##############ECHO OF PROBLEM################# ##############temp/mtest2postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 1 ) = y1 ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=64; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.2; x_end=0.6; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; 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)); } /* 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 step_error = 5.270462766947299e-15 est_needed_step_err = 5.270462766947299e-15 opt_iter = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 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 step_error = 5.270462766947299e-15 est_needed_step_err = 5.270462766947299e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 200000 step_error = 7.453559924999299e-15 est_needed_step_err = 7.453559924999299e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 100000 step_error = 1.05409255338946e-14 est_needed_step_err = 1.05409255338946e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 50000 step_error = 1.49071198499986e-14 est_needed_step_err = 1.49071198499986e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 25000 step_error = 2.10818510677892e-14 est_needed_step_err = 2.10818510677892e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 12500 step_error = 2.98142396999972e-14 est_needed_step_err = 2.98142396999972e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 7 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 6250 step_error = 4.216370213557839e-14 est_needed_step_err = 4.216370213557839e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 8 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 3125 step_error = 5.962847939999439e-14 est_needed_step_err = 5.962847939999439e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 1562.5 step_error = 8.432740427115678e-14 est_needed_step_err = 8.432740427115678e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 10 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 781.25 step_error = 1.192569587999888e-13 est_needed_step_err = 1.192569587999888e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 11 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 390.625 step_error = 1.686548085423136e-13 est_needed_step_err = 1.686548085423136e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 12 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 195.3125 step_error = 2.385139175999776e-13 est_needed_step_err = 2.385139175999776e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 13 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 97.65625 step_error = 3.373096170846271e-13 est_needed_step_err = 3.373096170846271e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 14 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 min_size = 0.9800665778412416 min_size = 0.1986693307950612 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.4 estimated_steps = 48.828125 step_error = 4.770278351999551e-13 est_needed_step_err = 4.770278351999551e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.2 y1[1] (analytic) = 0.9800665778412416 y1[1] (numeric) = 0.9800665778412416 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 y2[1] (analytic) = 0.1986693307950612 y2[1] (numeric) = 0.1986693307950612 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.21 y1[1] (analytic) = 0.9780309147241483 y1[1] (numeric) = 0.978079884533291 absolute error = 4.89698091427071e-05 relative error = 0.005006979677786457 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 y2[1] (analytic) = 0.2084598998460996 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.009790569051038367 relative error = 4.696619857472101 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.22 y1[1] (analytic) = 0.9758974493306055 y1[1] (numeric) = 0.9760931912253403 absolute error = 0.0001957418947348133 relative error = 0.02005762950493189 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 y2[1] (analytic) = 0.2182296230808694 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.01956029228580813 relative error = 8.963170081891072 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.23 y1[1] (analytic) = 0.9736663950053748 y1[1] (numeric) = 0.9741064979173897 absolute error = 0.0004401029120149058 relative error = 0.04520058556734685 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 y2[1] (analytic) = 0.2279775235351884 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.02930819274012722 relative error = 12.85573783136717 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.24 y1[1] (analytic) = 0.9713379748520296 y1[1] (numeric) = 0.972119804609439 absolute error = 0.0007818297574094801 relative error = 0.08048998161824997 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 y2[1] (analytic) = 0.2377026264271346 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.03903329563207342 relative error = 16.42106198773478 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.9689124217106447 y1[1] (numeric) = 0.9701331113014884 absolute error = 0.001220689590843649 relative error = 0.1259855445643357 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.247403959254523 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.04873462845946178 relative error = 19.69840280903703 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.9663899781345132 y1[1] (numeric) = 0.9681464179935377 absolute error = 0.001756439859024517 relative error = 0.1817526980583024 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.2570805518921552 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.05841122109709396 relative error = 22.72098012361408 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.9637708963658905 y1[1] (numeric) = 0.9661597246855871 absolute error = 0.002388828319696557 relative error = 0.2478626744908108 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.2667314366888312 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.06806210589376999 relative error = 25.51709192537782 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.9610554383107709 y1[1] (numeric) = 0.9641730313776364 absolute error = 0.003117593066865543 relative error = 