) = 1.393008957756343 absolute error = 7.682743330406083e-14 relative error = 5.515214591857261e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.919534642698801 y2[1] (numeric) = 1.919534642698833 absolute error = 3.175237850427948e-14 relative error = 1.654170641048536e-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] = 7.460084603899184 y1[1] (closed_form) = 1.3837899174958 y1[1] (numeric) = 1.383789917495723 absolute error = 7.72715225139109e-14 relative error = 5.584050117502421e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.923420434703806 y2[1] (numeric) = 1.923420434703837 absolute error = 3.086420008457935e-14 relative error = 1.604651771796956e-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] = 7.470089148750382 y1[1] (closed_form) = 1.374532463670548 y1[1] (numeric) = 1.374532463670471 absolute error = 7.749356711883593e-14 relative error = 5.637812795770374e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.927213801481012 y2[1] (numeric) = 1.927213801481043 absolute error = 3.108624468950438e-14 relative error = 1.613014843792393e-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] = 7.480093693601579 y1[1] (closed_form) = 1.365237522859983 y1[1] (numeric) = 1.365237522859904 absolute error = 7.904787935331115e-14 relative error = 5.790045909939307e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.930914363352024 y2[1] (numeric) = 1.930914363352053 absolute error = 2.953193245502916e-14 relative error = 1.529427353979718e-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] = 7.490098238452776 y1[1] (closed_form) = 1.355906025395501 y1[1] (numeric) = 1.355906025395422 absolute error = 7.971401316808624e-14 relative error = 5.879021973136718e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.934521749927297 y2[1] (numeric) = 1.934521749927325 absolute error = 2.864375403532904e-14 relative error = 1.480663323449609e-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] = 7.500102783303974 y1[1] (closed_form) = 1.346538905267457 y1[1] (numeric) = 1.346538905267377 absolute error = 8.01581023779363e-14 relative error = 5.952899100380234e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.93803560014321 y2[1] (numeric) = 1.938035600143238 absolute error = 2.753353101070388e-14 relative error = 1.42069273694814e-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] = 7.510107328155171 y1[1] (closed_form) = 1.33713710003168 y1[1] (numeric) = 1.337137100031599 absolute error = 8.08242361927114e-14 relative error = 6.044573603618993e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.941455562298205 y2[1] (numeric) = 1.941455562298232 absolute error = 2.731148640577885e-14 relative error = 1.40675310504912e-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] = 7.520111873006369 y1[1] (closed_form) = 1.327701550715634 y1[1] (numeric) = 1.327701550715553 absolute error = 8.08242361927114e-14 relative error = 6.087530450585598e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.944781294087986 y2[1] (numeric) = 1.944781294088011 absolute error = 2.55351295663786e-14 relative error = 1.313007773367823e-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] = 7.530116417857566 y1[1] (closed_form) = 1.318233201724232 y1[1] (numeric) = 1.318233201724151 absolute error = 8.149037000748649e-14 relative error = 6.1817870996496e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.948012462639782 y2[1] (numeric) = 1.948012462639807 absolute error = 2.531308496145357e-14 relative error = 1.299431366427267e-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] = 7.540120962708763 y1[1] (closed_form) = 1.30873300074531 y1[1] (numeric) = 1.308733000745228 absolute error = 8.171241461241152e-14 relative error = 6.243627582240009e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.951148744545666 y2[1] (numeric) = 1.951148744545691 absolute error = 2.509104035652854e-14 relative error = 1.285962458099067e-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] = 7.550125507559961 y1[1] (closed_form) = 1.29920189865477 y1[1] (numeric) = 1.299201898654688 absolute error = 8.215650382226158e-14 relative error = 6.323613281917823e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.954189825894922 y2[1] (numeric) = 1.954189825894947 absolute error = 2.531308496145357e-14 relative error = 1.295323751358773e-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] = 7.560130052411158 y1[1] (closed_form) = 1.28964084942141 y1[1] (numeric) = 1.289640849421328 absolute error = 8.237854842718662e-14 relative error = 6.387712397924219e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.957135402305465 y2[1] (numeric) = 1.95713540230549 absolute error = 2.486899575160351e-14 relative error = 1.270683455130817e-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] = 7.570134597262355 y1[1] (closed_form) = 1.280050810011439 y1[1] (numeric) = 1.280050810011357 absolute error = 8.260059303211165e-14 relative error = 6.452915180091444e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.959985178954309 y2[1] (numeric) = 1.959985178954333 absolute error = 2.398081733190338e-14 relative error = 1.223520340327146e-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] = 7.580139142113553 y1[1] (closed_form) = 1.270432740292697 y1[1] (numeric) = 1.270432740292614 absolute error = 8.326672684688674e-14 relative error = 6.55420190349493e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.962738870607073 y2[1] (numeric) = 1.962738870607097 absolute error = 2.375877272697835e-14 relative error = 1.210490762820109e-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] = 7.59014368696475 y1[1] (closed_form) = 1.260787602938578 y1[1] (numeric) = 1.260787602938495 absolute error = 8.326672684688674e-14 relative error = 6.604342131284682e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.965396201646532 y2[1] (numeric) = 1.965396201646554 absolute error = 2.264854970235319e-14 relative error = 1.152365598517954e-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] = 7.599986868189315 y1[1] (closed_form) = 1.251272553098482 y1[1] (numeric) = 1.251272553098398 absolute error = 8.37108160567368e-14 relative error = 6.690054524847259e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.967916372451345 y2[1] (numeric) = 1.967916372451366 absolute error = 2.109423746787797e-14 relative error = 1.071907209227688e-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] = 7.609991413040513 y1[1] (closed_form) = 1.241576576931396 y1[1] (numeric) = 1.241576576931313 absolute error = 8.348877145181177e-14 relative error = 6.724415795452379e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.970381758628072 y2[1] (numeric) = 1.970381758628093 absolute error = 2.087219286295294e-14 relative error = 1.059296898763706e-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] = 7.61999595789171 y1[1] (closed_form) = 1.231856421344715 y1[1] (numeric) = 1.231856421344631 absolute error = 8.37108160567368e-14 relative error = 6.795501050792647e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.972750019214198 y2[1] (numeric) = 1.972750019214218 absolute error = 2.065014825802791e-14 relative error = 1.046769639178787e-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] = 7.630000502742908 y1[1] (closed_form) = 1.222113059229616 y1[1] (numeric) = 1.222113059229532 absolute error = 8.415490526658687e-14 relative error = 6.886016365755525e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.975020917170325 y2[1] (numeric) = 1.975020917170345 absolute error = 2.042810365310288e-14 relative error = 1.034323407691847e-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] = 7.640005047594105 y1[1] (closed_form) = 1.21234746580002 y1[1] (numeric) = 1.212347465799937 absolute error = 8.304468224196171e-14 relative error = 6.849907686090725e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.977194225202088 y2[1] (numeric) = 1.977194225202107 absolute error = 1.931788062847772e-14 relative error = 9.770350521079058e-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] = 7.650009592445302 y1[1] (closed_form) = 1.202560618494983 y1[1] (numeric) = 1.2025606184949 absolute error = 8.282263763703668e-14 relative error = 6.887190247481249e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.979269725782907 y2[1] (numeric) = 1.979269725782926 absolute error = 1.887379141862766e-14 relative error = 9.535734909077169e-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] = 7.6600141372965 y1[1] (closed_form) = 1.192753496880862 y1[1] (numeric) = 1.19275349688078 absolute error = 8.260059303211165e-14 relative error = 6.925202336284759e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.981247211175756 y2[1] (numeric) = 1.981247211175774 absolute error = 1.820765760385257e-14 relative error = 9.189997846380499e-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] = 7.670018682147697 y1[1] (closed_form) = 1.182927082553272 y1[1] (numeric) = 1.18292708255319 absolute error = 8.215650382226158e-14 relative error = 6.94518749582874e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.983126483453959 y2[1] (numeric) = 1.983126483453977 absolute error = 1.754152378907747e-14 relative error = 8.845388297435199e-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] = 7.680023226998895 y1[1] (closed_form) = 1.173082359038837 y1[1] (numeric) = 1.173082359038755 absolute error = 8.215650382226158e-14 relative error = 7.003472790229013e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.984907354520998 y2[1] (numeric) = 1.984907354521015 absolute error = 1.709743457922741e-14 relative error = 8.613719194643922e-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] = 7.690027771850092 y1[1] (closed_form) = 1.163220311696749 y1[1] (numeric) = 1.163220311696666 absolute error = 8.260059303211165e-14 relative error = 7.101027397950527e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.98658964612934 y2[1] (numeric) = 1.986589646129356 absolute error = 1.665334536937735e-14 relative error = 8.382881387620556e-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] = 7.700032316701289 y1[1] (closed_form) = 1.153341927620143 y1[1] (numeric) = 1.15334192762006 absolute error = 8.260059303211165e-14 relative error = 7.16184776205556e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.988173189898278 y2[1] (numeric) = 1.988173189898295 absolute error = 1.620925615952729e-14 relative error = 8.152839119793485e-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] = 7.710036861552487 y1[1] (closed_form) = 1.143448195537299 y1[1] (numeric) = 1.143448195537216 absolute error = 8.304468224196171e-14 relative error = 7.262653661623868e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.989657827330786 y2[1] (numeric) = 1.989657827330801 absolute error = 1.509903313490213e-14 relative error = 7.588758693829355e-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] = 7.720041406403684 y1[1] (closed_form) = 1.133540105712682 y1[1] (numeric) = 1.133540105712599 absolute error = 8.304468224196171e-14 relative error = 7.326135336848063e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.991043409829381 y2[1] (numeric) = 1.991043409829395 absolute error = 1.465494392505207e-14 relative error = 7.360434158644437e-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] = 7.730045951254882 y1[1] (closed_form) = 1.123618649847823 y1[1] (numeric) = 1.12361864984774 absolute error = 8.348877145181177e-14 relative error = 7.430347606202429e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.992329798710994 y2[1] (numeric) = 1.992329798711007 absolute error = 1.332267629550188e-14 relative error = 6.686983402106138e-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] = 7.740050496106079 y1[1] (closed_form) = 1.113684820982061 y1[1] (numeric) = 1.113684820981977 absolute error = 8.37108160567368e-14 relative error = 7.516562539024244e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.993516865220856 y2[1] (numeric) = 1.993516865220869 absolute error = 1.287858708565182e-14 relative error = 6.460234829377795e-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] = 7.750055040957276 y1[1] (closed_form) = 1.10373961339315 y1[1] (numeric) = 1.103739613393065 absolute error = 8.43769498715119e-14 relative error = 7.644642708085626e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.994604490545382 y2[1] (numeric) = 1.994604490545395 absolute error = 1.221245327087672e-14 relative error = 6.122744297811886e-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] = 7.760059585808474 y1[1] (closed_form) = 1.093784022497741 y1[1] (numeric) = 1.093784022497656 absolute error = 8.43769498715119e-14 relative error = 7.71422402741179e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.995592565824064 y2[1] (numeric) = 1.995592565824076 absolute error = 1.154631945610163e-14 relative error = 5.785910237310223e-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] = 7.770064130659671 y1[1] (closed_form) = 1.083819044751752 y1[1] (numeric) = 1.083819044751667 absolute error = 8.504308368628699e-14 relative error = 7.846612780804759e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.996480992160364 