Abstract
AbstractIn this paper, we investigate the numerical performance of a family ofP-stable two-step Maruyama schemes in mean-square sense for stochastic differential equations with time delay proposed in 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.
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