Regarding the absolute stability of Størmer-Cowell methods

Syvert P. Nørsett; Andreas Asheim

doi:10.3934/dcds.2014.34.1131

Article Contents

2014, Volume 34, Issue 3: 1131-1146. Doi: 10.3934/dcds.2014.34.1131

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Regarding the absolute stability of Størmer-Cowell methods

Syvert P. Nørsett^1, and
Andreas Asheim^2,

1.
Dept. of Mathematical Sciences, NTNU Trondheim, N-7491 Trondheim
2.
Dept. Computer Science, University of Leuven, Belgium, BE-3001 Heverlee

Received: August 31, 2012

Revised: September 30, 2012

Published: February 2014

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Abstract

High order variants of the classical Størmer-Cowell methods are still a popular class of methods for computations in celestial mechanics. In this work we shall investigate the absolute stability of Størmer-Cowell methods close to zero, and present a characterization of the stability of methods of all orders. In particular, we show that many methods are not absolutely stable at any point in a neighborhood of the origin.

Keywords:

Multistep methods for second order problems,
Størmer-Cowell methods,
absolute stability.

Mathematics Subject Classification: Primary: 65L06, 70F15; Secondary: 65L20, 70M20.

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