@Article{JCM-13-64,
author = {Li , Wang-Yao},
title = {On Stability of Symplectic Algorithms},
journal = {Journal of Computational Mathematics},
year = {1995},
volume = {13},
number = {1},
pages = {64--69},
abstract = {<p style="text-align: justify;">The stability of symplectic algorithms is discussed in this paper. There are following conclusions. <br/>1. Symplectic Runge-Kutta methods and symplectic one-step methods with high order derivative are unconditionally critically stable for Hamiltonian systems. Only some of them are A-stable for non-Hamiltonian systems. The criterion of judging A-stability is given. <br/>2. The hopscotch schemes are conditionally critically stable for Hamiltonian systems. Their stability regions are only a segment on the imaginary axis for non-Hamiltonian systems. <br/>3. All linear symplectic multistep methods are conditionally critically stable except the trapezoidal formula which is unconditionally critically stable for Hamiltonian systems. Only the trapezoidal formula is A-stable, and others only have segments on the imaginary axis as their stability regions for non-Hamiltonian systems. &nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/9251.html}
}