##############ECHO OF PROBLEM################# ##############temp/multpostode.ode################# diff ( y , x , 1 ) = x * x ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=10.0; 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(1.0 + x * x * x / 3.0); } /* 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 = 9.9 estimated_steps = 9900000 step_error = 1.059402876939547e-21 est_needed_step_err = 1.059402876939547e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 9900000 step_error = 1.05975601123186e-21 est_needed_step_err = 1.05975601123186e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 4950000 step_error = 1.498721323890511e-21 est_needed_step_err = 1.498721323890511e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 2475000 step_error = 2.119512022463721e-21 est_needed_step_err = 2.119512022463721e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 1237500 step_error = 2.997442647781021e-21 est_needed_step_err = 2.997442647781021e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 618750 step_error = 4.239024044927441e-21 est_needed_step_err = 4.239024044927441e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 309375 step_error = 5.994885295562043e-21 est_needed_step_err = 5.994885295562043e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 154687.5 step_error = 8.478048089854883e-21 est_needed_step_err = 8.478048089854883e-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 = 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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 77343.75 step_error = 1.198977059112409e-20 est_needed_step_err = 1.198977059112409e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 38671.875 step_error = 1.695609617970977e-20 est_needed_step_err = 1.695609617970977e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 19335.9375 step_error = 2.397954118224817e-20 est_needed_step_err = 2.397954118224817e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 9667.96875 step_error = 3.391219235941953e-20 est_needed_step_err = 3.391219235941953e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 4833.984375 step_error = 4.795908236449634e-20 est_needed_step_err = 4.795908236449634e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 2416.9921875 step_error = 6.782438471883906e-20 est_needed_step_err = 6.782438471883906e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 1208.49609375 step_error = 9.591816472899268e-20 est_needed_step_err = 9.591816472899268e-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 = 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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 604.248046875 step_error = 1.356487694376781e-19 est_needed_step_err = 1.356487694376781e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 302.1240234375 step_error = 1.918363294579854e-19 est_needed_step_err = 1.918363294579854e-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 = 1.000333333333333 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1.000333333333333 desired_abs_gbl_error = 1.000333333333333e-16 range = 9.9 estimated_steps = 151.06201171875 step_error = 2.712975388753562e-19 est_needed_step_err = 2.712975388753562e-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] = 0.1 y[1] (closed_form) = 1.000333333333333 y[1] (numeric) = 1.000333333333333 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] = 0.2 y[1] (closed_form) = 1.002666666666667 y[1] (numeric) = 1.002666666666667 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] = 0.3 y[1] (closed_form) = 1.009 y[1] (numeric) = 1.009 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] = 0.4 y[1] (closed_form) = 1.021333333333333 y[1] (numeric) = 1.021333333333333 absolute error = 2.220446049250313e-16 relative error = 2.174065975114536e-14 % 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] = 0.5 y[1] (closed_form) = 1.041666666666667 y[1] (numeric) = 1.041666666666667 absolute error = 2.220446049250313e-16 relative error = 2.131628207280301e-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] = 0.6 y[1] (closed_form) = 1.072 y[1] (numeric) = 1.072 absolute error = 2.220446049250313e-16 relative error = 2.071311613106635e-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] = 0.7 y[1] (closed_form) = 1.114333333333333 y[1] (numeric) = 1.114333333333333 absolute error = 2.220446049250313e-16 relative error = 1.992622838094807e-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] = 0.7999999999999999 y[1] (closed_form) = 1.170666666666667 y[1] (numeric) = 1.170666666666667 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] = 0.8999999999999999 y[1] (closed_form) = 1.243 y[1] (numeric) = 1.243 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] = 0.9999999999999999 y[1] (closed_form) = 1.333333333333333 y[1] (numeric) = 1.333333333333333 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] = 