Journal of Applied Mathematics
Volume 2012 (2012), Article ID 675651, 32 pages
http://dx.doi.org/10.1155/2012/675651
Research Article

Approximations of Numerical Method for Neutral Stochastic Functional Differential Equations with Markovian Switching

Hua Yang1 and Feng Jiang2

1School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China
2School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China

Received 9 April 2012; Accepted 17 September 2012

Academic Editor: Zhenyu Huang

Copyright © 2012 Hua Yang and Feng Jiang. 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

Stochastic systems with Markovian switching have been used in a variety of application areas, including biology, epidemiology, mechanics, economics, and finance. In this paper, we study the Euler-Maruyama (EM) method for neutral stochastic functional differential equations with Markovian switching. The main aim is to show that the numerical solutions will converge to the true solutions. Moreover, we obtain the convergence order of the approximate solutions.