y2[1] (numeric) = 1.996480992160375 absolute error = 1.13242748511766e-14 relative error = 5.672117538631188e-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] = 7.780068675510869 y1[1] (closed_form) = 1.07384567755063 y1[1] (numeric) = 1.073845677550546 absolute error = 8.459899447643693e-14 relative error = 7.878133352401392e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.997269680631617 y2[1] (numeric) = 1.997269680631627 absolute error = 9.769962616701378e-15 relative error = 4.891659204285182e-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] = 7.790073220362066 y1[1] (closed_form) = 1.063864919129526 y1[1] (numeric) = 1.063864919129441 absolute error = 8.548717289613705e-14 relative error = 8.035528887077527e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.997958552297929 y2[1] (numeric) = 1.997958552297938 absolute error = 8.881784197001252e-15 relative error = 4.445429654577153e-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] = 7.800077765213263 y1[1] (closed_form) = 1.053877768463376 y1[1] (numeric) = 1.05387776846329 absolute error = 8.615330671091215e-14 relative error = 8.17488605310741e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.998547538210078 y2[1] (numeric) = 1.998547538210087 absolute error = 8.881784197001252e-15 relative error = 4.444119555422675e-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] = 7.810082310064461 y1[1] (closed_form) = 1.043885225166918 y1[1] (numeric) = 1.043885225166831 absolute error = 8.681944052568724e-14 relative error = 8.316952710179871e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999036579416414 y2[1] (numeric) = 1.999036579416423 absolute error = 8.881784197001252e-15 relative error = 4.443032352911793e-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] = 7.820086854915658 y1[1] (closed_form) = 1.033888289394638 y1[1] (numeric) = 1.03388828939455 absolute error = 8.748557434046234e-14 relative error = 8.461801457455999e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999425626968763 y2[1] (numeric) = 1.999425626968772 absolute error = 8.659739592076221e-15 relative error = 4.331113633471255e-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] = 7.830091399766856 y1[1] (closed_form) = 1.023887961740665 y1[1] (numeric) = 1.023887961740577 absolute error = 8.770761894538737e-14 relative error = 8.566134403639212e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999714641927323 y2[1] (numeric) = 1.999714641927331 absolute error = 7.771561172376096e-15 relative error = 3.886335084732825e-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] = 7.840095944618053 y1[1] (closed_form) = 1.013885243138622 y1[1] (numeric) = 1.013885243138534 absolute error = 8.79296635503124e-14 relative error = 8.672545945940977e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999903595364564 y2[1] (numeric) = 1.999903595364571 absolute error = 6.661338147750939e-15 relative error = 3.330829627583443e-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] = 7.85010048946925 y1[1] (closed_form) = 1.003881134761444 y1[1] (numeric) = 1.003881134761355 absolute error = 8.859579736508749e-14 relative error = 8.825327451356165e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999992468368119 y2[1] (numeric) = 1.999992468368124 absolute error = 5.329070518200751e-15 relative error = 2.664545293287515e-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] = 7.860105034320448 y1[1] (closed_form) = 0.993876637921166 y1[1] (numeric) = 0.9938766379210777 absolute error = 8.826273045769994e-14 relative error = 8.880652496502379e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999981252042683 y2[1] (numeric) = 1.999981252042688 absolute error = 4.884981308350689e-15 relative error = 2.442513550245238e-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] = 7.870109579171645 y1[1] (closed_form) = 0.9838727539687057 y1[1] (numeric) = 0.9838727539686178 absolute error = 8.781864124784988e-14 relative error = 8.925812905541966e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999869947510898 y2[1] (numeric) = 1.999869947510902 absolute error = 4.218847493575595e-15 relative error = 2.109560923612311e-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] = 7.880114124022843 y1[1] (closed_form) = 0.9738704841936365 y1[1] (numeric) = 0.9738704841935489 absolute error = 8.759659664292485e-14 relative error = 8.99468646649197e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999658565913245 y2[1] (numeric) = 1.999658565913248 absolute error = 2.886579864025407e-15 relative error = 1.443536368273503e-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] = 7.89011866887404 y1[1] (closed_form) = 0.9638708297239688 y1[1] (numeric) = 0.9638708297238812 absolute error = 8.759659664292485e-14 relative error = 9.088001622376162e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.999347128406924 y2[1] (numeric) = 1.999347128406926 absolute error = 1.110223024625157e-15 relative error = 5.552927797534488e-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] = 7.900123213725237 y1[1] (closed_form) = 0.9538747914259467 y1[1] (numeric) = 0.9538747914258591 absolute error = 8.759659664292485e-14 relative error = 9.183238453337966e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.998935666163743 y2[1] (numeric) = 1.998935666163743 absolute error = 4.440892098500626e-16 relative error = 2.221628326349974e-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] = 7.910127758576435 y1[1] (closed_form) = 0.9438833698038714 y1[1] (numeric) = 0.9438833698037836 absolute error = 8.781864124784988e-14 relative error = 9.303971661890561e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.99842422036699 y2[1] (numeric) = 1.998424220366989 absolute error = 6.661338147750939e-16 relative error = 3.333295343331885e-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] = 7.920132303427632 y1[1] (closed_form) = 0.9338975648999608 y1[1] (numeric) = 0.9338975648998731 absolute error = 8.770761894538737e-14 relative error = 9.391567366896671e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.997812842207317 y2[1] (numeric) = 1.997812842207316 absolute error = 1.110223024625157e-15 relative error = 5.557192351404188e-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] = 7.930136848278829 y1[1] (closed_form) = 0.9239183761942549 y1[1] (numeric) = 0.9239183761941676 absolute error = 8.72635297355373e-14 relative error = 9.444939291605782e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.997101592877617 y2[1] (numeric) = 1.997101592877614 absolute error = 3.33066907387547e-15 relative error = 1.667751448275758e-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] = 7.940141393130027 y1[1] (closed_form) = 0.9139468025045777 y1[1] (numeric) = 0.9139468025044899 absolute error = 8.781864124784988e-14 relative error = 9.608725694667553e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.996290543566893 y2[1] (numeric) = 1.996290543566888 absolute error = 4.218847493575595e-15 relative error = 2.113343424468427e-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] = 7.949984574354592 y1[1] (closed_form) = 0.9041444612263573 y1[1] (numeric) = 0.9041444612262698 absolute error = 8.748557434046234e-14 relative error = 9.676061524703614e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.995395256009599 y2[1] (numeric) = 1.995395256009594 absolute error = 5.10702591327572e-15 relative error = 2.55940566055508e-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] = 7.959989119205789 y1[1] (closed_form) = 0.894190947962025 y1[1] (numeric) = 0.8941909479619379 absolute error = 8.715250743307479e-14 relative error = 9.7465208780861e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.994386466373525 y2[1] (numeric) = 1.994386466373519 absolute error = 5.995204332975845e-15 relative error = 3.006039418166115e-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] = 7.969993664056987 y1[1] (closed_form) = 0.8842480251344758 y1[1] (numeric) = 0.8842480251343884 absolute error = 8.737455203799982e-14 relative error = 9.881226709521004e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.993278148513663 y2[1] (numeric) = 1.993278148513656 absolute error = 7.327471962526033e-15 relative error = 3.676091050308228e-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] = 7.979998208908184 y1[1] (closed_form) = 0.8743166879316788 y1[1] (numeric) = 0.8743166879315917 absolute error = 8.715250743307479e-14 relative error = 9.968070910238087e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.992070413361641 y2[1] (numeric) = 1.992070413361632 absolute error = 9.103828801926284e-15 relative error = 4.570033639806673e-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] = 7.990002753759382 y1[1] (closed_form) = 0.8643979303819975 y1[1] (numeric) = 0.8643979303819106 absolute error = 8.693046282814976e-14 relative error = 1.005676434113316e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.990763381799769 y2[1] (numeric) = 1.99076338179976 absolute error = 9.103828801926284e-15 relative error = 4.57303408589718e-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] = 8.00000729861058 y1[1] (closed_form) = 0.8544927452546958 y1[1] (numeric) = 0.8544927452546099 absolute error = 8.58202398035246e-14 relative error = 1.004341350820298e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.989357184648944 y2[1] (numeric) = 1.989357184648934 absolute error = 9.769962616701378e-15 relative error = 4.911115355297773e-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] = 8.010011843461832 y1[1] (closed_form) = 0.8446021239605208 y1[1] (numeric) = 0.8446021239604892 absolute error = 3.164135620181696e-14 relative error = 3.746303176866741e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.987851962655548 y2[1] (numeric) = 1.987851962655545 absolute error = 3.108624468950438e-15 relative error = 1.563810850782703e-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] = 8.020016388313085 y1[1] (closed_form) = 0.8347270564526309 y1[1] (numeric) = 0.8347270564526535 absolute error = 2.264854970235319e-14 relative error = 2.71328807749488e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.986247866477382 y2[1] (numeric) = 1.986247866477387 absolute error = 5.10702591327572e-15 relative error = 2.571192648948215e-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] = 8.030020933164337 y1[1] (closed_form) = 0.8248685311273508 y1[1] (numeric) = 0.8248685311274278 absolute error = 7.693845560652335e-14 relative error = 9.327359779548298e-12 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 14 h = 0.0001613636266322163 y2[1] (closed_form) = 1.984545056668565 y2[1] (numeric) = 1.98454505666858 absolute error = 1.48769885299771e-14 relative error = 7.496422658677723e-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] = 8.04002547801559 y1[1] (closed_form) = 0.8150275347252971 y1[1] (numeric) = 0.8150275347254281 absolute error = 1.310063169057685e-13 relative error = 1.607385165826622e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.982743703663473 y2[1] (numeric) = 1.982743703663498 absolute error = 2.575717417130363e-14 relative error = 1.299067253307256e-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] = 8.050030022866842 y1[1] (closed_form) = 0.8052050522326148 y1[1] (numeric) = 0.8052050522327996 absolute error = 1.84741111297626e-13 relative error = 2.294336216413312e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.980843987759675 y2[1] (numeric) = 1.980843987759713 absolute error = 3.819167204710538e-14 relative error = 1.928050481668674e-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] = 8.060034567718095 y1[1] (closed_form) = 0.7954020667823902 y1[1] (numeric) = 0.7954020667826284 absolute error = 2.381428387820961e-13 relative error = 2.993993210822877e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.978846099099896 y2[1] (numeric) = 1.978846099099946 absolute error = 5.084821452783217e-14 relative error = 2.569589143438752e-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] = 8.070039112569347 y1[1] (closed_form) = 0.7856195595562492 y1[1] (numeric) = 0.7856195595565398 absolute error = 2.90656387846866e-13 relative error = 3.699709157076497e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.976750237652975 y2[1] (numeric) = 1.97675023765304 absolute error = 6.52811138479592e-14 relative error = 3.302446237490703e-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] = 8.0800436574206 y1[1] (closed_form) = 0.7758585096861501 y1[1] (numeric) = 0.7758585096864943 absolute error = 3.441691376337985e-13 relative error = 4.43597812406571e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.97455661319386 y2[1] (numeric) = 1.97455661319394 absolute error = 8.01581023779363e-14 relative error = 4.05954946251351e-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] = 8.090048202271852 y1[1] (closed_form) = 0.766119894156383 y1[1] (numeric) = 0.7661198941567801 absolute error = 3.97015753605956e-13 relative error = 5.182162173756524e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.972265445282603 y2[1] (numeric) = 1.9722654452827 