On the Contractivity Region of Runge-Kutta Methods

On the Contractivity Region of Runge-Kutta Methods

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

Keywords: