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

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

Published online: 1983-01

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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 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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@Article{JCM-1-2, 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 = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9676.html} }
TY - JOUR T1 - On the Contractivity Region of Runge-Kutta Methods JO - Journal of Computational Mathematics VL - 1 SP - 2 EP - 11 PY - 1983 DA - 1983/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9676.html KW - AB -

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.

Ming-You Huang. (1970). On the Contractivity Region of Runge-Kutta Methods. Journal of Computational Mathematics. 1 (1). 2-11. doi:
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