absolute error = 9.703349235223868e-14 relative error = 4.919900238800507e-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] = 8.100052747123105 y1[1] (closed_form) = 0.7564046877057833 y1[1] (numeric) = 0.7564046877062326 absolute error = 4.493072580658009e-13 relative error = 5.940037989830209e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.969876963242391 y2[1] (numeric) = 1.969876963242506 absolute error = 1.143529715363911e-13 relative error = 5.805081924922237e-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] = 8.110057291974357 y1[1] (closed_form) = 0.746713862730169 y1[1] (numeric) = 0.7467138627306709 absolute error = 5.018208071305708e-13 relative error = 6.720389592015753e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.96739140613659 y2[1] (numeric) = 1.967391406136723 absolute error = 1.327826737451687e-13 relative error = 6.74917422791416e-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] = 8.120061836825609 y1[1] (closed_form) = 0.7370483891850148 y1[1] (numeric) = 0.7370483891855684 absolute error = 5.535572000781031e-13 relative error = 7.510459397247911e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.964809022744815 y2[1] (numeric) = 1.964809022744967 absolute error = 1.521005543736464e-13 relative error = 7.74123859433238e-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] = 8.130066381676862 y1[1] (closed_form) = 0.7274092344883685 y1[1] (numeric) = 0.7274092344889734 absolute error = 6.049605261182478e-13 relative error = 8.316646221074628e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.962130071538034 y2[1] (numeric) = 1.962130071538206 absolute error = 1.723066134218243e-13 relative error = 8.781610145078718e-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] = 8.140070926528114 y1[1] (closed_form) = 0.717797363424022 y1[1] (numeric) = 0.7177973634246783 absolute error = 6.5625282985593e-13 relative error = 9.142591813453959e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.959354820652696 y2[1] (numeric) = 1.95935482065289 absolute error = 1.940669847044774e-13 relative error = 9.904637111099164e-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] = 8.150075471379367 y1[1] (closed_form) = 0.7082137380449465 y1[1] (numeric) = 0.7082137380456537 absolute error = 7.072120666862247e-13 relative error = 9.985856369272263e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.0001613636266322163 y2[1] (closed_form) = 1.956483547863891 y2[1] (numeric) = 1.956483547864108 absolute error = 2.162714451969805e-13 relative error = 1.105408964123966e-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] = 8.160080016230619 y1[1] (closed_form) = 0.6986593175769999 y1[1] (numeric) = 0.6986593175777576 absolute error = 7.576161920042068e-13 relative error = 1.084385726983036e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.953516540557551 y2[1] (numeric) = 1.953516540557791 absolute error = 2.393640841091838e-13 relative error = 1.225298476566096e-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] = 8.170084561081872 y1[1] (closed_form) = 0.6891350583229183 y1[1] (numeric) = 0.6891350583237259 absolute error = 8.075762281123389e-13 relative error = 1.171869314090128e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.950454095701683 y2[1] (numeric) = 1.950454095701948 absolute error = 2.646771690706373e-13 relative error = 1.357002811057795e-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] = 8.180089105933124 y1[1] (closed_form) = 0.6796419135665995 y1[1] (numeric) = 0.6796419135674563 absolute error = 8.567591081032333e-13 relative error = 1.260603695859728e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.947296519816646 y2[1] (numeric) = 1.947296519816937 absolute error = 2.90434343241941e-13 relative error = 1.491474669041609e-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] = 8.190093650784377 y1[1] (closed_form) = 0.6701808334776884 y1[1] (numeric) = 0.6701808334785943 absolute error = 9.058309657916652e-13 relative error = 1.351621712443112e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.944044128944472 y2[1] (numeric) = 1.94404412894479 absolute error = 3.175237850427948e-13 relative error = 1.633315727329687e-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] = 8.200098195635629 y1[1] (closed_form) = 0.6607527650164748 y1[1] (numeric) = 0.6607527650174292 absolute error = 9.543477119677846e-13 relative error = 1.444334042164756e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.940697248617233 y2[1] (numeric) = 1.940697248617579 absolute error = 3.455014052633487e-13 relative error = 1.780295228993198e-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] = 8.210102740486882 y1[1] (closed_form) = 0.651358651839112 y1[1] (numeric) = 0.6513586518401143 absolute error = 1.002309346631591e-12 relative error = 1.538797932293629e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.937256213824458 y2[1] (numeric) = 1.937256213824833 absolute error = 3.743672039036028e-13 relative error = 1.932460978739313e-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] = 8.220107285338134 y1[1] (closed_form) = 0.6419994342031661 y1[1] (numeric) = 0.6419994342042158 absolute error = 1.049715869783086e-12 relative error = 1.635072889255684e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.933721368979604 y2[1] (numeric) = 1.933721368980009 absolute error = 4.04343225568482e-13 relative error = 2.091010794289603e-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] = 8.230111830189387 y1[1] (closed_form) = 0.6326760488735054 y1[1] (numeric) = 0.632676048874602 absolute error = 1.09667830372473e-12 relative error = 1.733396270772999e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.930093067885586 y2[1] (numeric) = 1.930093067886021 absolute error = 4.352074256530614e-13 relative error = 2.254852021875974e-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] = 8.240116375040639 y1[1] (closed_form) = 0.62338942902854 y1[1] (numeric) = 0.6233894290296832 absolute error = 1.143196648456524e-12 relative error = 1.83384028541842e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.926371673699359 y2[1] (numeric) = 1.926371673699826 absolute error = 4.676259379721159e-13 relative error = 2.427495920733189e-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] = 8.250120919891891 y1[1] (closed_form) = 0.6141405041668193 y1[1] (numeric) = 0.6141405041680087 absolute error = 1.18938192628093e-12 relative error = 1.936660940307982e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.922557558895576 y2[1] (numeric) = 1.922557558896077 absolute error = 5.013767179207207e-13 relative error = 2.607863237180475e-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] = 8.260125464743144 y1[1] (closed_form) = 0.6049302000139989 y1[1] (numeric) = 0.6049302000152337 absolute error = 1.234790047988099e-12 relative error = 2.041210784251678e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.918651105229304 y2[1] (numeric) = 1.918651105229839 absolute error = 5.349054532644004e-13 relative error = 2.787924557031292e-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] = 8.270130009594396 y1[1] (closed_form) = 0.5957594384301843 y1[1] (numeric) = 0.5957594384314638 absolute error = 1.279532035880493e-12 relative error = 2.147732714486299e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.914652703697814 y2[1] (numeric) = 1.914652703698384 absolute error = 5.702105454474804e-13 relative error = 2.978140862550266e-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] = 8.280134554445649 y1[1] (closed_form) = 0.5866291373176624 y1[1] (numeric) = 0.5866291373189865 absolute error = 1.324051979167962e-12 relative error = 2.257051167322058e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.910562754501446 y2[1] (numeric) = 1.910562754502052 absolute error = 6.059597268404104e-13 relative error = 3.171629539059728e-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] = 8.290139099296901 y1[1] (closed_form) = 0.5775402105290275 y1[1] (numeric) = 0.5775402105303958 absolute error = 1.368349877850505e-12 relative error = 2.369272048775782e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.906381667003554 y2[1] (numeric) = 1.906381667004196 absolute error = 6.423750420481156e-13 relative error = 3.369603543543298e-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] = 8.300143644148154 y1[1] (closed_form) = 0.5684935677757148 y1[1] (numeric) = 0.5684935677771265 absolute error = 1.411648575810887e-12 relative error = 2.483139046469947e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.902109859689533 y2[1] (numeric) = 1.902109859690212 absolute error = 6.792344464656708e-13 relative error = 3.570952765980284e-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] = 8.309986825372773 y1[1] (closed_form) = 0.5596349841057404 y1[1] (numeric) = 0.559634984107194 absolute error = 1.453615006141717e-12 relative error = 2.597434126575375e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.89781883070943 y2[1] (numeric) = 1.897818830710146 absolute error = 7.16315895488151e-13 relative error = 3.774416629749545e-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] = 8.319991370224026 y1[1] (closed_form) = 0.5506749032709053 y1[1] (numeric) = 0.5506749032724008 absolute error = 1.495470414170086e-12 relative error = 2.715704683992811e-10 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.893368321270342 y2[1] (numeric) = 1.893368321271097 absolute error = 7.545075675352564e-13 relative error = 3.985001539631891e-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] = 8.329995915075278 y1[1] (closed_form) = 0.5417597954222212 y1[1] (numeric) = 0.5417597954237579 absolute error = 1.536659688383679e-12 relative error = 2.836422527784812e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.888828394521977 y2[1] (numeric) = 1.888828394522772 absolute error = 7.94475596421762e-13 relative error = 4.206181984164989e-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] = 8.34000045992653 y1[1] (closed_form) = 0.5328905528735712 y1[1] (numeric) = 0.5328905528751484 absolute error = 1.577182828782497e-12 relative error = 2.959674965671019e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.884199504865979 y2[1] (numeric) = 1.884199504866814 absolute error = 8.351097591230427e-13 relative error = 4.432172691725887e-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] = 8.350005004777783 y1[1] (closed_form) = 0.5240680633481769 y1[1] (numeric) = 0.5240680633497937 absolute error = 1.616817790761615e-12 relative error = 3.085129401765214e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.879482115608297 y2[1] (numeric) = 1.879482115609173 absolute error = 8.766321002440236e-13 relative error = 4.66422155850257e-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] = 8.360009549629035 y1[1] (closed_form) = 0.5152932098897454 y1[1] (numeric) = 0.5152932098914016 absolute error = 1.656230708135809e-12 relative error = 3.214152013550079e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.874676698912812 y2[1] (numeric) = 1.874676698913731 absolute error = 9.194867089945546e-13 relative error = 4.904774831456517e-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] = 8.370014094480288 y1[1] (closed_form) = 0.5065668707740862 y1[1] (numeric) = 0.5065668707757812 absolute error = 1.694977491695226e-12 relative error = 3.346009361222392e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.86978373575408 y2[1] (numeric) = 1.869783735755042 absolute error = 9.625633623500107e-13 relative error = 5.147993021566266e-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] = 8.38001863933154 y1[1] (closed_form) = 0.4978899194212045 y1[1] (numeric) = 0.4978899194229379 absolute error = 1.733335697196026e-12 relative error = 3.481363308602478e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.864803715869188 y2[1] (numeric) = 1.864803715870196 absolute error = 1.007860461754717e-12 relative error = 5.404646361319329e-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] = 8.390023184182793 y1[1] (closed_form) = 0.4892632243078798 y1[1] (numeric) = 0.4892632243096504 absolute error = 1.770528168520968e-12 relative error = 3.618764052878873e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.85973713770874 y2[1] (numeric) = 1.859737137709794 absolute error = 1.053601650369274e-12 relative error = 5.665325647404917e-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] = 8.400027729034045 y1[1] (closed_form) = 0.4806876488807407 y1[1] (numeric) = 0.4806876488825475 absolute error = 1.806832461426211e-12 relative error = 3.758849360147568e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.854584508386963 y2[1] (numeric) = 1.854584508388062 absolute error = 1.09889874977398e-12 relative error = 5.925309657254467e-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] = 8.410032273885298 y1[1] (closed_form) = 0.4721640514698418 y1[1] (numeric) = 0.4721640514716842 absolute error = 1.842470620516679e-12 relative error = 3.902183181419862e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.849346343630953 y2[1] (numeric) = 1.849346343632098 absolute error = 