Comparison of a spectral collocation method and symplectic methods for Hamiltonian systems
N. Kanyamee 1, Z. Zhang 11 Department of Mathematics, Wayne State University, Detroit, MI 48202, USA.
Received by the editors June 1, 2009 and, in revised form, March 22, 2010.
We conduct a systematic comparison of a spectral collocation method with some symplectic methods in solving Hamiltonian dynamical systems. Our main emphasis is on non-linear problems. Numerical evidence has demonstrated that the proposed spectral collocation method preserves both energy and symplectic structure up to the machine error in each time (large) step, and therefore has a better long time behavior.AMS subject classifications: 65N20, 49J40
Key words: Hamiltonian systems, spectral method, collocation, symplectic structure, energy conservation.
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