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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| Format: | Article |
| Language: | English English |
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Hikari Ltd
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/17160/1/The%20expansion%20approach%20for%20solving%20cauchy%20integral%20equation%20of%20the%20first%20kind.pdf |
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| author | Yaghobifar, Mohammad Nik Long, Nik Mohd Asri Eshkuratov, Zainidin K. |
| author_facet | Yaghobifar, Mohammad Nik Long, Nik Mohd Asri Eshkuratov, Zainidin K. |
| author_sort | Yaghobifar, Mohammad |
| collection | UPM |
| 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. |
| first_indexed | 2024-03-06T07:39:36Z |
| format | Article |
| id | upm.eprints-17160 |
| institution | Universiti Putra Malaysia |
| language | English English |
| last_indexed | 2024-03-06T07:39:36Z |
| publishDate | 2010 |
| publisher | Hikari Ltd |
| record_format | dspace |
| spelling | 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 Cauchy integral formula Integral equations Mathematical physics English |
| spellingShingle | Cauchy integral formula Integral equations Mathematical physics Yaghobifar, Mohammad Nik Long, Nik Mohd Asri Eshkuratov, Zainidin K. The expansion approach for solving cauchy integral equation of the first kind |
| title | 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_short | 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 |
| topic | Cauchy integral formula Integral equations Mathematical physics |
| url | http://psasir.upm.edu.my/id/eprint/17160/1/The%20expansion%20approach%20for%20solving%20cauchy%20integral%20equation%20of%20the%20first%20kind.pdf |
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