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Numerische Mathematik

, Volume 70, Issue 4, pp 427–452 | Cite as

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

  • David Elliot
  • Siegfried Prössdorf

Summary.

The cruciform crack problem of elasticity gives rise to an integral equation of the second kind 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 number of derivatives vanish at the end points 0 and 1. If the transformed kernel is dominated near the origin by a Mellin kernel then we have given conditions under which the use of a modified Euler-Maclaurin quadrature rule and the Nyström method gives an approximate solution which converges to the exact solution of the original equation. The method is illustrated with a numerical example.

Mathematics Subject Classification (1991): 65R20, 45E99, 45L10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • David Elliot
    • 1
  • Siegfried Prössdorf
    • 2
  1. 1.Mathematics Department, University of Tasmania, GPO Box 252C, Hobart, Tasmania 7001, Australia AU
  2. 2.Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstrasse 39, D-10117 Berlin, Germany DE

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