##############ECHO OF PROBLEM################# ##############temp/mtest8postode.ode################# diff ( y2 , x , 4 ) = y1 - 1.0; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=1.4; // # // # Trouble about Pi/2 // # array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); array_y2_init[3 + 1] = exact_soln_y2ppp(x_start); glob_look_poles=true; glob_max_iter=20; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y1 (double x) { return(1.0 + sin(x)); } double exact_soln_y2 (double x) { return(1.0 + sin(x)); } double exact_soln_y2p (double x) { return( cos(x)); } double exact_soln_y2pp (double x) { return( -sin(x)); } double exact_soln_y2ppp (double x) { return( -cos(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 1300000 step_error = 7.692307692307694e-17 est_needed_step_err = 7.692307692307694e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.475466125514873e-184 estimated_step_error = 2.475466125514873e-184 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.661257502151857e-176 estimated_step_error = 1.661257502151857e-176 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.114851449339244e-168 estimated_step_error = 1.114851449339244e-168 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.481646952857925e-161 estimated_step_error = 7.481646952857925e-161 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.020855692025192e-153 estimated_step_error = 5.020855692025192e-153 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.369449168190196e-145 estimated_step_error = 3.369449168190196e-145 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.261212414751383e-137 estimated_step_error = 2.261212414751383e-137 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.517491888835743e-129 estimated_step_error = 1.517491888835743e-129 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.018395625965179e-121 estimated_step_error = 1.018395625965179e-121 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.834660257908665e-114 estimated_step_error = 6.834660257908665e-114 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.587096248204522e-106 estimated_step_error = 4.587096248204522e-106 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.078929868524915e-98 estimated_step_error = 3.078929868524915e-98 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.067015579248802e-90 estimated_step_error = 2.067015579248802e-90 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.388198528557741e-82 estimated_step_error = 1.388198528557741e-82 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.330106382801203e-75 estimated_step_error = 9.330106382801203e-75 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.280203627412157e-67 estimated_step_error = 6.280203627412157e-67 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.239904976716615e-59 estimated_step_error = 4.239904976716615e-59 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.879345661003232e-51 estimated_step_error = 2.879345661003232e-51 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (analytic) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.099833416646828 y1[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.11 y2[1] (analytic) = 1.109778300837175 y2[1] (numeric) = 1.109778300837175 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.109778300837175 y1[1] (numeric) = 1.109778300837175 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.12 y2[1] (analytic) = 1.119712207288919 y2[1] (numeric) = 1.119712207288919 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.119712207288919 y1[1] (numeric) = 1.119712207288919 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.13 y2[1] (analytic) = 1.129634142619695 y2[1] (numeric) = 1.129634142619695 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.129634142619695 y1[1] (numeric) = 1.129634142619695 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.14 y2[1] (analytic) = 1.139543114644237 y2[1] (numeric) = 1.139543114644237 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.139543114644237 y1[1] (numeric) = 1.139543114644237 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.15 y2[1] (analytic) = 1.149438132473599 y2[1] (numeric) = 1.149438132473599 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.149438132473599 y1[1] (numeric) = 1.149438132473599 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.16 y2[1] (analytic) = 1.159318206614246 y2[1] (numeric) = 1.159318206614246 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.159318206614246 y1[1] (numeric) = 1.159318206614246 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.17 y2[1] (analytic) = 1.169182349066996 y2[1] (numeric) = 1.169182349066996 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.169182349066996 y1[1] (numeric) = 1.169182349066996 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.18 y2[1] (analytic) = 1.179029573425824 y2[1] (numeric) = 1.179029573425824 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.179029573425824 y1[1] (numeric) = 1.179029573425824 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y2[1] (analytic) = 1.188858894976501 y2[1] (numeric) = 1.188858894976501 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.188858894976501 y1[1] (numeric) = 1.188858894976501 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y2[1] (analytic) = 1.198669330795061 y2[1] (numeric) = 1.198669330795061 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.198669330795061 y1[1] (numeric) = 1.198669330795061 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y2[1] (analytic) = 1.2084598998461 y2[1] (numeric) = 1.2084598998461 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.2084598998461 y1[1] (numeric) = 1.2084598998461 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y2[1] (analytic) = 1.218229623080869 y2[1] (numeric) = 1.218229623080869 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.218229623080869 y1[1] (numeric) = 1.218229623080869 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y2[1] (analytic) = 1.227977523535188 y2[1] (numeric) = 1.227977523535188 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.227977523535188 y1[1] (numeric) = 1.227977523535188 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y2[1] (analytic) = 