##############ECHO OF PROBLEM################# ##############temp/tan_sqrt_linpostode.ode################# diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.001; glob_type_given_pole=1; array_given_rad_poles[1][1]=-1.5; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; array_given_ord_poles[1][2]=0.0; /* 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(0.0); } /* 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 = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 4900 step_error = 3.571428571428571e-20 est_needed_step_err = 3.571428571428571e-20 opt_iter = 1 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 NO 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 4900 step_error = 3.571428571428571e-20 est_needed_step_err = 3.571428571428571e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.725554091601842e-113 estimated_step_error = 9.725554091601842e-113 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 NO 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 2450 step_error = 5.050762722761054e-20 est_needed_step_err = 5.050762722761054e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.680619765119502e-102 estimated_step_error = 6.680619765119502e-102 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 NO 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 1225 step_error = 7.142857142857142e-20 est_needed_step_err = 7.142857142857142e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.587139299919488e-91 estimated_step_error = 4.587139299919488e-91 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 NO 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 612.5 step_error = 1.010152544552211e-19 est_needed_step_err = 1.010152544552211e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.14712000169966e-80 estimated_step_error = 3.14712000169966e-80 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 NO 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 306.25 step_error = 1.428571428571428e-19 est_needed_step_err = 1.428571428571428e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.155657056932716e-69 estimated_step_error = 2.155657056932716e-69 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 NO 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 153.125 step_error = 2.020305089104421e-19 est_needed_step_err = 2.020305089104421e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.47179151966198e-58 estimated_step_error = 1.47179151966198e-58 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 NO 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.064 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 76.5625 step_error = 2.857142857142857e-19 est_needed_step_err = 2.857142857142857e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.985129424249694e-48 estimated_step_error = 9.985129424249694e-48 Double H and LOOP opt_iter = 8 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Desired digits = 16 Estimated correct digits = -16 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -0.4519111018010179 absolute error = 0.4519111018010179 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -0.8092693172240324 absolute error = 0.8092693172240324 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.493 Order of pole (three term test) = 0.001092 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 0 y[1] (numeric) = -1.104750851623186 absolute error = 1.104750851623186 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.63 Order of pole (three term test) = 0.003232 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (closed_form) = 0 y[1] (numeric) = -1.3563287277553 absolute error = 1.3563287277553 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.762 Order of pole (three term test) = 0.007307 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 0 y[1] (numeric) = -1.574950907947592 absolute error = 1.574950907947592 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.889 Order of pole (three term test) = 0.0139 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (closed_form) = 0 y[1] (numeric) = -1.767783943585915 absolute error = 1.767783943585915 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -1.939777418365157 absolute error = 1.939777418365157 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -2.094494586562222 absolute error = 2.094494586562222 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -2.234586880692176 absolute error = 2.234586880692176 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -2.362081087792797 absolute error = 2.362081087792797 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 2.6 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -2.478561476544245 absolute error = 2.478561476544245 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 2.7 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -2.585289863117036 absolute error = 2.585289863117036 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 2.8 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -2.68328738669675 absolute error = 2.68328738669675 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 2.9 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -2.773391777841391 absolute error = 2.773391777841391 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -2.856298439971313 absolute error = 2.856298439971313 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 0.5 NO 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 y[1] (numeric) = -2.9325905436145 absolute error = 2.9325905436145 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.002761482201959 absolute error = 3.002761482201959 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.06723190400727 absolute error = 3.06723190400727 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.126362819470379 absolute error = 3.126362819470379 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.180465820282413 absolute error = 3.180465820282413 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.229811140195037 absolute error = 3.229811140195037 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.274634080461202 absolute error = 3.274634080461202 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.315140180270594 absolute error = 3.315140180270594 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.351509412737963 absolute error = 3.351509412737963 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.383899616032892 absolute error = 3.383899616032892 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.412449318052531 absolute error = 3.412449318052531 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.437280075633107 absolute error = 3.437280075633107 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.458498421627179 absolute error = 3.458498421627179 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.476197492473868 absolute error = 3.476197492473868 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.490458393238037 absolute error = 3.490458393238037 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.501351345140954 absolute error = 3.501351345140954 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.508936651388003 absolute error = 3.508936651388003 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 4.8 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.513265509926099 absolute error = 3.513265509926099 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.514380696130838 absolute error = 3.514380696130838 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 5 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.512317133960198 absolute error = 3.512317133960198 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 5.1 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.507102370542636 absolute error = 3.507102370542636 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 5.2 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.498756966285938 absolute error = 3.498756966285938 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 5.3 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.487294810242789 absolute error = 3.487294810242789 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 5.4 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.472723368529943 absolute error = 3.472723368529943 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 5.5 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.455043871977423 absolute error = 3.455043871977423 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 5.6 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.434251447809875 absolute error = 3.434251447809875 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 5.7 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.410335198976474 absolute error = 3.410335198976474 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 5.8 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.383278233702124 absolute error = 3.383278233702124 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 5.9 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.353057646892814 absolute error = 3.353057646892814 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 6 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.319644454159572 absolute error = 3.319644454159572 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 6.1 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.283003478400083 absolute error = 3.283003478400083 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 6.2 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.243093188069306 absolute error = 3.243093188069306 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 6.3 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.199865485455978 absolute error = 3.199865485455978 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 6.4 Order of pole (given) = 0.5 NO 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) = 0 y[1] (numeric) = -3.153265442436901 absolute error = 3.153265442436901 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.1 Radius of convergence (given) for eq 1 = 6.5 Order of pole (given) = 0.5 NO 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 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 50 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 104.1 %