The optimal exponentially-fitted Numerov method for solving two-point boundary value problems

Authors:
D. Hollevoet;M. Van Daele;G. Vanden Berghe
Affiliations:
Vakgroep Toegepaste Wiskunde en Informatica, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium;Vakgroep Toegepaste Wiskunde en Informatica, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium;Vakgroep Toegepaste Wiskunde en Informatica, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

Second order boundary value problems are solved by means of exponentially-fitted Numerov methods. These methods, which depend on a parameter, can be constructed following a six-step flow chart of Ixaru and Vanden Berghe [L.Gr. Ixaru, G. Vanden Berghe, Exponential Fitting, Kluwer Academic Publishers, Dordrecht, 2004]. Special attention is paid to the expression of the error term of such methods. An algorithm concerning the choice of the best suited method and its parameter is discussed. Several numerical examples are given to sustain the theory.