The BDF2-Maruyama Scheme for Stochastic Evolution Equations with Monotone Drift [article]

Raphael Kruse, Rico Weiske
2021 arXiv   pre-print
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
more » ... etical results through various numerical experiments and compare the performance of the BDF2-Maruyama scheme to the backward Euler--Maruyama scheme.
arXiv:2105.08767v1 fatcat:lfxepcoasrbztomnsquxnc5bxa