Local structure-preserving algorithms for general multi-symplectic Hamiltonian PDEs - Cai, Jiaxiang; Wang, Yushun; Jiang, Chaolong (Computer physics communications, 2019)
Many PDEs can be recast into the general multi-symplectic formulation possessing three local conservation laws. We devote the present paper to some systematic methods, which hold the discrete versions of the local conservation laws respectively, for the general multi-symplectic PDEs. For the original problem subjected to appropriate boundary conditions, the proposed methods are globally conservative. The proposed methods are successfully applied to many one-dimensional and multi-dimensional Hamiltonian PDEs, such as KdV equation, G–P equation, Maxwell’s equations and so on. Numerical experiments are carried out to verify the theoretical analysis.