Long-time analysis of extended RKN integrators for Hamiltonian systems with a solution-dependent high frequency

2018/03/21 by Wang, Bin, Wu, Xinyuan
#65L05 #65P10 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1803.07861

Abstract

In this paper, we analyse the long-time behaviour of the extended RKN (ERKN) integrators 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.

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