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Recently, the numerical solution of stiffly/highly-oscillatory Hamiltonianproblems has been attacked by using Hamiltonian Boundary Value Methods (HBVMs)as spectral methods in time. While a theoretical analysis of this spectralapproach has been only partially addressed, there is enough numerical evidencethat it turns out to be very effective even when applied to a wider range ofproblems. Here we fill this gap by providing a thorough convergence analysis ofthe methods and confirm the theoretical results with the aid of a few numericaltests.

Analysis of Spectral Hamiltonian Boundary Value Methods (SHBVMs) for the numerical solution of ODE problems