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Integrators for highly oscillatory Hamiltonian systems: an homogenization approach

Abstract : We introduce a systematic way to construct symplectic schemes for the numerical integration of a large class of highly oscillatory Hamiltonian systems. The bottom line of our construction is to consider the Hamilton-Jacobi form of the Newton equations of motion, and to perform a two-scale expansion of the solution, for small times and high frequencies. The approximation obtained for the solution is then used as a generating function, from which the numerical scheme is derived. Several options for the derivation are presented, some of them also giving rise to non symplectic variants. The various integrators obtained are tested and compared to several existing algorithms. The numerical results demonstrate their efficiency.
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Contributor : Frederic Legoll Connect in order to contact the contributor
Submitted on : Monday, July 30, 2007 - 9:17:20 PM
Last modification on : Friday, February 4, 2022 - 3:09:17 AM
Long-term archiving on: : Tuesday, September 21, 2010 - 1:42:44 PM


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  • HAL Id : inria-00165293, version 2


Claude Le Bris, Frédéric Legoll. Integrators for highly oscillatory Hamiltonian systems: an homogenization approach. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2010, 13 (2), pp.347-373. ⟨inria-00165293v2⟩



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