Semi bounded solution of hypersingular integral equations of the first kind on the rectangle
A hypersingular integral equations (HSIEs) of the first kind on the interval [ 1 ; 1 ] with the assumption that kernel of the hypersingular integral is constant on the diagonal of the domain is considered. Truncated series of Chebyshev polynomials of the third and fourth kinds are used to find semi...
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| Format: | Article |
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Horizon Research Publishing
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/87558/ |
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| author | Eshkuvatov, Zainidin K. Kommuji, Massamdi Aloev, Rakhmatullo Nik Long, Nik Mohd Asri Khudoyberganov, Mirzoali |
| author_facet | Eshkuvatov, Zainidin K. Kommuji, Massamdi Aloev, Rakhmatullo Nik Long, Nik Mohd Asri Khudoyberganov, Mirzoali |
| author_sort | Eshkuvatov, Zainidin K. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A hypersingular integral equations (HSIEs) of the first kind on the interval [ 1 ; 1 ] with the assumption that kernel of the hypersingular integral is constant on the diagonal of the domain is considered. Truncated series of Chebyshev polynomials of the third and fourth kinds are used to find semi bounded (unbounded on the left and bounded on the right and vice versa) solutions of HSIEs of first kind. Exact calculations of singular and hypersingular integrals with respect to Chebyshev polynomials of third and forth kind with corresponding weights allows us to obtain high accurate approximate solution. Gauss-Chebyshev quadrature formula is extended for regular kernel integrals. Three examples are provided to verify the validity and accuracy of the proposed method. Numerical examples reveal that approximate solutions are exact if solution of HSIEs is of the polynomial forms with corresponding weights. |
| first_indexed | 2025-11-15T12:45:34Z |
| format | Article |
| id | upm-87558 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T12:45:34Z |
| publishDate | 2020 |
| publisher | Horizon Research Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-875582022-11-23T03:26:51Z http://psasir.upm.edu.my/id/eprint/87558/ Semi bounded solution of hypersingular integral equations of the first kind on the rectangle Eshkuvatov, Zainidin K. Kommuji, Massamdi Aloev, Rakhmatullo Nik Long, Nik Mohd Asri Khudoyberganov, Mirzoali A hypersingular integral equations (HSIEs) of the first kind on the interval [ 1 ; 1 ] with the assumption that kernel of the hypersingular integral is constant on the diagonal of the domain is considered. Truncated series of Chebyshev polynomials of the third and fourth kinds are used to find semi bounded (unbounded on the left and bounded on the right and vice versa) solutions of HSIEs of first kind. Exact calculations of singular and hypersingular integrals with respect to Chebyshev polynomials of third and forth kind with corresponding weights allows us to obtain high accurate approximate solution. Gauss-Chebyshev quadrature formula is extended for regular kernel integrals. Three examples are provided to verify the validity and accuracy of the proposed method. Numerical examples reveal that approximate solutions are exact if solution of HSIEs is of the polynomial forms with corresponding weights. Horizon Research Publishing 2020 Article PeerReviewed Eshkuvatov, Zainidin K. and Kommuji, Massamdi and Aloev, Rakhmatullo and Nik Long, Nik Mohd Asri and Khudoyberganov, Mirzoali (2020) Semi bounded solution of hypersingular integral equations of the first kind on the rectangle. Mathematics and Statistics, 8 (2). 106 - 120. ISSN 2332-2071; ESSN: 2332-2144 https://www.hrpub.org/journals/article_info.php?aid=8759 10.13189/ms.2020.080206 |
| spellingShingle | Eshkuvatov, Zainidin K. Kommuji, Massamdi Aloev, Rakhmatullo Nik Long, Nik Mohd Asri Khudoyberganov, Mirzoali Semi bounded solution of hypersingular integral equations of the first kind on the rectangle |
| title | Semi bounded solution of hypersingular integral equations of the first kind on the rectangle |
| title_full | Semi bounded solution of hypersingular integral equations of the first kind on the rectangle |
| title_fullStr | Semi bounded solution of hypersingular integral equations of the first kind on the rectangle |
| title_full_unstemmed | Semi bounded solution of hypersingular integral equations of the first kind on the rectangle |
| title_short | Semi bounded solution of hypersingular integral equations of the first kind on the rectangle |
| title_sort | semi bounded solution of hypersingular integral equations of the first kind on the rectangle |
| url | http://psasir.upm.edu.my/id/eprint/87558/ http://psasir.upm.edu.my/id/eprint/87558/ http://psasir.upm.edu.my/id/eprint/87558/ |