Uniformly accurate structure-preserving algorithms for nonlinear Hamiltonian systems with highly oscillatory solution
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Uniformly accurate algorithms and structure-preserving algorithms constitute two interesting classes of numerical methods. In this paper, we combine these two kinds of methods for solving Hamiltonian systems with highly oscillatory solution and the obtained algorithms respect the advantage of each method. Two kinds of algorithms are presented to preserve the symplecticity and energy of the Hamiltonian systems. Moreover, the algorithms are shown to be uniformly accurate for the highly oscillatory structure. A numerical experiment is carried out to support the theoretical results by showing the performance of the obtained algorithms.
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