Energy-conserving numerical methods for multi-symplectic Hamiltonian PDEs

Abstract

In this paper, the discrete gradient methods are investigated for ODEs with first integral, and the recursive formula is presented for deriving the high-order numerical methods. We generalize the idea of discrete gradient methods to PDEs and construct the high-order energypreserving numerical methods for multi-symplectic Hamiltonian PDEs. By integrating nonlinear Schrödinger equation, some numerical experiments are presented to demonstrate the conservative property of the proposed numerical methods.

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Cite this paper

@inproceedings{Hong2007EnergyconservingNM, title={Energy-conserving numerical methods for multi-symplectic Hamiltonian PDEs}, author={Jialin Hong and Yajuan Sun}, year={2007} }