1.1 y[1] (closed_form) = 1.443666666666666 y[1] (numeric) = 1.443666666666667 absolute error = 2.220446049250313e-16 relative error = 1.538060066439838e-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] = 1.2 y[1] (closed_form) = 1.576 y[1] (numeric) = 1.576 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] = 1.3 y[1] (closed_form) = 1.732333333333334 y[1] (numeric) = 1.732333333333334 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] = 1.4 y[1] (closed_form) = 1.914666666666667 y[1] (numeric) = 1.914666666666667 absolute error = 2.220446049250313e-16 relative error = 1.159703716530456e-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] = 1.5 y[1] (closed_form) = 2.125000000000001 y[1] (numeric) = 2.125 absolute error = 4.440892098500626e-16 relative error = 2.089831575765e-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] = 1.6 y[1] (closed_form) = 2.365333333333334 y[1] (numeric) = 2.365333333333334 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] = 1.7 y[1] (closed_form) = 2.637666666666668 y[1] (numeric) = 2.637666666666667 absolute error = 4.440892098500626e-16 relative error = 1.68364416725665e-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) = 2.944000000000002 y[1] (numeric) = 2.944000000000001 absolute error = 8.881784197001252e-16 relative error = 3.016910393003141e-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] = 1.900000000000001 y[1] (closed_form) = 3.286333333333336 y[1] (numeric) = 3.286333333333334 absolute error = 1.332267629550188e-15 relative error = 4.053963777919222e-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) = 3.666666666666668 y[1] (numeric) = 3.666666666666668 absolute error = 4.440892098500626e-16 relative error = 1.21115239050017e-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] = 2.100000000000001 y[1] (closed_form) = 4.087000000000002 y[1] (numeric) = 4.087000000000002 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] = 2.200000000000001 y[1] (closed_form) = 4.549333333333337 y[1] (numeric) = 4.549333333333335 absolute error = 1.77635683940025e-15 relative error = 3.904653076055647e-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] = 2.300000000000001 y[1] (closed_form) = 5.055666666666671 y[1] (numeric) = 5.055666666666669 absolute error = 1.77635683940025e-15 relative error = 3.513595647260992e-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] = 2.400000000000001 y[1] (closed_form) = 5.608000000000005 y[1] (numeric) = 5.608000000000002 absolute error = 2.664535259100376e-15 relative error = 4.751311089693961e-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] = 2.500000000000001 y[1] (closed_form) = 6.208333333333338 y[1] (numeric) = 6.208333333333336 absolute error = 2.664535259100376e-15 relative error = 4.291868873718723e-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] = 2.600000000000001 y[1] (closed_form) = 6.858666666666672 y[1] (numeric) = 6.85866666666667 absolute error = 2.664535259100376e-15 relative error = 3.88491727123888e-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] = 2.700000000000001 y[1] (closed_form) = 7.561000000000007 y[1] (numeric) = 7.561000000000003 absolute error = 3.552713678800501e-15 relative error = 4.698735192171006e-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] = 2.800000000000001 y[1] (closed_form) = 8.317333333333341 y[1] (numeric) = 8.317333333333337 absolute error = 3.552713678800501e-15 relative error = 4.271457613177899e-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] = 2.900000000000001 y[1] (closed_form) = 9.129666666666678 y[1] (numeric) = 9.129666666666672 absolute error = 5.329070518200751e-15 relative error = 5.837092100698176e-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] = 3.000000000000001 y[1] (closed_form) = 10.00000000000001 y[1] (numeric) = 10.00000000000001 absolute error = 5.329070518200751e-15 relative error = 5.329070518200745e-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) = 10.93033333333335 y[1] (numeric) = 10.93033333333334 absolute error = 5.329070518200751e-15 relative error = 4.87548765045355e-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] = 3.200000000000002 y[1] (closed_form) = 11.92266666666668 y[1] (numeric) = 11.92266666666668 absolute error = 5.329070518200751e-15 relative error = 4.469696811284454e-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] = 3.300000000000002 y[1] (closed_form) = 12.97900000000002 y[1] (numeric) = 12.97900000000001 absolute error = 8.881784197001252e-15 relative error = 6.843196083674582e-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] = 3.400000000000002 y[1] (closed_form) = 14.10133333333335 y[1] (numeric) = 14.10133333333334 absolute error = 8.881784197001252e-15 relative error = 6.29854212154967e-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] = 3.500000000000002 