Abstract
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.
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Acknowledgements
The idea of combining spectral accurate discretizations in space and time resulted from interesting discussions of the first author with Volker Mehrmann at the ANODE 2018 Conference. The authors wish also to thank the anonimous referees, for their comments.
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Dedicated to John Butcher, on the occasion of his 85-th birthday
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Brugnano, L., Iavernaro, F., Montijano, J.I. et al. Spectrally accurate space-time solution of Hamiltonian PDEs. Numer Algor 81, 1183–1202 (2019). https://doi.org/10.1007/s11075-018-0586-z
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DOI: https://doi.org/10.1007/s11075-018-0586-z
Keywords
- Multi-frequency highly oscillatory problems
- Stiffly oscillatory problems
- Hamiltonian problems
- Energy-conserving methods
- Spectral methods
- Legendre polynomials
- Hamiltonian boundary value methods