期刊
BIT NUMERICAL MATHEMATICS
卷 61, 期 3, 页码 977-1004出版社
SPRINGER
DOI: 10.1007/s10543-021-00846-3
关键词
Long-time energy conservation; Modulated Fourier expansions; Symmetric or symplectic methods; Extended RKN integrators; Highly oscillatory Hamiltonian systems
资金
- National Natural Science Foundation of China [11671200]
This paper presents a long-term analysis of one-stage extended Runge-Kutta-Nystrom integrators for highly oscillatory Hamiltonian systems, showing the near conservation of total and oscillatory energy over a long term for both symmetric and symplectic integrators. By establishing a relationship between ERKN integrators and trigonometric integrators, explicit integrators were proven to have near energy conservation. The technology of modulated Fourier expansion was used for the long-term analysis of implicit integrators, deriving near energy conservation through adaptations of this technology.
This paper presents a long-term analysis of one-stage extended Runge-Kutta-Nystrom (ERKN) integrators for highly oscillatory Hamiltonian systems. We study the long-time numerical energy conservation not only for symmetric integrators but also for symplectic integrators. In the analysis, we neither assume symplecticity for symmetric methods, nor assume symmetry for symplectic methods. It turns out that these both types of integrators have a near conservation of the total and oscillatory energy over a long term. To prove the result for explicit integrators, a relationship between ERKN integrators and trigonometric integrators is established. For the long-term analysis of implicit integrators, the above approach does not work anymore and we use the technology of modulated Fourier expansion. By taking some adaptations of this technology for implicit methods, we derive the modulated Fourier expansion and show the near energy conservation.
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