Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments

Abstract

In this paper, the asymptotic stability of the analytic and numerical solutions for differential equations with piecewise continuous arguments is investigated by using Lyapunov methods. In particular, the linear equations with variable coefficients are considered. The stability conditions of the analytic solutions of those equations and the numerical solutions of the $\theta$-methods are obtained. Some examples are illustrated.