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

TL;DR

This paper introduces Lawson schemes for highly oscillatory stochastic differential equations that preserve quadratic invariants and outperform standard methods in accuracy, offering a novel approach for efficient numerical discretization.

Contribution

The paper develops and analyzes Lawson schemes that preserve invariants and improve accuracy for highly oscillatory stochastic differential equations.

Findings

Midpoint Lawson schemes preserve quadratic invariants.

Numerical experiments show reduced integration error.

Lawson schemes outperform some standard methods.

Abstract

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