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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 325364, 9 pages
http://dx.doi.org/10.1155/2015/325364
Research Article

Stability Analysis of One-Leg Methods for Nonlinear Neutral Delay Integrodifferential Equations

Department of Mathematics, Xiangtan University, Xiangtan 411105, China

Received 8 April 2015; Revised 16 June 2015; Accepted 24 June 2015

Academic Editor: Antonia Vecchio

Copyright © 2015 Yuexin Yu and Liping Wen. 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 is concerned with the numerical solution of nonlinear neutral delay integrodifferential equations (NDIDEs). The adaptation of one-leg methods is considered. It is proved that an A-stable one-leg method can preserve the global stability and a strongly A-stable one-leg method can preserve the asymptotic stability of the analytical solution of nonlinear NDIDEs. Numerical tests are given to confirm the theoretical results.