Multi-symplectic Runge–Kutta-type methods for Hamiltonian wave equations

Abstract

The non-linear wave equation is taken as a model problem for the investigation. Different multi-symplectic reformulations of the equation are discussed. Multi-symplectic Runge–Kutta methods and multi-symplectic partitioned Runge–Kutta methods are explored based on these different reformulations. Some popular and efficient multi-symplectic schemes are collected and constructed. Stability analyses are performed for these schemes.