CLOSED NEWTON–COTES TRIGONOMETRICALLY-FITTED FORMULAE FOR LONG-TIME INTEGRATION

T. E. Simos ()
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T. E. Simos: Department of Computer Science and Technology, Faculty of Science and Technology, University of Peloponnese, University Campus, GR-221 00 Tripolis, Greece

International Journal of Modern Physics C (IJMPC), 2003, vol. 14, issue 08, 1061-1074

Abstract: The connection between closed Newton–Cotes, trigonometrically-fitted differential methods and symplectic integrators is investigated in this paper. It is known from the literature that several one-step symplectic integrators have been obtained based on symplectic geometry. However, the investigation of multistep symplectic integrators is very poor. Zhuet al.2presented the well known open Newton–Cotes differential methods as multilayer symplectic integrators. Chiou and Wu2also investigated the construction of multistep symplectic integrators based on the open Newton–Cotes integration methods. In this paper we investigate the closed Newton–Cotes formulae and we write them as symplectic multilayer structures. After this we construct trigonometrically-fitted symplectic methods which are based on the closed Newton–Cotes formulae. We apply the symplectic schemes in order to solve Hamilton's equations of motion which are linear in position and momentum. We observe that the Hamiltonian energy of the system remains almost constant as integration procceeds.

Keywords: Closed Newton–Cotes differential methods; symplectic integrators; multistep methods; trigonometric fitting; energy preservation (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S0129183103005248

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