@Article{JCM-1-1,
author = {},
title = {On the Contractivity Region of Runge-Kutta Methods},
journal = {Journal of Computational Mathematics},
year = {1983},
volume = {1},
number = {1},
pages = {2--11},
abstract = {<p style="text-align: justify;">In this paper we first introduce the definition of contractivity region of Runge-Kutta methods and then examine the general features of the contractivity regions. We find that the intersections of the contractivity region and the axis place is $C^s$ are always either the whole axis plane or a generalized disk introduced by Dahlquist and Jeltsch. We also define the AN-contractivity and show that it is equivalent to the algebraic stability and can be determined locally in a neighborhood of the origion. However, many implicit methods are only r-circle contractive but not AN-contractive. A simple bound for the radius r of the r-circle contractive methods is given. &nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/1983-JCM-9676},
url = {https://global-sci.com/article/86297/on-the-contractivity-region-of-runge-kutta-methods}
}