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On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems

Zur Korrektur der Differenzen-Eigenwertapproximationen bei Sturm-Liouville-Problemen

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Abstract

The use of algebraic eigenvalues to approximate the eigenvalues of Sturm-Liouville operators is known to be satisfactory only when approximations to the fundamental and the first few harmonics are required. In this paper, we show how the asymptotic error associated with related but simpler Sturm-Liouville operators can be used to correct certain classes of algebraic eigenvalues to yield uniformly valid approximations.

Zusammenfassung

Die Benutzung algebraischer Eigenwerte zur näherungsweisen Berechnung der Eigenwerte von Sturm-Liouville-Operatoren ist bekanntlich nur für die Grundschwingung und einige weitere Harmonische zufriedenstellend. In dieser Arbeit zeigen wir, wie man den asymptotischen Fehler, der bei verwandten aber einfachen Sturm-Liouville-Operatoren auftritt, dazu benutzen kann, um gewisse Klassen algebraischer Eigenwerte so zu korrigieren, daß die gleichmäßig gute Approximationen liefern.

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Author notes

  1. J. W. Paine

    Present address: Mathematics Department, The University of Bristol, Bristol, England

Authors and Affiliations

  1. Pure Mathematics, SGS, ANU, P.O. Box 4, 2600, Canberra, A.C.T.

    J. W. Paine

  2. DMS, CSIRO, P.O. Box 1965, 2601, Canberra City, A.C.T.

    F. R. de Hoog & R. S. Anderssen

Authors
  1. J. W. Paine
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  2. F. R. de Hoog
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  3. R. S. Anderssen
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Paine, J.W., de Hoog, F.R. & Anderssen, R.S. On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems. Computing 26, 123–139 (1981). https://doi.org/10.1007/BF02241779

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  • DOI: https://doi.org/10.1007/BF02241779

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