Stability of Runge-Kutta methods in the numerical solution of equation u′(t)=au(t)+a0u([t])+a1u([t−1])

This paper is concerned with the stability analysis of the Runge-Kutta methods for the equation u′(t)=au(t)+a0u([t])+a1u([t−1]). The stability regions for the Runge-Kutta methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given.