On the Numerical Stability of Some Symplectic Integrators
Fuyao Liu1; Xin Wu2; Benkui Lu1
Source PublicationChinese Astronomy and Astrophysics
AbstractIn this paper, we analyze the linear stabilities of several symplectic integrators, such as the first-order implicit Euler scheme, the second-order implicit mid-point Euler difference scheme, the first-order explicit Euler scheme, the second-order explicit leapfrog scheme and some of their combinations. For a linear Hamiltonian system, we find the stable regions of each scheme by theoretical analysis and check them by numerical tests. When the Hamiltonian is real symmetric quadratic, a diagonalizing by a similar transformation is suggested so that the theoretical analysis of the linear stability of the numerical method would be simplified. A Hamiltonian may be separated into a main part and a perturbation, or it may be spontaneously separated into kinetic and potential energy parts, but the former separation generally is much more charming because it has a much larger maximum step size for the symplectic being stable, no matter this Hamiltonian is linear or nonlinear.
Document Type期刊论文
First Author Affilication中国科学院紫金山天文台
Recommended Citation
GB/T 7714
Fuyao Liu,Xin Wu,Benkui Lu. On the Numerical Stability of Some Symplectic Integrators[J]. Chinese Astronomy and Astrophysics,2007,31(2):172.
APA Fuyao Liu,Xin Wu,&Benkui Lu.(2007).On the Numerical Stability of Some Symplectic Integrators.Chinese Astronomy and Astrophysics,31(2),172.
MLA Fuyao Liu,et al."On the Numerical Stability of Some Symplectic Integrators".Chinese Astronomy and Astrophysics 31.2(2007):172.
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