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Numerical solution of initial-value problems by collocation methods using generalized piecewise functions

Kollokationsverfahren mit allgemeineren Ansatzfunktionen zur numerischen Lösung von Anfangswertaufgaben

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Abstract

A general class of piecewise functions is described which leads to the same order of convergence of collocation methods as piecewise polynomials. This order only depends on the collocation points used.

Zusammenfassung

Es wird eine für Kollokationsverfahren geeignete allgemeine Klasse von Ansatzfunktionen charakterisiert, die die gleiche Konvergenzordnung wie ein Polynomansatz sichert. Dabei hängt diese Ordnung ausschließlich von der Wahl der Kollokationsstellen ab.

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Authors and Affiliations

  1. Sektion Mathematik WB Numerische Mathematik, Technische Universität Dresden, Mommsenstrasse 13, DDR-8027, Dresden, German Democratic Republic

    G. Keller

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  1. G. Keller
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Keller, G. Numerical solution of initial-value problems by collocation methods using generalized piecewise functions. Computing 28, 199–211 (1982). https://doi.org/10.1007/BF02241748

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  • DOI: https://doi.org/10.1007/BF02241748

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