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Journal of Applied Mathematics
Volume 2014, Article ID 607827, 9 pages
http://dx.doi.org/10.1155/2014/607827
Research Article

Stability Analysis of Runge-Kutta Methods for Nonlinear Functional Differential and Functional Equations

Department of Mathematics, Xiangtan University, Xiangtan 411105, China

Received 5 September 2013; Revised 15 April 2014; Accepted 18 April 2014; Published 6 May 2014

Academic Editor: Mehmet Sezer

Copyright © 2014 Yuexin Yu 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 is concerned with the numerical stability of Runge-Kutta methods for a class of nonlinear functional differential and functional equations. The sufficient conditions for the stability and asymptotic stability of -algebraically stable Runge-Kutta methods are derived. A numerical test is given to confirm the theoretical results.