##############ECHO OF PROBLEM################# ##############temp/add_lin_cpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + 0.3 ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-5.0; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(0.05 * x * x + 0.5 * x); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 10000000 step_error = 1.05409255338946e-21 est_needed_step_err = 1.05409255338946e-21 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 10000000 step_error = 1.317615691736825e-21 est_needed_step_err = 1.317615691736825e-21 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 5000000 step_error = 1.863389981249825e-21 est_needed_step_err = 1.863389981249825e-21 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 2500000 step_error = 2.63523138347365e-21 est_needed_step_err = 2.63523138347365e-21 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 1250000 step_error = 3.72677996249965e-21 est_needed_step_err = 3.72677996249965e-21 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 625000 step_error = 5.270462766947299e-21 est_needed_step_err = 5.270462766947299e-21 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 312500 step_error = 7.4535599249993e-21 est_needed_step_err = 7.4535599249993e-21 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 156250 step_error = 1.05409255338946e-20 est_needed_step_err = 1.05409255338946e-20 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 78125 step_error = 1.49071198499986e-20 est_needed_step_err = 1.49071198499986e-20 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 39062.5 step_error = 2.10818510677892e-20 est_needed_step_err = 2.10818510677892e-20 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 19531.25 step_error = 2.98142396999972e-20 est_needed_step_err = 2.98142396999972e-20 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 9765.625 step_error = 4.21637021355784e-20 est_needed_step_err = 4.21637021355784e-20 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 4882.8125 step_error = 5.96284793999944e-20 est_needed_step_err = 5.96284793999944e-20 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 2441.40625 step_error = 8.432740427115679e-20 est_needed_step_err = 8.432740427115679e-20 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 1220.703125 step_error = 1.192569587999888e-19 est_needed_step_err = 1.192569587999888e-19 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 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 610.3515625 step_error = 1.686548085423136e-19 est_needed_step_err = 1.686548085423136e-19 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 = 16 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 305.17578125 step_error = 2.385139175999776e-19 est_needed_step_err = 2.385139175999776e-19 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 = 17 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 min_size = 1.25 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1.25 desired_abs_gbl_error = 1.25e-16 range = 10 estimated_steps = 152.587890625 step_error = 3.373096170846272e-19 est_needed_step_err = 3.373096170846272e-19 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 = 18 SETTING H FOR MAX H 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 START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (closed_form) = -1.25 y[1] (numeric) = -1.25 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (closed_form) = -1.2495 y[1] (numeric) = -1.2495 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.800000000000001 y[1] (closed_form) = -1.248 y[1] (numeric) = -1.248 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.700000000000001 y[1] (closed_form) = -1.2455 y[1] (numeric) = -1.2455 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.600000000000001 y[1] (closed_form) = -1.242 y[1] (numeric) = -1.242 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.500000000000002 y[1] (closed_form) = -1.2375 y[1] (numeric) = -1.2375 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.400000000000002 y[1] (closed_form) = -1.232 y[1] (numeric) = -1.232 absolute error = 2.220446049250313e-16 relative error = 1.802310104910968e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.300000000000002 y[1] (closed_form) = -1.2255 y[1] (numeric) = -1.2255 absolute error = 2.220446049250313e-16 relative error = 1.811869481232405e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.200000000000003 y[1] (closed_form) = -1.218 y[1] (numeric) = -1.218 absolute error = 2.220446049250313e-16 relative error = 1.823026313013393e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.100000000000003 y[1] (closed_form) = -1.2095 y[1] (numeric) = -1.2095 absolute error = 2.220446049250313e-16 relative