##############ECHO OF PROBLEM################# ##############temp/sqrt_tonepostode.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=0.5; x_end=0.6; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.01; glob_min_h=0.001; 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 = 0.09999999999999998 estimated_steps = 99.99999999999997 step_error = 2.500000000000001e-19 est_needed_step_err = 2.500000000000001e-19 opt_iter = 1 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.2357022603955159 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.09999999999999998 estimated_steps = 99.99999999999997 step_error = 2.500000000000001e-19 est_needed_step_err = 2.500000000000001e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.285783216869341e-103 estimated_step_error = 9.285783216869341e-103 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.2357022603955159 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.09999999999999998 estimated_steps = 49.99999999999999 step_error = 3.535533905932738e-19 est_needed_step_err = 3.535533905932738e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.375202760816313e-92 estimated_step_error = 6.375202760816313e-92 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.2357022603955159 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.09999999999999998 estimated_steps = 24.99999999999999 step_error = 5.000000000000001e-19 est_needed_step_err = 5.000000000000001e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.372866438037111e-81 estimated_step_error = 4.372866438037111e-81 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.2357022603955159 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.09999999999999998 estimated_steps = 12.5 step_error = 7.071067811865476e-19 est_needed_step_err = 7.071067811865476e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.993886267121181e-70 estimated_step_error = 2.993886267121181e-70 Double H and LOOP opt_iter = 5 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3125 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] = 0.5 y[1] (closed_form) = 0.2357022603955159 y[1] (numeric) = 0.2357022603955159 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.009999999999999998 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (closed_form) = 0.2428085665704569 y[1] (numeric) = 0.2428085665704569 absolute error = 2.775557561562891e-17 relative error = 1.143105286920548e-14 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.009999999999999998 Radius of convergence (given) for eq 1 = 0.51 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.51 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (closed_form) = 0.2499848884321699 y[1] (numeric) = 0.24998488843217 absolute error = 2.775557561562891e-17 relative error = 1.110290137524054e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009999999999999998 Radius of convergence (given) for eq 1 = 0.52 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.52 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (closed_form) = 0.257230549421245 y[1] (numeric) = 0.257230549421245 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009999999999999998 Radius of convergence (given) for eq 1 = 0.53 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.53 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (closed_form) = 0.2645448922205832 y[1] (numeric) = 0.2645448922205832 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009999999999999998 Radius of convergence (given) for eq 1 = 0.54 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.54 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (closed_form) = 0.2719272778601743 y[1] (numeric) = 0.2719272778601743 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009999999999999998 Radius of convergence (given) for eq 1 = 0.55 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.55 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5600000000000001 y[1] (closed_form) = 0.279377084879121 y[1] (numeric) = 0.279377084879121 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009999999999999998 Radius of convergence (given) for eq 1 = 0.56 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.56 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5700000000000001 y[1] (closed_form) = 0.2868937085402886 y[1] (numeric) = 0.2868937085402885 absolute error = 5.551115123125783e-17 relative error = 1.934903052203474e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009999999999999998 Radius of convergence (given) for eq 1 = 0.57 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.57 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5800000000000001 y[1] (closed_form) = 0.2944765600934045 y[1] (numeric) = 0.2944765600934044 absolute error = 5.551115123125783e-17 relative error = 1.885078772098205e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009999999999999998 Radius of convergence (given) for eq 1 = 0.58 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.58 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5900000000000001 y[1] (closed_form) = 0.302125066082832 y[1] (numeric) = 0.3021250660828319 absolute error = 1.110223024625157e-16 relative error = 3.674713386147089e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.009999999999999998 Radius of convergence (given) for eq 1 = 0.59 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.59 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 = 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 %