Numerical Solutions to Neutral Stochastic Delay Differential Equations with Poisson Jumps under Local Lipschitz Condition. (4th June 2014)

• Record Type: Journal Article
• Authors: Tan, Jianguo; Wang, Hongli; Guo, Yongfeng; Zhu, Zhiwen
• Other Names: Abd El Aziz Mohamed Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2014(2014)
• Publication Date: 2014-06-04
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2014/976183
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Recently, Liu et al. (2011) studied the stability of a class of neutral stochastic delay differential equations with Poisson jumps (NSDDEwPJs) by fixed points theory. To the best of our knowledge to date, there are not any numerical methods that have been established for NSDDEwPJs yet. In this paper, we will develop the Euler-Maruyama method for NSDDEwPJs, and the main aim is to prove the convergence of the numerical method. It is proved that the proposed method is convergent with strong order 1/2 under the local Lipschitz condition. Finally, some numerical examples are simulated to verify the results obtained from theory.