Preservation of equilibria for symplectic methods applied to Hamiltonian systems |
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| Authors: | Ling-shu Wang Ying Wang |
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| Institution: | (1) Department of Informatics and Computer Technology, Technological Educational Institute of Western Macedonia at Kastoria, P.O. Box 30, 521 00 Kastoria, Greece;(2) Department of International Trade, Technological Educational Institute of Western Macedonia at Kastoria, P.O. Box 30, 521 00 Kastoria, Greece;(3) Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Science and Technology, University of Peloponnessos, 22100 Tripolis, Greece;(4) Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia; |
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| Abstract: | In this paper, the linear stability of symplectic methods for Hamiltonian systems is studied. In particular, three classes
of symplectic methods are considered: symplectic Runge-Kutta (SRK) methods, symplectic partitioned Runge-Kutta (SPRK) methods
and the composition methods based on SRK or SPRK methods. It is shown that the SRK methods and their compositions preserve
the ellipticity of equilibrium points unconditionally, whereas the SPRK methods and their compositions have some restrictions
on the time-step. |
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| Keywords: | Hamiltonian systems elliptic equilibrium points symplectic methods |
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