Exponentially fitted open Newton-Cotes differential methods as multilayer symplectic integrators.
Classical open and closed Newton-Cotes differential methods possessing the characteristics of multilayer symplectic structures have been constructed in the past. In this paper, we study the exponentially fitted open Newton-Cotes differential methods of order two, four, and six. It is shown that these integrators, just as their classical counterparts, preserve the volume in the phase space of a Hamiltonian system. They can be converted into a multilayer symplectic structure so that volume-preserving integrators of a Hamiltonian system are obtained. A numerical example has been carried out to show the effectiveness of the present differential method.
Vakgroep Toegepaste Wiskunde en Informatica, Universiteit Gent, Krijgslaan 281-S9, B-9000 Gent, Belgium. guido.vandenberghe@ugent.be
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Vanden Berghe
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Van Daele