1.145750161413162e-12 relative error = 6.195433134302086e-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] = 8.42003681873655 y1[1] (closed_form) = 0.4636932852027542 y1[1] (numeric) = 0.4636932852046313 absolute error = 1.877109578884983e-12 relative error = 4.048170717124359e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.844023167729053 y2[1] (numeric) = 1.844023167730247 absolute error = 1.193933840681893e-12 relative error = 6.474614102339309e-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] = 8.430041363587803 y1[1] (closed_form) = 0.4552761979191752 y1[1] (numeric) = 0.4552761979210864 absolute error = 1.911248936892207e-12 relative error = 4.197998809574292e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.838615513478382 y2[1] (numeric) = 1.838615513479625 absolute error = 1.24322774297525e-12 relative error = 6.761760323795223e-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] = 8.440045908439055 y1[1] (closed_form) = 0.4469136320860682 y1[1] (numeric) = 0.4469136320880128 absolute error = 1.944666649933424e-12 relative error = 4.351325424682757e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.833123922131501 y2[1] (numeric) = 1.833123922132793 absolute error = 1.292077556058757e-12 relative error = 7.048500870341426e-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] = 8.450050453290308 y1[1] (closed_form) = 0.4386064247133401 y1[1] (numeric) = 0.4386064247153175 absolute error = 1.977418229159866e-12 relative error = 4.508411454420092e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.827548943342242 y2[1] (numeric) = 1.827548943343586 absolute error = 1.343591904401364e-12 relative error = 7.351879189315655e-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] = 8.46005499814156 y1[1] (closed_form) = 0.4303554072700652 y1[1] (numeric) = 0.4303554072720742 absolute error = 2.009059585361683e-12 relative error = 4.668373050326095e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.821891135110695 y2[1] (numeric) = 1.82189113511209 absolute error = 1.395328297348897e-12 relative error = 7.658680974174228e-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] = 8.470059542992812 y1[1] (closed_form) = 0.4221614056012625 y1[1] (numeric) = 0.4221614056033026 absolute error = 2.040145830051188e-12 relative error = 4.832620421910701e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.816151063727354 y2[1] (numeric) = 1.816151063728801 absolute error = 1.446620601086579e-12 relative error = 7.965309879661806e-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] = 8.480064087844065 y1[1] (closed_form) = 0.4140252398452381 y1[1] (numeric) = 0.4140252398473083 absolute error = 2.070177362867298e-12 relative error = 5.000123576140254e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.810329303716439 y2[1] (numeric) = 1.810329303717938 absolute error = 1.498801083243961e-12 relative error = 8.279162692483964e-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] = 8.490068632695317 y1[1] (closed_form) = 0.4059477243514962 y1[1] (numeric) = 0.4059477243535956 absolute error = 2.099431739566171e-12 relative error = 5.171680030772498e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.804426437778393 y2[1] (numeric) = 1.804426437779945 absolute error = 1.552091788425969e-12 relative error = 8.601579737087549e-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] = 8.50007317754657 y1[1] (closed_form) = 0.3979296675992319 y1[1] (numeric) = 0.3979296676013596 absolute error = 2.127742426694113e-12 relative error = 5.347031397611279e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.798443056731555 y2[1] (numeric) = 1.79844305673316 absolute error = 1.605604538212901e-12 relative error = 8.927747432442408e-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] = 8.510077722397822 y1[1] (closed_form) = 0.3899718721164096 y1[1] (numeric) = 0.3899718721185647 absolute error = 2.155109424251123e-12 relative error = 5.5263201742094e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.79237975945303 y2[1] (numeric) = 1.79237975945469 absolute error = 1.660005466419534e-12 relative error = 9.261460679103562e-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] = 8.520082267249075 y1[1] (closed_form) = 0.3820751343994383 y1[1] (numeric) = 0.3820751344016201 absolute error = 2.181810287993358e-12 relative error = 5.710422091253906e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.786237152818746 y2[1] (numeric) = 1.786237152820461 absolute error = 1.715072528440942e-12 relative error = 9.601594758761435e-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] = 8.530086812100327 y1[1] (closed_form) = 0.3742402448334503 y1[1] (numeric) = 0.3742402448356579 absolute error = 2.207567462164661e-12 relative error = 5.898797611002804e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.780015851642708 y2[1] (numeric) = 1.780015851644479 absolute error = 1.770805724277125e-12 relative error = 9.948258172211871e-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] = 8.54009135695158 y1[1] (closed_form) = 0.3664679876131912 y1[1] (numeric) = 0.3664679876154237 absolute error = 2.232491969067496e-12 relative error = 6.091915377405086e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.773716478615468 y2[1] (numeric) = 1.773716478617297 absolute error = 1.828537321557633e-12 relative error = 1.030907331359382e-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] = 8.550095901802832 y1[1] (closed_form) = 0.3587591406645301 y1[1] (numeric) = 0.3587591406667865 absolute error = 2.256472786399399e-12 relative error = 6.289659358141319e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.767339664241793 y2[1] (numeric) = 1.767339664243679 absolute error = 1.885602785023366e-12 relative error = 1.066915898044029e-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] = 8.560100446654085 y1[1] (closed_form) = 0.3511144755665965 y1[1] (numeric) = 0.351114475568876 absolute error = 2.279509914160371e-12 relative error = 6.492212861579992e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.760886046777562 y2[1] (numeric) = 1.760886046779506 absolute error = 1.943556426908799e-12 relative error = 1.103737763420594e-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] = 8.570104991505337 y1[1] (closed_form) = 0.3435347574745533 y1[1] (numeric) = 0.3435347574768547 absolute error = 2.301436818896718e-12 relative error = 6.699283751709441e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.754356272165882 y2[1] (numeric) = 1.754356272167885 absolute error = 2.002620291818857e-12 relative error = 1.141512886288755e-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] = 8.58010953635659 y1[1] (closed_form) = 0.3360207450430123 y1[1] (numeric) = 0.3360207450453348 absolute error = 2.322531056364596e-12 relative error = 6.911868063584292e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.747750993972434 y2[1] (numeric) = 1.747750993974496 absolute error = 2.061240067519066e-12 relative error = 1.179367126454385e-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] = 8.590114081207842 y1[1] (closed_form) = 0.3285731903501 y1[1] (numeric) = 0.3285731903524427 absolute error = 2.342681604261543e-12 relative error = 7.129862304850186e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.74107087332006 y2[1] (numeric) = 1.741070873322182 absolute error = 2.121414155453749e-12 relative error = 1.218453647098472e-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] = 8.600118626059094 y1[1] (closed_form) = 0.3211928388221827 y1[1] (numeric) = 0.3211928388245446 absolute error = 2.361832951436327e-12 relative error = 7.353317589822959e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.73431657882259 y2[1] (numeric) = 1.734316578824773 absolute error = 2.182698466413058e-12 relative error = 1.258535202318639e-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] = 8.610123170910347 y1[1] (closed_form) = 0.3138804291592563 y1[1] (numeric) = 0.3138804291616358 absolute error = 2.379541008679098e-12 relative error = 7.581042931070319e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.727488786517918 y2[1] (numeric) = 1.727488786520162 absolute error = 2.243760732767441e-12 relative error = 1.298856901578022e-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] = 8.620127715761599 y1[1] (closed_form) = 0.3066366932610094 y1[1] (numeric) = 0.3066366932634062 absolute error = 2.396804976712019e-12 relative error = 7.816432375468701e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.720588179800344 y2[1] (numeric) = 1.720588179802649 absolute error = 2.305267088331675e-12 relative error = 1.339813393696089e-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] = 8.630132260612852 y1[1] (closed_form) = 0.2994623561535681 y1[1] (numeric) = 0.2994623561559811 absolute error = 2.413014232871546e-12 relative error = 8.057821570181336e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.713615449352163 y2[1] (numeric) = 1.713615449354531 absolute error = 2.367883666920534e-12 relative error = 1.381805741664922e-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] = 8.640136805464104 y1[1] (closed_form) = 0.2923581359169279 y1[1] (numeric) = 0.2923581359193561 absolute error = 2.428113266006449e-12 relative error = 8.305270035982117e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.706571293074545 y2[1] (numeric) = 1.706571293076976 absolute error = 2.430722290114318e-12 relative error = 1.424330937698564e-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] = 8.650141350315357 y1[1] (closed_form) = 0.2853247436130808 y1[1] (numeric) = 0.285324743615523 absolute error = 2.442213098419188e-12 relative error = 8.55941572922603e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.699456416017675 y2[1] (numeric) = 1.69945641602017 absolute error = 2.494449091727802e-12 relative error = 1.467792329486758e-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] = 8.659984531539976 y1[1] (closed_form) = 0.2784746000541789 y1[1] (numeric) = 0.2784746000566339 absolute error = 2.454980663202377e-12 relative error = 8.815815383969476e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.6923879672792 y2[1] (numeric) = 1.692387967281758 absolute error = 2.557287714921586e-12 relative error = 1.511052881705876e-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] = 8.669989076391229 y1[1] (closed_form) = 0.2715837979044182 y1[1] (numeric) = 0.2715837979068852 absolute error = 2.466971071868329e-12 relative error = 9.083645971902051e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.685134903887292 y2[1] (numeric) = 1.685134903889914 absolute error = 2.622124739559695e-12 relative error = 1.556032536926831e-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] = 8.679993621242481 y1[1] (closed_form) = 0.264765902992663 y1[1] (numeric) = 0.2647659029951409 absolute error = 2.477906768660887e-12 relative error = 9.358859054934852e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.677813265286101 y2[1] (numeric) = 1.677813265288788 absolute error = 2.686961764197804e-12 relative error = 1.601466515845924e-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] = 8.689998166093734 y1[1] (closed_form) = 0.2580215977225797 y1[1] (numeric) = 0.2580215977250676 absolute error = 2.487898775882513e-12 relative error = 9.642211341383361e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.670423784299041 y2[1] (numeric) = 1.670423784301793 absolute error = 2.752020833440838e-12 relative error = 1.647498592457882e-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] = 8.700002710944986 y1[1] (closed_form) = 0.2513515571322417 y1[1] (numeric) = 0.2513515571347384 absolute error = 2.496725048928283e-12 relative error = 9.93319905161638e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.0001613636266322163 y2[1] (closed_form) = 1.662967200539876 y2[1] (numeric) = 1.662967200542695 absolute error = 2.818856259523272e-12 relative error = 1.695076282086707e-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] = 8.710007255796238 y1[1] (closed_form) = 0.2447564488265639 y1[1] (numeric) = 0.2447564488290684 absolute error = 2.504524365676275e-12 relative error = 1.023272063998199e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.655444260338694 y2[1] (numeric) = 1.65544426034158 absolute error = 2.886135774815557e-12 relative error = 1.74342069012041e-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] = 8.720011800647491 y1[1] (closed_form) = 0.2382369329104831 y1[1] (numeric) = 0.2382369329129942 absolute error = 2.51115794824841e-12 relative error = 1.054059048515358e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.647855716667201 y2[1] (numeric) = 1.647855716670154 absolute error = 2.953859379317691e-12 relative error = 1.792547338605526e-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] = 8.730016345498743 y1[1] (closed_form) = 0.2317936619228872 y1[1] (numeric) = 0.2317936619254041 absolute error = 2.516931107976461e-12 relative error = 1.085849840369574e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.640202329063362 y2[1] (numeric) = 1.640202329066383 absolute error = 3.020916850005051e-12 relative