  It is well-known that a numerical method which is at the same time geometric
structure-preserving and physical property-preserving cannot exist in general
for Hamiltonian partial differential equations. In this paper, we present a
novel class of parametric multi-symplectic Runge-Kutta methods for Hamiltonian
wave equations, which can also conserve energy simultaneously in a weaker sense
with a suitable parameter. The existence of such a parameter, which enforces
the energy-preserving property, is proved under certain assumptions on the
fixed step sizes and the fixed initial condition. We compare the proposed
method with the classical multi-symplectic Runge-Kutta method in numerical
experiments, which shows the remarkable energy-preserving property of the
proposed method and illustrate the validity of theoretical results.

Numerical Analysis;Numerical Analysis