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

被引：3
|
作者：
Cao, Wanrong [1 ,2 ]
Zhang, Zhongqiang [2 ]
机构：
[1] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China
[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2012年 / 4卷 / 06期
关键词：
P-stability in mean-square sense; two-step Maruyama methods; nonlinear stochastic delay differential system; Burgers' equation; EXPONENTIAL STABILITY; NUMERICAL-SOLUTIONS; MULTISTEP METHODS; CONVERGENCE;
D O I：
10.4208/aamm.12-12S11
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：821 / 832
页数：12
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