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Numerical solution of differential eigenvalue problems with an operational approach to the Tau method

Numerische Lösung in Differentialgleichungs-Eigenwertproblemen mit einem operationalen Zugang zum Tau-Verfahren

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Abstract

A technique for the numerical solution of eigenvalue problems defined by differential equations, based on an operational approach to the Tau method recently proposed by the authors, is shown to be equivalent to a method of Chaves and Oritz. The technique discussed here leads to an algorithmic formulation of remarkable simplicity and to numerical results of high accuracy. It requires no shooting and can deal with complex multipoint boundary conditions and a nonlinear dependence on the eigenvalue parameter.

Zusammenfassung

Es wird gezeigt, daß eine Technik zur numerischen Lösung von Eigenwertproblemen bei Differentialgleichungen, die sich auf einen operationalen Zugang zum Tau-Verfahren stützt, zu einer Methode von Chaves und Ortiz äquivalent ist. Die hier diskutierte Technik führt zu einer algorithmischen Formulierung in bemerkenswerter Einfachheit und zu numerischen Resultaten von hoher Genauigkeit. Sie erfordert keine Vorwärtsrechnung und kann auch bei komplizierten Mehrpunkt-Randbedingungen und einer nichtlinearen Abhängigkeit von Eigenwertparameter eingesetzt werden.

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Ortiz, E.L., Samara, H. Numerical solution of differential eigenvalue problems with an operational approach to the Tau method. Computing 31, 95–103 (1983). https://doi.org/10.1007/BF02259906

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  • DOI: https://doi.org/10.1007/BF02259906

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