Abstract: A numerical method is presented for digital simulation of dynamic systems with functions containing discontinuities.The method is suitable for both off-line and in-line simulation.And it can achieve medium and high accuracy.The effectiveness of the method consists in:1.A suitable integration method for each type of problem,2.A flexible hybrid algorithm for searching the zeros of the function;3.Hermite interpolation for function approximation;4.Special treatment for evaluating the condition functions;5.Inverse continuous fraction interpolation together with rational extrapolation for greater accuracy in integration.Four examples are given to compare results obtained with those given elsewhere.