##############ECHO OF PROBLEM################# ##############temp/mtest7postode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 4 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=0.5; /* # */ /* # Trouble about Pi/4??? */ /* # */ array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); array_y2_init[3 + 1] = exact_soln_y2ppp(x_start); array_y2_init[4 + 1] = exact_soln_y2pppp(x_start); glob_look_poles=true; glob_max_iter=200000; glob_max_h=0.0001; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=30.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y1 (double x) { return( cos(x) ); } double exact_soln_y2 (double x) { return( sin(x) + 10.0 * x + 10.0); } double exact_soln_y2p (double x) { return( cos(x) + 10.0); } double exact_soln_y2pp (double x) { return( -sin(x)); } double exact_soln_y2ppp (double x) { return( -cos(x)); } double exact_soln_y2pppp (double x) { return( sin(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 400000.0000000001 step_error = 2.5e-16 est_needed_step_err = 2.5e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.467208610116497e-183 estimated_step_error = 2.467208610116497e-183 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.65571567075937e-175 estimated_step_error = 1.65571567075937e-175 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.111131977716593e-167 estimated_step_error = 1.111131977716593e-167 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.45668047786339e-160 estimated_step_error = 7.45668047786339e-160 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.004093560803892e-152 estimated_step_error = 5.004093560803892e-152 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.358190342152641e-144 estimated_step_error = 3.358190342152641e-144 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.253643389576351e-136 estimated_step_error = 2.253643389576351e-136 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.512394477355783e-128 estimated_step_error = 1.512394477355783e-128 best_h = 0.0001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (analytic) = 11.09983341664683 y2[1] (numeric) = 11.09983341664683 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 y1[1] (analytic) = 0.9950041652780258 y1[1] (numeric) = 0.9950041652780258 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09933 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09933 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1100000000000003 y2[1] (analytic) = 11.20977830083718 y2[1] (numeric) = 11.20977830083718 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 y1[1] (analytic) = 0.9939560979566968 y1[1] (numeric) = 0.9939560979566964 absolute error = 4.440892098500626e-16 relative error = 4.467895621979574e-14 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1091 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1091 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1200000000000006 y2[1] (analytic) = 11.31971220728893 y2[1] (numeric) = 11.31971220728892 absolute error = 1.06581410364015e-14 relative error = 9.415558312108475e-14 % Correct digits = 16 h = 0.0001 y1[1] (analytic) = 0.9928086358538661 y1[1] (numeric) = 0.9928086358538654 absolute error = 7.771561172376096e-16 relative error = 7.827854121849127e-14 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1189 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1189 Order of pole (three term test) = 22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1300000000000002 y2[1] (analytic) = 11.4296341426197 y2[1] (numeric) = 11.4296341426197 absolute error = 1.77635683940025e-15 relative error = 1.554167716336986e-14 % Correct digits = 16 h = 0.0001 y1[1] (analytic) = 0.991561893714788 y1[1] (numeric) = 0.9915618937147874 absolute error = 5.551115123125783e-16 relative error = 5.598354634554463e-14 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1285 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1285 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1400999999999991 y2[1] (analytic) = 11.54064213554597 y2[1] (numeric) = 11.54064213554598 absolute error = 8.881784197001252e-15 relative error = 7.696091857527364e-14 % Correct digits = 16 h = 0.0001 y1[1] (analytic) = 0.9902020369501161 y1[1] (numeric) = 0.9902020369501152 absolute error = 8.881784197001252e-16 relative error = 8.969668679290643e-14 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1383 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1383 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.150099999999998 y2[1] (analytic) = 11.65053700883401 y2[1] (numeric) = 11.65053700883403 absolute error = 1.598721155460225e-14 relative error = 1.372229584136762e-13 % Correct digits = 15 h = 0.0001 y1[1] (analytic) = 0.9887561291789647 y1[1] (numeric) = 0.9887561291789638 absolute error = 8.881784197001252e-16 relative error = 8.982785476512228e-14 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1479 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1479 Order of pole (three term test) = 22.