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

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

Year:    2012

Author:    Wanrong Cao, Zhongqiang Zhang

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 6 : pp. 821–832

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 [8, 10] 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.12-12S11

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 6 : pp. 821–832

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    P-stability in mean-square sense two-step Maruyama methods nonlinear stochastic delay differential system Burgers' equation.

Author Details

Wanrong Cao

Zhongqiang Zhang