On the semi-bounded solution of cauchy type singular integral equations of the first kind.
This paper presents an efficient approximate method to obtain a numerical solution, which is bounded at the end point x = −1, for Cauchy type singular integral equations of the first kind on the interval [−1,1]. The solution is derived by approximating the unknown density function using the weighte...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English English |
| Published: |
2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/15930/ http://psasir.upm.edu.my/id/eprint/15930/1/On%20the%20semi.pdf |
| _version_ | 1848842817728675840 |
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| author | Mahiub, Mohammad Abdulkawi Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri |
| author_facet | Mahiub, Mohammad Abdulkawi Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri |
| author_sort | Mahiub, Mohammad Abdulkawi |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper presents an efficient approximate method to obtain a numerical solution, which is bounded at the end point x = −1, for Cauchy type singular integral equations of
the first kind on the interval [−1,1]. The solution is derived by approximating the unknown density function using the weighted Chebyshev polynomials of the third kind, and then computing the Cauchy singular integral which is obtained analytically. The known force function is interpolated using the Chebyshev polynomials of the fourth kind. The exactness of this approximate method is shown for characteristic equation when the force function is a cubic.
Particular result is also given to show the exactness of this method. |
| first_indexed | 2025-11-15T08:05:10Z |
| format | Article |
| id | upm-15930 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T08:05:10Z |
| publishDate | 2009 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-159302015-10-23T00:25:09Z http://psasir.upm.edu.my/id/eprint/15930/ On the semi-bounded solution of cauchy type singular integral equations of the first kind. Mahiub, Mohammad Abdulkawi Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri This paper presents an efficient approximate method to obtain a numerical solution, which is bounded at the end point x = −1, for Cauchy type singular integral equations of the first kind on the interval [−1,1]. The solution is derived by approximating the unknown density function using the weighted Chebyshev polynomials of the third kind, and then computing the Cauchy singular integral which is obtained analytically. The known force function is interpolated using the Chebyshev polynomials of the fourth kind. The exactness of this approximate method is shown for characteristic equation when the force function is a cubic. Particular result is also given to show the exactness of this method. 2009 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/15930/1/On%20the%20semi.pdf Mahiub, Mohammad Abdulkawi and Eshkuvatov, Zainidin K. and Nik Long, Nik Mohd Asri (2009) On the semi-bounded solution of cauchy type singular integral equations of the first kind. European Journal of Pure and Applied Mathematics, 2 (3). pp. 462-472. ISSN 1307-5543 http://www.ejpam.com/index.php/ejpam/article/viewArticle/304 English |
| spellingShingle | Mahiub, Mohammad Abdulkawi Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri On the semi-bounded solution of cauchy type singular integral equations of the first kind. |
| title | On the semi-bounded solution of cauchy type singular integral equations of the first kind. |
| title_full | On the semi-bounded solution of cauchy type singular integral equations of the first kind. |
| title_fullStr | On the semi-bounded solution of cauchy type singular integral equations of the first kind. |
| title_full_unstemmed | On the semi-bounded solution of cauchy type singular integral equations of the first kind. |
| title_short | On the semi-bounded solution of cauchy type singular integral equations of the first kind. |
| title_sort | on the semi-bounded solution of cauchy type singular integral equations of the first kind. |
| url | http://psasir.upm.edu.my/id/eprint/15930/ http://psasir.upm.edu.my/id/eprint/15930/ http://psasir.upm.edu.my/id/eprint/15930/1/On%20the%20semi.pdf |