Trigonometric polynomial or exponential fitting approach?

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

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Abstract

The application of a trigonometric polynomial and an exponential fitting approach is compared for a three-point formula for second-order derivatives, for Simpson's quadrature rule and for Numerov's scheme for second-order differential equations. The expressions for the occurring parameters are constructed in both the approaches and the behaviour of these parameters with respect to the introduced frequency is studied. The errors for specific problems obtained in both the approaches as a function of the frequency are compared.