Exponential Discrete Gradient Schemes for Stochastic Differential Equations

TL;DR

This paper introduces exponential discrete gradient schemes for stochastic differential equations, analyzing their error properties and structure-preserving features, supported by numerical experiments.

Contribution

The paper proposes a new class of stochastic exponential discrete gradient schemes tailored for SDEs with specific coefficient structures, with theoretical and numerical validation.

Findings

Root mean-square errors are rigorously analyzed.

Schemes preserve structure for special SDEs.

Numerical tests confirm theoretical predictions.

Abstract

In this paper, we propose a class of stochastic exponential discrete gradient schemes for SDEs with linear and gradient components in the coefficients. The root mean-square errors of the schemes are analyzed, and the structure-preserving properties of the schemes for SDEs with special structures are investigated. Numerical tests are performed to verify the theoretical results and illustrate the numerical behavior of the proposed methods.