1999 | OriginalPaper | Buchkapitel
On Some Difficulties in Integrating Highly Oscillatory Hamiltonian Systems
verfasst von : Uri M. Ascher, Sebastian Reich
Erschienen in: Computational Molecular Dynamics: Challenges, Methods, Ideas
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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The numerical integration of highly oscillatory Hamiltonian systems, such as those arising in molecular dynamics or Hamiltonian partial differential equations, is a challenging task. Various methods have been suggested to overcome the step-size restrictions of explicit methods such as the Verlet method. Among these are multiple-time-stepping, constrained dynamics, and implicit methods. In this paper, we investigate the suitability of time-reversible, semi-implicit methods. Here semi-implicit means that only the highly oscillatory part is integrated by an implicit method such as the midpoint method or an energy-conserving variant of it. The hope is that such methods will allow one to use a step-size k which is much larger than the period e of the fast oscillations.