Symplectic schemes for highly oscillatory Hamiltonian systems: the homogenization approach beyond the constant frequency case

Abstract : We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach considers the Hamilton-Jacobi form of the equations of motion, formally homogenizes it and infers an appropriate symplectic integrator for the original system. In our previous work, the case of a system exhibiting a single constant fast frequency was considered. The present work successfully extends the approach to systems that have either one varying fast frequency or several constant frequencies. Some related issues are also examined.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00524814
Contributor : Frederic Legoll <>
Submitted on : Friday, October 8, 2010 - 6:24:10 PM
Last modification on : Thursday, February 7, 2019 - 4:21:42 PM

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  • HAL Id : hal-00524814, version 1
  • ARXIV : 1008.1030

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Matthew Dobson, Claude Le Bris, Frédéric Legoll. Symplectic schemes for highly oscillatory Hamiltonian systems: the homogenization approach beyond the constant frequency case. IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2013, 33 (1), pp.30-56. ⟨hal-00524814⟩

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