The BDF2-Maruyama Scheme for Stochastic Evolution Equations with Monotone Drift
Numerical Analysis
2021-05-20 v1 Numerical Analysis
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.
Cite
@article{arxiv.2105.08767,
title = {The BDF2-Maruyama Scheme for Stochastic Evolution Equations with Monotone Drift},
author = {Raphael Kruse and Rico Weiske},
journal= {arXiv preprint arXiv:2105.08767},
year = {2021}
}