Year: 1983
Journal of Computational Mathematics, Vol. 1 (1983), Iss. 1 : pp. 2–11
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1983-JCM-9676
Journal of Computational Mathematics, Vol. 1 (1983), Iss. 1 : pp. 2–11
Published online: 1983-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10