1.237702626427135 y2[1] (numeric) = 1.237702626427135 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.237702626427135 y1[1] (numeric) = 1.237702626427135 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y2[1] (analytic) = 1.247403959254523 y2[1] (numeric) = 1.247403959254523 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.247403959254523 y1[1] (numeric) = 1.247403959254523 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y2[1] (analytic) = 1.257080551892155 y2[1] (numeric) = 1.257080551892155 absolute error = 2.220446049250313e-16 relative error = 1.766351444947662e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.257080551892155 y1[1] (numeric) = 1.257080551892155 absolute error = 2.220446049250313e-16 relative error = 1.766351444947662e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y2[1] (analytic) = 1.266731436688831 y2[1] (numeric) = 1.266731436688831 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.266731436688831 y1[1] (numeric) = 1.266731436688831 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y2[1] (analytic) = 1.276355648564114 y2[1] (numeric) = 1.276355648564114 absolute error = 2.220446049250313e-16 relative error = 1.739676595428782e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.276355648564114 y1[1] (numeric) = 1.276355648564114 absolute error = 2.220446049250313e-16 relative error = 1.739676595428782e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y2[1] (analytic) = 1.285952225104836 y2[1] (numeric) = 1.285952225104835 absolute error = 2.220446049250313e-16 relative error = 1.726694045005672e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.285952225104836 y1[1] (numeric) = 1.285952225104835 absolute error = 2.220446049250313e-16 relative error = 1.726694045005672e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y2[1] (analytic) = 1.29552020666134 y2[1] (numeric) = 1.295520206661339 absolute error = 4.440892098500626e-16 relative error = 3.427883313333386e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.29552020666134 y1[1] (numeric) = 1.295520206661339 absolute error = 4.440892098500626e-16 relative error = 3.427883313333386e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y2[1] (analytic) = 1.305058636443444 y2[1] (numeric) = 1.305058636443443 absolute error = 2.220446049250313e-16 relative error = 1.701414777271227e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.305058636443444 y1[1] (numeric) = 1.305058636443443 absolute error = 2.220446049250313e-16 relative error = 1.701414777271227e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y2[1] (analytic) = 1.314566560616118 y2[1] (numeric) = 1.314566560616118 absolute error = 2.220446049250313e-16 relative error = 1.689108878754396e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.314566560616118 y1[1] (numeric) = 1.314566560616118 absolute error = 2.220446049250313e-16 relative error = 1.689108878754396e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y2[1] (analytic) = 1.324043028394869 y2[1] (numeric) = 1.324043028394868 absolute error = 2.220446049250313e-16 relative error = 1.677019554222607e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.324043028394869 y1[1] (numeric) = 1.324043028394868 absolute error = 2.220446049250313e-16 relative error = 1.677019554222607e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y2[1] (analytic) = 1.333487092140815 y2[1] (numeric) = 1.333487092140814 absolute error = 2.220446049250313e-16 relative error = 1.665142514192283e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.333487092140815 y1[1] (numeric) = 1.333487092140814 absolute error = 2.220446049250313e-16 relative error = 1.665142514192283e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y2[1] (analytic) = 1.342897807455452 y2[1] (numeric) = 1.342897807455451 absolute error = 2.220446049250313e-16 relative error = 1.653473582965823e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.342897807455452 y1[1] (numeric) = 1.342897807455451 absolute error = 2.220446049250313e-16 relative error = 1.653473582965823e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y2[1] (analytic) = 1.35227423327509 y2[1] (numeric) = 1.35227423327509 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.35227423327509 y1[1] (numeric) = 1.35227423327509 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y2[1] (analytic) = 1.361615431964962 y2[1] (numeric) = 1.361615431964962 absolute error = 2.220446049250313e-16 relative error = 1.630743892235389e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.361615431964962 y1[1] (numeric) = 1.361615431964962 absolute error = 2.220446049250313e-16 relative error = 1.630743892235389e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y2[1] (analytic) = 1.370920469412983 y2[1] (numeric) = 1.370920469412983 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.370920469412983 y1[1] (numeric) = 1.370920469412983 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y2[1] (analytic) = 1.380188415123162 y2[1] (numeric) = 1.380188415123162 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.380188415123162 y1[1] (numeric) = 1.380188415123162 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y2[1] (analytic) = 1.389418342308651 y2[1] (numeric) = 1.389418342308651 absolute error = 2.220446049250313e-16 relative error = 1.59811194485948e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.389418342308651 y1[1] (numeric) = 1.389418342308651 absolute error = 2.220446049250313e-16 relative error = 1.59811194485948e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y2[1] (analytic) = 1.398609327984423 y2[1] (numeric) = 1.398609327984423 absolute error = 2.220446049250313e-16 relative error = 1.587609924245438e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.398609327984423 y1[1] (numeric) = 1.398609327984423 absolute error = 2.220446049250313e-16 relative error = 1.587609924245438e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y2[1] (analytic) = 1.40776045305957 y2[1] (numeric) = 1.40776045305957 absolute error = 2.220446049250313e-16 relative error = 1.57728969046153e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.40776045305957 y1[1] (numeric) = 1.40776045305957 absolute error = 2.220446049250313e-16 relative error = 1.57728969046153e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y2[1] (analytic) = 1.416870802429211 y2[1] (numeric) = 1.416870802429211 absolute error = 2.220446049250313e-16 relative error = 1.567147862348056e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.416870802429211 y1[1] (numeric) = 1.416870802429211 absolute error = 2.220446049250313e-16 relative error = 1.567147862348056e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y2[1] (analytic) = 1.425939465066 y2[1] (numeric) = 1.425939465066 absolute error = 2.220446049250313e-16 relative error = 1.557181145237143e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.425939465066 y1[1] (numeric) = 1.425939465066 absolute error = 2.220446049250313e-16 relative error = 1.557181145237143e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y2[1] (analytic) = 1.43496553411123 y2[1] (numeric) = 1.43496553411123 absolute error = 2.220446049250313e-16 relative error = 1.547386328428845e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.43496553411123 y1[1] (numeric) = 1.43496553411123 absolute error = 2.220446049250313e-16 relative error = 1.547386328428845e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y2[1] (analytic) = 1.44394810696552 y2[1] (numeric) = 1.44394810696552 absolute error = 2.220446049250313e-16 relative error = 1.537760282754632e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.44394810696552 y1[1] (numeric) = 1.44394810696552 absolute error = 2.220446049250313e-16 relative error = 1.537760282754632e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y2[1] (analytic) = 1.452886285379068 y2[1] (numeric) = 1.452886285379068 absolute error = 2.220446049250313e-16 relative error = 1.528299958224867e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.452886285379068 y1[1] (numeric) = 1.452886285379068 absolute error = 2.220446049250313e-16 relative error = 1.528299958224867e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y2[1] (analytic) = 1.461779175541483 y2[1] (numeric) = 1.461779175541483 absolute error = 2.220446049250313e-16 relative error = 1.519002381757011e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.461779175541483 y1[1] (numeric) = 1.461779175541483 absolute error = 2.220446049250313e-16 relative error = 1.519002381757011e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y2[1] (analytic) = 1.470625888171158 y2[1] (numeric) = 1.470625888171158 absolute error = 2.220446049250313e-16 relative error = 1.509864654981435e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.470625888171158 y1[1] (numeric) = 1.470625888171158 absolute error = 2.220446049250313e-16 relative error = 1.509864654981435e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y2[1] (analytic) = 1.479425538604203 y2[1] (numeric) = 1.479425538604203 absolute error = 2.220446049250313e-16 relative error = 1.500883952121877e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.479425538604203 y1[1] (numeric) = 1.479425538604203 absolute error = 2.220446049250313e-16 relative error = 1.500883952121877e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y2[1] (analytic) = 1.488177246882908 y2[1] (numeric) = 1.488177246882908 absolute error = 2.220446049250313e-16 relative error = 1.492057517947673e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.488177246882908 y1[1] (numeric) = 1.488177246882908 absolute error = 2.220446049250313e-16 relative error = 1.492057517947673e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y2[1] (analytic) = 1.496880137843737 y2[1] (numeric) = 1.496880137843737 absolute error = 2.220446049250313e-16 relative error = 1.483382665795056e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.496880137843737 y1[1] (numeric) = 1.496880137843737 absolute error = 2.220446049250313e-16 relative error = 1.483382665795056e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y2[1] (analytic) = 1.505533341204847 y2[1] (numeric) = 1.505533341204847 absolute error = 2.220446049250313e-16 relative error = 1.474856775654889e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.505533341204847 y1[1] (numeric) = 1.505533341204847 absolute error = 2.220446049250313e-16 relative error = 1.474856775654889e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y2[1] (analytic) = 1.514135991653113 y2[1] (numeric) = 1.514135991653113 absolute error = 2.220446049250313e-16 relative error = 1.466477292324357e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.514135991653113 y1[1] (numeric) = 1.514135991653113 absolute error = 2.220446049250313e-16 relative error = 1.466477292324357e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y2[1] (analytic) = 1.522687228930659 y2[1] (numeric) = 1.522687228930659 absolute error = 2.220446049250313e-16 relative error = 1.458241723620201e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.522687228930659 y1[1] (numeric) = 1.522687228930659 absolute error = 2.220446049250313e-16 relative error = 1.458241723620201e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y2[1] (analytic) = 1.531186197920884 y2[1] (numeric) = 1.531186197920883 absolute error = 4.440892098500626e-16 relative error = 2.900295277302445e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.531186197920884 y1[1] (numeric) = 1.531186197920883 absolute error = 4.440892098500626e-16 relative error = 2.900295277302445e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y2[1] (analytic) = 1.53963204873397 y2[1] (numeric) = 1.539632048733969 absolute error = 4.440892098500626e-16 relative error = 2.884385332295691e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.53963204873397 y1[1] (numeric) = 1.539632048733969 absolute error = 4.440892098500626e-16 relative error = 2.884385332295691e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y2[1] (analytic) = 1.548023936791874 y2[1] (numeric) = 1.548023936791874 absolute error = 4.440892098500626e-16 relative error = 2.868748985693292e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.548023936791874 y1[1] (numeric) = 1.548023936791874 absolute error = 4.440892098500626e-16 relative error = 2.868748985693292e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y2[1] (analytic) = 1.556361022912784 y2[1] (numeric) = 1.556361022912784 absolute error = 4.440892098500626e-16 relative error = 2.853381723855652e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.556361022912784 y1[1] (numeric) = 1.556361022912784 absolute error = 4.440892098500626e-16 relative error = 2.853381723855652e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y2[1] (analytic) = 1.564642473395036 y2[1] (numeric) = 1.564642473395035 absolute error = 4.440892098500626e-16 relative error = 2.838279143007391e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.564642473395036 y1[1] (numeric) = 1.564642473395035 absolute error = 4.440892098500626e-16 relative error = 2.838279143007391e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y2[1] (analytic) = 1.572867460100482 y2[1] (numeric) = 1.572867460100481 absolute error = 4.440892098500626e-16 relative error = 2.823436946312643e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.572867460100482 y1[1] (numeric) = 1.572867460100481 absolute error = 4.440892098500626e-16 relative error = 2.823436946312643e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y2[1] (analytic) = 1.581035160537305 y2[1] (numeric) = 1.581035160537305 absolute error = 4.440892098500626e-16 relative error = 2.808850941045116e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.581035160537305 y1[1] (numeric) = 1.581035160537305 absolute error = 4.440892098500626e-16 relative error = 2.808850941045116e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y2[1] (analytic) = 1.58914475794227 y2[1] (numeric) = 1.58914475794227 absolute error = 4.440892098500626e-16 relative error = 2.794517035849514e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.58914475794227 y1[1] (numeric) = 1.58914475794227 absolute error = 4.440892098500626e-16 relative error = 2.794517035849514e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y2[1] (analytic) = 1.597195441362392 y2[1] (numeric) = 1.597195441362392 absolute error = 2.220446049250313e-16 relative error = 1.390215619045528e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.597195441362392 y1[1] (numeric) = 1.597195441362392 absolute error = 2.220446049250313e-16 relative error = 1.390215619045528e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y2[1] (analytic) = 1.60518640573604 y2[1] (numeric) = 1.60518640573604 absolute error = 2.220446049250313e-16 relative error = 1.383294825644971e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.60518640573604 y1[1] (numeric) = 1.60518640573604 absolute error = 2.220446049250313e-16 relative error = 1.383294825644971e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y2[1] (analytic) = 1.613116851973434 y2[1] (numeric) = 1.613116851973434 absolute error = 4.440892098500626e-16 relative error = 2.752988472637791e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.613116851973434 y1[1] (numeric) = 1.613116851973434 absolute error = 4.440892098500626e-16 relative error = 2.752988472637791e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y2[1] (analytic) = 1.62098598703656 y2[1] (numeric) = 1.62098598703656 absolute error = 4.440892098500626e-16 relative error = 2.739623990593119e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.62098598703656 y1[1] (numeric) = 1.62098598703656 absolute error = 4.440892098500626e-16 relative error = 2.739623990593119e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y2[1] (analytic) = 1.628793024018469 y2[1] (numeric) = 1.628793024018468 absolute error = 4.440892098500626e-16 relative error = 2.726492582553123e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.628793024018469 y1[1] (numeric) = 1.628793024018468 absolute error = 4.440892098500626e-16 relative error = 2.726492582553123e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y2[1] (analytic) = 1.636537182221968 y2[1] (numeric) = 1.636537182221968 absolute error = 4.440892098500626e-16 relative error = 2.713590712599095e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.636537182221968 y1[1] (numeric) = 1.636537182221968 absolute error = 4.440892098500626e-16 relative error = 2.713590712599095e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y2[1] (analytic) = 1.644217687237691 y2[1] (numeric) = 1.644217687237691 absolute error = 4.440892098500626e-16 relative error = 2.70091492931291e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.644217687237691 y1[1] (numeric) = 1.644217687237691 absolute error = 4.440892098500626e-16 relative error = 2.70091492931291e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y2[1] (analytic) = 1.651833771021537 y2[1] (numeric) = 1.651833771021537 absolute error = 4.440892098500626e-16 relative error = 2.688461863662142e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.651833771021537 y1[1] (numeric) = 1.651833771021537 absolute error = 4.440892098500626e-16 relative error = 2.688461863662142e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y2[1] (analytic) = 1.659384671971474 y2[1] (numeric) = 1.659384671971473 absolute error = 4.440892098500626e-16 relative error = 2.676228226951448e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.659384671971474 y1[1] (numeric) = 1.659384671971473 absolute error = 4.440892098500626e-16 relative error = 2.676228226951448e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.91 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y2[1] (analytic) = 1.666869635003698 y2[1] (numeric) = 1.666869635003698 absolute error = 4.440892098500626e-16 relative error = 2.664210808837953e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.666869635003698 y1[1] (numeric) = 1.666869635003698 absolute error = 4.440892098500626e-16 relative error = 2.664210808837953e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y2[1] (analytic) = 1.674287911628145 y2[1] (numeric) = 1.674287911628145 absolute error = 4.440892098500626e-16 relative error = 2.652406475408475e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.674287911628145 y1[1] (numeric) = 1.674287911628145 absolute error = 4.440892098500626e-16 relative error = 2.652406475408475e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y2[1] (analytic) = 1.681638760023335 y2[1] (numeric) = 1.681638760023334 absolute error = 4.440892098500626e-16 relative error = 2.640812167316483e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.681638760023335 y1[1] (numeric) = 1.681638760023334 absolute error = 4.440892098500626e-16 relative error = 2.640812167316483e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y2[1] (analytic) = 1.688921445110552 y2[1] (numeric) = 1.688921445110551 absolute error = 2.220446049250313e-16 relative error = 1.314712448988395e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.688921445110552 y1[1] (numeric) = 1.688921445110551 absolute error = 2.220446049250313e-16 relative error = 1.314712448988395e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y2[1] (analytic) = 1.696135238627357 y2[1] (numeric) = 1.696135238627357 absolute error = 2.220446049250313e-16 relative error = 1.309120875908025e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.696135238627357 y1[1] (numeric) = 1.696135238627357 absolute error = 2.220446049250313e-16 relative error = 1.309120875908025e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y2[1] (analytic) = 1.703279419200411 y2[1] (numeric) = 1.70327941920041 absolute error = 2.220446049250313e-16 relative error = 1.303629941288601e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.703279419200411 y1[1] (numeric) = 1.70327941920041 absolute error = 2.220446049250313e-16 relative error = 1.303629941288601e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y2[1] (analytic) = 1.710353272417608 y2[1] (numeric) = 1.710353272417608 absolute error = 2.220446049250313e-16 relative error = 1.298238255838036e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.710353272417608 y1[1] (numeric) = 1.710353272417608 absolute error = 2.220446049250313e-16 relative error = 1.298238255838036e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y2[1] (analytic) = 1.717356090899523 y2[1] (numeric) = 1.717356090899523 absolute error = 2.220446049250313e-16 relative error = 1.292944463304218e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.717356090899523 y1[1] (numeric) = 1.717356090899523 absolute error = 2.220446049250313e-16 relative error = 1.292944463304218e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y2[1] (analytic) = 1.724287174370143 y2[1] (numeric) = 1.724287174370143 absolute error = 2.220446049250313e-16 relative error = 1.287747239702928e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.724287174370143 y1[1] (numeric) = 1.724287174370143 absolute error = 2.220446049250313e-16 relative error = 1.287747239702928e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y2[1] (analytic) = 1.731145829726896 y2[1] (numeric) = 1.731145829726896 absolute error = 2.220446049250313e-16 relative error = 1.282645292569378e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.731145829726896 y1[1] (numeric) = 1.731145829726896 absolute error = 2.220446049250313e-16 relative error = 1.282645292569378e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y2[1] (analytic) = 1.737931371109963 y2[1] (numeric) = 1.737931371109963 absolute error = 2.220446049250313e-16 relative error = 1.277637360232575e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.737931371109963 y1[1] (numeric) = 1.737931371109963 absolute error = 2.220446049250313e-16 relative error = 1.277637360232575e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y2[1] (analytic) = 1.74464311997086 y2[1] (numeric) = 1.744643119970859 absolute error = 2.220446049250313e-16 relative error = 1.272722211111806e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.74464311997086 y1[1] (numeric) = 1.744643119970859 absolute error = 2.220446049250313e-16 relative error = 1.272722211111806e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y2[1] (analytic) = 1.751280405140293 y2[1] (numeric) = 1.751280405140293 absolute error = 2.220446049250313e-16 relative error = 1.267898643034515e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.751280405140293 y1[1] (numeric) = 1.751280405140293 absolute error = 2.220446049250313e-16 relative error = 1.267898643034515e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y2[1] (analytic) = 1.757842562895277 y2[1] (numeric) = 1.757842562895277 absolute error = 2.220446049250313e-16 relative error = 1.263165482574901e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.757842562895277 y1[1] (numeric) = 1.757842562895277 absolute error = 2.220446049250313e-16 relative error = 1.263165482574901e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y2[1] (analytic) = 1.764328937025506 y2[1] (numeric) = 1.764328937025505 absolute error = 2.220446049250313e-16 relative error = 1.258521584412586e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.764328937025506 y1[1] (numeric) = 1.764328937025505 absolute error = 2.220446049250313e-16 relative error = 1.258521584412586e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y2[1] (analytic) = 1.77073887889897 y2[1] (numeric) = 1.77073887889897 absolute error = 2.220446049250313e-16 relative error = 1.253965830710718e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.77073887889897 y1[1] (numeric) = 1.77073887889897 absolute error = 2.220446049250313e-16 relative error = 1.253965830710718e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y2[1] (analytic) = 1.777071747526824 y2[1] (numeric) = 1.777071747526824 absolute error = 2.220446049250313e-16 relative error = 1.249497130512901e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.777071747526824 y1[1] (numeric) = 1.777071747526824 absolute error = 2.220446049250313e-16 relative error = 1.249497130512901e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y2[1] (analytic) = 1.783326909627484 y2[1] (numeric) = 1.783326909627484 absolute error = 2.220446049250313e-16 relative error = 1.245114419158369e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.783326909627484 y1[1] (numeric) = 1.783326909627484 absolute error = 2.220446049250313e-16 relative error = 1.245114419158369e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y2[1] (analytic) = 1.789503739689951 y2[1] (numeric) = 1.78950373968995 absolute error = 4.440892098500626e-16 relative error = 2.481633315429704e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.789503739689951 y1[1] (numeric) = 1.78950373968995 absolute error = 4.440892098500626e-16 relative error = 2.481633315429704e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y2[1] (analytic) = 1.795601620036366 y2[1] (numeric) = 1.795601620036366 absolute error = 4.440892098500626e-16 relative error = 2.473205664857155e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.795601620036366 y1[1] (numeric) = 1.795601620036366 absolute error = 4.440892098500626e-16 relative error = 2.473205664857155e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y2[1] (analytic) = 1.801619940883778 y2[1] (numeric) = 1.801619940883777 absolute error = 4.440892098500626e-16 relative error = 2.464943908381789e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.801619940883778 y1[1] (numeric) = 1.801619940883777 absolute error = 4.440892098500626e-16 relative error = 2.464943908381789e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 11.