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Computational Methods in Applied Mathematics

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Volume 18, Issue 4


Approximate Solution of a Singular Integral Equation with a Cauchy Kernel on the Euclidean Plane

Dorota Pylak
  • Corresponding author
  • Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Aleje Racławickie 14, 20-950 Lublin, Poland
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/ Paweł KarczmarekORCID iD: http://orcid.org/0000-0002-6215-297X / Paweł Wójcik
  • Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Aleje Racławickie 14, 20-950 Lublin, Poland
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  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-12-05 | DOI: https://doi.org/10.1515/cmam-2017-0052


Multidimensional singular integral equations (SIEs) play a key role in many areas of applied science such as aerodynamics, fluid mechanics, etc. Solving an equation with a singular kernel can be a challenging problem. Therefore, a plethora of methods have been proposed in the theory so far. However, many of them are discussed in the simplest cases of one–dimensional equations defined on the finite intervals. In this study, a very efficient method based on trigonometric interpolating polynomials is proposed to derive an approximate solution of a SIE with a multiplicative Cauchy kernel defined on the Euclidean plane. Moreover, an estimation of the error of the approximated solution is presented and proved. This assessment and an illustrating example show the effectiveness of our proposal.

Keywords: Singular Integral Equation; Cauchy Kernel; Trigonometric Interpolating Polynomials,Approximate Solution

MSC 2010: 65R20; 45E05


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About the article

Received: 2017-06-01

Revised: 2017-09-11

Accepted: 2017-11-03

Published Online: 2017-12-05

Published in Print: 2018-10-01

Citation Information: Computational Methods in Applied Mathematics, Volume 18, Issue 4, Pages 741–752, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2017-0052.

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