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Structure-preserving algorithms and algorithms with uniform error bound haveconstituted two interesting classes of numerical methods. In this paper, weblend these two kinds of methods for solving nonlinear Hamiltonian systems withhighly oscillatory solution, and the blended algorithms inherit and respect theadvantage of each method. Two kinds of algorithms are presented to preserve thesymplecticity and energy of the Hamiltonian systems, respectively. Moreover,the proposed algorithms are shown to have uniform error bound for the highlyoscillatory structure. A numerical experiment is carried out to support thetheoretical results established in this paper by showing the performance of theblended algorithms.

Structure-preserving algorithms with uniform error bound and long-time energy conservation for highly oscillatory Hamiltonian systems