@Article{JCM-24-45,
author = {},
title = {Expansions of Step-Transition Operators of Multi-Step Methods and Order Barriers for Dahlquist Pairs},
journal = {Journal of Computational Mathematics},
year = {2006},
volume = {24},
number = {1},
pages = {45--58},
abstract = { Using least parameters, we expand the step-transition operator of any linear multi-step method ({LMSM}) up to $O(\tau ^{s+5})$ with order $s=1$ and rewrite the expansion of the step-transition operator for $s=2$ (obtained by the second author in a former paper). We prove that in the conjugate relation $G_3^{\lambda\tau} \circ G_1^{\tau}=G_2^{\tau}\circ G_3^{\lambda\tau}$ with $G_1$ being an {LMSM}, (1) the order of $G_2$ can not be higher than that of $G_1$; (2) if $G_3$ is also an {LMSM} and $G_2$ is a symplectic $B$-series, then the orders of $G_1$, $G_2$ and $G_3$ must be $2$, $2$ and $1$ respectively. },
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/8733.html}
}