High order numerical integrators for single integrand Stratonovich SDEs
Journal article, 2020
We show that applying any deterministic B-series method of order pd with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and weak sense with order left perpendicular pd/2 right perpendicular. 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.
Strong error
High order
Weak error
Stratonovich stochastic differential equation
Geometric numerical integration
B-series methods
Single integrand SDEs
Author
David Cohen
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Umeå University
Kristian Debrabant
University of Southern Denmark
Andreas Rößler
Universitaet Zu Lübeck
Applied Numerical Mathematics
0168-9274 (ISSN)
Vol. 158 264-270Numerical analysis and simulation of PDEs with random dispersion
Swedish Research Council (VR) (2018-04443), 2019-01-01 -- 2022-12-31.
Subject Categories
Computational Mathematics
DOI
10.1016/j.apnum.2020.08.002