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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

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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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