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Commun. Comput. Phys., 14 (2013), pp. 393-411.
Published online: 2014-08
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In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations, and develop a stochastic multi-symplectic method for numerically solving a kind of stochastic nonlinear Schrödinger equations. It is shown that the stochastic multi-symplectic method preserves the multi-symplectic structure, the discrete charge conservation law, and deduces the recurrence relation of the discrete energy. Numerical experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision.
In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations, and develop a stochastic multi-symplectic method for numerically solving a kind of stochastic nonlinear Schrödinger equations. It is shown that the stochastic multi-symplectic method preserves the multi-symplectic structure, the discrete charge conservation law, and deduces the recurrence relation of the discrete energy. Numerical experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision.