@Article{AAMM-4-821,
author = {Cao , Wanrong and Zhang , Zhongqiang},
title = {Simulations of Two-Step Maruyama Methods for Nonlinear Stochastic Delay Differential Equations},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2012},
volume = {4},
number = {6},
pages = {821--832},
abstract = {<p style="text-align: justify;">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&#39; 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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.12-12S11},
url = {http://global-sci.org/intro/article_detail/aamm/151.html}
}