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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 642318, 21 pages
http://dx.doi.org/10.1155/2012/642318
Research Article

A Class of New Pouzet-Runge-Kutta-Type Methods for Nonlinear Functional Integro-Differential Equations

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

Received 2 October 2011; Accepted 7 February 2012

Academic Editor: Shaher Momani

Copyright © 2012 Chengjian Zhang. 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 presents a class of new numerical methods for nonlinear functional-integrodifferential equations, which are derived by an adaptation of Pouzet-Runge-Kutta methods originally introduced for standard Volterra integrodifferential equations. Based on the nonclassical Lipschitz condition, analytical and numerical stability is studied and some novel stability criteria are obtained. Numerical experiments further illustrate the theoretical results and the effectiveness of the methods. In the end, a comparison between the presented methods and the existed related methods is given.