Simulations of Two-Step Maruyama Methods for Nonlinear Stochastic Delay Differential Equations (Advances in Applied Mathematics and Mechanics, 2021)
In this paper, we investigate the numerical performance of a family of P-stable two-step Maruyama schemes in mean-square sense for stochastic differentialequations with time delay proposed in [8, 10] for a certainclass of nonlinear stochastic delay differential equationswith multiplicative white noises.We also test the convergence of one of the schemes fora time-delayed Burgers' equation with an additive white noise. Numerical results show thatthis family of two-step Maruyama methods exhibit similar stability for nonlinear equationsas that for linear equations.