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Asymptotic errox expansions for Defect Correction Iterates

Asymptotische Fehlerentwicklungen für Defektkorrektur-Näherungen

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Abstract

Asymptotic error expansions are shown to exist for Iterated Defect Correction (IDeC) methods applied to differential equations. Only weak assumptions are needed to guarantee the existence of these error expansions. The results are derived in a very general way which can easily be extended to other types of operator equations.

Zusammenfassung

Für das Verfharen der Iterierten Defektkorrektur (IDeC), angewendet auf Differentialgleichungen, wird die Existenz asymptotischer Fehlerentwicklungen nachgewiesen. Es werden nur schwache Voraussetzungen benötigt, um die Existenz dieser Fehlerentwicklung zu gewährleisten. Die Herleitung der Resultate erfolgt so allgemein, daß eine Erweiterung auf andere Operatorgleichungen leicht durchzuführen ist.

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References

  1. Boehmer, K.: Discrete Newton methods and iterated defect corrections. Num. Math.37, 167–192 (1981).

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  2. Frank, R., Ueberhuber, C. W.: Iterated defect correction for differential equations. Part I: Theoretical Results. Computing20, 207–228 (1978); Part II: Numerical Experiments. (To appear in Computing.)

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  3. Macsek, F.: Asymptotische Entwicklungen bei der Defektkorrektur. Dissertation, TU Wien, January 1981.

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Authors and Affiliations

  1. Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Gusshausstrasse 27-29, A-1040, Wien, Austria

    R. Frank,  F. Macsek &  C. W. Ueberhuber

Authors
  1. R. Frank
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  2. F. Macsek
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  3. C. W. Ueberhuber
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Frank, R., Macsek, F. & Ueberhuber, C.W. Asymptotic errox expansions for Defect Correction Iterates. Computing 32, 115–125 (1984). https://doi.org/10.1007/BF02253686

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  • DOI: https://doi.org/10.1007/BF02253686

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