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arXiv · 1803.00139

Stochastic multi-symplectic Runge-Kutta methods for stochastic Hamiltonian PDEs

Liying Zhang·Lihai Ji
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Abstract

In this paper, we consider stochastic Runge-Kutta methods for stochastic Hamiltonian partial differential equations and present some sufficient conditions for multisymplecticity of stochastic Runge-Kutta methods of stochastic Hamiltonian partial differential equations. Particularly, we apply these ideas to stochastic Maxwell equations with multiplicative noise, possessing the stochastic multi-symplectic conservation law and energy conservation law. Theoretical analysis shows that the methods can preserve both the discrete stochastic multi-symplectic conservation law and discrete energy conservation law almost surely.

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Liying Zhang, Lihai Ji. 2018-02-28. Stochastic multi-symplectic Runge-Kutta methods for stochastic Hamiltonian PDEs. https://arxiv.org/abs/1803.00139

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