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y2[1] (analytic) = 1.807558100405115 y2[1] (numeric) = 1.807558100405114 absolute error = 4.440892098500626e-16 relative error = 2.456846116042036e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.807558100405115 y1[1] (numeric) = 1.807558100405114 absolute error = 4.440892098500626e-16 relative error = 2.456846116042036e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 11.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y2[1] (analytic) = 1.813415504789374 y2[1] (numeric) = 1.813415504789374 absolute error = 4.440892098500626e-16 relative error = 2.448910405128818e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.813415504789374 y1[1] (numeric) = 1.813415504789374 absolute error = 4.440892098500626e-16 relative error = 2.448910405128818e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y2[1] (analytic) = 1.819191568300999 y2[1] (numeric) = 1.819191568300998 absolute error = 4.440892098500626e-16 relative error = 2.441134939212651e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.819191568300999 y1[1] (numeric) = 1.819191568300998 absolute error = 4.440892098500626e-16 relative error = 2.441134939212651e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y2[1] (analytic) = 1.82488571333845 y2[1] (numeric) = 1.82488571333845 absolute error = 4.440892098500626e-16 relative error = 2.43351792720019e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.82488571333845 y1[1] (numeric) = 1.82488571333845 absolute error = 4.440892098500626e-16 relative error = 2.43351792720019e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y2[1] (analytic) = 1.830497370491971 y2[1] (numeric) = 1.83049737049197 absolute error = 4.440892098500626e-16 relative error = 2.426057622419352e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.830497370491971 y1[1] (numeric) = 1.83049737049197 absolute error = 4.440892098500626e-16 relative error = 2.426057622419352e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y2[1] (analytic) = 1.836025978600521 y2[1] (numeric) = 1.836025978600521 absolute error = 2.220446049250313e-16 relative error = 1.209376160866095e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.836025978600521 y1[1] (numeric) = 1.836025978600521 absolute error = 2.220446049250313e-16 relative error = 1.209376160866095e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y2[1] (analytic) = 1.841470984807897 y2[1] (numeric) = 1.841470984807897 absolute error = 2.220446049250313e-16 relative error = 1.205800182337356e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.841470984807897 y1[1] (numeric) = 1.841470984807897 absolute error = 2.220446049250313e-16 relative error = 1.205800182337356e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.010000000000001 y2[1] (analytic) = 1.846831844618016 y2[1] (numeric) = 1.846831844618015 absolute error = 2.220446049250313e-16 relative error = 1.202300066311437e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.846831844618016 y1[1] (numeric) = 1.846831844618015 absolute error = 2.220446049250313e-16 relative error = 1.202300066311437e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.020000000000001 y2[1] (analytic) = 1.852108021949363 y2[1] (numeric) = 1.852108021949363 absolute error = 2.220446049250313e-16 relative error = 1.198875023991997e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.852108021949363 y1[1] (numeric) = 1.852108021949363 absolute error = 2.220446049250313e-16 relative error = 1.198875023991997e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.030000000000001 y2[1] (analytic) = 1.857298989188604 y2[1] (numeric) = 1.857298989188604 absolute error = 2.220446049250313e-16 relative error = 1.195524286706448e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.857298989188604 y1[1] (numeric) = 1.857298989188604 absolute error = 2.220446049250313e-16 relative error = 1.195524286706448e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.040000000000001 y2[1] (analytic) = 1.862404227243339 y2[1] (numeric) = 1.862404227243339 absolute error = 2.220446049250313e-16 relative error = 1.19224710552603e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.862404227243339 y1[1] (numeric) = 1.862404227243339 absolute error = 2.220446049250313e-16 relative error = 1.19224710552603e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.050000000000001 y2[1] (analytic) = 1.867423225594017 y2[1] (numeric) = 1.867423225594017 absolute error = 2.220446049250313e-16 relative error = 1.189042750897564e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.867423225594017 y1[1] (numeric) = 1.867423225594017 absolute error = 2.220446049250313e-16 relative error = 1.189042750897564e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.060000000000001 y2[1] (analytic) = 1.872355482344987 y2[1] (numeric) = 1.872355482344986 absolute error = 2.220446049250313e-16 relative error = 1.185910512286571e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.872355482344987 y1[1] (numeric) = 1.872355482344986 absolute error = 2.220446049250313e-16 relative error = 1.185910512286571e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.070000000000001 y2[1] (analytic) = 1.877200504274682 y2[1] (numeric) = 1.877200504274682 absolute error = 2.220446049250313e-16 relative error = 