Exponentially-fitted Numerov methods

Authors:
G. Vanden Berghe;M. Van Daele
Affiliations:
Vakgroep Toegepaste Wiskunde en Informatica, Universiteit Gent, Krijgslaan 281-S9, B 9000, Gent;Vakgroep Toegepaste Wiskunde en Informatica, Universiteit Gent, Krijgslaan 281-S9, B 9000, Gent
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

The error in the estimate of the kth eigenvalue of a regular Sturm-Liouville problem obtained by Numerov's method with mesh length h is O(k^6h^4). It is shown that the error can be reduced to O(k^3h^4) by using one of the three versions of the exponentially-fitted Numerov method. Numerical examples demonstrate the usefulness of this approach even for low values of k.