error = 1.841795244694078e-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] = 8.740020890349996 y1[1] (closed_form) = 0.2254272807713033 y1[1] (numeric) = 0.2254272807738247 absolute error = 2.521399755650577e-12 relative error = 1.118498057122264e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.632484863555376 y2[1] (numeric) = 1.632484863558464 absolute error = 3.08841840990226e-12 relative error = 1.891851176602041e-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] = 8.750025435201248 y1[1] (closed_form) = 0.2191384266673481 y1[1] (numeric) = 0.2191384266698727 absolute error = 2.52461940242199e-12 relative error = 1.152066043740635e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.624704092585006 y2[1] (numeric) = 1.624704092588162 absolute error = 3.15591996979947e-12 relative error = 1.942458312379951e-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] = 8.760029980052501 y1[1] (closed_form) = 0.2129277290629498 y1[1] (numeric) = 0.2129277290654767 absolute error = 2.526923115198088e-12 relative error = 1.186751545380466e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.616860794930262 y2[1] (numeric) = 1.616860794933486 absolute error = 3.22386561890653e-12 relative error = 1.993904255094256e-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] = 8.770034524903753 y1[1] (closed_form) = 0.206795809587346 y1[1] (numeric) = 0.2067958095898741 absolute error = 2.528061093798328e-12 relative error = 1.22249145127408e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.608955755627456 y2[1] (numeric) = 1.608955755630748 absolute error = 3.291811268013589e-12 relative error = 2.045930260356885e-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] = 8.780039069755006 y1[1] (closed_form) = 0.2007432819848651 y1[1] (numeric) = 0.2007432819873931 absolute error = 2.528005582647097e-12 relative error = 1.25932263219533e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.600989765892627 y2[1] (numeric) = 1.600989765895989 absolute error = 3.361755318564974e-12 relative error = 2.09979813124579e-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] = 8.790043614606258 y1[1] (closed_form) = 0.194770752053496 y1[1] (numeric) = 0.1947707520560232 absolute error = 2.527145159803013e-12 relative error = 1.297497254161088e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.592963623042348 y2[1] (numeric) = 1.592963623045778 absolute error = 3.429923012276959e-12 relative error = 2.15317095925032e-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] = 8.800048159457511 y1[1] (closed_form) = 0.1888788175842545 y1[1] (numeric) = 0.1888788175867794 absolute error = 2.524896958178147e-12 relative error = 1.336781429739652e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.584878130413921 y2[1] (numeric) = 1.58487813041742 absolute error = 3.499867062828343e-12 relative error = 2.208287814479646e-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] = 8.810052704308763 y1[1] (closed_form) = 0.1830680683013496 y1[1] (numeric) = 0.1830680683038711 absolute error = 2.521483022377424e-12 relative error = 1.377347259832771e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.576734097284972 y2[1] (numeric) = 1.576734097288542 absolute error = 3.570033157984653e-12 relative error = 2.264194808834289e-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] = 8.820057249160016 y1[1] (closed_form) = 0.1773390858031583 y1[1] (numeric) = 0.1773390858056751 absolute error = 2.51687559682523e-12 relative error = 1.419244711579767e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.568532338792453 y2[1] (numeric) = 1.568532338796094 absolute error = 3.640643342350813e-12 relative error = 2.321050865392799e-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] = 8.830061794011268 y1[1] (closed_form) = 0.1716924435040134 y1[1] (numeric) = 0.1716924435065245 absolute error = 2.511185703824026e-12 relative error = 1.46260700388094e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.56027367585105 y2[1] (numeric) = 1.560273675854762 absolute error = 3.711697615926823e-12 relative error = 2.378876009622017e-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] = 8.84006633886252 y1[1] (closed_form) = 0.1661287065768102 y1[1] (numeric) = 0.1661287065793146 absolute error = 2.504385587798197e-12 relative error = 1.507497192630152e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.551958935071022 y2[1] (numeric) = 1.551958935074804 absolute error = 3.781641666478208e-12 relative error = 2.436689258343778e-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] = 8.850070883713773 y1[1] (closed_form) = 0.160648431896439 y1[1] (numeric) = 0.1606484318989352 absolute error = 2.496280959718433e-12 relative error = 1.553878198654093e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.543588948675461 y2[1] (numeric) = 1.543588948679314 absolute error = 3.853140029264068e-12 relative error = 2.496221570237602e-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] = 8.860075428565025 y1[1] (closed_form) = 0.1552521679840462 y1[1] (numeric) = 0.1552521679865331 absolute error = 2.486955086311582e-12 relative error = 1.601881067816807e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.535164554417 y2[1] (numeric) = 1.535164554420924 absolute error = 3.923972258235153e-12 relative error = 2.55605970509483e-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] = 8.870079973416278 y1[1] (closed_form) = 0.1499404549521339 y1[1] (numeric) = 0.1499404549546104 absolute error = 2.47649123430449e-12 relative error = 1.651649806648292e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.526686595493957 y2[1] (numeric) = 1.526686595497952 absolute error = 3.994804487206238e-12 relative error = 2.616650004655164e-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] = 8.88008451826753 y1[1] (closed_form) = 0.1447138244504994 y1[1] (numeric) = 0.1447138244529643 absolute error = 2.464889403697157e-12 relative error = 1.703285372393909e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.518155920465943 y2[1] (numeric) = 1.518155920470009 absolute error = 4.066302849992098e-12 relative error = 2.678448764830488e-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] = 8.890089063118783 y1[1] (closed_form) = 0.1395727996130226 y1[1] (numeric) = 0.1395727996154748 absolute error = 2.452149594489583e-12 relative error = 1.756896473588246e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.509573383168929 y2[1] (numeric) = 1.509573383173067 absolute error = 4.138023257382883e-12 relative error = 2.741187214560087e-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] = 8.900093607970035 y1[1] (closed_form) = 0.1345178950053053 y1[1] (numeric) = 0.1345178950077436 absolute error = 2.438244051106153e-12 relative error = 1.812579695073276e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.500939842629784 y2[1] (numeric) = 1.500939842633993 absolute error = 4.209299575563819e-12 relative error = 2.804442560595061e-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] = 8.910098152821288 y1[1] (closed_form) = 0.1295496165731685 y1[1] (numeric) = 0.1295496165755915 absolute error = 2.422950728941942e-12 relative error = 1.870287842630147e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.492256162980294 y2[1] (numeric) = 1.492256162984575 absolute error = 4.280575893744754e-12 relative error = 2.868526195392419e-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] = 8.92010269767254 y1[1] (closed_form) = 0.1246684615920119 y1[1] (numeric) = 0.1246684615944185 absolute error = 2.406588817116528e-12 relative error = 1.930391043881084e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.483523213370677 y2[1] (numeric) = 1.48352321337503 absolute error = 4.353406524160164e-12 relative error = 2.934505159692713e-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] = 8.930107242523793 y1[1] (closed_form) = 0.119874918617042 y1[1] (numeric) = 0.119874918619431 absolute error = 2.389005659964027e-12 relative error = 1.992915355042747e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.474741867882581 y2[1] (numeric) = 1.474741867887006 absolute error = 4.425571020760799e-12 relative error = 3.000912306853394e-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] = 8.940111787375045 y1[1] (closed_form) = 0.1151694674343721 y1[1] (numeric) = 0.1151694674367424 absolute error = 2.370340035362517e-12 relative error = 2.058132322886035e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.465913005441603 y2[1] (numeric) = 1.465913005446102 absolute error = 4.498623695781134e-12 relative error = 3.068820372751883e-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] = 8.950116332226298 y1[1] (closed_form) = 0.110552579013001 y1[1] (numeric) = 0.1105525790153512 absolute error = 2.350217243041186e-12 relative error = 2.125881878128597e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.457037509729318 y2[1] (numeric) = 1.457037509733889 absolute error = 4.57167637080147e-12 relative error = 3.137651803933844e-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] = 8.96012087707755 y1[1] (closed_form) = 0.106024715457673 y1[1] (numeric) = 0.106024715460002 absolute error = 2.329039738846461e-12 relative error = 2.196695109053376e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.448116269094825 y2[1] (numeric) = 1.448116269099468 absolute error = 4.64361882279718e-12 relative error = 3.206661593339995e-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] = 8.970125421928802 y1[1] (closed_form) = 0.1015863299626266 y1[1] (numeric) = 0.1015863299649333 absolute error = 2.306710378263688e-12 relative error = 2.270689746457344e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.439150176465839 y2[1] (numeric) = 1.439150176470555 absolute error = 4.71556127479289e-12 relative error = 3.276629049494351e-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] = 8.980129966780055 y1[1] (closed_form) = 0.09723786676623369 y1[1] (numeric) = 0.09723786676851678 absolute error = 2.283090383414788e-12 relative error = 2.347943717135927e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.430140129259314 y2[1] (numeric) = 1.430140129264102 absolute error = 4.787725771393525e-12 relative error = 3.347731927411297e-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] = 8.990134511631307 y1[1] (closed_form) = 0.09297976110653561 y1[1] (numeric) = 0.092979761108794 absolute error = 2.258387921116878e-12 relative error = 2.428902692629239e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.421087029291622 y2[1] (numeric) = 1.421087029296481 absolute error = 4.859668223389235e-12 relative error = 3.41968375139675e-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] = 9.00013905648256 y1[1] (closed_form) = 0.08881243917768078 y1[1] (numeric) = 0.08881243917991309 absolute error = 2.232311557825994e-12 relative error = 2.51351227203654e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.411991782688287 y2[1] (numeric) = 1.411991782693219 absolute error = 4.93227680919972e-12 relative error = 3.493134216269428e-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] = 9.010143601333812 y1[1] (closed_form) = 0.08473631808726612 y1[1] (numeric) = 0.08473631808947113 absolute error = 2.205013949208023e-12 relative error = 2.602206467051329e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.402855299793295 y2[1] (numeric) = 1.402855299798301 absolute error = 5.005551528824981e-12 relative error = 3.568116775523839e-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] = 9.019986782558432 y1[1] (closed_form) = 0.08081534317180006 y1[1] (numeric) = 0.08081534317397709 absolute error = 2.177036328987469e-12 relative error = 2.693840356972129e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.39382682317438 y2[1] (numeric) = 1.393826823179457 absolute error = 5.076827847005916e-12 relative error = 3.642366298736927e-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] = 9.029991327409684 y1[1] (closed_form) = 0.07692135141695644 y1[1] (numeric) = 0.07692135141910371 absolute error = 2.147268474139707e-12 relative error = 2.791511634396957e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.38461124337453 y2[1] (numeric) = 1.38461124337968 absolute error = 5.149436432816401e-12 relative error = 3.719048546988799e-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] = 9.039995872260937 y1[1] (closed_form) = 0.07311975068051202 y1[1] (numeric) = 0.07311975068262826 absolute error = 2.116237740601434e-12 relative error = 2.894208091392545e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.375357167803472 y2[1] (numeric) = 1.375357167808693 absolute error = 5.221378884812111e-12 relative error = 3.796380319994236e-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] = 9.050000417112189 y1[1] (closed_form) = 0.06941092146499928 y1[1] (numeric) = 0.06941092146708336 absolute error = 2.084082906250728e-12 relative error = 3.002528798442238e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.366065522702396 y2[1] (numeric) = 1.366065522707689 absolute error = 5.293543381412746e-12 relative error = 3.875028901205913e-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] = 