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The BDF2-Maruyama Scheme for Stochastic Evolution Equations with Monotone Drift (2105.08767v1)
Published 18 May 2021 in math.NA and cs.NA
Abstract: We study the numerical approximation of stochastic evolution equations with a monotone drift driven by an infinite-dimensional Wiener process. To discretize the equation, we combine a drift-implicit two-step BDF method for the temporal discretization with an abstract Galerkin method for the spatial discretization. After proving well-posedness of the BDF2-Maruyama scheme, we establish a convergence rate of the strong error for equations under suitable Lipschitz conditions. We illustrate our theoretical results through various numerical experiments and compare the performance of the BDF2-Maruyama scheme to the backward Euler--Maruyama scheme.