The expansion approach for solving cauchy integral equation of the first kind

In this paper we expand the kernel of Cauchy integral equation of first kind as a series of Chebyshev polynomials of the second kind times some unknown functions. These unknown functions are determined by applying the orthogonality of the Chebyshev polynomial. Whereas the unknown function in the in...

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Main Authors: Yaghobifar, Mohammad, Nik Long, Nik Mohd Asri, Eshkuratov, Zainidin K.
Format: Article
Language:English
English
Published: Hikari Ltd 2010
Online Access:http://psasir.upm.edu.my/id/eprint/17160/1/The%20expansion%20approach%20for%20solving%20cauchy%20integral%20equation%20of%20the%20first%20kind.pdf
http://psasir.upm.edu.my/id/eprint/17160/
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spelling my.upm.eprints.171602015-11-03T01:11:16Z http://psasir.upm.edu.my/id/eprint/17160/ The expansion approach for solving cauchy integral equation of the first kind Yaghobifar, Mohammad Nik Long, Nik Mohd Asri Eshkuratov, Zainidin K. In this paper we expand the kernel of Cauchy integral equation of first kind as a series of Chebyshev polynomials of the second kind times some unknown functions. These unknown functions are determined by applying the orthogonality of the Chebyshev polynomial. Whereas the unknown function in the integral is expanded using Chebyshev polynomials of the first kind with some unknown coefficients. These two expansions in the integral can be simplified by the used of the property of orthogonality. The advantage of this approach is that the unknown coefficients are stability computed. Hikari Ltd 2010 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/17160/1/The%20expansion%20approach%20for%20solving%20cauchy%20integral%20equation%20of%20the%20first%20kind.pdf Yaghobifar, Mohammad and Nik Long, Nik Mohd Asri and Eshkuratov, Zainidin K. (2010) The expansion approach for solving cauchy integral equation of the first kind. Applied Mathematical Sciences, 4 (52). pp. 2581-2586. ISSN 1312-885X English
institution Universiti Putra Malaysia
building UPM Library
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continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
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language English
English
description In this paper we expand the kernel of Cauchy integral equation of first kind as a series of Chebyshev polynomials of the second kind times some unknown functions. These unknown functions are determined by applying the orthogonality of the Chebyshev polynomial. Whereas the unknown function in the integral is expanded using Chebyshev polynomials of the first kind with some unknown coefficients. These two expansions in the integral can be simplified by the used of the property of orthogonality. The advantage of this approach is that the unknown coefficients are stability computed.
format Article
author Yaghobifar, Mohammad
Nik Long, Nik Mohd Asri
Eshkuratov, Zainidin K.
spellingShingle Yaghobifar, Mohammad
Nik Long, Nik Mohd Asri
Eshkuratov, Zainidin K.
The expansion approach for solving cauchy integral equation of the first kind
author_facet Yaghobifar, Mohammad
Nik Long, Nik Mohd Asri
Eshkuratov, Zainidin K.
author_sort Yaghobifar, Mohammad
title The expansion approach for solving cauchy integral equation of the first kind
title_short The expansion approach for solving cauchy integral equation of the first kind
title_full The expansion approach for solving cauchy integral equation of the first kind
title_fullStr The expansion approach for solving cauchy integral equation of the first kind
title_full_unstemmed The expansion approach for solving cauchy integral equation of the first kind
title_sort expansion approach for solving cauchy integral equation of the first kind
publisher Hikari Ltd
publishDate 2010
url http://psasir.upm.edu.my/id/eprint/17160/1/The%20expansion%20approach%20for%20solving%20cauchy%20integral%20equation%20of%20the%20first%20kind.pdf
http://psasir.upm.edu.my/id/eprint/17160/
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