Numerical integrations of stochastic contact Hamiltonian systems via stochastic contact Hamilton-Jacobi equation

TL;DR

This paper develops structure-preserving numerical schemes for stochastic contact Hamiltonian systems based on the stochastic contact Hamilton-Jacobi equation, ensuring accurate and convergent simulations of dissipative stochastic dynamics.

Contribution

The paper introduces a novel numerical approximation method for the stochastic contact Hamilton-Jacobi equation with proven convergence, enabling structure-preserving simulations of stochastic contact Hamiltonian systems.

Findings

Numerical schemes preserve the contact structure in stochastic systems.

The proposed method has a proven convergence order.

Numerical tests confirm the effectiveness and accuracy of the approach.

Abstract

Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of the stochastic contact Hamiltonian systems via structure-preserving methods. The contact structure-preserving schemes are constructed by the stochastic contact Hamilton-Jacobi equation. A general numerical approximation method of the stochastic contact Hamilton-Jacobi equation is devised, and the convergent order theorem is provided, too. Numerical tests are shown to confirm the theoretical results and the usability of proposed approach.