Error analysis of discrete conservation laws for Hamiltonian PDEs under the central box discretizations

The central box scheme has been the most successful of the multisymplectic integrators for Hamiltonian PDEs. In this paper, we investigate conservative properties of the central box scheme for Hamiltonian PDEs and derive the error formulas of discrete local and global conservation laws of energy and momentum. We apply these results to the nonlinear Schrödinger equation and Klein-Gordon equation. Numerical experiments are presented to verify the theoretical predications.