y[1] (closed_form) = 15.29166666666669 y[1] (numeric) = 15.29166666666668 absolute error = 8.881784197001252e-15 relative error = 5.808251245995361e-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] = 3.600000000000002 y[1] (closed_form) = 16.55200000000002 y[1] (numeric) = 16.55200000000001 absolute error = 7.105427357601002e-15 relative error = 4.292790815370344e-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] = 3.700000000000002 y[1] (closed_form) = 17.88433333333336 y[1] (numeric) = 17.88433333333335 absolute error = 1.06581410364015e-14 relative error = 5.959484671724686e-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] = 3.800000000000002 y[1] (closed_form) = 19.2906666666667 y[1] (numeric) = 19.29066666666668 absolute error = 1.06581410364015e-14 relative error = 5.525024728574174e-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] = 3.900000000000002 y[1] (closed_form) = 20.77300000000003 y[1] (numeric) = 20.77300000000002 absolute error = 1.06581410364015e-14 relative error = 5.130766396958305e-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] = 4.000000000000002 y[1] (closed_form) = 22.33333333333336 y[1] (numeric) = 22.33333333333336 absolute error = 3.552713678800501e-15 relative error = 1.590767318865894e-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) = 23.97366666666669 y[1] (numeric) = 23.97366666666669 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] = 4.200000000000001 y[1] (closed_form) = 25.69600000000002 y[1] (numeric) = 25.69600000000003 absolute error = 1.06581410364015e-14 relative error = 4.147782159247158e-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] = 4.300000000000001 y[1] (closed_form) = 27.50233333333334 y[1] (numeric) = 27.50233333333336 absolute error = 1.77635683940025e-14 relative error = 6.458931385459111e-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] = 4.4 y[1] (closed_form) = 29.39466666666668 y[1] (numeric) = 29.39466666666669 absolute error = 1.77635683940025e-14 relative error = 6.043126324730959e-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] = 4.5 y[1] (closed_form) = 31.375 y[1] (numeric) = 31.37500000000003 absolute error = 2.842170943040401e-14 relative error = 9.05871216905307e-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] = 4.6 y[1] (closed_form) = 33.44533333333332 y[1] (numeric) = 33.44533333333336 absolute error = 3.552713678800501e-14 relative error = 1.062244960572627e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 4.699999999999999 y[1] (closed_form) = 35.60766666666665 y[1] (numeric) = 35.60766666666669 absolute error = 3.552713678800501e-14 relative error = 9.977384118028427e-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] = 4.799999999999999 y[1] (closed_form) = 37.86399999999997 y[1] (numeric) = 37.86400000000002 absolute error = 4.973799150320701e-14 relative error = 1.313595803486347e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 4.899999999999999 y[1] (closed_form) = 40.2163333333333 y[1] (numeric) = 40.21633333333335 absolute error = 4.973799150320701e-14 relative error = 1.236760971989997e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 4.999999999999998 y[1] (closed_form) = 42.66666666666662 y[1] (numeric) = 42.66666666666669 absolute error = 6.394884621840902e-14 relative error = 1.498801083243963e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 5.099999999999998 y[1] (closed_form) = 45.21699999999993 y[1] (numeric) = 45.21700000000002 absolute error = 8.526512829121202e-14 relative error = 1.885687424889138e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 5.199999999999998 y[1] (closed_form) = 47.86933333333327 y[1] (numeric) = 47.86933333333335 absolute error = 8.526512829121202e-14 relative error = 1.78120567707674e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 5.299999999999997 y[1] (closed_form) = 50.6256666666666 y[1] (numeric) = 50.62566666666668 absolute error = 8.526512829121202e-14 relative error = 1.684227268603122e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 5.399999999999997 y[1] (closed_form) = 53.48799999999991 y[1] (numeric) = 53.48800000000001 absolute error = 1.06581410364015e-13 relative error = 1.99262283809481e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 5.499999999999996 y[1] (closed_form) = 56.45833333333323 y[1] (numeric) = 56.45833333333334 absolute error = 1.13686837721616e-13 relative error = 2.013641406139328e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 5.599999999999996 y[1] (closed_form) = 59.53866666666655 y[1] (numeric) = 59.53866666666667 absolute error = 1.20792265079217e-13 relative error = 2.028803663936331e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 5.699999999999996 y[1] (closed_form) = 62.73099999999986 y[1] (numeric) = 62.731 absolute error = 1.4210854715202e-13 relative error = 