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Mathematical Problems in Engineering
Volume 2013, Article ID 724241, 7 pages
http://dx.doi.org/10.1155/2013/724241
Research Article

Mean-Square Stability of Milstein Methods for Stochastic Pantograph Equations

1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
2School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China

Received 1 June 2013; Revised 22 September 2013; Accepted 27 September 2013

Academic Editor: Guo-Cheng Wu

Copyright © 2013 Feiyan Xiao 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 deals with nonlinear stochastic pantograph equations. For solving the equations, a class of extended Milstein methods are suggested. A mean-square stability criterion for this type of equations is presented. It is proved that under the suitable conditions the Milstein methods preserve the mean-square stability. Numerical examples further illustrate the obtained theoretical results.