9.060004961963442 y1[1] (closed_form) = 0.06579523498744178 y1[1] (numeric) = 0.0657952349894924 absolute error = 2.050623559846088e-12 relative error = 3.116674878108554e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.35673723807283 y2[1] (numeric) = 1.356737238078195 absolute error = 5.365485833408457e-12 relative error = 3.954697846305031e-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] = 9.070009506814694 y1[1] (closed_form) = 0.06227305314219844 y1[1] (numeric) = 0.06227305314421442 absolute error = 2.015977662583879e-12 relative error = 3.237319451770674e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.347373247583555 y2[1] (numeric) = 1.347373247588993 absolute error = 5.438094419218942e-12 relative error = 4.036071243786297e-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] = 9.080014051665946 y1[1] (closed_form) = 0.05884472846474198 y1[1] (numeric) = 0.05884472846672204 absolute error = 1.980061947737255e-12 relative error = 3.364892658012093e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.337974488477155 y2[1] (numeric) = 1.337974488482665 absolute error = 5.510036871214652e-12 relative error = 4.118192774726236e-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] = 9.090018596517199 y1[1] (closed_form) = 0.05551060409637332 y1[1] (numeric) = 0.05551060409831623 absolute error = 1.942911109775736e-12 relative error = 3.5000719977801e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.328541901476208 y2[1] (numeric) = 1.328541901481789 absolute error = 5.580869100185737e-12 relative error = 4.200747521763943e-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] = 9.100023141368451 y1[1] (closed_form) = 0.05227101374987664 y1[1] (numeric) = 0.05227101375178117 absolute error = 1.904532087593225e-12 relative error = 3.643572127195868e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.319076430689127 y2[1] (numeric) = 1.31907643069478 absolute error = 5.652367462971597e-12 relative error = 4.285094731029817e-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] = 9.110027686219704 y1[1] (closed_form) = 0.0491262816761181 y1[1] (numeric) = 0.04912628167798305 absolute error = 1.864945697871434e-12 relative error = 3.796228076382271e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.309579023515669 y2[1] (numeric) = 1.309579023521392 absolute error = 5.723421736547607e-12 relative error = 4.370428690269204e-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] = 9.120032231070956 y1[1] (closed_form) = 0.04607672263159146 y1[1] (numeric) = 0.04607672263341558 absolute error = 1.824124185034748e-12 relative error = 3.958884401609064e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.300050630552102 y2[1] (numeric) = 1.300050630557896 absolute error = 5.794031920913767e-12 relative error = 4.456774055371344e-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] = 9.130036775922209 y1[1] (closed_form) = 0.04312264184691406 y1[1] (numeric) = 0.04312264184869614 absolute error = 1.782081426870974e-12 relative error = 4.132588706409469e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.29049220549607 y2[1] (numeric) = 1.290492205501935 absolute error = 5.864642105279927e-12 relative error = 4.544500214959096e-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] = 9.140041320773461 y1[1] (closed_form) = 0.04026433499627635 y1[1] (numeric) = 0.04026433499801514 absolute error = 1.738789667804497e-12 relative error = 4.318436323275425e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.280904705051127 y2[1] (numeric) = 1.280904705057062 absolute error = 5.935252289646087e-12 relative error = 4.633640790170401e-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] = 9.150045865624714 y1[1] (closed_form) = 0.03750208816784784 y1[1] (numeric) = 0.03750208816954208 absolute error = 1.694248907835316e-12 relative error = 4.517745519269162e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.271289088830986 y2[1] (numeric) = 1.271289088836991 absolute error = 6.004752250987622e-12 relative error = 4.723357026928699e-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] = 9.160050410475966 y1[1] (closed_form) = 0.03483617783514237 y1[1] (numeric) = 0.03483617783679082 absolute error = 1.648452208069529e-12 relative error = 4.732012265727347e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.261646319263473 y2[1] (numeric) = 1.261646319269547 absolute error = 6.074696301539007e-12 relative error = 4.814896384816713e-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] = 9.170054955327219 y1[1] (closed_form) = 0.03226687082934587 y1[1] (numeric) = 0.03226687083094737 absolute error = 1.601496713021788e-12 relative error = 4.963284854896028e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.251977361494191 y2[1] (numeric) = 1.251977361500334 absolute error = 6.143530129065766e-12 relative error = 4.907061675407357e-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] = 9.180059500178471 y1[1] (closed_form) = 0.02979442431260948 y1[1] (numeric) = 0.02979442431416277 absolute error = 1.553288747624393e-12 relative error = 5.213353785013446e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.242283183289925 y2[1] (numeric) = 1.242283183296137 absolute error = 6.212586001197451e-12 relative error = 5.000941882465743e-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] = 9.190064045029724 y1[1] (closed_form) = 0.02741908575230989 y1[1] (numeric) = 0.02741908575381371 absolute error = 1.503817903536486e-12 relative error = 5.484566178176816e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.232564754941774 y2[1] (numeric) = 1.232564754948055 absolute error = 6.280975739514361e-12 relative error = 5.095858626763243e-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] = 9.200068589880976 y1[1] (closed_form) = 0.0251410928962803 y1[1] (numeric) = 0.02514109289773344 absolute error = 1.453132753015396e-12 relative error = 5.779910837648554e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.222823049168036 y2[1] (numeric) = 1.222823049174385 absolute error = 6.349143433226345e-12 relative error = 5.192201306269185e-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] = 9.210073134732228 y1[1] (closed_form) = 0.02296067374901434 y1[1] (numeric) = 0.0229606737504156 absolute error = 1.401261051636737e-12 relative error = 6.102874275180584e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.21305904101685 y2[1] (numeric) = 1.213059041023268 absolute error = 6.41731112693833e-12 relative error = 5.290188614033989e-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] = 9.220077679583481 y1[1] (closed_form) = 0.02087804654884506 y1[1] (numeric) = 0.02087804655019327 absolute error = 1.348206268847463e-12 relative error = 6.457530716263506e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.2032737077686 y2[1] (numeric) = 1.203273707775085 absolute error = 6.484368597625689e-12 relative error = 5.388938988495448e-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] = 9.230082224434733 y1[1] (closed_form) = 0.01889341974610148 y1[1] (numeric) = 0.01889341974739544 absolute error = 1.293957996306716e-12 relative error = 6.848723067054681e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.193468028838102 y2[1] (numeric) = 1.193468028844654 absolute error = 6.551870157522899e-12 relative error = 5.489774337651472e-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] = 9.240086769285986 y1[1] (closed_form) = 0.01700699198224476 y1[1] (numeric) = 0.01700699198348317 absolute error = 1.238415620052891e-12 relative error = 7.281802809960706e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.183642985676571 y2[1] (numeric) = 1.18364298568319 absolute error = 6.619149672815183e-12 relative error = 5.592184259032865e-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] = 9.250091314137238 y1[1] (closed_form) = 0.01521895206998591 y1[1] (numeric) = 0.01521895207116761 absolute error = 1.181695366558877e-12 relative error = 7.764630318334202e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.173799561673392 y2[1] (numeric) = 1.173799561680077 absolute error = 6.685318965082843e-12 relative error = 5.69545191817257e-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] = 9.260095858988491 y1[1] (closed_form) = 0.01352947897438794 y1[1] (numeric) = 0.01352947897551171 absolute error = 1.123771214972535e-12 relative error = 8.306093805237415e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.163938742057689 y2[1] (numeric) = 1.16393874206444 absolute error = 6.751266212745577e-12 relative error = 5.800362140030013e-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] = 9.270100403839743 y1[1] (closed_form) = 0.01193874179495291 y1[1] (numeric) = 0.01193874179601755 absolute error = 1.06464143057039e-12 relative error = 8.917534601681944e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.154061513799713 y2[1] (numeric) = 1.15406151380653 absolute error = 6.816769371198461e-12 relative error = 5.90676431861457e-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] = 9.280104948690996 y1[1] (closed_form) = 0.01044689974869684 y1[1] (numeric) = 0.0104468997497012 absolute error = 1.004363259227148e-12 relative error = 9.613983893666003e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 1.14416886551206 y2[1] (numeric) = 1.144168865518941 absolute error = 6.88116230662672e-12 relative error = 6.014114274598038e-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] = 9.290109493542248 y1[1] (closed_form) = 0.009054102154213761 y1[1] (numeric) = 0.009054102155156634 absolute error = 9.42872516174198e-13 relative error = 1.041376052660712e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 1.134261787350715 y2[1] (numeric) = 1.134261787357661 absolute error = 6.946221375869754e-12 relative error = 6.124001930889325e-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] = 9.300114038393501 y1[1] (closed_form) = 0.007760488416730271 y1[1] (numeric) = 0.00776048841761047 absolute error = 8.801986917106319e-13 relative error = 1.134205277354806e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 1.124341270915953 y2[1] (numeric) = 1.124341270922962 absolute error = 7.008837954458613e-12 relative error = 6.233728260058276e-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] = 9.310118583244753 y1[1] (closed_form) = 0.006566188014152541 y1[1] (numeric) = 0.006566188014968857 absolute error = 8.1631576498431e-13 relative error = 1.243211073494774e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 1.114408309153085 y2[1] (numeric) = 1.114408309160157 absolute error = 7.072120666862247e-12 relative error = 6.346076755508791e-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] = 9.320123128096006 y1[1] (closed_form) = 0.005471320484106701 y1[1] (numeric) = 0.005471320484858015 absolute error = 7.513139416159831e-13 relative error = 1.373185767125922e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 1.104463896253077 y2[1] (numeric) = 1.104463896260212 absolute error = 7.135181334660956e-12 relative error = 6.460311974766441e-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] = 9.330127672947258 y1[1] (closed_form) = 0.004475995411974631 y1[1] (numeric) = 0.004475995412659721 absolute error = 6.850900055588305e-13 relative error = 1.530586925370855e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 1.09450902755304 y2[1] (numeric) = 1.094509027560237 absolute error = 7.19713177943504e-12 relative error = 6.575671463875856e-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] = 9.34013221779851 y1[1] (closed_form) = 0.00358031241992518 y1[1] (numeric) = 0.003580312420542903 absolute error = 6.177224530501402e-13 relative error = 1.725331145998284e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 1.084544699436607 y2[1] (numeric) = 1.084544699443865 absolute error = 7.258416090394348e-12 relative error = 6.692592840262748e-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] = 9.350136762649763 y1[1] (closed_form) = 0.00278436115694336 y1[1] (numeric) = 0.002784361157492434 absolute error = 5.49073807254441e-13 relative error = 1.971992052414666e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 1.074571909234204 y2[1] (numeric) = 1.074571909241523 absolute error = 7.319034267538882e-12 relative error = 6.811116319572144e-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] = 9.360141307501015 y1[1] (closed_form) = 0.002088221289856751 y1[1] (numeric) = 0.002088221290336169 absolute error = 4.794177208000683e-13 relative error = 2.295818566397988e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 1.064591655123228 y2[1] (numeric) = 1.064591655130607 absolute error = 7.37898631086864e-12 relative error = 6.931283253403401e-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] = 9.369984488725635 y1[1] (closed_form) = 0.001500786745519789 y1[1] (numeric) = 0.001500786745929499 absolute error = 4.097106768435888e-13 relative error = 2.72997264978968e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 1.054766058194688 y2[1] (numeric) = 1.054766058202126 absolute error = 7.437384041963924e-12 relative error = 