@Article{JCM-25-6,
author = {},
title = {Non-Existence of Conjugate-Symplectic Multi-Step Methods of Odd Order},
journal = {Journal of Computational Mathematics},
year = {2007},
volume = {25},
number = {6},
pages = {690--696},
abstract = {<p style="text-align: justify;">We prove that any linear multi-step method $G_1^{\tau}$ of the form $$\sum^{m}_{k=0}\alpha _k Z_{k}=\tau \sum^{m}_{k=0}\beta _k J^{-1}\nabla H(Z_k)$$ with odd order $u$ ($u\ge 3$) cannot be conjugate to a symplectic method $G_2^{\tau}$ of order $w$ ($w\ge u$) via any generalized linear multi-step method $G_3^{\tau}$ of the form $$\sum^m_{k=0} \alpha_k Z_k = \tau\sum^m_{k=0} \beta_k J^{-1}\nabla H(\sum^m_{l=0}\gamma_{kl}Z_l).$$ We also give a necessary condition for this kind of generalized linear multi-step methods to be conjugate-symplectic. We also demonstrate that these results can be easily extended to the case when $G_3^{\tau}$ is a more general operator.</p>},
issn = {1991-7139},
doi = {https://doi.org/2007-JCM-8722},
url = {https://global-sci.com/article/85043/non-existence-of-conjugate-symplectic-multi-step-methods-of-odd-order}
}