Skip to main content
SpringerLink
Log in

Second order parallel algorithms for piecewise smooth displacement kernels

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

Abstract

Second order parallel algorithms for Fredholm integral equations with piecewise smooth displacement kernels are derived. One is based on a difference scheme of Runge-Kutta type for an unusual partial differential equations for continuous functions of two variables. The other is based on the trapezoidal quadrature rule applied to a modified integral equations. It is found that the Runge-Kutta type algorithm exhibits certain advantages.

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

  • [B] Baker, C.T.H., “The Numerical Treatment of Integral Equations”, Oxford; New York, Clarendon Press, 1977.

    Google Scholar 

  • [C] Carnahan, B., H.A. Luther and J.O. Wilkes, “Applied Numerical Methods”, John Wiley & Sons, Inc., New York, 1969.

    Google Scholar 

  • [DM] Delves, L.M. and J.L. Mohammed, “Computational Methods for Integral Equations”, Cambridge University Press, 1985.

  • [GK] Gohberg, I. and I. Koltracht, “Numerical Solution of Integral Equations, Fast Algorithms and Krein-Sobolev Equation”, Numer. Math. 47, 1985, pp. 233–288.

    Google Scholar 

  • [GKL1] Gohberg, I., I. Koltracht and P. Lancaster, “Second Order Parallel Algorithms for Fredholm Integral Equations with Continuous Displacement Kernels”, Int. Eq. Oper. Theory, V. 10, 1987, pp. 578–594.

    Google Scholar 

  • [GKL2] Gohberg I., I. Koltracht and P. Lancaster, “On the Numerical Solution of Integral Equations with Piecewise Continuous Displacement Kernels, Int. Eq. Oper. Theory, V. 12, 1989, p.p. 511–536.

    Google Scholar 

  • [GKKL] Gohberg, I., I. Koltracht, T. Kailath and P. Lancaster, “Linear Complexity Parallel Algorithms for Linear Systems of Equations with Recursive Structure”, Lin. Alg. Appl., V. 88/89, 1987, pp. 271–315.

    Google Scholar 

  • [K] Kailath, T., “A View of Three Decades of Linear Filtering Theory”, IEEE Trans. Inf. Theory, Vol. IT-20, No. 2, 1974 p.p. 145–181.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, ISRAEL

    I. Gohberg

  2. Department of Mathematics, University of Connecticut, 06268, Storrs, Connecticut, USA

    I. Koltracht

  3. Department of Mathematics & Statistics, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, Alberta, CANADA

    P. Lancaster

Authors
  1. I. Gohberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Koltracht
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Lancaster
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The work of these authors was supported in part by the NSF Grant DMS-9007030

The work of this author was supported in part by a grant from the National Science and Engineering Research Council of Canada

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gohberg, I., Koltracht, I. & Lancaster, P. Second order parallel algorithms for piecewise smooth displacement kernels. Integr equ oper theory 15, 16–29 (1992). https://doi.org/10.1007/BF01193764

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01193764

MSC 1991

Search

Navigation