TY - JOUR
T1 - On Stability of Symplectic Algorithms
AU - Li , Wang-Yao
JO - Journal of Computational Mathematics
VL - 1
SP - 64
EP - 69
PY - 1995
DA - 1995/02
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9251.html
KW - 
AB - <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>