High Order Multisymplectic Runge-Kutta Methods

We study the spatial semidiscretizations obtained by applying Runge–Kutta (RK) and partitioned Runge–Kutta (PRK) methods to multisymplectic Hamiltonian partial differential equations. These methods can be regarded as multisymplectic hp-finite element methods for wave equations. All the methods we consider are multisymplectic; we determine their properties with regard to existence of solutions, dispersion, and order. The Lobatto IIIA–IIIB PRK method can lead to explicit ODEs and exhibits a surprisingly high order of 2 higher than the number of degrees of freedom per cell.