Advertisement

A Collocation Method for Cauchy Integral Equations in L2

  • M. Ahues
  • A. Mennouni

Abstract

In this paper we present a collocation method based on trigonometric polynomials combined with a regularization procedure, for solving Cauchy integral equations of the second kind, in L 2(0,2π). A system of linear equations is involved. We prove the existence of the solution for a double projection scheme, and we perform the error analysis. Some numerical examples illustrate the theoretical results.

Keywords

Integral Equation Collocation Method Singular Integral Equation Trigonometric Polynomial Fredholm Integral Equation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AhLaLi01]
    Ahues, M., Largillier, A., Limaye, B.V.: Spectral Computations for Bounded Operators, CRC Press, Boca Raton (2001). MATHCrossRefGoogle Scholar
  2. [Mu53]
    Mushkelishvili, N.I.: Singular Integral Equations, Noordhoff, Groningen (1953). Google Scholar
  3. [PoSt90]
    Porter, D., Stirling, D.: Integral Equations: A Practical Treatment, from Spectral Theory to Applications, Cambridge University Press (1990). MATHGoogle Scholar
  4. [Se93]
    Sengupta, A.: A note on a reduction of Cauchy singular integral equation to Fredholm equation in L p, Applied Mathematics and Computation, 56, 97–100 (1993). MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Université Jean MonnetUniversité de LyonSaint-ÉtienneFrance
  2. 2.University of Bordj Bou-ArreridjBordj Bou-ArreridjAlgeria

Personalised recommendations