TY - JOUR
T1 - Long-time analysis of an extended RKN integrator for Hamiltonian systems with a solution-dependent high frequency
AU - Wang, Bin
AU - Wu, Xinyuan
N1 - Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/12/15
Y1 - 2022/12/15
N2 - In this paper, we analyse the long-time behaviour of an extended RKN (ERKN) integrator for solving highly oscillatory Hamiltonian systems with a slowly varying, solution-dependent high frequency. We prove that a symmetric ERKN integrator approximately conserves a modified action and a modified total energy over long time intervals based on the technique of varying-frequency modulated Fourier expansion. An illustrative numerical experiment is carried out and the numerical results strongly support the theoretical analysis presented in this paper. As a byproduct of this work, similar long-time behaviour is also investigated for an RKN method.
AB - In this paper, we analyse the long-time behaviour of an extended RKN (ERKN) integrator for solving highly oscillatory Hamiltonian systems with a slowly varying, solution-dependent high frequency. We prove that a symmetric ERKN integrator approximately conserves a modified action and a modified total energy over long time intervals based on the technique of varying-frequency modulated Fourier expansion. An illustrative numerical experiment is carried out and the numerical results strongly support the theoretical analysis presented in this paper. As a byproduct of this work, similar long-time behaviour is also investigated for an RKN method.
KW - Highly oscillatory Hamiltonian systems
KW - Long-time analysis of extended RKN integrators
KW - RKN methods
KW - Solution-dependent high frequency
KW - Störmer–Verlet method
UR - https://www.scopus.com/pages/publications/85134166008
U2 - 10.1016/j.cam.2022.114545
DO - 10.1016/j.cam.2022.114545
M3 - 文章
AN - SCOPUS:85134166008
SN - 0377-0427
VL - 416
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 114545
ER -