An Isaac Newton Institute Workshop

Effective Computational Methods for Highly Oscillatory Problems: The Interplay between Mathematical Theory and Applications

Partitioned Runge-Kutta methods in space and time

Author: Robert McLachlan (IFS, Massey University)

Abstract

In a partitioned RK (PRK) method, different coefficients are used for different variables. This allows, for example, explicit symplectic integrators for separable Hamiltonians; in fact, these are a special case of splitting methods. There also exist implicit symplectic PRK methods, but these seem to have no clear application, since non- partitioned (Gauss) methods dominate them. Recently, a possible application has emerged for implicit symplectic PRK methods in the spatial discretization of Hamiltonian PDEs. Here they can yield stable multisymplectic methods, while by contrast, explicit PRK methods are unconditionally unstable.