High order numerical integrators for single integrand Stratonovich SDEs

David Cohen; Kristian Debrabant; Andreas Rößler

doi:10.1016/j.apnum.2020.08.002

paper

High order numerical integrators for single integrand Stratonovich SDEs

arXiv:2004.12887 · doi:10.1016/j.apnum.2020.08.002

Abstract

We show that applying any deterministic B-series method of order $p_{d}$ with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and weak sense with order $⌊ p_{d} /2 ⌋$ .As an application, we derive high order energy-preserving methods for stochastic Poisson systems as well as further geometric numerical schemes for this wide class of Stratonovich SDEs.