Abstract and Applied Analysis
Volume 2012 (2012), Article ID 258329, 14 pages
http://dx.doi.org/10.1155/2012/258329
Research Article

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

Minghui Song and M. Z. Liu

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 17 January 2012; Accepted 13 February 2012

Academic Editor: Norio Yoshida

Copyright © 2012 Minghui Song and M. Z. Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 𝜃 -methods are obtained. Some examples are illustrated.