##############ECHO OF PROBLEM################# ##############temp/sqrtpostode.ode################# diff ( y , x , 1 ) = sqrt ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=0.2; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.001; glob_max_h=0.01; glob_type_given_pole=1; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=1.5; 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(2.0*expt(x,1.5)/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 = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 100 step_error = 2.5e-19 est_needed_step_err = 2.5e-19 opt_iter = 1 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0210818510677892 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 100 step_error = 2.5e-19 est_needed_step_err = 2.5e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.204116264324181e-78 estimated_step_error = 1.204116264324181e-78 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0210818510677892 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 50 step_error = 3.535533905932737e-19 est_needed_step_err = 3.535533905932737e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.236403653689294e-68 estimated_step_error = 8.236403653689294e-68 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0210818510677892 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 25 step_error = 4.999999999999999e-19 est_needed_step_err = 4.999999999999999e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.608205902107171e-57 estimated_step_error = 5.608205902107171e-57 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0210818510677892 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.1 estimated_steps = 12.5 step_error = 7.071067811865474e-19 est_needed_step_err = 7.071067811865474e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.784643348666978e-46 estimated_step_error = 3.784643348666978e-46 Double H and LOOP opt_iter = 5 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0625 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.0210818510677892 y[1] (numeric) = 0.0210818510677892 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1125000000000001 y[1] (closed_form) = 0.02515576474687267 y[1] (numeric) = 0.02515576474687267 absolute error = 3.469446951953614e-18 relative error = 1.379185640692928e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1125 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1125 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1250000000000002 y[1] (closed_form) = 0.02946278254943955 y[1] (numeric) = 0.02946278254943955 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.125 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.125 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1312500000000002 y[1] (closed_form) = 0.03169988663228948 y[1] (numeric) = 0.03169988663228948 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1313 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1312 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1437500000000003 y[1] (closed_form) = 0.03633461150274712 y[1] (numeric) = 0.03633461150274713 absolute error = 6.938893903907228e-18 relative error = 1.909720131005833e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1438 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1438 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1500000000000003 y[1] (closed_form) = 0.03872983346207429 y[1] (numeric) = 0.03872983346207431 absolute error = 1.387778780781446e-17 relative error = 3.58322940412437e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.15 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.15 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1625000000000004 y[1] (closed_form) = 0.04367056280328397 y[1] (numeric) = 0.04367056280328399 absolute error = 2.081668171172169e-17 relative error = 4.76675370672262e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1625 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1625 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1750000000000005 y[1] (closed_form) = 0.04880516821448794 y[1] (numeric) = 0.04880516821448797 absolute error = 2.775557561562891e-17 relative error = 5.68701566474462e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.175 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.175 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1812500000000005 y[1] (closed_form) = 0.05144293798040288 y[1] (numeric) = 0.05144293798040292 absolute error = 3.469446951953614e-17 relative error = 6.744262843765446e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1813 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1813 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1937500000000006 y[1] (closed_form) = 0.05685534611577413 y[1] (numeric) = 0.05685534611577418 absolute error = 4.85722573273506e-17 relative error = 8.543129300179311e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.006250000000000044 Radius of convergence (given) for eq 1 = 0.1938 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1938 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( x ) ; Iterations = 16 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 106.3 %