Half-bounded numerical solution of singular integral equations with Cauchy kernel.
In this study, a numerical solution for singular integral equations of the first kind with Cauchy kernel over the finite segment [-1,1] is presented. The numerical solution is bounded at x =1 and unbounded at x = -1. The numerical solution is derived by approximating the unknown density function usi...
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| Format: | Article |
| Language: | English English |
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Science Publications
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/24851/ http://psasir.upm.edu.my/id/eprint/24851/1/Half-bounded%20numerical%20solution%20of%20singular%20integral%20equations%20with%20Cauchy%20kernel..pdf |
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| author | Mahiub, Mohammad Abdulkawi Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri |
| author_facet | Mahiub, Mohammad Abdulkawi Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri |
| author_sort | Mahiub, Mohammad Abdulkawi |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this study, a numerical solution for singular integral equations of the first kind with Cauchy kernel over the finite segment [-1,1] is presented. The numerical solution is bounded at x =1 and unbounded at x = -1. The numerical solution is derived by approximating the unknown density function using the weighted Chebyshev polynomials of the fourth kind. The force function is approximated by using the Chebyshev polynomials of the third kind. The exactness of the numerical solution is shown for characteristic equation when the force function is a cubic. |
| first_indexed | 2025-11-15T08:42:13Z |
| format | Article |
| id | upm-24851 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T08:42:13Z |
| publishDate | 2011 |
| publisher | Science Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-248512015-10-19T23:58:09Z http://psasir.upm.edu.my/id/eprint/24851/ Half-bounded numerical solution of singular integral equations with Cauchy kernel. Mahiub, Mohammad Abdulkawi Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri In this study, a numerical solution for singular integral equations of the first kind with Cauchy kernel over the finite segment [-1,1] is presented. The numerical solution is bounded at x =1 and unbounded at x = -1. The numerical solution is derived by approximating the unknown density function using the weighted Chebyshev polynomials of the fourth kind. The force function is approximated by using the Chebyshev polynomials of the third kind. The exactness of the numerical solution is shown for characteristic equation when the force function is a cubic. Science Publications 2011 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/24851/1/Half-bounded%20numerical%20solution%20of%20singular%20integral%20equations%20with%20Cauchy%20kernel..pdf Mahiub, Mohammad Abdulkawi and Eshkuratov, Zainidin K. and Nik Long, Nik Mohd Asri (2011) Half-bounded numerical solution of singular integral equations with Cauchy kernel. Journal of Mathematics and Statistics, 7 (1). pp. 81-85. ISSN 1549-3644 http://www.thescipub.com/ 10.3844/jmssp.2011.81.85 English |
| spellingShingle | Mahiub, Mohammad Abdulkawi Eshkuratov, Zainidin K. Nik Long, Nik Mohd Asri Half-bounded numerical solution of singular integral equations with Cauchy kernel. |
| title | Half-bounded numerical solution of singular integral equations with Cauchy kernel. |
| title_full | Half-bounded numerical solution of singular integral equations with Cauchy kernel. |
| title_fullStr | Half-bounded numerical solution of singular integral equations with Cauchy kernel. |
| title_full_unstemmed | Half-bounded numerical solution of singular integral equations with Cauchy kernel. |
| title_short | Half-bounded numerical solution of singular integral equations with Cauchy kernel. |
| title_sort | half-bounded numerical solution of singular integral equations with cauchy kernel. |
| url | http://psasir.upm.edu.my/id/eprint/24851/ http://psasir.upm.edu.my/id/eprint/24851/ http://psasir.upm.edu.my/id/eprint/24851/ http://psasir.upm.edu.my/id/eprint/24851/1/Half-bounded%20numerical%20solution%20of%20singular%20integral%20equations%20with%20Cauchy%20kernel..pdf |