Numerical stability of coupled differential equation with piecewise constant arguments

This paper deals with the stability of numerical solutions for a coupled differential equation with piecewise constant arguments. A sufficient condition such that the system is asymptotically stable is derived. Furthermore, when the linear  θ-method is applied to this system, it is shown that the linear θ-method is asymptotically stable if and only if 1/2<θ≤1. Finally, some numerical experiments are given