Symplectic schemes for highly oscillatory Hamiltonian systems with varying fast frequencies |
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| Authors: | Matthew Dobson Claude Le Bris Frédéric Legoll |
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| Affiliation: | 1. CERMICS, École des Ponts ParisTech, 77455 Marne-La-Vallée cedex 2, France;2. Institut Navier, LAMI, École des Ponts ParisTech, 77455 Marne-La-Vallée cedex 2, France;3. INRIA Rocquencourt, MICMAC project, domaine de Voluceau, B.P. 105, 78153 Le Chesnay cedex, France |
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| Abstract: | We derive symplectic integrators for a class of highly oscillatory Hamiltonian systems. Our approach is based upon a two-scale expansion of the solution to the Hamilton–Jacobi equation associated to the original dynamics. This Note presents an extension of the approach previously introduced in Le Bris and Legoll (2007, 2010) [10], [11] to the case where the fast frequencies of the system, instead of being constant, explicitly depend on the slow degrees of freedom. |
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