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Numerical integrators for highly oscillatory Hamiltonian systems: a review. (English) Zbl 1367.65191
Mielke, Alexander (ed.), Analysis, modeling and simulation of multiscale problems. Berlin: Springer (ISBN 3-540-35656-8/hbk). 553-576 (2006).
Summary: Numerical methods for oscillatory, multi-scale Hamiltonian systems are reviewed. The construction principles are described, and the algorithmic and analytical distinction between problems with nearly constant high frequencies and with time- or state-dependent frequencies is emphasized. Trigonometric integrators for the first case and adiabatic integrators for the second case are discussed in more detail.
For the entire collection see [Zbl 1105.35002].

MSC:
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
70-08 Computational methods for problems pertaining to mechanics of particles and systems
70H05 Hamilton’s equations
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