0.3243926356990682 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.2763556485641138 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.0776863177690526 relative error = 28.11099326997457 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.9582438755126972 y1[1] (numeric) = 0.9621863380696858 absolute error = 0.003942462556988602 relative error = 0.4114258027351579 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.2859522251048356 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.08728289430977443 relative error = 30.52359333024068 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000000000000001 y1[1] (analytic) = 0.955336489125606 y1[1] (numeric) = 0.9601996447617351 absolute error = 0.004863155636129157 relative error = 0.5090515950647163 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.2955202066613397 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.09685087586627844 relative error = 32.77301304044757 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3100000000000001 y1[1] (analytic) = 0.9523335698857134 y1[1] (numeric) = 0.9582129514537845 absolute error = 0.005879381568071107 relative error = 0.6173657795951343 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.3050586364434436 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1063893056483824 relative error = 34.87503480928541 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200000000000001 y1[1] (analytic) = 0.9492354180824408 y1[1] (numeric) = 0.9562262581458338 absolute error = 0.006990840063393011 relative error = 0.7364706299639842 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.3145665606161179 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1158972298210567 relative error = 36.84346791154707 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3300000000000001 y1[1] (analytic) = 0.9460423435283869 y1[1] (numeric) = 0.9542395648378832 absolute error = 0.008197221309496294 relative error = 0.8664750965505096 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.3240430283948685 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1253736975998073 relative error = 38.69044744484701 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3400000000000001 y1[1] (analytic) = 0.9427546655283462 y1[1] (numeric) = 0.9522528715299325 absolute error = 0.009498206001586351 relative error = 1.007494987708524 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.3334870921408145 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1348177613457533 relative error = 40.42668052916023 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500000000000001 y1[1] (analytic) = 0.9393727128473789 y1[1] (numeric) = 0.9502661782219819 absolute error = 0.01089346537460301 relative error = 1.159653162756164 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.3428978074554515 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1442284766603903 relative error = 42.06165030061562 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.9358968236779348 y1[1] (numeric) = 0.9482794849140312 absolute error = 0.01238266123609644 relative error = 1.323079737297796 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.3522742332750901 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1536049024800289 relative error = 43.60378590621449 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.9323273456060344 y1[1] (numeric) = 0.9462927916060806 absolute error = 0.01396544600004623 relative error = 1.497912301496249 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.3616154319649622 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1629461011699009 relative error = 45.06060493173013 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.9286646355765101 y1[1] (numeric) = 0.9443060982981299 absolute error = 0.01564146272161981 relative error = 1.684296151959063 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.3709204694129828 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1722511386179216 relative error = 46.43883334088451 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.924909059857313 y1[1] (numeric) = 0.9423194049901793 absolute error = 0.01741034513286632 relative error = 1.882384537951465 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.3801884151231616 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1815190843281004 relative error = 47.74450696223805 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.921060994002885 y1[1] (numeric) = 0.9403327116822287 absolute error = 0.01927171767934366 relative error = 2.092338922701496 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.3894183423086507 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1907490115135895 relative error = 48.98305775294039 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4100000000000002 y1[1] (analytic) = 0.917120822816605 y1[1] (numeric) = 0.938346018374278 absolute error = 0.02122519555767299 relative error = 2.314329260618844 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.3986093279844231 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.1999399971893618 relative error = 50.15938743841317 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4200000000000002 y1[1] (analytic) = 0.9130889403123081 y1[1] (numeric) = 0.9363593250663274 absolute error = 0.02327038475401921 relative error = 2.548534291310103 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.4077604530595704 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2090911222645092 relative error = 51.27793063197394 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4300000000000002 y1[1] (analytic) = 0.9089657496748851 y1[1] (numeric) = 0.9343726317583767 absolute error = 0.02540688208349162 relative error = 2.795141851338078 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.416870802429211 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2182014716341498 relative error = 52.3427091469671 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4400000000000002 y1[1] (analytic) = 0.9047516632199634 y1[1] (numeric) = 0.9323859384504261 absolute error = 0.02763427523046269 relative error = 3.054349204743517 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.4259394650659998 