7.051216697941122e-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] = 9.379989033576887 y1[1] (closed_form) = 0.001002856334548441 y1[1] (numeric) = 0.001002856334886193 absolute error = 3.377517449748568e-13 relative error = 3.367897607456778e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 1.044773953904799 y2[1] (numeric) = 1.044773953912296 absolute error = 7.496669951478907e-12 relative error = 7.175398968801256e-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] = 9.38999357842814 y1[1] (closed_form) = 0.0006049156304376302 y1[1] (numeric) = 0.0006049156307023412 absolute error = 2.647109961784189e-13 relative error = 4.37599861631798e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 1.034777368186155 y2[1] (numeric) = 1.03477736819371 absolute error = 7.555289727179115e-12 relative error = 7.301367385356201e-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] = 9.399998123279392 y1[1] (closed_form) = 0.000307004463105498 y1[1] (numeric) = 0.0003070044632959932 absolute error = 1.904952432775497e-13 relative error = 6.204966577703745e-08 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 1.024777301597848 y2[1] (numeric) = 1.02477730160546 absolute error = 7.612133146039923e-12 relative error = 7.428085237808226e-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] = 9.410002668130645 y1[1] (closed_form) = 0.0001091526505054841 y1[1] (numeric) = 0.0001091526506205792 absolute error = 1.150951079234575e-13 relative error = 1.054441714337251e-07 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 9 h = 0.0001613636266322163 y2[1] (closed_form) = 1.014774755047372 y2[1] (numeric) = 1.01477475505504 absolute error = 7.667644297271181e-12 relative error = 7.556006157162668e-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] = 9.420007212981897 y1[1] (closed_form) = 1.137999564182479e-05 y1[1] (numeric) = 1.137999568042158e-05 absolute error = 3.859678418885459e-14 relative error = 3.391634355904337e-07 % Desired digits = 8 Estimated correct digits = 6 Correct digits = 9 h = 0.0001613636266322163 y2[1] (closed_form) = 1.004770729690439 y2[1] (numeric) = 1.004770729698162 absolute error = 7.722711359292589e-12 relative error = 7.686043324203807e-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] = 9.430011757833149 y1[1] (closed_form) = 1.369628458758321e-05 y1[1] (numeric) = 1.369628454864341e-05 absolute error = 3.89397969571088e-14 relative error = 2.843091986596926e-07 % Desired digits = 8 Estimated correct digits = 6 Correct digits = 9 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9947662268307768 y2[1] (numeric) = 0.994766226838555 absolute error = 7.778222510523847e-12 relative error = 7.81914614783864e-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] = 9.440016302684402 y1[1] (closed_form) = 0.0001161012855052102 y1[1] (numeric) = 0.0001161012853876985 absolute error = 1.175116861457104e-13 relative error = 1.012148019157264e-07 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 9 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9847622478199042 y2[1] (numeric) = 0.9847622478277366 absolute error = 7.832401394125554e-12 relative error = 7.953596323848885e-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] = 9.450020847535654 y1[1] (closed_form) = 0.000318584748669859 y1[1] (numeric) = 0.0003185847484725728 absolute error = 1.972861977950213e-13 relative error = 6.19258136551489e-08 % Desired digits = 8 Estimated correct digits = 7 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9747597939569096 y2[1] (numeric) = 0.9747597939647956 absolute error = 7.886025166214949e-12 relative error = 8.090224089160124e-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] = 9.460025392386907 y1[1] (closed_form) = 0.0006211264074947875 y1[1] (numeric) = 0.0006211264072166677 absolute error = 2.781198665466333e-13 relative error = 4.477669330923872e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9647598663882286 y2[1] (numeric) = 0.9647598663961677 absolute error = 7.939093826792032e-12 relative error = 8.229087986955361e-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] = 9.470029937238159 y1[1] (closed_form) = 0.001023695980560291 y1[1] (numeric) = 0.001023695980200303 absolute error = 3.59987647330362e-13 relative error = 3.516548410528418e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9547634660074399 y2[1] (numeric) = 0.9547634660154307 absolute error = 7.990830219739564e-12 relative error = 8.369434424585845e-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] = 9.480034482089412 y1[1] (closed_form) = 0.00152625317464461 y1[1] (numeric) = 0.001526253174201572 absolute error = 4.430373169023172e-13 relative error = 2.902777365265623e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9447715933550856 y2[1] (numeric) = 0.9447715933631274 absolute error = 8.041789456569859e-12 relative error = 8.511887437271212e-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] = 9.490039026940664 y1[1] (closed_form) = 0.002128747688756261 y1[1] (numeric) = 0.002128747688229302 absolute error = 5.269586850209507e-13 relative error = 2.475439845709619e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9347852485185273 y2[1] (numeric) = 0.934785248526619 absolute error = 8.091749492677991e-12 relative error = 8.656265709693229e-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] = 9.500043571791917 y1[1] (closed_form) = 0.002831119219169786 y1[1] (numeric) = 0.002831119218557677 absolute error = 6.121093215627482e-13 relative error = 2.162075399079261e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9248054310318468 y2[1] (numeric) = 0.9248054310399876 absolute error = 8.140821350366423e-12 relative error = 8.802739557101589e-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] = 9.510048116643169 y1[1] (closed_form) = 0.003633297465460261 y1[1] (numeric) = 0.003633297464762046 absolute error = 6.98214923378071e-13 relative error = 1.921711420591383e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9148331397758029 y2[1] (numeric) = 0.9148331397839918 absolute error = 8.188894007332692e-12 relative error = 8.951243293765609e-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] = 9.520052661494422 y1[1] (closed_form) = 0.004535202137540661 y1[1] (numeric) = 0.004535202136755297 absolute error = 7.853648287259318e-13 relative error = 1.731708543319345e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.9048693728778536 y2[1] (numeric) = 0.9048693728860905 absolute error = 8.236855641996499e-12 relative error = 9.102811841006331e-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] = 9.530057206345674 y1[1] (closed_form) = 0.00553674296369755 y1[1] (numeric) = 0.005536742962824104 absolute error = 8.734454132186542e-13 relative error = 1.577543727324032e-08 % Desired digits = 8 Estimated correct digits = 8 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.894915127612253 y2[1] (numeric) = 0.8949151276205366 absolute error = 8.283596031333218e-12 relative error = 9.256292329569735e-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] = 9.540061751196927 y1[1] (closed_form) = 0.006637819699626846 y1[1] (numeric) = 0.006637819698664226 absolute error = 9.6261974086298e-13 relative error = 1.45020471242552e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8849714003002344 y2[1] (numeric) = 0.8849714003085631 absolute error = 8.328782108435462e-12 relative error = 9.411357367718153e-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] = 9.550066296048179 y1[1] (closed_form) = 0.007838322138466691 y1[1] (numeric) = 0.007838322137413964 absolute error = 1.052727349737381e-12 relative error = 1.343051907207417e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.875039186210288 y2[1] (numeric) = 0.8750391862186611 absolute error = 8.373080007118006e-12 relative error = 9.568805762152235e-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] = 9.560070840899431 y1[1] (closed_form) = 0.009138130121828736 y1[1] (numeric) = 0.009138130120684785 absolute error = 1.143951253168574e-12 relative error = 1.251843908893305e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8651194794585447 y2[1] (numeric) = 0.8651194794669615 absolute error = 8.416822794288237e-12 relative error = 9.729087130896767e-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] = 9.570075385750684 y1[1] (closed_form) = 0.01053711355182396 y1[1] (numeric) = 0.01053711355058798 absolute error = 1.235980068292619e-12 relative error = 1.172977838962998e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8552132729092753 y2[1] (numeric) = 0.8552132729177346 absolute error = 8.45934433613138e-12 relative error = 9.891502627589345e-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] = 9.580079930601936 y1[1] (closed_form) = 0.01203513240408527 y1[1] (numeric) = 0.01203513240275616 absolute error = 1.329112167547386e-12 relative error = 1.104360237113989e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8453215580755136 y2[1] (numeric) = 0.8453215580840143 absolute error = 8.500755654949899e-12 relative error = 1.005623904151101e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.590084475453189 y1[1] (closed_form) = 0.01363203674178148 y1[1] (numeric) = 0.01363203674035833 absolute error = 1.423149792456613e-12 relative error = 1.043974440073751e-08 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 10 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8354453250198168 y2[1] (numeric) = 0.8354453250283586 absolute error = 8.541722884558567e-12 relative error = 1.022415546386109e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.600089020304441 y1[1] (closed_form) = 0.01532766673062524 y1[1] (numeric) = 0.01532766672910707 absolute error = 1.518176209747146e-12 relative error = 9.904809625810653e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8255855622551695 y2[1] (numeric) = 0.825585562263751 absolute error = 8.581468868840147e-12 relative error = 1.039440278654947e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.610093565155694 y1[1] (closed_form) = 0.01712185265487043 y1[1] (numeric) = 0.01712185265325633 absolute error = 1.614094274904332e-12 relative error = 9.427100603188473e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8157432566460436 y2[1] (numeric) = 0.8157432566546636 absolute error = 8.61999360779464e-12 relative error = 1.056704243346864e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.620098110006946 y1[1] (closed_form) = 0.01901441493429934 y1[1] (numeric) = 0.01901441493258838 absolute error = 1.710957764355925e-12 relative error = 8.998214093190935e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.8059193933096228 y2[1] (numeric) = 0.8059193933182799 absolute error = 8.657075056817121e-12 relative error = 1.074186218706763e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.630102654858199 y1[1] (closed_form) = 0.02100516414219655 y1[1] (numeric) = 0.02100516414038789 absolute error = 1.808660859969891e-12 relative error = 8.610553327391209e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7961149555172021 y2[1] (numeric) = 0.7961149555258952 absolute error = 8.693046282814976e-12 relative error = 1.091933548361426e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.640107199709451 y1[1] (closed_form) = 0.02309390102430908 y1[1] (numeric) = 0.02309390102240175 absolute error = 1.907328461836499e-12 relative error = 8.259013753582857e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7863309245957724 y2[1] (numeric) = 0.7863309246045003 absolute error = 8.727907285788206e-12 relative error = 1.109953457607552e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.650111744560704 y1[1] (closed_form) = 0.02528041651878921 y1[1] (numeric) = 0.02528041651678244 absolute error = 2.006766280926442e-12 relative error = 7.938026968167038e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7765682798297989 y2[1] (numeric) = 0.776568279838561 absolute error = 8.76210215494666e-12 relative error = 1.128310591937525e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.660116289411956 y1[1] (closed_form) = 0.02756449177712017 y1[1] (numeric) = 0.02756449177501299 absolute error = 2.107179014609883e-12 relative error = 7.644541505238059e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7668279983632051 y2[1] (numeric) = 0.7668279983719999 absolute error = 8.79474271187064e-12 relative error = 1.146899008727254e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.670120834263209 y1[1] (closed_form) = 0.02994589818602011 y1[1] (numeric) = 0.02994589818381163 absolute error = 2.208479926713025e-12 relative error = 7.374899603926483e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7571110551015697 y2[1] (numeric) = 0.7571110551103966 absolute error = 8.826828157282307e-12 relative error = 1.16585646158583e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.680125379114461 y1[1] (closed_form) = 0.03242439739032421 y1[1] (numeric) = 0.03242439738801361 absolute error = 2.310596158849876e-12 relative error = 7.126103628187651e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7474184226145488 y2[1] (numeric) = 0.7474184226234063 absolute error = 8.857470312761961e-12 