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On the solvability of ordinary differential equations with only partially continuous right-hand-side by difference methods

Über die Lösbarkeit gewöhnlicher Differentialgleichungen mit nur partiell stetiger rechter Seite durch Differenzenverfahren

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Abstract

An example shows that even strongly stable difference methods need not yield a solution of initial value problems for ordinary differential equations with only partially continuous right-hand-side.

Zusammenfassung

Ein Beispiel zeigt, daß sogar die durch stark stabile Differenzenverfahren bestimmten Näherungslösungen gewöhnlicher Differentialgleichungen nicht gegen eine Lösung der Differentialgleichung konvergieren müssen, falls die rechte Seite der Differentialgleichung nur partiell stetig ist.

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References

  1. Dieudonné, J.: Elements d'analyse, 11. Paris: Gauthier-Villars 1974.

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  2. Taubert, K.: Eine Erweiterung der Theorie von G. Dahlquist. Computing17, 177–185 (1976).

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Authors and Affiliations

  1. Institut für Angewandte Analysis, Universität Bonn, Beringstrasse 6, D-5300, Bonn 1, Federal Republic of Germany

    M. Struwe

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  1. M. Struwe
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Additional information

This research was supported by the Sonderforschungsbereich 72 of the Deutsche Forschungsgemeinschaft.

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Struwe, M. On the solvability of ordinary differential equations with only partially continuous right-hand-side by difference methods. Computing 27, 165–167 (1981). https://doi.org/10.1007/BF02243550

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  • DOI: https://doi.org/10.1007/BF02243550

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