Year: 2004
Author: Hongyu Liu, Geng Sun
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 5 : pp. 769–776
Abstract
Properties of symplectic Runge-Kutta (RK) methods and symplectic partitioned Runge- Kutta (PRK) methods with real eigenvalues are discussed in this paper. It is shown that an $s$ stage such method can't reach order more than $s + 1$. Particularly, we prove that no symplectic RK method with real eigenvalues exists in stage $s$ of order $s + 1$ when $s$ is even. But an example constructed by using the W-transformation shows that PRK method of this type does not necessarily meet this order barrier. Another useful way other than W-transformation to construct symplectic PRK method with real eigenvalues is then presented. Finally, a class of efficient symplectic methods is recommended.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JCM-10302
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 5 : pp. 769–776
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Runge-Kutta method Partitioned Runge-Kutta method Symplectic Real eigenvalues.