relative error = 1.185075192791956e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.690129923965713 y1[1] (closed_form) = 0.0349997413168418 y1[1] (numeric) = 0.03499974131442835 absolute error = 2.413458322081397e-12 relative error = 6.89564617130483e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7377510710385307 y2[1] (numeric) = 0.7377510710474178 absolute error = 8.887113267519453e-12 relative error = 1.204622211528488e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.700134468816966 y1[1] (closed_form) = 0.0376716721991861 y1[1] (numeric) = 0.03767167219666884 absolute error = 2.517264174883849e-12 relative error = 6.682114246413076e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7281099679795355 y2[1] (numeric) = 0.7281099679884507 absolute error = 8.91520191004247e-12 relative error = 1.224430690707567e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.710139013668218 y1[1] (closed_form) = 0.04043992260357354 y1[1] (numeric) = 0.0404399226009518 absolute error = 2.62174310039498e-12 relative error = 6.48305667173385e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7184960784163671 y2[1] (numeric) = 0.7184960784253096 absolute error = 8.942513396448248e-12 relative error = 1.244615477395282e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.720143558519471 y1[1] (closed_form) = 0.04330421545559204 y1[1] (numeric) = 0.04330421545286494 absolute error = 2.727103265431907e-12 relative error = 6.29754687099347e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.7089103646040281 y2[1] (numeric) = 0.7089103646129964 absolute error = 8.968270570619552e-12 relative error = 1.265078212762329e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.72998673974409 y1[1] (closed_form) = 0.04621576312150555 y1[1] (numeric) = 0.04621576311867397 absolute error = 2.831582190943038e-12 relative error = 6.126875333635722e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6995076881480859 y2[1] (numeric) = 0.6995076881570788 absolute error = 8.992806499463768e-12 relative error = 1.285590802192869e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.739991284595343 y1[1] (closed_form) = 0.04926973395440548 y1[1] (numeric) = 0.04926973395146697 absolute error = 2.938510546002249e-12 relative error = 5.964129111639946e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6899807083020914 y2[1] (numeric) = 0.6899807083111077 absolute error = 9.016343227585821e-12 relative error = 1.306752945277744e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.749995829446595 y1[1] (closed_form) = 0.05241886345838676 y1[1] (numeric) = 0.05241886345534071 absolute error = 3.046049523725003e-12 relative error = 5.810979717526955e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.680484758312683 y2[1] (numeric) = 0.6804847583217221 absolute error = 9.039102799590637e-12 relative error = 1.328332881695076e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.760000374297848 y1[1] (closed_form) = 0.05566283643681669 y1[1] (numeric) = 0.05566283643366225 absolute error = 3.154435046504034e-12 relative error = 5.667039713444458e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6710207886302819 y2[1] (numeric) = 0.6710207886393419 absolute error = 9.05997499245359e-12 relative error = 1.350177989410317e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.7700049191491 y1[1] (closed_form) = 0.05900132820017112 y1[1] (numeric) = 0.05900132819690754 absolute error = 3.263576908718591e-12 relative error = 5.531361764681639e-09 % Desired digits = 8 Estimated correct digits = 9 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6615897465043975 y2[1] (numeric) = 0.6615897465134772 absolute error = 9.079736962291918e-12 relative error = 1.372411983448351e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.780009464000353 y1[1] (closed_form) = 0.06243400459853277 y1[1] (numeric) = 0.0624340045951594 absolute error = 3.373364088066211e-12 relative error = 5.403087804086632e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6521925758888174 y2[1] (numeric) = 0.6521925758979155 absolute error = 9.098055642198233e-12 relative error = 1.394995278779319e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.790014008851605 y1[1] (closed_form) = 0.06596052205503677 y1[1] (numeric) = 0.06596052205155281 absolute error = 3.483963118000588e-12 relative error = 5.281891363888244e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.642830217347127 y2[1] (numeric) = 0.6428302173562422 absolute error = 9.115264099079923e-12 relative error = 1.417989362214082e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.800018553702857 y1[1] (closed_form) = 0.06958052760025857 y1[1] (numeric) = 0.06958052759666346 absolute error = 3.595110320553374e-12 relative error = 5.16683394700217e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6335036079585682 y2[1] (numeric) = 0.6335036079676992 absolute error = 9.1310292660296e-12 relative error = 1.441353948315126e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.81002309855411 y1[1] (closed_form) = 0.07329365890754347 y1[1] (numeric) = 0.07329365890383648 absolute error = 3.706993045859974e-12 relative error = 5.057726822638467e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6242136812242473 y2[1] (numeric) = 0.6242136812333923 absolute error = 9.145018076139877e-12 relative error = 1.465046081368177e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.820027643405362 y1[1] (closed_form) = 0.07709954432927135 y1[1] (numeric) = 0.07709954432545184 absolute error = 3.819514149405734e-12 relative error = 4.954003532230514e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6149613669737004 y2[1] (numeric) = 0.6149613669828587 absolute error = 9.158340752435379e-12 relative error = 1.489254649849744e-09 % Desired digits = 8 Estimated correct digits = 11 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] = 9.830032188256615 y1[1] (closed_form) = 0.0809978029340549 y1[1] (numeric) = 0.08099780293012231 absolute error = 3.932590364463806e-12 relative error = 4.855181525930475e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.6057475912718278 y2[1] (numeric) = 0.6057475912809978 absolute error = 9.169998094193943e-12 relative error = 1.513831540780973e-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] = 9.840036733107867 y1[1] (closed_form) = 0.08498804454486764 y1[1] (numeric) = 0.08498804454082126 absolute error = 4.046374346700077e-12 relative error = 4.76111006950381e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5965732763262022 y2[1] (numeric) = 0.5965732763353827 absolute error = 9.180545212927882e-12 relative error = 1.538879728147263e-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] = 9.85004127795912 y1[1] (closed_form) = 0.08906986977809617 y1[1] (numeric) = 0.08906986977393541 absolute error = 4.160755073812084e-12 relative error = 4.671338449441952e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5874393403947665 y2[1] (numeric) = 0.5874393404039562 absolute error = 9.189649041729808e-12 relative error = 1.564357102054869e-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] = 9.860045822810372 y1[1] (closed_form) = 0.09324287008351473 y1[1] (numeric) = 0.09324287007923911 absolute error = 4.275621523497364e-12 relative error = 4.585467521181859e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.578346697693925 y2[1] (numeric) = 0.5783466977031227 absolute error = 9.197753669809572e-12 relative error = 1.590352933021716e-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] = 9.870050367661625 y1[1] (closed_form) = 0.09750662778517716 y1[1] (numeric) = 0.09750662778078599 absolute error = 4.391167984785227e-12 relative error = 4.503455902976851e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5692962583070386 y2[1] (numeric) = 0.5692962583162425 absolute error = 9.203970918747473e-12 relative error = 1.616727808139483e-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] = 9.880054912512877 y1[1] (closed_form) = 0.1018607161232219 y1[1] (numeric) = 0.1018607161187146 absolute error = 4.507311190948826e-12 relative error = 4.424974968265772e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5602889280933352 y2[1] (numeric) = 0.5602889281025445 absolute error = 9.209299989265674e-12 relative error = 1.643669815251382e-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] = 9.89005945736413 y1[1] (closed_form) = 0.1063046992965865 y1[1] (numeric) = 0.1063046992919625 absolute error = 4.623967875261314e-12 relative error = 4.349730450166273e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.551325608597242 y2[1] (numeric) = 0.5513256086064547 absolute error = 9.212741680642011e-12 relative error = 1.671016462319305e-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] = 9.900064002215382 y1[1] (closed_form) = 0.110838132506627 y1[1] (numeric) = 0.110838132501886 absolute error = 4.741027015420229e-12 relative error = 4.277433143450666e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5424071969581501 y2[1] (numeric) = 0.5424071969673651 absolute error = 9.214962126691262e-12 relative error = 1.698901153666339e-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] = 9.910068547066635 y1[1] (closed_form) = 0.1154605620016379 y1[1] (numeric) = 0.1154605619967792 absolute error = 4.858655144879265e-12 relative error = 4.208064693821897e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5335345858206187 y2[1] (numeric) = 0.533534585829835 absolute error = 9.216294394320812e-12 relative error = 1.727403366015235e-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] = 9.920073091917887 y1[1] (closed_form) = 0.1201715251222681 y1[1] (numeric) = 0.1201715251172914 absolute error = 4.97672736354815e-12 relative error = 4.141353251932681e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.524708663245032 y2[1] (numeric) = 0.5247086632542476 absolute error = 9.215628260506037e-12 relative error = 1.756332400443417e-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] = 9.930077636769139 y1[1] (closed_form) = 0.1249705503478288 y1[1] (numeric) = 0.1249705503427335 absolute error = 5.095243671426886e-12 relative error = 4.077155503632948e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5159303126187114 y2[1] (numeric) = 0.5159303126279249 absolute error = 9.213518836759249e-12 relative error = 1.785806844725623e-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] = 9.940082181620392 y1[1] (closed_form) = 0.1298571573434876 y1[1] (numeric) = 0.1298571573382732 absolute error = 5.214356724181357e-12 relative error = 4.015455775293745e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.5072004125674984 y2[1] (numeric) = 0.5072004125767083 absolute error = 9.209966123080449e-12 relative error = 1.815843578765777e-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] = 9.950086726471644 y1[1] (closed_form) = 0.1348308570083453 y1[1] (numeric) = 0.1348308570030115 absolute error = 5.33384447720664e-12 relative error = 3.955952365471135e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4985198368678121 y2[1] (numeric) = 0.4985198368770171 absolute error = 9.205025630620867e-12 relative error = 1.846471283561316e-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] = 9.960091271322897 y1[1] (closed_form) = 0.1398911515243908 y1[1] (numeric) = 0.139891151518937 absolute error = 5.453804075017388e-12 relative error = 3.898605462595314e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4898894543591934 y2[1] (numeric) = 0.4898894543683918 absolute error = 9.198419803624347e-12 relative error = 1.877652135961258e-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] = 9.970095816174149 y1[1] (closed_form) = 0.1450375344063265 y1[1] (numeric) = 0.1450375344007525 absolute error = 5.573985717433061e-12 relative error = 3.843133255297482e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4813101288573425 y2[1] (numeric) = 0.4813101288665329 absolute error = 9.190426197847046e-12 relative error = 1.909460376341059e-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] = 9.980100361025402 y1[1] (closed_form) = 0.1502694905522637 y1[1] (numeric) = 0.150269490546569 absolute error = 5.694694715785431e-12 relative error = 3.789654636384635e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4727827190676595 y2[1] (numeric) = 0.4727827190768406 absolute error = 9.181155835591426e-12 relative error = 1.941939809834191e-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] = 9.990104905876654 y1[1] (closed_form) = 0.1555864962952782 y1[1] (numeric) = 0.1555864962894625 absolute error = 5.815681269893958e-12 relative error = 3.73790875710494e-09 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 11 h = 0.0001613636266322163 y2[1] (closed_form) = 0.4643080784992967 y2[1] (numeric) = 0.4643080785084668 absolute error = 9.170164627647637e-12 relative error = 1.975017246584808e-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 Finished! diff ( y1 , x , 1 ) = neg ( y2 ) + 1.0 ; diff ( y2 , x , 1 ) = y1 - 1.0 ; Iterations = 53726 Total Elapsed Time = 5.0 Seconds Elapsed Time(since restart) = 5.0 Seconds Time to Timeout = 2 Minutes 55.0 Seconds Percent Done = 100 %