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Analysis, Modeling and Simulation of Multiscale Problems pp 553–576Cite as

Numerical Integrators for Highly Oscillatory Hamiltonian Systems: A Review

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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.

Keywords

  • Hamiltonian System
  • Slow Variable
  • Oscillatory Integral
  • Oscillatory Energy
  • Slow Time Scale

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/3-540-35657-6_20
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Author information

Authors and Affiliations

  1. Mathematisches Institut, Univiversität Tübingen, 72076, Tübingen

    David Cohen, Katina Lorenz & Christian Lubich

  2. Institut für Mathematik II, BioComputing Group, Freie Universität Berlin, Arnimallee 2-6, 14195, Berlin

    Tobias Jahnke

Authors
  1. David Cohen
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  2. Tobias Jahnke
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  3. Katina Lorenz
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  4. Christian Lubich
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Editor information

Editors and Affiliations

  1. Weierstraß-Institut für Angewandte, Analysis und Stochastik, Mohrenstraße 39, 10117, Berlin, Germany

    Alexander Mielke

  2. Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489, Berlin, Germany

    Alexander Mielke

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Cohen, D., Jahnke, T., Lorenz, K., Lubich, C. (2006). Numerical Integrators for Highly Oscillatory Hamiltonian Systems: A Review. In: Mielke, A. (eds) Analysis, Modeling and Simulation of Multiscale Problems. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-35657-6_20

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