Journal of Applied Mathematics
Volume 2012 (2012), Article ID 989867, 27 pages
http://dx.doi.org/10.1155/2012/989867
Research Article

On the One-Leg Methods for Solving Nonlinear Neutral Differential Equations with Variable Delay

Wansheng Wang1 and Shoufu Li2

1School of Mathematics and Computational Sciences, Changsha University of Science & Technology, Yuntang Campus, Changsha 410114, China
2School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

Received 9 December 2011; Revised 2 July 2012; Accepted 21 July 2012

Academic Editor: Yuantong Gu

Copyright © 2012 Wansheng Wang and Shoufu Li. 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

Based on A-stable one-leg methods and linear interpolations, we introduce four algorithms for solving neutral differential equations with variable delay. A natural question is which algorithm is better. To answer this question, we analyse the error behavior of the four algorithms and obtain their error bounds under a one-sided Lipschitz condition and some classical Lipschitz conditions. After extensively numerically experimenting, we give a positive conclusion.