1.182849697831429e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.877200504274682 y1[1] (numeric) = 1.877200504274682 absolute error = 2.220446049250313e-16 relative error = 1.182849697831429e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.080000000000001 y2[1] (analytic) = 1.881957806884948 y2[1] (numeric) = 1.881957806884948 absolute error = 2.220446049250313e-16 relative error = 1.179859634008287e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.881957806884948 y1[1] (numeric) = 1.881957806884948 absolute error = 2.220446049250313e-16 relative error = 1.179859634008287e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.090000000000001 y2[1] (analytic) = 1.886626914449488 y2[1] (numeric) = 1.886626914449487 absolute error = 2.220446049250313e-16 relative error = 1.176939665306446e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.886626914449488 y1[1] (numeric) = 1.886626914449487 absolute error = 2.220446049250313e-16 relative error = 1.176939665306446e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.100000000000001 y2[1] (analytic) = 1.891207360061436 y2[1] (numeric) = 1.891207360061435 absolute error = 2.220446049250313e-16 relative error = 1.174089153913922e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.891207360061436 y1[1] (numeric) = 1.891207360061435 absolute error = 2.220446049250313e-16 relative error = 1.174089153913922e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.110000000000001 y2[1] (analytic) = 1.895698685680048 y2[1] (numeric) = 1.895698685680048 absolute error = 2.220446049250313e-16 relative error = 1.171307479412936e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.895698685680048 y1[1] (numeric) = 1.895698685680048 absolute error = 2.220446049250313e-16 relative error = 1.171307479412936e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.120000000000001 y2[1] (analytic) = 1.900100442176505 y2[1] (numeric) = 1.900100442176505 absolute error = 2.220446049250313e-16 relative error = 1.168594038485072e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.900100442176505 y1[1] (numeric) = 1.900100442176505 absolute error = 2.220446049250313e-16 relative error = 1.168594038485072e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.130000000000001 y2[1] (analytic) = 1.904412189378826 y2[1] (numeric) = 1.904412189378826 absolute error = 2.220446049250313e-16 relative error = 1.165948244625849e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.904412189378826 y1[1] (numeric) = 1.904412189378826 absolute error = 2.220446049250313e-16 relative error = 1.165948244625849e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.140000000000001 y2[1] (analytic) = 1.908633496115884 y2[1] (numeric) = 1.908633496115883 absolute error = 2.220446049250313e-16 relative error = 1.163369527868486e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.908633496115884 y1[1] (numeric) = 1.908633496115883 absolute error = 2.220446049250313e-16 relative error = 1.163369527868486e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.150000000000001 y2[1] (analytic) = 1.912763940260521 y2[1] (numeric) = 1.912763940260521 absolute error = 4.440892098500626e-16 relative error = 2.321714669033216e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.912763940260521 y1[1] (numeric) = 1.912763940260521 absolute error = 2.220446049250313e-16 relative error = 1.160857334516608e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.160000000000001 y2[1] (analytic) = 1.916803108771767 y2[1] (numeric) = 1.916803108771767 absolute error = 4.440892098500626e-16 relative error = 2.316822253771397e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.916803108771767 y1[1] (numeric) = 1.916803108771767 absolute error = 2.220446049250313e-16 relative error = 1.158411126885699e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.170000000000001 y2[1] (analytic) = 1.920750597736136 y2[1] (numeric) = 1.920750597736135 absolute error = 4.440892098500626e-16 relative error = 2.312060766106134e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.920750597736136 y1[1] (numeric) = 1.920750597736136 absolute error = 2.220446049250313e-16 relative error = 1.156030383053067e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.180000000000001 y2[1] (analytic) = 1.924606012408021 y2[1] (numeric) = 1.92460601240802 absolute error = 4.440892098500626e-16 relative error = 2.307429193232276e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.924606012408021 y1[1] (numeric) = 1.92460601240802 absolute error = 2.220446049250313e-16 relative error = 1.153714596616138e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.190000000000001 y2[1] (analytic) = 1.928368967249167 y2[1] (numeric) = 1.928368967249167 absolute error = 4.440892098500626e-16 relative error = 2.302926552917719e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.928368967249167 y1[1] (numeric) = 1.928368967249167 absolute error = 2.220446049250313e-16 relative error = 1.15146327645886e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.200000000000001 y2[1] (analytic) = 1.932039085967227 y2[1] (numeric) = 1.932039085967226 absolute error = 4.440892098500626e-16 relative error = 2.298551893052104e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.932039085967227 y1[1] (numeric) = 1.932039085967227 absolute error = 2.220446049250313e-16 relative error = 1.149275946526052e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.210000000000001 y2[1] (analytic) = 1.935616001553386 y2[1] (numeric) = 1.935616001553386 absolute error = 4.440892098500626e-16 relative error = 2.294304291211007e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.935616001553386 y1[1] (numeric) = 1.935616001553386 absolute error = 2.220446049250313e-16 relative error = 1.147152145605504e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.220000000000001 y2[1] (analytic) = 1.939099356319068 y2[1] (numeric) = 1.939099356319067 absolute error = 4.440892098500626e-16 relative error = 2.290182854235295e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.939099356319068 y1[1] (numeric) = 1.939099356319068 absolute error = 2.220446049250313e-16 relative error = 1.145091427117647e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.230000000000001 