On the polynomials interpolating approximate solutions of singular integral equations

Abstract

A direct approach to the solution of singular integral equations with Cauchy principal value integrals is to replace the integrals by a quadrature formula, and to satisfy the resulting equation at a discrete set of collocation points. For the canonical equation, i.e. the integral equation of the first kind with only the principal part, interpolatory polynomials are explicitly constructed from the discrete values of the solution obtained from Gauss-Chebyshev and Lobatto-Chebyshev formulae, and are shown to converge to the analytic solution under fairly reasonable conditions.

†This work was supported by the U.S. Army Research Office under Contract No. DAAG

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†This work was supported by the U.S. Army Research Office under Contract No. DAAG

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Notes

†This work was supported by the U.S. Army Research Office under Contract No. DAAG

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Additional information

Notes on contributors

David Colton