##############ECHO OF PROBLEM################# ##############temp/sing1postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-2.0); x_end=c(-1.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.001); glob_min_h=c(0.001); glob_type_given_pole=2; array_given_rad_poles[1][1]=c(0.0); array_given_rad_poles[1][2]=c(0.001); array_given_ord_poles[1][1]=c(1.0); array_given_ord_poles[1][2]=c(0.0); /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(5.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.1); glob_lower_ratio_limit=c(0.9); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(1.0) / (c(x) * c(x) + c(0.000001))) ; } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 8 estimated_h = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-08 range = 0.5 estimated_steps = 500 step_error = 1.49071198499986e-11 est_needed_step_err = 1.49071198499986e-11 opt_iter = 1 SETTING H FOR MIN H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] = -2 y[1] (closed_form) = 0.2499999375000156 y[1] (numeric) = 0.2499999375000156 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.923 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 2 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.95 y[1] (closed_form) = 0.2629848092084657 y[1] (numeric) = 0.2629848092084657 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.875 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.95 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.95 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.9 y[1] (closed_form) = 0.2770082335157248 y[1] (numeric) = 0.2770082335157248 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.827 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.9 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.85 y[1] (closed_form) = 0.2921839905963505 y[1] (numeric) = 0.2921839905963505 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.779 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.85 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.85 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.8 y[1] (closed_form) = 0.3086418800488025 y[1] (numeric) = 0.3086418800488025 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.731 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.8 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.75 y[1] (closed_form) = 0.3265305056226921 y[1] (numeric) = 0.3265305056226921 absolute error = 5.551115123125783e-17 relative error = 1.700029561568783e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.75 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.683 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.75 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.75 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.7 y[1] (closed_form) = 0.3460206415153491 y[1] (numeric) = 0.346020641515349 absolute error = 5.551115123125783e-17 relative error = 1.604272825694863e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.635 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.7 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.65 y[1] (closed_form) = 0.3673093233023607 y[1] (numeric) = 0.3673093233023607 absolute error = 5.551115123125783e-17 relative error = 1.511291647382506e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.587 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.65 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.65 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.6 y[1] (closed_form) = 0.3906248474121691 y[1] (numeric) = 0.3906248474121691 absolute error = 5.551115123125783e-17 relative error = 1.421086026631712e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.538 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.6 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.55 y[1] (closed_form) = 0.4162329172807838 y[1] (numeric) = 0.4162329172807838 absolute error = 5.551115123125783e-17 relative error = 1.333655963442481e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.55 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.49 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.55 Order of pole (three term test) = 2 Radius of convergence (six term test) for eq 1 = 1.55 Order of pole (six term test) = 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 0.000001 ) / ( x * x + 0.000001 ) ; Iterations = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 5 Minutes 0.0 Seconds Percent Done = 110 %