##############ECHO OF PROBLEM################# ##############temp/expt_lin_linpostode.ode################# diff ( y , x , 1 ) = expt((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(0.0 ) ; } /* 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 = 3.434498166590288e-196 estimated_step_error = 3.434498166590288e-196 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 = 7.888963080470786e-155 estimated_step_error = 7.888963080470786e-155 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 = 5.294188822888208e-147 estimated_step_error = 5.294188822888208e-147 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 = 3.552863693272892e-139 estimated_step_error = 3.552863693272892e-139 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 = 2.384278030118841e-131 estimated_step_error = 2.384278030118841e-131 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 = 1.600050580939044e-123 estimated_step_error = 1.600050580939044e-123 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 = 1.073760575605909e-115 estimated_step_error = 1.073760575605909e-115 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 = 7.205681339566228e-108 estimated_step_error = 7.205681339566228e-108 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 = 4.835377238257454e-100 estimated_step_error = 4.835377238257454e-100 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 = 3.244599507499652e-92 estimated_step_error = 3.244599507499652e-92 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 = 2.176921154685293e-84 estimated_step_error = 2.176921154685293e-84 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 = 1.460246195288808e-76 estimated_step_error = 1.460246195288808e-76 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 = 9.790688492033759e-69 estimated_step_error = 9.790688492033759e-69 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 = 6.558563503158904e-61 estimated_step_error = 6.558563503158904e-61 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 = 4.385551339199762e-53 estimated_step_error = 4.385551339199762e-53 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 = 2.922086198286034e-45 estimated_step_error = 2.922086198286034e-45 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 = 1.933411158647845e-37 estimated_step_error = 1.933411158647845e-37 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 = 1.262175510289223e-29 estimated_step_error = 1.262175510289223e-29 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.054 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.441 Order of pole (six term test) = -0.8519 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0 y[1] (numeric) = 0.06036451654195045 absolute error = 0.06036451654195045 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.103 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.523 Order of pole (six term test) = -0.8488 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0 y[1] (numeric) = 0.119696276768172 absolute error = 0.119696276768172 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.153 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.601 Order of pole (six term test) = -0.8401 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0 y[1] (numeric) = 0.1782179791478993 absolute error = 0.1782179791478993 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.203 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.679 Order of pole (six term test) = -0.8322 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0 y[1] (numeric) = 0.2360003371237854 absolute error = 0.2360003371237854 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.253 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.757 Order of pole (six term test) = -0.8251 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0 y[1] (numeric) = 0.2931088357103154 absolute error = 0.2931088357103154 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.303 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.834 Order of pole (six term test) = -0.8186 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0 y[1] (numeric) = 0.3496043405819411 absolute error = 0.3496043405819411 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.353 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.911 Order of pole (six term test) = -0.8128 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y[1] (analytic) = 0 y[1] (numeric) = 0.4055436222526872 absolute error = 0.4055436222526872 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.403 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.989 Order of pole (six term test) = -0.8074 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y[1] (analytic) = 0 y[1] (numeric) = 0.4609798097426998 absolute error = 0.4609798097426998 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.453 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.066 Order of pole (six term test) = -0.8026 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y[1] (analytic) = 0 y[1] (numeric) = 0.5159627852939054 absolute error = 0.5159627852939054 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.503 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.143 Order of pole (six term test) = -0.7982 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0 y[1] (numeric) = 0.5705395294968438 absolute error = 0.5705395294968438 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.554 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.22 Order of pole (six term test) = -0.7942 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 0 y[1] (numeric) = 0.624754424466352 absolute error = 0.624754424466352 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.604 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.297 Order of pole (six term test) = -0.7906 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0 y[1] (numeric) = 0.6786495213405375 absolute error = 0.6786495213405375 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.654 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.374 Order of pole (six term test) = -0.7873 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0 y[1] (numeric) = 0.7322647772911114 absolute error = 0.7322647772911114 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.704 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.451 Order of pole (six term test) = -0.7844 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 0 y[1] (numeric) = 0.785638266360938 absolute error = 0.785638266360938 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.754 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.529 Order of pole (six term test) = -0.7818 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 0 y[1] (numeric) = 0.8388063677395139 absolute error = 0.8388063677395139 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.804 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.606 Order of pole (six term test) = -0.7795 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 0 y[1] (numeric) = 0.891803934513295 absolute error = 0.891803934513295 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.854 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.683 Order of pole (six term test) = -0.7775 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0 y[1] (numeric) = 0.9446644454580337 absolute error = 0.9446644454580337 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.904 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.761 Order