Stochastic conformal multi-symplectic method for damped stochastic nonlinear Schrodinger equation
For researchers in numerical methods for stochastic PDEs, this work provides a structure-preserving scheme for damped stochastic Hamiltonian systems, but it is incremental as it extends existing conformal multi-symplectic ideas to the stochastic setting.
The paper proposes a stochastic conformal multi-symplectic method for damped stochastic Hamiltonian PDEs, applied to the damped stochastic nonlinear Schrödinger equation, and shows it preserves discrete conservation laws and charge dissipation. Numerical experiments demonstrate better performance than a Crank-Nicolson method.
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.