error = 1.8358379902855e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.000000000000004 y[1] (closed_form) = -1.2 y[1] (numeric) = -1.2 absolute error = 4.440892098500626e-16 relative error = 3.700743415417187e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.900000000000003 y[1] (closed_form) = -1.1895 y[1] (numeric) = -1.1895 absolute error = 2.220446049250313e-16 relative error = 1.866705379781683e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.800000000000003 y[1] (closed_form) = -1.178 y[1] (numeric) = -1.178 absolute error = 4.440892098500626e-16 relative error = 3.76985746901581e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.700000000000003 y[1] (closed_form) = -1.1655 y[1] (numeric) = -1.1655 absolute error = 4.440892098500626e-16 relative error = 3.810289230802767e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.600000000000003 y[1] (closed_form) = -1.152000000000001 y[1] (numeric) = -1.152 absolute error = 6.661338147750939e-16 relative error = 5.782411586589354e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.500000000000003 y[1] (closed_form) = -1.137500000000001 y[1] (numeric) = -1.1375 absolute error = 6.661338147750939e-16 relative error = 5.856121448572251e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.400000000000003 y[1] (closed_form) = -1.122 y[1] (numeric) = -1.122 absolute error = 4.440892098500626e-16 relative error = 3.958014348039772e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.300000000000003 y[1] (closed_form) = -1.105500000000001 y[1] (numeric) = -1.1055 absolute error = 6.661338147750939e-16 relative error = 6.025633783582937e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.200000000000003 y[1] (closed_form) = -1.088000000000001 y[1] (numeric) = -1.088 absolute error = 6.661338147750939e-16 relative error = 6.122553444624022e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.100000000000003 y[1] (closed_form) = -1.069500000000001 y[1] (numeric) = -1.0695 absolute error = 6.661338147750939e-16 relative error = 6.228460166200033e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.000000000000003 y[1] (closed_form) = -1.05 y[1] (numeric) = -1.05 absolute error = 6.661338147750939e-16 relative error = 6.344131569286606e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.900000000000003 y[1] (closed_form) = -1.029500000000001 y[1] (numeric) = -1.0295 absolute error = 6.661338147750939e-16 relative error = 6.47045958985035e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.800000000000002 y[1] (closed_form) = -1.008 y[1] (numeric) = -1.008 absolute error = 6.661338147750939e-16 relative error = 6.608470384673548e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.700000000000002 y[1] (closed_form) = -0.9855000000000005 y[1] (numeric) = -0.9854999999999998 absolute error = 6.661338147750939e-16 relative error = 6.759348703958331e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.600000000000002 y[1] (closed_form) = -0.9620000000000006 y[1] (numeric) = -0.9619999999999999 absolute error = 7.771561172376096e-16 relative error = 8.078545917230863e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.500000000000002 y[1] (closed_form) = -0.9375000000000006 y[1] (numeric) = -0.9374999999999999 absolute error = 6.661338147750939e-16 relative error = 7.105427357600998e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.400000000000002 y[1] (closed_form) = -0.9120000000000006 y[1] (numeric) = -0.9119999999999999 absolute error = 6.661338147750939e-16 relative error = 7.304098846218131e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.300000000000002 y[1] (closed_form) = -0.8855000000000006 y[1] (numeric) = -0.8855 absolute error = 6.661338147750939e-16 relative error = 7.522685655280559e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.200000000000002 y[1] (closed_form) = -0.8580000000000005 y[1] (numeric) = -0.858 absolute error = 5.551115123125783e-16 relative error = 6.469831145834241e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.100000000000002 y[1] (closed_form) = -0.8295000000000006 y[1] (numeric) = -0.8295 absolute error = 5.551115123125783e-16 relative error = 6.692121908530173e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.000000000000002 y[1] (closed_form) = -0.8000000000000005 y[1] (numeric) = -0.8 absolute error = 4.440892098500626e-16 relative error = 5.55111512312578e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.900000000000002 y[1] (closed_form) = -0.7695000000000005 y[1] (numeric) = -0.7695000000000001 absolute error = 4.440892098500626e-16 relative error = 5.771139829110621e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.800000000000002 y[1] (closed_form) = -0.7380000000000005 