@Article{JCM-22-5,
author = {Liu, Hongyu and Sun, Geng},
title = {Symplectic RK Methods and Symplectic PRK Methods with Real Eigenvalues},
journal = {Journal of Computational Mathematics},
year = {2004},
volume = {22},
number = {5},
pages = {769--776},
abstract = {<p style="text-align: justify;">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&#39;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.</p>},
issn = {1991-7139},
doi = {https://doi.org/2004-JCM-10302},
url = {https://global-sci.com/article/85260/symplectic-rk-methods-and-symplectic-prk-methods-with-real-eigenvalues}
}