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

Autores: D. Hollevoet, M. Van Daele, G. vanden Berghe
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 230, Nº 1, 2009, págs. 260-269
Idioma: inglés
DOI: 10.1016/j.cam.2008.11.011
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Resumen
- 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.