Exponential Discrete Gradient Schemes for Stochastic Differential Equations
This work provides new numerical methods for solving stochastic differential equations, which is relevant for researchers in computational mathematics and physics.
The paper proposes exponential discrete gradient schemes for SDEs with linear and gradient components, analyzes their root mean-square errors, and investigates structure-preserving properties. Numerical tests confirm theoretical results.
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.