Stochastic conformal multi-symplectic method for damped stochastic nonlinear Schrodinger equation

TL;DR

This paper introduces a stochastic conformal multi-symplectic numerical method tailored for damped stochastic nonlinear Schrödinger equations, preserving key properties and demonstrating superior performance through numerical experiments.

Contribution

The paper develops a novel stochastic conformal multi-symplectic method that maintains intrinsic properties of damped stochastic Hamiltonian PDEs, with proven conservation laws and convergence analysis.

Findings

Preserves discrete stochastic conformal multi-symplectic law

Almost surely maintains discrete charge exponential dissipation

Numerical experiments confirm good performance and convergence

Abstract

In this paper, we propose a stochastic conformal multi-symplectic method for a class of damped stochastic Hamiltonian partial differential equations in order to inherit the intrinsic properties, and apply the numerical method to solve a kind of damped stochastic nonlinear Schrodinger equation with multiplicative noise. It is shown that the stochastic conformal multi-symplectic method preserves the discrete stochastic conformal multi-symplectic conservation law, the discrete charge exponential dissipation law almost surely, and we also deduce the recurrence relation of the discrete global energy. Numerical experiments are preformed to verify the good performance of the proposed stochastic conformal multi-symplectic method, compared with a Crank-Nicolson type method. Finally, we present the mean square convergence result of the proposed numerical method in temporal direction numerically.