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On the numerical solution of integral equations with piecewise continuous displacement kernels

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Abstract

Solution of a Fredholm integral equation with a piecewise continuous displacement kernel is considered. It is shown that this problem is equivalent to the solution of an initial value problem for an unusual partial differential equation for continuous functions of two variables. The difference scheme for the numerical solution of the initial value problem is derived. This scheme allows implementation on parallel processors and is of linear complexity. The approach based on the numerical solution of the initial value problem is compared with a corresponding quadrature method and demonstrates certain advantages.

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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
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  2. I. Koltracht
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  3. P. Lancaster
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Additional information

This work was supported by the NSF grant DMS-8801961

This work was supported by a research grant from the NSERC of Canada

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Gohberg, I., Koltracht, I. & Lancaster, P. On the numerical solution of integral equations with piecewise continuous displacement kernels. Integr equ oper theory 12, 511–538 (1989). https://doi.org/10.1007/BF01199457

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  • DOI: https://doi.org/10.1007/BF01199457

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