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Numerical evaluation of a 2-D Cauchy principal value integral based on quasi-interpolating splines

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Approximation Theory and its Applications

Abstract

In this paper the author presents a method for the numerical solution of a 2-D Cauchy principal value of the form

where S is a domain with a continuous boundary. By using polar coordinates, the integral is reduced to the form

where

the finite-part of the integral. We construct the relative product rule based on quasi-inter polating splines.

Convergence results are proved and numerical examples are given.

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Authors and Affiliations

  1. Università degli Studi di L' Aquila, Italy

    M. G. Cimoroni

  2. Facoltà di Ingegneria, Dipartimento di Energetica, Località Monteluco, 67040, Roio Poggio-L'Aquila, Italy

    M. G. Cimoroni

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  1. M. G. Cimoroni
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Cimoroni, M.G. Numerical evaluation of a 2-D Cauchy principal value integral based on quasi-interpolating splines. Approx. Theory & its Appl. 13, 1–12 (1997). https://doi.org/10.1007/BF02836806

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  • DOI: https://doi.org/10.1007/BF02836806

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