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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 232484, 9 pages
http://dx.doi.org/10.1155/2013/232484
Research Article

Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations

1School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China
2CSIB Software Technology Center, Administrative Commission of Guangzhou Tianhe Software Park, Guangzhou 510635, China

Received 17 January 2013; Revised 2 April 2013; Accepted 6 April 2013

Academic Editor: Chengming Huang

Copyright © 2013 Qi Wang et al. 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

This paper focuses on the stability and oscillations of Euler-Maclaurin method for linear differential equations with piecewise constant arguments . The necessary and sufficient conditions under which the numerical stability region contains the analytical stability region are given. Furthermore, the conditions of oscillation for the Euler-Maclaurin method are obtained. We prove that the Euler-Maclaurin method preserves the oscillations of the analytic solution. Moreover, the relationships between stability and oscillations are discussed for analytic solution and numerical solution, respectively. Finally, some numerical experiments for verifying the theoretical analysis are also provided.