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Simulations of Two-Step Maruyama Methods for Nonlinear Stochastic Delay Differential Equations

Published online by Cambridge University Press:  03 June 2015

Wanrong Cao  and
Zhongqiang Zhang
Wanrong Cao*
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210096, China Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Zhongqiang Zhang*
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
*
Corresponding author. Email: wrcao@seu.edu.cn
Email: zhongqiang_zhang@brown.edu
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Abstract

In this paper, we investigate the numerical performance of a family of P-stable two-step Maruyama schemes in mean-square sense for stochastic differential equations with time delay proposed in for a certain class of nonlinear stochastic delay differential equations with multiplicative white noises. We also test the convergence of one of the schemes for a time-delayed Burgers’ equation with an additive white noise. Numerical results show that this family of two-step Maruyama methods exhibit similar stability for nonlinear equations as that for linear equations.

Keywords

65C2065C3065Q20P-stability in mean-square sensetwo-step Maruyama methodsnonlinear stochastic delay differential systemBurgers’ equation
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 6 , December 2012 , pp. 821 - 832
Copyright
Copyright © Global-Science Press 2012

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