Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Regarding the absolute stability of Størmer-Cowell methods

Pages: 1131 - 1146, Volume 34, Issue 3, March 2014      doi:10.3934/dcds.2014.34.1131

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Syvert P. Nørsett - Dept. of Mathematical Sciences, NTNU Trondheim, N-7491 Trondheim, Norway (email)
Andreas Asheim - Dept. Computer Science, University of Leuven, Belgium, BE-3001 Heverlee, Belgium (email)

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.

Received: September 2012;      Revised: October 2012;      Available Online: August 2013.