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