On Some Difficulties in Integrating Highly Oscillatory Hamiltonian Systems

Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 4)


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.


Hamiltonian System Vibrational Energy Oscillatory System Implicit Method Symplectic Integrator 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and Department of Computer ScienceUniversity of British ColumbiaVancouverCanada
  2. 2.Konrad-Zuse-ZentrumBerlinGermany

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