HIGH ORDER MULTISYMPLECTIC RUNGE-KUTTA METHODS

摘要

We study the spatial semidiscretizations obtained by applying Runge-Kutta (RK) and partitioned Runge-Kutta (PRK) methods to multisymplectic Hamiltonian PDEs. 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.