Symplectic RK Methods and Symplectic PRK Methods with Real Eigenvalues

Symplectic RK Methods and Symplectic PRK Methods with Real Eigenvalues

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.

Author Details

Hongyu Liu

Geng Sun