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An algorithm for the approximate solution of integral equations of Mellin type

journal contribution
posted on 2023-05-16, 09:42 authored by David ElliottDavid Elliott, Prossdorf, S
The cruciform crack problem ofelasticity gives rise to an integral equation of the secondkind on [0,1] whose kernel has a fixed singularity at (0,0). We introduce a transformation of[0,1] onto itself such that an arbitrary numberof derivatives vanish at theend points 0 and 1. If the transformed kernelis dominated near the origin by a Mellin kernel then we have given conditions under which the use of amodified Euler-Maclaurin quadrature rule and theNyström method gives an approximate solutionwhich converges to the exact solution of theoriginal equation. The method is illustrated with a numerical example. © 1995, Springer-Verlag Berlin Heidelberg. All rights reserved.

History

Publication title

Numerische Mathematik

Volume

70

Issue

4

Pagination

427-452

ISSN

0029-599X

Department/School

School of Natural Sciences

Publisher

Springer-Verlag

Place of publication

175 Fifth Ave, New York, USA, Ny, 10010

Repository Status

  • Restricted

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