Journal of Applied Mathematics
Volume 2012 (2012), Article ID 241984, 11 pages
http://dx.doi.org/10.1155/2012/241984
Research Article

On the Convergence of Continuous-Time Waveform Relaxation Methods for Singular Perturbation Initial Value Problems

Yongxiang Zhao1,2 and Li Li1

1School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China
2Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, Xiangtan, China

Received 26 April 2012; Revised 24 June 2012; Accepted 12 July 2012

Academic Editor: Jesus Vigo-Aguiar

Copyright © 2012 Yongxiang Zhao and Li 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

This paper extends the continuous-time waveform relaxation method to singular perturbation initial value problems. The sufficient conditions for convergence of continuous-time waveform relaxation methods for singular perturbation initial value problems are given.