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HIGH-ORDER SYMPLECTIC AND SYMMETRIC COMPOSITION METHODS FOR MULTI-FREQUENCY AND MULTI-DIMENSIONAL OSCILLATORY HAMILTONIAN SYSTEMS
Ist Teil von
Journal of computational mathematics, 2015-07, Vol.33 (4), p.356-378
Ort / Verlag
Chinese Academy of Mathematices and System Sciences (AMSS) Chinese Academy of Sciences
Erscheinungsjahr
2015
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
The multi-frequency and multi-dimensional adapted Runge-Kutta~NystrSm （ARKN） integrators, and multi-frequency and multi-dimensional extended Runge-Kutta-NystrSm （ERKN） integrators have been developed to efficiently solve multi-frequency oscillatory Hamiltonian systems. The aim of this paper is to analyze and derive high-order sym- plectic and symmetric composition methods based on the ARKN integrators and ERKN integrators. We first consider the symplecticity conditions for the multi-frequency and multi-dimensional ARKN integrators. We then analyze the symplecticity of the adjoint in- tegrators of the multi-frequency and multi~dimensional symplectic ARKN integrators and ERKN integrators, respectively. On the basis of the theoretical analysis and by using the idea of composition methods, we derive and propose four new high-order symplectic and symmetric methods for the multi-frequency oscillatory Hamiltonian systems. The numer- ical results accompanied in this paper quantitatively show the advantage and efficiency of the proposed high-order symplectic and symmetric methods.