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Journal Articles IMA Journal of Numerical Analysis Year : 2013

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.

Dates and versions

hal-00524814 , version 1 (08-10-2010)

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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, 2013, 33 (1), pp.30-56. ⟨10.1093/imanum/drs005⟩. ⟨hal-00524814⟩
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