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.
基金
This work was supported by the NSF of China(No.10901036)and AIRFORCE MURI.The authors thank the referees for their helpful suggestions for improving the paper.The first author also would like to thank Professor George Em Karniadakis for his hospitality when she was visiting Division of Applied Mathematics at Brown University.
