Volume 1, Issue 1
On the Contractivity Region of Runge-Kutta Methods

J. Comp. Math., 1 (1983), pp. 2-11

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• 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 jettesch. 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.

• History

Published online: 1983-01

• Keywords