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Integrators for highly oscillatory Hamiltonian systems: An homogenization approach

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  • We introduce a systematic way to build 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. The various integrators obtained are tested and compared to several existing algorithms. The numerical results demonstrate their efficiency.
    Mathematics Subject Classification: Primary: 70K70, 37M15, 70H20, 65P10.


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