10.1186/2251-7456-6-36

Adapted linear approximation for singular integrals

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  • Mostefa Nadir*1,
  1. Laboratory of Pure and Applied Mathematics, University of Msila, Msila, 28000, DZ Laboratory of Signals Analysis and Systems, University of Msila, Msila, 28000, DZ Department of Mathematics, Faculty of Mathematics and Informatics, University of Msila, Msila, 28000, DZ

Published in Issue 2012-09-18

How to Cite

Nadir, M. (2012). Adapted linear approximation for singular integrals. Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-36
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Abstract

Abstract Purpose The purpose of this work is to present an approximation for singular integrals of Cauchy type kernel on a smooth-oriented contour. Methods For the method, we use a small modification of the spline functions in order to eliminate the singularity. Noting that this approximation is due to the idea of Sanikidze’s Approximate solution of singular integral equations in the case of closed contours of integrations . Results This approximation represents a good approach for any singular integral given on the curve in the sense of Cauchy principal value. Conclusions This approximation is destined to solve numerically the singular integral equations with Cauchy type kernel on a smooth-oriented contour.

Keywords

  • Singular integral,
  • Interpolation; Hőlder space,
  • Hőlder condition,
  • Approximation theory,
  • Spline functions,
  • 45D05;,
  • 45E05;,
  • 45L05;,
  • 45L10;,
  • 65R20
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References

  1. Nadir (1985) Problèmes aux limites qui se reduisent aux equations intégrales de Fredholm
  2. Muskhelishvili (1953) Noordhoff
  3. Nadir (1998) Opérateurs intégraux et bases d’ondelettes 6(6) (pp. 977-995)
  4. Sanikidze (1970) On the approximate calculation of singular line integral
  5. Sanikidze (1971) Approximate solution of singular integral equations in the case of closed contours of integration
  6. Antidze (1975) On the approximate solution of singular integral equations
  7. Nadir (2004) On the approximation of singular integrals of Cauchy types