2.265363969202155e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 5.799999999999995 y[1] (closed_form) = 66.03733333333317 y[1] (numeric) = 66.03733333333334 absolute error = 1.70530256582424e-13 relative error = 2.582331053885042e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 5.899999999999995 y[1] (closed_form) = 69.45966666666648 y[1] (numeric) = 69.45966666666666 absolute error = 1.84741111297626e-13 relative error = 2.659688998857273e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 5.999999999999995 y[1] (closed_form) = 72.99999999999982 y[1] (numeric) = 72.99999999999999 absolute error = 1.70530256582424e-13 relative error = 2.336030912088006e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 6.099999999999994 y[1] (closed_form) = 76.66033333333313 y[1] (numeric) = 76.66033333333331 absolute error = 1.84741111297626e-13 relative error = 2.409865744965365e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 6.199999999999994 y[1] (closed_form) = 80.44266666666644 y[1] (numeric) = 80.44266666666664 absolute error = 1.989519660128281e-13 relative error = 2.473214455175056e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 6.299999999999994 y[1] (closed_form) = 84.34899999999975 y[1] (numeric) = 84.34899999999996 absolute error = 2.131628207280301e-13 relative error = 2.527152909080495e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 6.399999999999993 y[1] (closed_form) = 88.38133333333307 y[1] (numeric) = 88.38133333333329 absolute error = 2.131628207280301e-13 relative error = 2.411853416196829e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 6.499999999999993 y[1] (closed_form) = 92.54166666666636 y[1] (numeric) = 92.54166666666661 absolute error = 2.557953848736361e-13 relative error = 2.764110417364829e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 6.599999999999993 y[1] (closed_form) = 96.83199999999967 y[1] (numeric) = 96.83199999999994 absolute error = 2.700062395888381e-13 relative error = 2.788398872158367e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 6.699999999999992 y[1] (closed_form) = 101.254333333333 y[1] (numeric) = 101.2543333333333 absolute error = 2.842170943040401e-13 relative error = 2.806962279514369e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 6.799999999999992 y[1] (closed_form) = 105.8106666666663 y[1] (numeric) = 105.8106666666666 absolute error = 2.984279490192421e-13 relative error = 2.820395697528067e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 6.899999999999991 y[1] (closed_form) = 110.5029999999996 y[1] (numeric) = 110.5029999999999 absolute error = 3.126388037344441e-13 relative error = 2.829233629262963e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 6.999999999999991 y[1] (closed_form) = 115.3333333333329 y[1] (numeric) = 115.3333333333332 absolute error = 3.410605131648481e-13 relative error = 2.957172079464012e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 7.099999999999991 y[1] (closed_form) = 120.3036666666662 y[1] (numeric) = 120.3036666666666 absolute error = 3.694822225952521e-13 relative error = 3.07124656157823e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 7.19999999999999 y[1] (closed_form) = 125.4159999999995 y[1] (numeric) = 125.4159999999999 absolute error = 3.836930773104541e-13 relative error = 3.059363058225869e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 7.29999999999999 y[1] (closed_form) = 130.6723333333328 y[1] (numeric) = 130.6723333333332 absolute error = 3.979039320256561e-13 relative error = 3.045051097470194e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 7.39999999999999 y[1] (closed_form) = 136.0746666666661 y[1] (numeric) = 136.0746666666665 absolute error = 4.263256414560601e-13 relative error = 3.133027270244242e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 7.499999999999989 y[1] (closed_form) = 141.6249999999994 y[1] (numeric) = 141.6249999999999 absolute error = 4.547473508864641e-13 relative error = 3.210925690283961e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 7.599999999999989 y[1] (closed_form) = 147.3253333333327 y[1] (numeric) = 147.3253333333332 absolute error = 4.547473508864641e-13 relative error = 3.086688084102753e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 7.699999999999989 y[1] (closed_form) = 153.177666666666 y[1] (numeric) = 153.1776666666665 absolute error = 4.831690603168681e-13 relative error = 3.154304872447921e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 7.799999999999988 y[1] (closed_form) = 159.1839999999993 y[1] (numeric) = 159.1839999999998 absolute error = 5.115907697472721e-13 relative error = 3.213832858498809e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 7.899999999999988 y[1] (closed_form) = 165.3463333333326 y[1] (numeric) = 165.3463333333331 absolute error = 5.400124791776761e-13 relative error = 3.265947712847247e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 