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1600999999999969 y2[1] (analytic) = 11.76041692854579 y2[1] (numeric) = 11.76041692854583 absolute error = 3.375077994860476e-14 relative error = 2.869862535798561e-13 % Correct digits = 15 h = 0.0001 y1[1] (analytic) = 0.9872113466188561 y1[1] (numeric) = 0.9872113466188553 absolute error = 7.771561172376096e-16 relative error = 7.872236476002084e-14 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1574 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1574 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1700999999999958 y2[1] (analytic) = 11.87028090669756 y2[1] (numeric) = 11.87028090669761 absolute error = 4.440892098500626e-14 relative error = 3.74118534633409e-13 % Correct digits = 15 h = 0.0001 y1[1] (analytic) = 0.9855678437467591 y1[1] (numeric) = 0.9855678437467585 absolute error = 5.551115123125783e-16 relative error = 5.632402841008414e-14 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1668 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1668 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1800999999999947 y2[1] (analytic) = 11.98012795689973 y2[1] (numeric) = 11.98012795689979 absolute error = 6.217248937900877e-14 relative error = 5.189634835511225e-13 % Correct digits = 15 h = 0.0001 y1[1] (analytic) = 0.9838257849115911 y1[1] (numeric) = 0.9838257849115905 absolute error = 6.661338147750939e-16 relative error = 6.770851353880243e-14 % Correct digits = 16 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1762 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1762 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1900999999999936 y2[1] (analytic) = 12.08995709445548 y2[1] (numeric) = 12.08995709445555 absolute error = 6.927791673660977e-14 relative error = 5.730203688512755e-13 % Correct digits = 15 h = 0.0001 y1[1] (analytic) = 0.9819853443177842 y1[1] (numeric) = 0.9819853443177832 absolute error = 9.992007221626409e-16 relative error = 1.01753119631008e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1856 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1856 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2000999999999925 y2[1] (analytic) = 12.19976733645925 y2[1] (numeric) = 12.19976733645934 absolute error = 8.526512829121202e-14 relative error = 6.989078229090112e-13 % Correct digits = 15 h = 0.0001 y1[1] (analytic) = 0.9800467060078638 y1[1] (numeric) = 0.9800467060078623 absolute error = 1.554312234475219e-15 relative error = 1.585957306878339e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1948 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1948 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2100999999999913 y2[1] (analytic) = 12.30955770189501 y2[1] (numeric) = 12.30955770189511 absolute error = 9.947598300641403e-14 relative error = 8.081198806282052e-13 % Correct digits = 15 h = 0.0001 y1[1] (analytic) = 0.9780100638440457 y1[1] (numeric) = 0.9780100638440441 absolute error = 1.554312234475219e-15 relative error = 1.589259959520285e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.204 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.204 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2200999999999902 y2[1] (analytic) = 12.41932721173438 y2[1] (numeric) = 12.4193272117345 absolute error = 1.154631945610163e-13 relative error = 9.29705712656649e-13 % Correct digits = 15 h = 0.0001 y1[1] (analytic) = 0.9758756214888487 y1[1] (numeric) = 0.9758756214888464 absolute error = 2.220446049250313e-15 relative error = 2.275337143746537e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2131 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2131 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2300999999999891 y2[1] (analytic) = 12.52907488903452 y2[1] (numeric) = 12.52907488903464 absolute error = 1.190159082398168e-13 relative error = 9.499177656283292e-13 % Correct digits = 15 h = 0.0001 y1[1] (analytic) = 0.9736435923847299 y1[1] (numeric) = 0.9736435923847273 absolute error = 2.55351295663786e-15 relative error = 2.622636226037888e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2221 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2221 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.240099999999988 y2[1] (analytic) = 12.63879975903581 y2[1] (numeric) = 12.63879975903595 absolute error = 1.403321903126198e-13 relative error = 1.110328456721475e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9713141997327395 y1[1] (numeric) = 0.9713141997327365 absolute error = 2.997602166487923e-15 relative error = 3.086130283396169e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.231 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.231 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2500999999999869 y2[1] (analytic) = 12.74850084925937 y2[1] (numeric) = 12.74850084925952 absolute error = 1.49213974509621e-13 relative error = 1.170443303679034e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9688876764702017 y1[1] (numeric) = 0.9688876764701982 absolute error = 3.441691376337985e-15 relative error = 3.552208847238687e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2398 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2398 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2600999999999858 y2[1] (analytic) = 12.85817718960425 y2[1] (numeric) = 12.85817718960442 absolute error = 1.70530256582424e-13 relative error = 1.326239746643845e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9663642652474206 y1[1] (numeric) = 0.966364265247417 absolute error = 3.552713678800501e-15 relative error = 3.676371122736923e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2485 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2485 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2700999999999847 y2[1] (analytic) = 12.96782781244448 y2[1] (numeric) = 12.96782781244466 absolute error = 1.740829702612245e-13 relative error = 1.342421975206727e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9637442184034157 y1[1] (numeric) = 0.9637442184034118 absolute error = 3.885780586188048e-15 relative error = 4.031962539422977e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2572 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2572 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2800999999999836 y2[1] (analytic) = 13.07745175272583 y2[1] (numeric) = 13.07745175272601 absolute error = 1.811883976188255e-13 relative error = 1.385502321437043e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9610277979406879 y1[1] (numeric) = 0.9610277979406836 absolute error = 4.329869796038111e-15 relative error = 4.505457391884245e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2657 