Numerical stability analysis of differential equations with piecewise constant arguments with complex coefficients

In this paper we consider the analytical and numerical stability regions of Runge–Kutta methods for differential equations with piecewise continuous arguments with complex coefficients. It is shown that the analytical stability region contained in the numerical one is violated for a∉Ra∉R by the geometric technique. And we give the conditions under which the analytical stability region is contained in the union of the numerical stability regions of two Runge–Kutta methods. At last, some experiments are given.