y2[1] (analytic) = 1.942488801931698 y2[1] (numeric) = 1.942488801931697 absolute error = 2.220446049250313e-16 relative error = 1.14309335891265e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.942488801931698 y1[1] (numeric) = 1.942488801931698 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.240000000000001 y2[1] (analytic) = 1.945783999449539 y2[1] (numeric) = 1.945783999449539 absolute error = 2.220446049250313e-16 relative error = 1.141157523074748e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.945783999449539 y1[1] (numeric) = 1.945783999449539 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.250000000000001 y2[1] (analytic) = 1.948984619355586 y2[1] (numeric) = 1.948984619355586 absolute error = 2.220446049250313e-16 relative error = 1.139283515733686e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.948984619355586 y1[1] (numeric) = 1.948984619355586 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.260000000000001 y2[1] (analytic) = 1.952090341590516 y2[1] (numeric) = 1.952090341590516 absolute error = 2.220446049250313e-16 relative error = 1.137470946883097e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.952090341590516 y1[1] (numeric) = 1.952090341590516 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.270000000000001 y2[1] (analytic) = 1.955100855584692 y2[1] (numeric) = 1.955100855584692 absolute error = 2.220446049250313e-16 relative error = 1.13571944020569e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.955100855584692 y1[1] (numeric) = 1.955100855584692 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.280000000000001 y2[1] (analytic) = 1.958015860289225 y2[1] (numeric) = 1.958015860289225 absolute error = 2.220446049250313e-16 relative error = 1.13402863290511e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.958015860289225 y1[1] (numeric) = 1.958015860289225 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.290000000000001 y2[1] (analytic) = 1.960835064206073 y2[1] (numeric) = 1.960835064206073 absolute error = 2.220446049250313e-16 relative error = 1.132398175544333e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.960835064206073 y1[1] (numeric) = 1.960835064206073 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.300000000000001 y2[1] (analytic) = 1.963558185417193 y2[1] (numeric) = 1.963558185417193 absolute error = 2.220446049250313e-16 relative error = 1.130827731890481e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.963558185417193 y1[1] (numeric) = 1.963558185417193 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.310000000000001 y2[1] (analytic) = 1.966184951612734 y2[1] (numeric) = 1.966184951612734 absolute error = 2.220446049250313e-16 relative error = 1.129316978765922e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.966184951612734 y1[1] (numeric) = 1.966184951612734 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.320000000000001 y2[1] (analytic) = 1.968715100118265 y2[1] (numeric) = 1.968715100118265 absolute error = 2.220446049250313e-16 relative error = 1.12786560590556e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.968715100118265 y1[1] (numeric) = 1.968715100118266 absolute error = 2.220446049250313e-16 relative error = 1.12786560590556e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.330000000000001 y2[1] (analytic) = 1.971148377921045 y2[1] (numeric) = 1.971148377921045 absolute error = 2.220446049250313e-16 relative error = 1.126473315820192e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.971148377921045 y1[1] (numeric) = 1.971148377921045 absolute error = 2.220446049250313e-16 relative error = 1.126473315820192e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.340000000000001 y2[1] (analytic) = 1.97348454169532 y2[1] (numeric) = 1.973484541695319 absolute error = 2.220446049250313e-16 relative error = 1.12513982366583e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.97348454169532 y1[1] (numeric) = 1.97348454169532 absolute error = 4.440892098500626e-16 relative error = 2.25027964733166e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.350000000000001 y2[1] (analytic) = 1.975723357826659 y2[1] (numeric) = 1.975723357826659 absolute error = 4.440892098500626e-16 relative error = 2.247729714237781e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.975723357826659 y1[1] (numeric) = 1.97572335782666 absolute error = 4.440892098500626e-16 relative error = 2.247729714237781e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.360000000000001 y2[1] (analytic) = 1.977864602435316 y2[1] (numeric) = 1.977864602435316 absolute error = 4.440892098500626e-16 relative error = 2.245296312514325e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.977864602435316 y1[1] (numeric) = 1.977864602435317 absolute error = 4.440892098500626e-16 relative error = 2.245296312514325e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.370000000000001 y2[1] (analytic) = 1.979908061398614 y2[1] (numeric) = 1.979908061398614 absolute error = 4.440892098500626e-16 relative error = 2.242978946892899e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.979908061398614 y1[1] (numeric) = 1.979908061398615 absolute error = 4.440892098500626e-16 relative error = 2.242978946892899e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.380000000000001 y2[1] (analytic) = 1.98185353037236 y2[1] (numeric) = 1.981853530372359 absolute error = 4.440892098500626e-16 relative error = 2.240777146465637e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.98185353037236 y1[1] (numeric) = 1.98185353037236 absolute error = 4.440892098500626e-16 relative error = 2.240777146465637e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.390000000000001 y2[1] (analytic) = 1.983700814811277 y2[1] (numeric) = 1.983700814811276 absolute error = 4.440892098500626e-16 relative error = 2.238690464480713e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.983700814811277 y1[1] (numeric) = 1.983700814811277 absolute error = 4.440892098500626e-16 relative error = 2.238690464480713e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 4 ) = y1 - 1.0; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; Iterations = 130 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 100.8 %