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The Approximate Solution of Singular Integral Equations

  • D. Elliott
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 18)

Abstract

We present a survey of numerical methods for solving Cauchy singular integral equations on both open and closed arcs in the plane. For completeness, necessary theory is reviewed, particularly the method of regularization. For closed arcs we discuss collocation methods based on piecewise polynomial or rational representations of the solution. Emphasis here, as for the open arc case, is on regularizable equations. For open arcs a detailed discussion is given of a degenerate kernel method developed recently by Dow and Elliott. In addition to this, a generalization of a Galerkin method due to Karpenko is presented. Attention is drawn to the relation of Cauchy singular equations and solving rectangular systems of linear equations. The possibility of exploiting this for the direct solution of such equations is discussed, and some direction for future research is given.

Keywords

Approximate Solution Singular Integral Equation Linear Algebraic Equation Fredholm Integral Equation Closed Contour 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • D. Elliott
    • 1
  1. 1.The University of TasmaniaHobartAustralia

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