B-series for SDEs with application to exponential integrators for non-autonomous semi-linear problems

Abstract

In this paper a set of previous general results for the development of B–series for a broad class of stochastic differential equations has been col- lected. The applicability of these results is demonstrated by the derivation of B–series for non-autonomous semi-linear SDEs and exponential Runge-Kutta methods applied to this class of SDEs, which is a significant generalization of existing theory on such methods.

B-series for SDEs with application to exponential integrators for non-autonomous semi-linear problems