Numerical Dispersion Relation of Multi-symplectic Runge-Kutta Methods for Hamiltonian PDEs

摘要

Numerical dispersion relation of the multi-symplectic Runge-Kutta (MSRK) method for linear Hamiltonian PDEs is derived in the present paper, which is shown to be a discrete counterpart to that possessed by the differential equation. This provides further understanding of MSRK methods. However, much still remains to be investigated further.