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, Volume 4, Issue 1, pp 10–23 | Cite as

Invariant imbedding and the calculation of eigenvalues for Sturm-Liouville systems

  • M. R. Scott
  • L. F. Shampine
  • G. M. Wing
Article

Summary

A new technique based upon an invariant imbedding-Ricatti transformation approach is presented for the calculation of eigenvalues ofSturm-Liouville type systems of differential equations.

A very simple numerical procedure is developed which is easily programmed and which uses reliable subroutines. The method is capable of handling a large class of problems. Included among these are problems in which the eigenvalues appears in a non-linear fashion, cases in which the eigenvalue occurs in the boundary condition, and equations which have singularities.

The numerical computations are generally well-conditioned and very accurate results were obtained.

Keywords

Eigenvalue Problem Characteristic Length Phase Function Transport Theory Singular Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Invariante Einbettung und die Berechnung von Eigenwerten für Sturm-Liouville-Systeme

Zusammenfassung

Es wird eine neue Technik, basierend auf einer Methode, welche invariante Einbettung (Invariant Imbedding) mit derRicatti-Transformation kombiniert, dargestellt zum Zwecke der Berechnung der Eigenwerte von Differentialgleichungssystemen, welche vomSturm-Liouville-Typ sind.

Eine sehr einfache numerische Prozedur ist entwickelt worden, die leicht zu programmieren ist und verläßliche Unterprogramme benutzt. Dieses Verfahren vermag eine umfangreiche Klasse von Problemen zu handhaben. Unter ihnen sind solche inbegriffen, bei denen der Eigenwert in einer nichtlinearen Form auftritt; auch Fälle, wo der Eigenwert in der Randbedingung vorkommt; und schließlich auch Gleichungen, die Singularitäten aufweisen.

Es sei betont, daß die hier von uns behandelten numerischen Berechnungen im allgemeinen stabil sind und sehr genaue Ergebnisse hervorzubringen vermögen.

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Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • M. R. Scott
    • 1
  • L. F. Shampine
    • 2
  • G. M. Wing
    • 2
  1. 1.Sandia LaboratoryAlbuquerqueUSA
  2. 2.Department of Mathematics and StatisticsThe University of New MexicoAlbuquerqueUSA

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