y[1] (numeric) = -0.7380000000000001 absolute error = 4.440892098500626e-16 relative error = 6.017468968158026e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.700000000000002 y[1] (closed_form) = -0.7055000000000005 y[1] (numeric) = -0.7055000000000001 absolute error = 3.33066907387547e-16 relative error = 4.721005065734185e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.600000000000001 y[1] (closed_form) = -0.6720000000000005 y[1] (numeric) = -0.6720000000000002 absolute error = 3.33066907387547e-16 relative error = 4.95635278850516e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.500000000000001 y[1] (closed_form) = -0.6375000000000005 y[1] (numeric) = -0.6375000000000002 absolute error = 3.33066907387547e-16 relative error = 5.224578939412497e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.400000000000001 y[1] (closed_form) = -0.6020000000000004 y[1] (numeric) = -0.6020000000000002 absolute error = 2.220446049250313e-16 relative error = 3.688448586794538e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.300000000000001 y[1] (closed_form) = -0.5655000000000004 y[1] (numeric) = -0.5655000000000002 absolute error = 2.220446049250313e-16 relative error = 3.926518212644229e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.200000000000001 y[1] (closed_form) = -0.5280000000000004 y[1] (numeric) = -0.5280000000000002 absolute error = 1.110223024625157e-16 relative error = 2.102695122396128e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.100000000000001 y[1] (closed_form) = -0.4895000000000004 y[1] (numeric) = -0.4895000000000003 absolute error = 1.110223024625157e-16 relative error = 2.268075637640768e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.000000000000001 y[1] (closed_form) = -0.4500000000000003 y[1] (numeric) = -0.4500000000000003 absolute error = 5.551115123125783e-17 relative error = 1.233581138472395e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.9000000000000009 y[1] (closed_form) = -0.4095000000000004 y[1] (numeric) = -0.4095000000000003 absolute error = 5.551115123125783e-17 relative error = 1.355583668650984e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.8000000000000009 y[1] (closed_form) = -0.3680000000000004 y[1] (numeric) = -0.3680000000000003 absolute error = 5.551115123125783e-17 relative error = 1.50845519650157e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.700000000000001 y[1] (closed_form) = -0.3255000000000004 y[1] (numeric) = -0.3255000000000003 absolute error = 5.551115123125783e-17 relative error = 1.705411712173817e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.600000000000001 y[1] (closed_form) = -0.2820000000000004 y[1] (numeric) = -0.2820000000000004 absolute error = 5.551115123125783e-17 relative error = 1.968480540115523e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.500000000000001 y[1] (closed_form) = -0.2375000000000005 y[1] (numeric) = -0.2375000000000004 absolute error = 8.326672684688674e-17 relative error = 3.505967446184698e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.400000000000001 y[1] (closed_form) = -0.1920000000000005 y[1] (numeric) = -0.1920000000000004 absolute error = 8.326672684688674e-17 relative error = 4.336808689942007e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.300000000000001 y[1] (closed_form) = -0.1455000000000005 y[1] (numeric) = -0.1455000000000004 absolute error = 8.326672684688674e-17 relative error = 5.722799096005942e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.200000000000001 y[1] (closed_form) = -0.0980000000000005 y[1] (numeric) = -0.09800000000000042 absolute error = 8.326672684688674e-17 relative error = 8.496604780294522e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.100000000000001 y[1] (closed_form) = -0.04950000000000051 y[1] (numeric) = -0.04950000000000043 absolute error = 7.632783294297951e-17 relative error = 1.541976423090479e-13 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.02695629777827e-15 y[1] (closed_form) = -5.134781488891348e-16 y[1] (numeric) = -4.440892098500626e-16 absolute error = 6.938893903907219e-17 relative error = 13.5135135135135 % Desired digits = 16 Estimated correct digits = -2 Correct digits = 2 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.09999999999999898 y[1] (closed_form) = 0.05049999999999948 y[1] (numeric) = 0.05049999999999955 absolute error = 6.938893903907228e-17 relative error = 1.374038396813327e-13 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.199999999999999 y[1] (closed_form) = 0.1019999999999995 y[1] (numeric) = 0.1019999999999995 absolute error = 6.938893903907228e-17 relative error = 6.802837160693397e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.299999999999999 y[1] (closed_form) = 