Computing eigenvalues of Sturm–Liouville problems by Hermite interpolations

Computing eigenvalues of Sturm–Liouville problems by Hermite interpolations

We establish a new method to compute the eigenvalues of Sturm–Liouville problems by the use of Hermite interpolations at equidistant nodes. We rigorously give estimates for the error by considering both truncation and amplitude errors. We compare the results of the new technique with those involving...

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Veröffentlicht in:Numerical algorithms 2012-07, Vol.60 (3), p.355-367
Hauptverfasser: Annaby, Mahmoud H., Asharabi, Rashad M.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Algorithms
Computer Science
Eigenvalues
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
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Zusammenfassung:We establish a new method to compute the eigenvalues of Sturm–Liouville problems by the use of Hermite interpolations at equidistant nodes. We rigorously give estimates for the error by considering both truncation and amplitude errors. We compare the results of the new technique with those involving the classical sinc method as well as a SLEIGN2-based method. We also introduce curves that illustrate the enclosure intervals.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-011-9518-x