Skip to main content
SpringerLink
Log in

Numerical implementations of Cauchy-type integral equations

  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In this paper, a good interpolation formulae are applied to the numerical solution of Cauchy integral equations of the first kind with using some Chebyshev quadrature rules. To demonstrate the effectiveness of the Radau-Chebyshev with respect to the olds, [6], [7], [8] and [12], some examples are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Delves,L.M. & Mohamed,J.L.Computational methods for integral equations, Cambridge University Press, 1985.

  2. Du JinyuanOn methods for numerical solutions for singular integral equation (I), Acta Math. Sci.(Chinese Ed.),7:2(1987), 169–189.

    Google Scholar 

  3. Du JinyuanOn methods for numerical solutions for singular integral equation (II), Acta Math. Sci.(Chinese Ed.),8:1(1988), 33–45.

    Google Scholar 

  4. Du JinyuanSingular integral operators and singular quadrature operators associated with singular integral equations of the first kind and their applications, Acta Math. Sci.,15:2 (1995) 219–234.

    Article  MathSciNet  MATH  Google Scholar 

  5. Hu JichengBoundary behavior of Cauchy singular integrals, J. of Math.15(1995), 97–110.

    MATH  Google Scholar 

  6. Gerasoulis,A.Singular integral equations — the convergence of the Nyström interpolant of the Gauss-Chebyshev method, Bit22(1982), 200–210.

    Article  MathSciNet  MATH  Google Scholar 

  7. Ioakimidis,N.I. & Theocaris,P.S.On convergence of two direct methods for solution of Cauchy type singular integral equations of the first kind, Bit20(1980), 83–87.

    Article  MathSciNet  MATH  Google Scholar 

  8. Krenk,S.On the use of the interpolation polynomial for solution of singular integral equations, Q. Applied Math.32(1975), 479–484.

    Article  MathSciNet  MATH  Google Scholar 

  9. Lu LiankeBoundary value problems for analytic functions, World Scientific Co., 1993.

  10. Muskhelishvili,N.I.Singular integral equations, P. Noordhoff, Groningen, 1953.

    MATH  Google Scholar 

  11. Paget,D.F. & Elliott, D.An algorithm for the numerical evaluation of certain Cauchy principal value integrals, Numer. Math.19(1972), 373–385.

    Article  MathSciNet  MATH  Google Scholar 

  12. Theocaris, P.S. & Ioakimidis, N.I.Numerical integration methods for the solution of singular integral equations, Q. Applied Math.35(1977), 173–182.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Imam Khomeini International University, P.O.Box 288, Qazvin, Iran

    S. Abbasbandy

  2. Department of Mathematics, Wuhan University, 430072, Wuchan, China

    Du Jin-Yuan

Authors
  1. S. Abbasbandy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Du Jin-Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Abbasbandy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abbasbandy, S., Jin-Yuan, D. Numerical implementations of Cauchy-type integral equations. Korean J. Comput. & Appl. Math. 9, 253–260 (2002). https://doi.org/10.1007/BF03012353

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03012353

AMS Mathematics Subject Classification

Key words and phrases

Search

Navigation