Stability of Runge-Kutta methods for delay differential systems with multiple delays

The stability of Runge-Kutta methods for systems of delay differential equations (DDEs) with multiple delays is considered. The stability regions of explicit and implicit Runge-Kutta methods are discussed when they are applied to asymptotically stable linear DDEs with multiple delays. A simple estimate on the stability regions of explicit Runge-Kutta methods is presented. It is shown that the stable step-size for numerical integration of DDEs with multiple delays can be easily selected by means of the estimate.