Year: 1998
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 3 : pp. 193–202
Abstract
In this paper, we propose a new definition of symplectic multistep methods. This definition differs from the old ones in that it is given via the one step method defined directly on $M$ which is corresponding to the $m$ step scheme defined on $M$ while the old definitions are given out by defining a corresponding one step method on $M\times M \times \cdots \times M=M^m$ with a set of new variables. The new definition gives out a step-transition operator $g: M\longrightarrow M$. Under our new definition, the Leap-frog method is symplectic only for linear Hamiltonian systems. The transition operator $g$ will be constructed via continued fractions and rational approximations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1998-JCM-9152
Journal of Computational Mathematics, Vol. 16 (1998), Iss. 3 : pp. 193–202
Published online: 1998-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Multi-step methods Explike and loglike function Fractional and rational approximation Simplecticity of LMM Nonexistence of SLMM.