On quadrature for Cauchy principal value integrals of oscillatory functions

Authors:
M. R. Capobianco;G. Criscuolo
Affiliations:
Istituto per le Applicazioni del Calcolo "Mauro Picone"-C.N.R. Sezione di Napoli, Via Pietro Castellino, 111, 80131 Napoli, Italy;Istituto per le Applicazioni del Calcolo "Mauro Picone"-C.N.R. Sezione di Napoli, Italy and Dipartimento di Matematica e Applicazioni, Universitá degli Studi di Napoli "Federico II", Napoli, ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

The authors develop an algorithm for the numerical evaluation of Cauchy principal value integrals of oscillatory functions. The method is based on an interpolatory procedure at the zeros of the orthogonal polynomials with respect to a Jacobi weight. A numerically stable procedure is obtained and the corresponding algorithm can be implemented in a fast way yielding satisfactory numerical results. Bounds of the error and of the amplification factor are also provided.