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P-stable Obrechkoff methods of arbitrary order for second-order differential equations

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Abstract

Following the ideas of Ananthakrishnaiah we develop a family of P-stable Obrechkoff methods of arbitrary even order. The coefficients of these methods follow from a recursive algorithm. It is also shown that the stability functions of the thus obtained methods can be expressed as Padé approximants of the exponential function with a complex argument. A numerical example is given to illustrate the performance of the methods.

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  1. Vakgroep Toegepaste Wiskunde en Informatica, Universiteit Gent, Krijgslaan 281-S9, B-9000, Gent, Belgium

    Marnix Van Daele & Guido Vanden Berghe

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  1. Marnix Van Daele
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  2. Guido Vanden Berghe
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Correspondence to Marnix Van Daele.

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Van Daele, M., Vanden Berghe, G. P-stable Obrechkoff methods of arbitrary order for second-order differential equations. Numer Algor 44, 115–131 (2007). https://doi.org/10.1007/s11075-007-9084-4

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