of pole (six term test) = -0.7757 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (analytic) = 0 y[1] (numeric) = 0.9974201420535014 absolute error = 0.9974201420535014 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.954 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.839 Order of pole (six term test) = -0.7742 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0 y[1] (numeric) = 1.05010215258079 absolute error = 1.05010215258079 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.004 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.888 Order of pole (six term test) = -0.7729 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.102740604896001 absolute error = 1.102740604896001 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.054 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.911 Order of pole (six term test) = -0.7718 TOP MAIN SOLVE Loop x[1] = 2.200000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.155364729251436 absolute error = 1.155364729251436 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.104 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.924 Order of pole (six term test) = -0.771 TOP MAIN SOLVE Loop x[1] = 2.300000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.208002952348412 absolute error = 1.208002952348412 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.154 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.925 Order of pole (six term test) = -0.7704 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.260682983648116 absolute error = 1.260682983648116 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.204 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.914 Order of pole (six term test) = -0.7699 TOP MAIN SOLVE Loop x[1] = 2.500000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.313431894833417 absolute error = 1.313431894833417 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.254 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.888 Order of pole (six term test) = -0.7697 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.366276193201058 absolute error = 1.366276193201058 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.304 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.844 Order of pole (six term test) = -0.7697 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.419241889666867 absolute error = 1.419241889666867 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.354 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.78 Order of pole (six term test) = -0.7698 TOP MAIN SOLVE Loop x[1] = 2.800000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.472354561983793 absolute error = 1.472354561983793 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.404 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.525639413701423 absolute error = 1.525639413701423 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.454 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.000000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.57912132933441 absolute error = 1.57912132933441 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.504 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y[1] (analytic) = 0 y[1] (numeric) = 1.632824926154313 absolute error = 1.632824926154313 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.554 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.200000000000002 y[1] (analytic) = 0 y[1] (numeric) = 1.686774602973522 absolute error = 1.686774602973522 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.605 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.300000000000002 y[1] (analytic) = 0 y[1] (numeric) = 1.740994586250187 absolute error = 1.740994586250187 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.655 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.400000000000002 y[1] (analytic) = 0 y[1] (numeric) = 1.795508973808411 absolute error = 1.795508973808411 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.705 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.500000000000002 y[1] (analytic) = 0 y[1] (numeric) = 1.850341776437789 absolute error = 1.850341776437789 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.755 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.600000000000002 y[1] (analytic) = 0 y[1] (numeric) = 1.905516957609958 absolute error = 1.905516957609958 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.805 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.700000000000002 y[1] (analytic) = 0 y[1] (numeric) = 1.961058471526716 absolute error = 1.961058471526716 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.855 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.800000000000002 y[1] (analytic) = 0 y[1] (numeric) = 2.016990299693987 absolute error = 2.016990299693987 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.905 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.900000000000002 y[1] (analytic) = 0 y[1] (numeric) = 2.073336486198064 absolute error = 2.073336486198064 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.955 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.000000000000002 y[1] (analytic) = 0 y[1] (numeric) = 2.130121171844916 absolute error = 2.130121171844916 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.005 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.187368627309509 absolute error = 2.187368627309509 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.055 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.200000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.245103285429901 absolute error = 2.245103285429901 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.105 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.300000000000001 y[1] (analytic) = 0 y[1] (numeric) = 2.303349772770154 absolute error = 2.303349772770154 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.155 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 0 y[1] (numeric) = 2.362132940566573 absolute error = 2.362132940566573 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.205 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 0 y[1] (numeric) = 2.421477895163427 absolute error = 2.421477895163427 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.255 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 0 y[1] (numeric) = 2.481410028036894 absolute error = 2.481410028036894 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.306 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.699999999999999 y[1] (analytic) = 0 y[1] (numeric) = 2.541955045499431 absolute error = 2.541955045499431 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.356 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.799999999999999 y[1] (analytic) = 0 y[1] (numeric) = 2.603138998171008 absolute error = 2.603138998171008 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.406 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999999 y[1] (analytic) = 0 y[1] (numeric) = 2.664988310298577 absolute error = 2.664988310298577 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.456 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.999999999999998 y[1] (analytic) = 0 y[1] (numeric) = 2.727529809000654 absolute error = 2.727529809000654 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.506 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = expt((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 %