##############ECHO OF PROBLEM################# ##############temp/lin_tanhpostode.ode################# diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms = 30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 1.1; x_end = 2.0 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 10; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_h = 0.005 ; glob_display_interval = 0.1; glob_look_poles = true; glob_max_iter = 10000; glob_max_minutes = 10; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(ln(cosh(3.0*x + 1.0))/3.0); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 1.1 y[1] (analytic) = 1.20234563609611 y[1] (numeric) = 1.20234563609611 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 1.53 Order of pole = 2.181 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.204999999999998 y[1] (analytic) = 1.307316955956456 y[1] (numeric) = 1.307316955956493 absolute error = 3.663735981263017e-14 relative error = 2.802484863804557e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 1.666 Order of pole = 2.785 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.304999999999996 y[1] (analytic) = 1.407302210249728 y[1] (numeric) = 1.407302210249785 absolute error = 5.639932965095795e-14 relative error = 4.007620341969746e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 1.837 Order of pole = 4.106 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.404999999999994 y[1] (analytic) = 1.507294117357051 y[1] (numeric) = 1.50729411735712 absolute error = 6.861178292183467e-14 relative error = 4.551983725786794e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 1.984 Order of pole = 4.998 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.504999999999991 y[1] (analytic) = 1.607289675799871 y[1] (numeric) = 1.607289675799947 absolute error = 7.593925488436071e-14 relative error = 4.724677575407767e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.036 Order of pole = 4.122 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.604999999999989 y[1] (analytic) = 1.707287238196455 y[1] (numeric) = 1.707287238196535 absolute error = 8.08242361927114e-14 relative error = 4.734073703853874e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.059 Order of pole = 2.512 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.704999999999987 y[1] (analytic) = 1.807285900403759 y[1] (numeric) = 1.807285900403843 absolute error = 8.415490526658687e-14 relative error = 4.656424600434615e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.172 Order of pole = 2.003 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.804999999999985 y[1] (analytic) = 1.907285166205277 y[1] (numeric) = 1.907285166205364 absolute error = 8.72635297355373e-14 relative error = 4.575274389049871e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.349 Order of pole = 2.587 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 1.904999999999983 y[1] (analytic) = 2.007284763267919 y[1] (numeric) = 2.007284763268009 absolute error = 8.970602038971265e-14 relative error = 4.469023131708955e-12 % Correct digits = 13 h = 0.005 TOP MAIN SOLVE Loop Complex estimate of poles used Radius of convergence = 2.371 Order of pole = 1.946 Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used Complex estimate of poles used x[1] = 2.004999999999981 y[1] (analytic) = 2.107284542131001 y[1] (numeric) = 2.107284542131093 absolute error = 9.192646643896296e-14 relative error = 4.362318642835101e-12 % Correct digits = 13 h = 0.005 Finished! diff ( y , x , 1 ) = tanh (3.0 * x + 1.0 ) ; Iterations = 181 Total Elapsed Time = 7 Seconds Elapsed Time(since restart) = 6 Seconds Time to Timeout = 9 Minutes 53 Seconds Percent Done = 101.1 %