##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrt_tonepostode.ode################# diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.5; x_end=1.5; 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]=-2.0; 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(0.8 * (x + 2.0) * sqrt(sqrt(0.1 * x + 0.2))); } // 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 = 1 estimated_steps = 1000 step_error = 7.905694150420949e-20 est_needed_step_err = 7.905694150420949e-20 opt_iter = 1 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.414213562373095 glob_desired_digits_correct = 16 estimated_h = 0.001 estimated_answer = 1.414213562373095 desired_abs_gbl_error = 1.414213562373095e-16 range = 1 estimated_steps = 1000 step_error = 1.118033988749895e-19 est_needed_step_err = 1.118033988749895e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.581160759120225e-127 estimated_step_error = 5.581160759120225e-127 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.414213562373095 glob_desired_digits_correct = 16 estimated_h = 0.002 estimated_answer = 1.414213562373095 desired_abs_gbl_error = 1.414213562373095e-16 range = 1 estimated_steps = 500 step_error = 1.58113883008419e-19 est_needed_step_err = 1.58113883008419e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.834624317884502e-116 estimated_step_error = 3.834624317884502e-116 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.414213562373095 glob_desired_digits_correct = 16 estimated_h = 0.004 estimated_answer = 1.414213562373095 desired_abs_gbl_error = 1.414213562373095e-16 range = 1 estimated_steps = 250 step_error = 2.23606797749979e-19 est_needed_step_err = 2.23606797749979e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.634144555525965e-105 estimated_step_error = 2.634144555525965e-105 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.414213562373095 glob_desired_digits_correct = 16 estimated_h = 0.008 estimated_answer = 1.414213562373095 desired_abs_gbl_error = 1.414213562373095e-16 range = 1 estimated_steps = 125 step_error = 3.16227766016838e-19 est_needed_step_err = 3.16227766016838e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.808812326998184e-94 estimated_step_error = 1.808812326998184e-94 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.414213562373095 glob_desired_digits_correct = 16 estimated_h = 0.016 estimated_answer = 1.414213562373095 desired_abs_gbl_error = 1.414213562373095e-16 range = 1 estimated_steps = 62.5 step_error = 4.47213595499958e-19 est_needed_step_err = 4.47213595499958e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.241144108238969e-83 estimated_step_error = 1.241144108238969e-83 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.414213562373095 glob_desired_digits_correct = 16 estimated_h = 0.032 estimated_answer = 1.414213562373095 desired_abs_gbl_error = 1.414213562373095e-16 range = 1 estimated_steps = 31.25 step_error = 6.324555320336759e-19 est_needed_step_err = 6.324555320336759e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.503597565314252e-73 estimated_step_error = 8.503597565314252e-73 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 min_size = 1.414213562373095 glob_desired_digits_correct = 16 estimated_h = 0.064 estimated_answer = 1.414213562373095 desired_abs_gbl_error = 1.414213562373095e-16 range = 1 estimated_steps = 15.625 step_error = 8.94427190999916e-19 est_needed_step_err = 8.94427190999916e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.808920981709633e-62 estimated_step_error = 5.808920981709633e-62 Double H and LOOP opt_iter = 8 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.953 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (closed_form) = 1.414213562373095 y[1] (numeric) = 1.414213562373095 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 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 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 1.485274318892232 y[1] (numeric) = 1.485274318892232 absolute error = 0 relative error = 0 % 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 Radius of convergence (three term test) for eq 1 = 2.6 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (closed_form) = 1.557021796359321 y[1] (numeric) = 1.557021796359321 absolute error = 2.220446049250313e-16 relative error = 1.42608539870298e-14 % 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 Radius of convergence (three term test) for eq 1 = 2.7 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y[1] (closed_form) = 1.62943682162873 y[1] (numeric) = 1.62943682162873 absolute error = 2.220446049250313e-16 relative error = 1.362707666708323e-14 % 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 Radius of convergence (three term test) for eq 1 = 2.8 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y[1] (closed_form) = 1.702501426076371 y[1] (numeric) = 1.702501426076371 absolute error = 0 relative error = 0 % 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 Radius of convergence (three term test) for eq 1 = 2.9 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y[1] (closed_form) = 1.776198730781485 y[1] (numeric) = 1.776198730781485 absolute error = 0 relative error = 0 % 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 Radius of convergence (three term test) for eq 1 = 3 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 1.850512846136167 y[1] (numeric) = 1.850512846136167 absolute error = 2.220446049250313e-16 relative error = 1.199908476121395e-14 % 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 Radius of convergence (three term test) for eq 1 = 3.1 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 1.925428783660234 y[1] (numeric) = 1.925428783660234 absolute error = 2.220446049250313e-16 relative error = 1.1532215930777e-14 % 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 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 2.000932378200509 y[1] (numeric) = 2.000932378200509 absolute error = 4.440892098500626e-16 relative error = 2.21941138385418e-14 % 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 Radius of convergence (three term test) for eq 1 = 3.3 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = 2.077010219012499 y[1] (numeric) = 2.077010219012499 absolute error = 0 relative error = 0 % 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 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = 1.25 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 110 %