TY - JOUR T1 - Simulations of Two-Step Maruyama Methods for Nonlinear Stochastic Delay Differential Equations AU - Cao , Wanrong AU - Zhang , Zhongqiang JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 821 EP - 832 PY - 2012 DA - 2012/12 SN - 4 DO - http://doi.org/10.4208/aamm.12-12S11 UR - https://global-sci.org/intro/article_detail/aamm/151.html KW - P-stability in mean-square sense, two-step Maruyama methods, nonlinear stochastic delay differential system, Burgers' equation. AB -

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.