TY - JOUR
T1 - Symplectic RK Methods and Symplectic PRK Methods with Real Eigenvalues
AU - Liu , Hongyu
AU - Sun , Geng
JO - Journal of Computational Mathematics
VL - 5
SP - 769
EP - 776
PY - 2004
DA - 2004/10
SN - 22
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/10302.html
KW - Runge-Kutta method, Partitioned Runge-Kutta method, Symplectic, Real eigenvalues.
AB - <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>