Numerical treatment of the Cauchy integral equation by discrete Fourier transform | Zendy

Kolybasova Valentina | Zendy; Krutitskii Pavel | Zendy; Prozorov Konstantin | Zendy; Vainikko Gennadi | Zendy

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Numerical treatment of the Cauchy integral equation by discrete Fourier transform

Author(s) -

Kolybasova Valentina,

Krutitskii Pavel,

Prozorov Konstantin,

Vainikko Gennadi

Publication year - 2011

Publication title -

international journal for numerical methods in biomedical engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.741

H-Index - 63

eISSN - 2040-7947

pISSN - 2040-7939

DOI - 10.1002/cnm.1336

Subject(s) - mathematics , mathematical analysis , integral equation , fourier transform , cauchy distribution , laplace transform , convergence (economics) , cauchy problem , electric field integral equation , cauchy's integral formula , integral transform , initial value problem , economics , economic growth

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.

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