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

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