0.1544999999999995 y[1] (numeric) = 0.1544999999999995 absolute error = 5.551115123125783e-17 relative error = 3.59295477224971e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.399999999999999 y[1] (closed_form) = 0.2079999999999995 y[1] (numeric) = 0.2079999999999995 absolute error = 5.551115123125783e-17 relative error = 2.668805347656633e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.499999999999999 y[1] (closed_form) = 0.2624999999999995 y[1] (numeric) = 0.2624999999999995 absolute error = 5.551115123125783e-17 relative error = 2.114710523095541e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.599999999999999 y[1] (closed_form) = 0.3179999999999994 y[1] (numeric) = 0.3179999999999995 absolute error = 5.551115123125783e-17 relative error = 1.745633686517545e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.699999999999999 y[1] (closed_form) = 0.3744999999999994 y[1] (numeric) = 0.3744999999999995 absolute error = 1.110223024625157e-16 relative error = 2.964547462283467e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.7999999999999989 y[1] (closed_form) = 0.4319999999999994 y[1] (numeric) = 0.4319999999999995 absolute error = 1.110223024625157e-16 relative error = 2.569960705150829e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.8999999999999989 y[1] (closed_form) = 0.4904999999999994 y[1] (numeric) = 0.4904999999999995 absolute error = 1.110223024625157e-16 relative error = 2.263451630224583e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.9999999999999989 y[1] (closed_form) = 0.5499999999999994 y[1] (numeric) = 0.5499999999999995 absolute error = 1.110223024625157e-16 relative error = 2.018587317500287e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.099999999999999 y[1] (closed_form) = 0.6104999999999994 y[1] (numeric) = 0.6104999999999995 absolute error = 1.110223024625157e-16 relative error = 1.818547132883141e-14 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.199999999999999 y[1] (closed_form) = 0.6719999999999995 y[1] (numeric) = 0.6719999999999995 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.299999999999999 y[1] (closed_form) = 0.7344999999999995 y[1] (numeric) = 0.7344999999999995 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.399999999999999 y[1] (closed_form) = 0.7979999999999995 y[1] (numeric) = 0.7979999999999995 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.499999999999999 y[1] (closed_form) = 0.8624999999999996 y[1] (numeric) = 0.8624999999999995 absolute error = 1.110223024625157e-16 relative error = 1.287215101014675e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.599999999999999 y[1] (closed_form) = 0.9279999999999996 y[1] (numeric) = 0.9279999999999995 absolute error = 1.110223024625157e-16 relative error = 1.19636101791504e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = 0.9944999999999997 y[1] (numeric) = 0.9944999999999995 absolute error = 2.220446049250313e-16 relative error = 2.232726042483976e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (closed_form) = 1.062 y[1] (numeric) = 1.061999999999999 absolute error = 4.440892098500626e-16 relative error = 4.18163097787253e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = 1.1305 y[1] (numeric) = 1.130499999999999 absolute error = 4.440892098500626e-16 relative error = 3.928254841663535e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 1.2 y[1] (numeric) = 1.199999999999999 absolute error = 4.440892098500626e-16 relative error = 3.70074341541719e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = 1.2705 y[1] (numeric) = 1.270499999999999 absolute error = 4.440892098500626e-16 relative error = 3.495389294372788e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 1.342 y[1] (numeric) = 1.341999999999999 absolute error = 6.661338147750939e-16 relative error = 4.963739305328569e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 1.4145 y[1] (numeric) = 1.414499999999999 absolute error = 6.661338147750939e-16 relative error = 4.709323540297589e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = 1.488 y[1] (numeric) = 1.487999999999999 absolute error = 8.881784197001252e-16 relative error = 5.968940992608368e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = 1.5625 y[1] (numeric) = 1.562499999999999 absolute error = 8.881784197001252e-16 relative error = 5.684341886080801e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = 1.638 y[1] (numeric) = 1.637999999999999 absolute error = 1.110223024625157e-15 relative error = 6.777918343254924e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = 1.7145 y[1] (numeric) = 1.714499999999999 absolute error = 1.110223024625157e-15 relative error = 6.475491540537512e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = 1.792 y[1] (numeric) = 1.791999999999999 absolute error = 1.332267629550188e-15 relative error = 7.434529182757743e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = 1.8705 y[1] (numeric) = 1.870499999999999 absolute error = 1.332267629550188e-15 relative error = 7.122521408982559e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = 1.95 y[1] (numeric) = 1.949999999999999 absolute error = 1.554312234475219e-15 relative error = 7.970831971667789e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y[1] (closed_form) = 2.0305 y[1] (numeric) = 2.030499999999999 absolute error = 1.332267629550188e-15 relative error = 6.561278648363396e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.200000000000001 y[1] (closed_form) = 2.112000000000001 y[1] (numeric) = 2.111999999999999 absolute error = 1.332267629550188e-15 relative error = 6.308085367188388e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.300000000000001 y[1] (closed_form) = 2.194500000000001 y[1] (numeric) = 2.194499999999999 absolute error = 1.332267629550188e-15 relative error = 6.070939300752734e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.400000000000001 y[1] (closed_form) = 2.278 y[1] (numeric) = 2.277999999999999 absolute error = 1.332267629550188e-15 relative error = 5.848409260536381e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.500000000000001 y[1] (closed_form) = 2.362500000000001 y[1] (numeric) = 2.362499999999999 absolute error = 1.77635683940025e-15 relative error = 7.518970748784127e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.600000000000001 y[1] (closed_form) = 2.448000000000001 y[1] (numeric) = 2.447999999999999 absolute error = 1.77635683940025e-15 relative error = 7.256359638072916e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.700000000000001 y[1] (closed_form) = 2.534500000000001 y[1] (numeric) = 2.534499999999999 absolute error = 1.77635683940025e-15 relative error = 7.008707198264943e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.800000000000001 y[1] (closed_form) = 2.622000000000001 y[1] (numeric) = 2.621999999999999 absolute error = 1.77635683940025e-15 relative error = 6.774816321129863e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.900000000000001 y[1] (closed_form) = 2.710500000000001 y[1] (numeric) = 2.710499999999999 absolute error = 2.220446049250313e-15 relative error = 8.192016414869257e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.000000000000001 y[1] (closed_form) = 2.800000000000001 y[1] (numeric) = 2.799999999999999 absolute error = 1.77635683940025e-15 relative error = 6.344131569286608e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y[1] (closed_form) = 2.8905 y[1] (numeric) = 2.890499999999999 absolute error = 1.332267629550188e-15 relative error = 4.609125167099767e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = 2.982 y[1] (numeric) = 2.981999999999999 absolute error = 1.332267629550188e-15 relative error = 4.467698288230006e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = 3.0745 y[1] (numeric) = 3.074499999999999 absolute error = 1.332267629550188e-15 relative error = 4.333282255814565e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.399999999999999 y[1] (closed_form) = 3.167999999999999 y[1] (numeric) = 3.167999999999999 absolute error = 4.440892098500626e-16 relative error = 1.401796748264087e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.499999999999999 y[1] (closed_form) = 3.262499999999999 y[1] (numeric) = 3.262499999999999 absolute error = 4.440892098500626e-16 relative error = 1.361192980383334e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.599999999999999 y[1] (closed_form) = 3.357999999999999 y[1] (numeric) = 3.357999999999999 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.699999999999998 y[1] (closed_form) = 3.454499999999999 y[1] (numeric) = 3.454499999999999 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.799999999999998 y[1] (closed_form) = 3.551999999999998 y[1] (numeric) = 3.551999999999999 absolute error = 8.881784197001252e-16 relative error = 2.500502307714318e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.899999999999998 y[1] (closed_form) = 3.650499999999997 y[1] (numeric) = 3.650499999999999 absolute error = 1.332267629550188e-15 relative error = 3.649548362005722e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.999999999999997 y[1] (closed_form) = 3.749999999999997 y[1] (numeric) = 3.749999999999999 absolute error = 1.332267629550188e-15 relative error = 3.552713678800503e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 Finished! diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + 0.3 ; Iterations = 101 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 102 %