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Recently, the numerical solution of multi-frequency, highly-oscillatoryHamiltonian problems has been attacked by using Hamiltonian Boundary ValueMethods (HBVMs) as spectral methods in time. When the problem derives from thespace semi- discretization of (possibly Hamiltonian) partial differentialequations (PDEs), the resulting problem may be stiffly-oscillatory, rather thanhighly-oscillatory. In such a case, a different implementation of the methodsis needed, in order to gain the maximum efficiency.

Spectrally accurate space-time solution of Hamiltonian PDEs