7.999999999999988 y[1] (closed_form) = 171.6666666666659 y[1] (numeric) = 171.6666666666664 absolute error = 5.684341886080801e-13 relative error = 3.311267118105337e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 8.099999999999987 y[1] (closed_form) = 178.1469999999991 y[1] (numeric) = 178.1469999999997 absolute error = 5.968558980384842e-13 relative error = 3.350356155525982e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 8.199999999999987 y[1] (closed_form) = 184.7893333333325 y[1] (numeric) = 184.789333333333 absolute error = 5.968558980384842e-13 relative error = 3.229926139523676e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 8.299999999999986 y[1] (closed_form) = 191.5956666666657 y[1] (numeric) = 191.5956666666663 absolute error = 6.252776074688882e-13 relative error = 3.263526875880411e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 8.399999999999986 y[1] (closed_form) = 198.567999999999 y[1] (numeric) = 198.5679999999997 absolute error = 6.821210263296962e-13 relative error = 3.435201172040307e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 8.499999999999986 y[1] (closed_form) = 205.7083333333323 y[1] (numeric) = 205.708333333333 absolute error = 6.536993168992922e-13 relative error = 3.177796962848509e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 8.599999999999985 y[1] (closed_form) = 213.0186666666656 y[1] (numeric) = 213.0186666666663 absolute error = 7.105427357601002e-13 relative error = 3.335589067750419e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 8.699999999999985 y[1] (closed_form) = 220.5009999999989 y[1] (numeric) = 220.5009999999996 absolute error = 7.389644451905042e-13 relative error = 3.351297477972925e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 8.799999999999985 y[1] (closed_form) = 228.1573333333322 y[1] (numeric) = 228.1573333333329 absolute error = 7.673861546209082e-13 relative error = 3.363407800264637e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 8.899999999999984 y[1] (closed_form) = 235.9896666666654 y[1] (numeric) = 235.9896666666662 absolute error = 7.958078640513122e-13 relative error = 3.372214874032548e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 8.999999999999984 y[1] (closed_form) = 243.9999999999987 y[1] (numeric) = 243.9999999999995 absolute error = 8.242295734817162e-13 relative error = 3.377990055252953e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 9.099999999999984 y[1] (closed_form) = 252.190333333332 y[1] (numeric) = 252.1903333333329 absolute error = 8.810729923425242e-13 relative error = 3.493682651102919e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 9.199999999999983 y[1] (closed_form) = 260.5626666666652 y[1] (numeric) = 260.5626666666662 absolute error = 9.663381206337363e-13 relative error = 3.70865916056179e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 9.299999999999983 y[1] (closed_form) = 269.1189999999985 y[1] (numeric) = 269.1189999999995 absolute error = 1.023181539494544e-12 relative error = 3.801966934681498e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 9.399999999999983 y[1] (closed_form) = 277.8613333333318 y[1] (numeric) = 277.8613333333328 absolute error = 1.023181539494544e-12 relative error = 3.682345892535905e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 9.499999999999982 y[1] (closed_form) = 286.791666666665 y[1] (numeric) = 286.7916666666661 absolute error = 1.080024958355352e-12 relative error = 3.76588682268322e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 9.599999999999982 y[1] (closed_form) = 295.9119999999983 y[1] (numeric) = 295.9119999999994 absolute error = 1.080024958355352e-12 relative error = 3.649818048458185e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 9.699999999999982 y[1] (closed_form) = 305.2243333333316 y[1] (numeric) = 305.2243333333327 absolute error = 1.080024958355352e-12 relative error = 3.538462830143594e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 9.799999999999981 y[1] (closed_form) = 314.7306666666649 y[1] (numeric) = 314.730666666666 absolute error = 1.13686837721616e-12 relative error = 3.612194481258579e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 9.899999999999981 y[1] (closed_form) = 324.4329999999981 y[1] (numeric) = 324.4329999999993 absolute error = 1.193711796076968e-12 relative error = 3.679378472834068e-13 % Desired digits = 16 Estimated correct digits = 13 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] = 9.99999999999998 y[1] (closed_form) = 334.3333333333314 y[1] (numeric) = 334.3333333333326 absolute error = 1.250555214937776e-12 relative error = 3.740444311877718e-13 % Desired digits = 16 Estimated correct digits = 13 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 Finished! diff ( y , x , 1 ) = x * x ; Iterations = 100 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 102 %