Year: 1995
Author: Wang-Yao Li
Journal of Computational Mathematics, Vol. 13 (1995), Iss. 1 : pp. 64–69
Abstract
The stability of symplectic algorithms is discussed in this paper. There are following conclusions.
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.
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.
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1995-JCM-9251
Journal of Computational Mathematics, Vol. 13 (1995), Iss. 1 : pp. 64–69
Published online: 1995-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 6