Volume 4, Issue 6
Simulations of Two-Step Maruyama Methods for Nonlinear Stochastic Delay Differential Equations

Wanrong Cao and Zhongqiang Zhang

10.4208/aamm.12-12S11

Adv. Appl. Math. Mech., 4 (2012), pp. 821-832.

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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 [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.

  • History

Published online: 2012-12

  • AMS Subject Headings

65C20, 65C30, 65Q20

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