Numerical treatment of the Cauchy integral equation by discrete Fourier transform

The uniquely solvable system of the Cauchy integral equation of the first kind and index 1 and an additional integral condition are treated. Such a system arises, for example, when solving the skew derivative problem for the Laplace equation outside an open arc in a plane. This problem models the el...

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Bibliographic Details
Published in:International journal for numerical methods in biomedical engineering Vol. 27; no. 7; pp. 1096 - 1106
Main Authors: Kolybasova, Valentina, Krutitskii, Pavel, Prozorov, Konstantin, Vainikko, Gennadi
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 01.07.2011
Subjects:
Convergence
Derivatives
discrete Fourier transform
Electrodes
Fourier transforms
Integral equations
Mathematical models
Numerical analysis
numerical method
Semiconductors
singular integral equation
ISSN:2040-7939, 2040-7947, 2040-7947
Online Access:Get full text
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Summary:The uniquely solvable system of the Cauchy integral equation of the first kind and index 1 and an additional integral condition are treated. Such a system arises, for example, when solving the skew derivative problem for the Laplace equation outside an open arc in a plane. This problem models the electric current from a thin electrode in a semiconductor film placed in a magnetic field. A fast and accurate numerical method based on the discrete Fourier transform is proposed. Some computational tests are given. It is shown that the convergence is close to exponential. Copyright © 2009 John Wiley & Sons, Ltd.
Bibliography:Russian Science Support Foundation
Russian Foundation for Basic Research - No. 08-01-00082
ArticleID:CNM1336
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ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:2040-7939
2040-7947
2040-7947
DOI:10.1002/cnm.1336