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Regarding the absolute stability of Størmer-Cowell methods

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

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