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Volume 8, Issue 1
Comparison of a Spectral Collocation Method and Symplectic Methods for Hamiltonian Systems

N. Kanyamee & Z. Zhang

Int. J. Numer. Anal. Mod., 8 (2011), pp. 86-104.

Published online: 2011-08

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  • Abstract

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.

  • Keywords

Hamiltonian systems, spectral method, collocation, symplectic structure, energy conservation.

  • AMS Subject Headings

65N20, 49J40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-86, author = {N. Kanyamee and Z. Zhang}, title = {Comparison of a Spectral Collocation Method and Symplectic Methods for Hamiltonian Systems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {1}, pages = {86--104}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/675.html} }
TY - JOUR T1 - Comparison of a Spectral Collocation Method and Symplectic Methods for Hamiltonian Systems AU - N. Kanyamee & Z. Zhang JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 86 EP - 104 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/675.html KW - Hamiltonian systems, spectral method, collocation, symplectic structure, energy conservation. AB -

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.

N. Kanyamee and Z. Zhang. (2011). Comparison of a Spectral Collocation Method and Symplectic Methods for Hamiltonian Systems. International Journal of Numerical Analysis and Modeling. 8 (1). 86-104. doi:
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