A modified Runge–Kutta method for increasing stability properties

Abstract

In control theory, we are interested mainly in investigating asymptotic stability of systems. In this paper explicit Runge–Kutta methods are investigated for numerical solutions of nonlinear ODEs with known strict Lyapunov functions. In order to increase stability properties, a modified version of explicit Runge–Kutta methods is presented. The modified Runge–Kutta method is explicit. It is different from the projection methods in literature which are implicit. Comparing with the standard Runge–Kutta method, the modified Runge–Kutta one has better stability properties. Numerical examples are provided to illustrate the effectiveness of the modified Runge–Kutta method.