On the general solution of first-kind hypersingular integral equations
A new algorithm is presented to provide a general solution for a first type Hyper singular Integral Equation (HSIE). The singular integral has been converted into a regular form by cancelling the singularity and then transforming it into a system of algebraic equation based orthogonal poly- nomials....
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Science Publications
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/53431/ http://psasir.upm.edu.my/id/eprint/53431/1/On%20the%20general%20solution%20of%20first-kind%20Hypersingular%20Integr.pdf |
| _version_ | 1848852282270023680 |
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| author | Obaiys, Suzan Jabbar Abbas, Zulkifly Nik Long, Nik Mohd Asri Ahmad, Ahmad Fahad Ahmedov, Anvarjon Raad, Haider Khaleel |
| author_facet | Obaiys, Suzan Jabbar Abbas, Zulkifly Nik Long, Nik Mohd Asri Ahmad, Ahmad Fahad Ahmedov, Anvarjon Raad, Haider Khaleel |
| author_sort | Obaiys, Suzan Jabbar |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A new algorithm is presented to provide a general solution for a first type Hyper singular Integral Equation (HSIE). The singular integral has been converted into a regular form by cancelling the singularity and then transforming it into a system of algebraic equation based orthogonal poly- nomials. We applied the convergence method presented by (Obaiys, 2013) to conform the numerical solution of the regularized Hadamard equation, which has shown an absolute agreement with the exact solution within small values of n. The proposed method has been examined by various HSIEs where the displacement function satisfies the HÓ§lder-continuous first derivative. Such equations are particularly important inmany physics and engineering problems, such as fracture mechanics, acoustics and elasticity. |
| first_indexed | 2025-11-15T10:35:36Z |
| format | Article |
| id | upm-53431 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:35:36Z |
| publishDate | 2016 |
| publisher | Science Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-534312017-12-04T09:27:48Z http://psasir.upm.edu.my/id/eprint/53431/ On the general solution of first-kind hypersingular integral equations Obaiys, Suzan Jabbar Abbas, Zulkifly Nik Long, Nik Mohd Asri Ahmad, Ahmad Fahad Ahmedov, Anvarjon Raad, Haider Khaleel A new algorithm is presented to provide a general solution for a first type Hyper singular Integral Equation (HSIE). The singular integral has been converted into a regular form by cancelling the singularity and then transforming it into a system of algebraic equation based orthogonal poly- nomials. We applied the convergence method presented by (Obaiys, 2013) to conform the numerical solution of the regularized Hadamard equation, which has shown an absolute agreement with the exact solution within small values of n. The proposed method has been examined by various HSIEs where the displacement function satisfies the HÓ§lder-continuous first derivative. Such equations are particularly important inmany physics and engineering problems, such as fracture mechanics, acoustics and elasticity. Science Publications 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/53431/1/On%20the%20general%20solution%20of%20first-kind%20Hypersingular%20Integr.pdf Obaiys, Suzan Jabbar and Abbas, Zulkifly and Nik Long, Nik Mohd Asri and Ahmad, Ahmad Fahad and Ahmedov, Anvarjon and Raad, Haider Khaleel (2016) On the general solution of first-kind hypersingular integral equations. American Journal of Engineering and Applied Sciences, 9 (2). pp. 195-201. ISSN 1941-7020; ESSN: 1941-7039 http://thescipub.com/abstract/10.3844/ajeassp.2016.195.201 10.3844/ajeassp.2016.195.201 |
| spellingShingle | Obaiys, Suzan Jabbar Abbas, Zulkifly Nik Long, Nik Mohd Asri Ahmad, Ahmad Fahad Ahmedov, Anvarjon Raad, Haider Khaleel On the general solution of first-kind hypersingular integral equations |
| title | On the general solution of first-kind hypersingular integral equations |
| title_full | On the general solution of first-kind hypersingular integral equations |
| title_fullStr | On the general solution of first-kind hypersingular integral equations |
| title_full_unstemmed | On the general solution of first-kind hypersingular integral equations |
| title_short | On the general solution of first-kind hypersingular integral equations |
| title_sort | on the general solution of first-kind hypersingular integral equations |
| url | http://psasir.upm.edu.my/id/eprint/53431/ http://psasir.upm.edu.my/id/eprint/53431/ http://psasir.upm.edu.my/id/eprint/53431/ http://psasir.upm.edu.my/id/eprint/53431/1/On%20the%20general%20solution%20of%20first-kind%20Hypersingular%20Integr.pdf |