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Abstract and Applied Analysis
Volume 2014, Article ID 304071, 7 pages
http://dx.doi.org/10.1155/2014/304071
Research Article

Stepsize Restrictions for Nonlinear Stability Properties of Neutral Delay Differential Equations

1School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China
2School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
3School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

Received 22 May 2014; Accepted 9 July 2014; Published 21 July 2014

Academic Editor: Ali H. Bhrawy

Copyright © 2014 Wei Gu 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

The present paper is concerned with the relationship between stepsize restriction and nonlinear stability of Runge-Kutta methods for delay differential equations. We obtain a special stepsize condition guaranteeing global and asymptotical stability properties of numerical methods. Some confirmations of the conditions on Runge-Kutta methods are illustrated at last.