##############ECHO OF PROBLEM################# ##############temp/mult_lin_linpostode.ode################# diff ( y , x , 1 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3); ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.1; 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_y (double x) { return(0.06 * x + 2.0/300.0 * x * x * x + 0.035 * x * 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 = 4.9 estimated_steps = 4900000.000000001 step_error = 2.040816326530612e-17 est_needed_step_err = 2.040816326530612e-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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 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 = 0 estimated_step_error = 0 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.006356666666666667 y[1] (numeric) = 0.006356666666666667 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0.01345333333333333 y[1] (numeric) = 0.01345333333333333 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0.02133 y[1] (numeric) = 0.02133 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0.03002666666666667 y[1] (numeric) = 0.03002666666666667 absolute error = 3.469446951953614e-18 relative error = 1.155455245988104e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0.03958333333333333 y[1] (numeric) = 0.03958333333333334 absolute error = 6.938893903907228e-18 relative error = 1.752983723092352e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0.05003999999999999 y[1] (numeric) = 0.05004000000000001 absolute error = 1.387778780781446e-17 relative error = 2.773338890450531e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0.06143666666666666 y[1] (numeric) = 0.06143666666666667 absolute error = 1.387778780781446e-17 relative error = 2.258877077936269e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y[1] (analytic) = 0.07381333333333333 y[1] (numeric) = 0.07381333333333334 absolute error = 1.387778780781446e-17 relative error = 1.88011937425232e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y[1] (analytic) = 0.08720999999999998 y[1] (numeric) = 0.08721000000000001 absolute error = 2.775557561562891e-17 relative error = 3.182613876347772e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y[1] (analytic) = 0.1016666666666666 y[1] (numeric) = 0.1016666666666667 absolute error = 4.163336342344337e-17 relative error = 4.09508492689607e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0.1172233333333333 y[1] (numeric) = 0.1172233333333333 absolute error = 2.775557561562891e-17 relative error = 2.367751779989387e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 0.13392 y[1] (numeric) = 0.13392 absolute error = 2.775557561562891e-17 relative error = 2.072548955766795e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0.1517966666666667 y[1] (numeric) = 0.1517966666666667 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0.1708933333333334 y[1] (numeric) = 0.1708933333333334 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 0.19125 y[1] (numeric) = 0.19125 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 0.2129066666666667 y[1] (numeric) = 0.2129066666666667 absolute error = 5.551115123125783e-17 relative error = 2.607299813592395e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 0.2359033333333335 y[1] (numeric) = 0.2359033333333334 absolute error = 1.110223024625157e-16 relative error = 4.706262556520987e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0.2602800000000002 y[1] (numeric) = 0.26028 absolute error = 1.665334536937735e-16 relative error = 6.398242419462631e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (analytic) = 0.2860766666666669 y[1] (numeric) = 0.2860766666666667 absolute error = 1.665334536937735e-16 relative error = 5.821287546244249e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0.3133333333333335 y[1] (numeric) = 0.3133333333333334 absolute error = 1.110223024625157e-16 relative error = 3.543264972207945e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (analytic) = 0.3420900000000002 y[1] (numeric) = 0.34209 absolute error = 1.665334536937735e-16 relative error = 4.868118147089169e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.200000000000001 y[1] (analytic) = 0.3723866666666669 y[1] (numeric) = 0.3723866666666667 absolute error = 1.665334536937735e-16 relative error = 4.472057369412798e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.300000000000001 y[1] (analytic) = 0.4042633333333335 y[1] (numeric) = 0.4042633333333334 absolute error = 1.665334536937735e-16 relative error = 4.119430083372391e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y[1] (analytic) = 0.4377600000000003 y[1] (numeric) = 0.43776 absolute error = 2.220446049250313e-16 relative error = 5.072290865429257e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.500000000000001 y[1] (analytic) = 0.472916666666667 y[1] (numeric) = 0.4729166666666667 absolute error = 2.775557561562891e-16 relative error = 5.869020394494216e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (analytic) = 0.5097733333333336 y[1] (numeric) = 0.5097733333333334 absolute error = 2.220446049250313e-16 relative error = 4.35575167247596e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y[1] (analytic) = 