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Preservation of equilibria for symplectic methods applied to Hamiltonian systems

Preservation of equilibria for symplectic methods applied to Hamiltonian systems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Preservation of equilibria for symplectic methods applied to Hamiltonian systems

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Publisher
Springer Journals
Copyright
Copyright © 2010 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Theoretical, Mathematical and Computational Physics; Math Applications in Computer Science; Applications of Mathematics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-009-7145-2
Publisher site
See Article on Publisher Site

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.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 18, 2010

References