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A Chebyshev polynomial method for line integrals with singularities

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Abstract

In this paper we consider a Chebyshev polynomial method for the calculation of line integrals along curves with Cauchy principal value or Hadamard finite part singularities. The major point we address is how to reconstruct the value of the integral when the parametrization of the curve is unknown and only empirical data are available at some discrete set of nodes.

We replace the curve by a near‐minimax parametric polynomial approximation, and express the integrand by means of a sum of Chebyshev polynomials. We make use of a mapping property of the Hadamard finite part operator to calculate the value of the integral.

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Authors and Affiliations

  1. School of Computing and Mathematics, University of Huddersfield, Queensgate, Huddersfield, West Yorkshire, HD1 3DH, UK

    J.C. Mason & E. Venturino

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  1. J.C. Mason
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  2. E. Venturino
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Mason, J., Venturino, E. A Chebyshev polynomial method for line integrals with singularities. Advances in Computational Mathematics 10, 187–208 (1999). https://doi.org/10.1023/A:1018978615805

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