0.5483700000000005 y[1] (numeric) = 0.5483700000000001 absolute error = 3.33066907387547e-16 relative error = 6.073762375541089e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.800000000000001 y[1] (analytic) = 0.5887466666666672 y[1] (numeric) = 0.5887466666666669 absolute error = 3.33066907387547e-16 relative error = 5.657219416175831e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.900000000000001 y[1] (analytic) = 0.6309433333333339 y[1] (numeric) = 0.6309433333333335 absolute error = 3.33066907387547e-16 relative error = 5.278871965060994e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.000000000000001 y[1] (analytic) = 0.6750000000000006 y[1] (numeric) = 0.6750000000000003 absolute error = 3.33066907387547e-16 relative error = 4.93432455388958e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y[1] (analytic) = 0.7209566666666674 y[1] (numeric) = 0.720956666666667 absolute error = 3.33066907387547e-16 relative error = 4.619790935944555e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.200000000000002 y[1] (analytic) = 0.7688533333333341 y[1] (numeric) = 0.7688533333333337 absolute error = 3.33066907387547e-16 relative error = 4.331995361762278e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.300000000000002 y[1] (analytic) = 0.8187300000000008 y[1] (numeric) = 0.8187300000000004 absolute error = 4.440892098500626e-16 relative error = 5.424122846971067e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.400000000000002 y[1] (analytic) = 0.8706266666666675 y[1] (numeric) = 0.8706266666666671 absolute error = 4.440892098500626e-16 relative error = 5.100799537307175e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.500000000000002 y[1] (analytic) = 0.9245833333333344 y[1] (numeric) = 0.9245833333333339 absolute error = 5.551115123125783e-16 relative error = 6.003910002479434e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.600000000000002 y[1] (analytic) = 0.9806400000000012 y[1] (numeric) = 0.9806400000000006 absolute error = 5.551115123125783e-16 relative error = 5.660706399010622e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.700000000000002 y[1] (analytic) = 1.038836666666668 y[1] (numeric) = 1.038836666666667 absolute error = 6.661338147750939e-16 relative error = 6.412305573623314e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.800000000000002 y[1] (analytic) = 1.099213333333335 y[1] (numeric) = 1.099213333333334 absolute error = 6.661338147750939e-16 relative error = 6.060095839222229e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.900000000000002 y[1] (analytic) = 1.161810000000001 y[1] (numeric) = 1.161810000000001 absolute error = 6.661338147750939e-16 relative error = 5.733586513931651e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.000000000000002 y[1] (analytic) = 1.226666666666668 y[1] (numeric) = 1.226666666666667 absolute error = 4.440892098500626e-16 relative error = 3.620292471603767e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y[1] (analytic) = 1.293823333333334 y[1] (numeric) = 1.293823333333334 absolute error = 2.220446049250313e-16 relative error = 1.71618952297736e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.200000000000001 y[1] (analytic) = 1.363320000000001 y[1] (numeric) = 1.363320000000001 absolute error = 2.220446049250313e-16 relative error = 1.628704962334824e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.300000000000001 y[1] (analytic) = 1.435196666666667 y[1] (numeric) = 1.435196666666668 absolute error = 2.220446049250313e-16 relative error = 1.547137128187063e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 1.509493333333334 y[1] (numeric) = 1.509493333333334 absolute error = 4.440892098500626e-16 relative error = 2.941975297561627e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 1.58625 y[1] (numeric) = 1.586250000000001 absolute error = 8.881784197001252e-16 relative error = 5.599233536328606e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 1.665506666666666 y[1] (numeric) = 1.665506666666668 absolute error = 1.332267629550188e-15 relative error = 7.999173201849615e-14 % Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.699999999999999 y[1] (analytic) = 1.747303333333333 y[1] (numeric) = 1.747303333333335 absolute error = 1.77635683940025e-15 relative error = 1.016627625846448e-13 % Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.799999999999999 y[1] (analytic) = 1.831679999999999 y[1] (numeric) = 1.831680000000001 absolute error = 1.998401444325282e-15 relative error = 1.091021054073464e-13 % Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.899999999999999 y[1] (analytic) = 1.918676666666665 y[1] (numeric) = 1.918676666666668 absolute error = 2.442490654175344e-15 relative error = 1.273007952099978e-13 % Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.999999999999998 y[1] (analytic) = 2.008333333333332 y[1] (numeric) = 2.008333333333335 absolute error = 2.664535259100376e-15 relative error = 1.326739548099773e-13 % Correct digits = 15 h = 0.1 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 Finished! diff ( y , x , 1 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3); Iterations = 50 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 104.1 %