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2272701342709386 relative error = 53.3573789025919 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500000000000002 y1[1] (analytic) = 0.9004471023526768 y1[1] (numeric) = 0.9303992451424754 absolute error = 0.02995214278979863 relative error = 3.326363393423117 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.4349655341112304 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2362962033161692 relative error = 54.32527057551714 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4600000000000002 y1[1] (analytic) = 0.8960524975255252 y1[1] (numeric) = 0.9284125518345248 absolute error = 0.03236005430899958 relative error = 3.611401608539991 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.44394810696552 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2452787761704588 relative error = 55.24942494900846 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.8915682881953289 y1[1] (numeric) = 0.9264258585265741 absolute error = 0.03485757033124526 relative error = 3.909691584231011 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.4528862853790685 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2542169545840073 relative error = 56.13262374929861 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.886994922779284 y1[1] (numeric) = 0.9244391652186235 absolute error = 0.03744424243933941 relative error = 4.221472014970809 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.4617791755414831 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2631098447464219 relative error = 56.97741662730867 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 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 y1[1] (analytic) = 0.8823328586101213 y1[1] (numeric) = 0.9224524719106728 absolute error = 0.04011961330055147 relative error = 4.546992998056216 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.4706258881711582 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.271956557376097 relative error = 57.7861448363825 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000000000000002 y1[1] (analytic) = 0.8775825618903726 y1[1] (numeric) = 0.9204657786027222 absolute error = 0.04288321671234951 relative error = 4.88651650278649 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.4794255386042032 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.280756207809142 relative error = 58.56096206859026 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5100000000000002 y1[1] (analytic) = 0.8727445076457512 y1[1] (numeric) = 0.9184790852947715 absolute error = 0.04573457764902034 relative error = 5.240316868036263 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.4881772468829077 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2895079160878465 relative error = 59.30385283959921 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5200000000000002 y1[1] (analytic) = 0.8678191796776498 y1[1] (numeric) = 0.9164923919868209 absolute error = 0.0486732123091711 relative error = 5.608681330049734 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.4968801378437369 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.2982108070486757 relative error = 60.01664875211002 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5300000000000002 y1[1] (analytic) = 0.8628070705147609 y1[1] (numeric) = 0.9145056986788702 absolute error = 0.05169862816410931 relative error = 5.991910582427806 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.5055333412048472 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3068640104097859 relative error = 60.70104291804595 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5400000000000003 y1[1] (analytic) = 0.8577086813638241 y1[1] (numeric) = 0.9125190053709196 absolute error = 0.05481032400709551 relative error = 6.390319370435053 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.5141359916531133 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3154666608580521 relative error = 61.35860277817253 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5500000000000003 y1[1] (analytic) = 0.8525245220595056 y1[1] (numeric) = 0.9105323120629689 absolute error = 0.05800779000346334 relative error = 6.804237121922277 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.5226872289306594 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3240178981355982 relative error = 61.99078152310911 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5600000000000003 y1[1] (analytic) = 0.847255111013416 y1[1] (numeric) = 0.9085456187550183 absolute error = 0.06129050774160227 relative error = 7.234008617344506 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.5311861979208836 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3325168671258224 relative error = 62.59892829055555 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5700000000000003 y1[1] (analytic) = 0.8419009751622686 y1[1] (numeric) = 0.9065589254470676 absolute error = 0.06465795028479904 relative error = 7.679994701554635 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.5396320487339695 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3409627179389083 relative error = 63.18429728902142 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5800000000000003 y1[1] (analytic) = 0.8364626499151868 y1[1] (numeric) = 0.904572232139117 absolute error = 0.06810958222393015 relative error = 8.142573040270971 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.5480239367918738 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3493546059968126 relative error = 63.7480559776149 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5900000000000003 y1[1] (analytic) = 0.8309406791001633 y1[1] (numeric) = 0.9025855388311663 absolute error = 0.07164485973100299 relative error = 8.622138924355966 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 y2[1] (analytic) = 0.556361022912784 y2[1] (numeric) = 0.1986693307950612 absolute error = 0.3576916921177228 relative error = 64.29129241388196 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 1 ) = y1 ; Iterations = 40 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102.5 %