Semi-bounded solutions of singular integral equations of Cauchy type
In this work, semi-bounded numerical solutions of the Cauchy type singular integral equations of the first kind over the interval [−1, 1] is presented. In the integral equation, the truncated Chebyshev series of the third kind Vj and fourth kind Wj with the weight functions ω1(x) = (1 + x)1/2(1 − x...
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| Format: | Article |
| Language: | English English |
| Published: |
Hikari Ltd
2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/16664/ http://psasir.upm.edu.my/id/eprint/16664/1/eshkuvatovIJCMS21-24-2009.pdf |
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| author | Nik Long, Nik Mohd Asri Eshkuvatov, Zainidin K. Mahiub, Mohammad Abdulkawi |
| author_facet | Nik Long, Nik Mohd Asri Eshkuvatov, Zainidin K. Mahiub, Mohammad Abdulkawi |
| author_sort | Nik Long, Nik Mohd Asri |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this work, semi-bounded numerical solutions of the Cauchy type singular integral equations of the first kind over the interval [−1, 1] is presented. In the integral equation, the truncated Chebyshev series of the third kind Vj and fourth kind Wj with the weight functions ω1(x) =
(1 + x)1/2(1 − x)−1/2 and ω2(x) = (1 + x)−1/2(1 − x)1/2, respectively,are used to approximate the unknown function. The exactness of the method is shown for characteristic singular integral equation when the forcing function is linear. The numerical results are given to show the
efficiency and accuracy of the method presented. |
| first_indexed | 2025-11-15T08:08:27Z |
| format | Article |
| id | upm-16664 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T08:08:27Z |
| publishDate | 2009 |
| publisher | Hikari Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-166642014-09-22T12:57:09Z http://psasir.upm.edu.my/id/eprint/16664/ Semi-bounded solutions of singular integral equations of Cauchy type Nik Long, Nik Mohd Asri Eshkuvatov, Zainidin K. Mahiub, Mohammad Abdulkawi In this work, semi-bounded numerical solutions of the Cauchy type singular integral equations of the first kind over the interval [−1, 1] is presented. In the integral equation, the truncated Chebyshev series of the third kind Vj and fourth kind Wj with the weight functions ω1(x) = (1 + x)1/2(1 − x)−1/2 and ω2(x) = (1 + x)−1/2(1 − x)1/2, respectively,are used to approximate the unknown function. The exactness of the method is shown for characteristic singular integral equation when the forcing function is linear. The numerical results are given to show the efficiency and accuracy of the method presented. Hikari Ltd 2009 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/16664/1/eshkuvatovIJCMS21-24-2009.pdf Nik Long, Nik Mohd Asri and Eshkuvatov, Zainidin K. and Mahiub, Mohammad Abdulkawi (2009) Semi-bounded solutions of singular integral equations of Cauchy type. International Journal of Contemporary Mathematical Sciences, 4 (22). 1059 - 1066. ISSN 1312-7586 Integral equations Chebyshev polynomials English |
| spellingShingle | Integral equations Chebyshev polynomials Nik Long, Nik Mohd Asri Eshkuvatov, Zainidin K. Mahiub, Mohammad Abdulkawi Semi-bounded solutions of singular integral equations of Cauchy type |
| title | Semi-bounded solutions of singular integral equations of Cauchy type |
| title_full | Semi-bounded solutions of singular integral equations of Cauchy type |
| title_fullStr | Semi-bounded solutions of singular integral equations of Cauchy type |
| title_full_unstemmed | Semi-bounded solutions of singular integral equations of Cauchy type |
| title_short | Semi-bounded solutions of singular integral equations of Cauchy type |
| title_sort | semi-bounded solutions of singular integral equations of cauchy type |
| topic | Integral equations Chebyshev polynomials |
| url | http://psasir.upm.edu.my/id/eprint/16664/ http://psasir.upm.edu.my/id/eprint/16664/1/eshkuvatovIJCMS21-24-2009.pdf |