Spectrally accurate space-time solution of Hamiltonian PDEs

Recently, the numerical solution of multi-frequency, highly oscillatory Hamiltonian problems has been attacked by using Hamiltonian boundary value methods (HBVMs) as spectral methods in time. When the problem derives from the space semi-discretization of (possibly Hamiltonian) partial differential equations (PDEs), the resulting problem may be stiffly oscillatory, rather than highly oscillatory. In such a case, a different implementation of the methods is needed, in order to gain the maximum efficiency.