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

This paper is concerned with the stability analysis of the Runge–Kutta methods for the equation u′(t)=au(t)+a0u([t]). 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.