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2657 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2900999999999825 y2[1] (analytic) = 13.18704804806227 y2[1] (numeric) = 13.18704804806246 absolute error = 1.865174681370263e-13 relative error = 1.414398942486855e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.95821527549902 y1[1] (numeric) = 0.9582152754990146 absolute error = 5.329070518200751e-15 relative error = 5.561454356303675e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2741 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2741 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000999999999814 y2[1] (analytic) = 13.29661573883229 y2[1] (numeric) = 13.29661573883249 absolute error = 2.060573933704291e-13 relative error = 1.549698039093104e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9553069323283122 y1[1] (numeric) = 0.9553069323283064 absolute error = 5.773159728050814e-15 relative error = 6.043251161153242e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2824 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2824 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3100999999999803 y2[1] (analytic) = 13.40615386827476 y2[1] (numeric) = 13.40615386827499 absolute error = 2.220446049250313e-13 relative error = 1.65628865002432e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9523030592604581 y1[1] (numeric) = 0.9523030592604516 absolute error = 6.550315845288424e-15 relative error = 6.878394206120985e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2906 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2906 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200999999999792 y2[1] (analytic) = 13.51566148258471 y2[1] (numeric) = 13.51566148258494 absolute error = 2.344791028008331e-13 relative error = 1.734869603703568e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9492039566802611 y1[1] (numeric) = 0.9492039566802544 absolute error = 6.772360450213455e-15 relative error = 7.134778993019644e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2987 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2987 Order of pole (three term test) = 22.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3300999999999781 y2[1] (analytic) = 13.62513763100861 y2[1] (numeric) = 13.62513763100885 absolute error = 2.415845301584341e-13 relative error = 1.773079558540581e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9460099344953968 y1[1] (numeric) = 0.9460099344953896 absolute error = 7.216449660063518e-15 relative error = 7.628302195275341e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3066 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3066 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.340099999999977 y2[1] (analytic) = 13.73458136593952 y2[1] (numeric) = 13.73458136593978 absolute error = 2.575717417130363e-13 relative error = 1.875351966327784e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9427213121054221 y1[1] (numeric) = 0.9427213121054143 absolute error = 7.771561172376096e-15 relative error = 8.243752498837135e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3145 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3145 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500999999999759 y2[1] (analytic) = 13.84399174301183 y2[1] (numeric) = 13.84399174301209 absolute error = 2.629008122312371e-13 relative error = 1.899024624627822e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9393384183698352 y1[1] (numeric) = 0.9393384183698268 absolute error = 8.43769498715119e-15 relative error = 8.982593304119613e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3222 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3222 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3600999999999748 y2[1] (analytic) = 13.95336782119566 y2[1] (numeric) = 13.95336782119594 absolute error = 2.824407374646398e-13 relative error = 2.024176106327552e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9358615915751908 y1[1] (numeric) = 0.9358615915751819 absolute error = 8.881784197001252e-15 relative error = 9.490489060515799e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3298 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3298 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3700999999999737 y2[1] (analytic) = 14.062708662891 y2[1] (numeric) = 14.0627086628913 absolute error = 2.948752353404416e-13 relative error = 2.096859448696147e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9322911794012709 y1[1] (numeric) = 0.9322911794012618 absolute error = 9.103828801926284e-15 relative error = 9.765005829801883e-13 % Correct digits = 15 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3372 Order of pole (three term test) = 22.87 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3372 Order of pole (three term test) = 22.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3800999999999726 y2[1] (analytic) = 14.17201333402148 y2[1] (numeric) = 14.17201333402178 absolute error = 2.984279490192421e-13 relative error = 2.105755491372795e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9286275388863178 y1[1] (numeric) = 0.9286275388863074 absolute error = 1.032507412901396e-14 relative error = 1.111863874013104e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3445 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3445 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3900999999999715 y2[1] (analytic) = 14.28128090412774 y2[1] (numeric) = 14.28128090412804 absolute error = 3.037570195374428e-13 relative error = 2.126959210287975e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9248710363913296 y1[1] (numeric) = 0.9248710363913184 absolute error = 1.121325254871408e-14 relative error = 1.212412553480543e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3517 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3517 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4000999999999704 y2[1] (analytic) = 14.39051044646048 y2[1] (numeric) = 14.3905104464608 absolute error = 3.197442310920451e-13 relative error = 2.221910280956643e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9210220475634256 y1[1] (numeric) = 0.9210220475634139 absolute error = 1.176836406102666e-14 relative error = 1.277750526402707e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3587 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3587 Order of pole (three term test) = 22.