Long-time energy analysis of extended RKN integrators for muti-frequency highly oscillatory Hamiltonian systems

2018/04/23 by Wang, Bin, Wu, Xinuan
#65L05 #65P10 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1804.08318

Abstract

In this paper, we study the long-time near conservation of the total and oscillatory energies for extended RKN (ERKN) integrators when applied to muti-frequency highly oscillatory Hamiltonian systems. We consider one-stage explicit symmetric integrators and show their long-time behaviour of numerical energy conservations by using modulated multi-frequency Fourier expansions. Numerical experiments are carried out and the numerical results demonstrate the remarkable long-time near conservation of the energies for the ERKN integrators and support our theoretical analysis presented in this paper.

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