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.
P-stability in mean-square sense two-step Maruyama methods nonlinear stochastic delay differential system Burgers' equation