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4100999999999693 y2[1] (analytic) = 14.49970103807317 y2[1] (numeric) = 14.49970103807351 absolute error = 3.428368700042483e-13 relative error = 2.364440957120638e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9170809572982812 y1[1] (numeric) = 0.917080957298269 absolute error = 1.221245327087672e-14 relative error = 1.331665778652147e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3656 Order of pole (three term test) = 22.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3656 Order of pole (three term test) = 22.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4200999999999682 y2[1] (analytic) = 14.6088517599143 y2[1] (numeric) = 14.60885175991466 absolute error = 3.570477247194503e-13 relative error = 2.444050570073995e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9130481597016386 y1[1] (numeric) = 0.9130481597016253 absolute error = 1.321165399303936e-14 relative error = 1.446983256322055e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3724 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3724 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4300999999999671 y2[1] (analytic) = 14.71796169691931 y2[1] (numeric) = 14.71796169691968 absolute error = 3.677058657558518e-13 relative error = 2.498347755809271e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9089240580498966 y1[1] (numeric) = 0.9089240580498827 absolute error = 1.387778780781446e-14 relative error = 1.526836888616344e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.379 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.379 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.440099999999966 y2[1] (analytic) = 14.8270299381021 y2[1] (numeric) = 14.82702993810249 absolute error = 3.854694341498544e-13 relative error = 2.599775111799601e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.904709064749784 y1[1] (numeric) = 0.9047090647497693 absolute error = 1.465494392505207e-14 relative error = 1.619851562900522e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3854 Order of pole (three term test) = 22.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3854 Order of pole (three term test) = 22.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500999999999649 y2[1] (analytic) = 14.9360555766461 y2[1] (numeric) = 14.93605557664651 absolute error = 4.050093593832571e-13 relative error = 2.711621935958289e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.9004036012971181 y1[1] (numeric) = 0.900403601297103 absolute error = 1.509903313490213e-14 relative error = 1.676918341191719e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3917 Order of pole (three term test) = 22.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3917 Order of pole (three term test) = 22.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4600999999999638 y2[1] (analytic) = 15.04503770999499 y2[1] (numeric) = 15.0450377099954 absolute error = 4.103384299014579e-13 relative error = 2.727400474568797e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.8960080982346562 y1[1] (numeric) = 0.89600809823464 absolute error = 1.620925615952729e-14 relative error = 1.809052417211773e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3979 Order of pole (three term test) = 22.8 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3979 Order of pole (three term test) = 22.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4700999999999627 y2[1] (analytic) = 15.1539754399429 y2[1] (numeric) = 15.15397543994333 absolute error = 4.263256414560601e-13 relative error = 2.81329241389919e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.891522995109042 y1[1] (numeric) = 0.8915229951090253 absolute error = 1.665334536937735e-14 relative error = 1.86796588094068e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4038 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4038 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4800999999999616 y2[1] (analytic) = 15.2628678727243 y2[1] (numeric) = 15.26286787272474 absolute error = 4.405364961712621e-13 relative error = 2.886328440007847e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.8869487404268501 y1[1] (numeric) = 0.8869487404268325 absolute error = 1.765254609153999e-14 relative error = 1.990255500339803e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4097 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4097 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4900999999999605 y2[1] (analytic) = 15.37171411910331 y2[1] (numeric) = 15.37171411910376 absolute error = 4.494182803682634e-13 relative error = 2.923670560654946e-12 % Correct digits = 14 h = 0.0001 y1[1] (analytic) = 0.8822857916097371 y1[1] (numeric) = 0.8822857916097188 absolute error = 1.831867990631508e-14 relative error = 2.076275066482995e-12 % Correct digits = 14 h = 0.0001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4153 Order of pole (three term test) = 22.78 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4153 Order of pole (three term test) = 22.22 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 4 ) ; Iterations = 4001 Total Elapsed Time = 2.0 Seconds Elapsed Time(since restart) = 2.0 Seconds Time to Timeout = 29 Minutes 58.0 Seconds Percent Done = 100 %