Lawson schemes for highly oscillatory stochastic differential equations and conservation of invariants

Abstract

In this paper, we consider a class of stochastic midpoint and trapezoidal Lawson schemes for the numerical discretization of highly oscillatory stochastic differen- tial equations. These Lawson schemes incorporate both the linear drift and diffusion terms in the exponential operator. We prove that the midpoint Lawson schemes pre- serve quadratic invariants and discuss this property as well for the trapezoidal Lawson scheme. Numerical experiments demonstrate that the integration error for highly oscil- latory problems is smaller than that of some standard methods.

Lawson schemes for highly oscillatory stochastic differential equations and conservation of invariants