@Article{JCM-16-193,
author = {K. Feng},
title = {The Step-Transition Operators for Multi-Step Methods of ODE's},
journal = {Journal of Computational Mathematics},
year = {1998},
volume = {16},
number = {3},
pages = {193--202},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/9152.html}
}