Homotopy perturbation method for the hypersingular integral equations of the first kind
Simple and efficient convex homotopy perturbation method (HPM) is presented to obtain an approximate solution of hyper-singular integral equations of the first kind. Convergence and error estimate of HPM are obtained. Three numerical examples were provided to verify the effectiveness of the HPM. Com...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/74519/1/Homotopy%20perturbation%20method%20for%20the%20hypersingular%20integral%20equations%20of%20the%20first%20kind.pdf |
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| author | K.Eshkuvatov, Zainidin Zulkarnain, Fatimah Samihah Nik Long, Nik Mohd Asri Muminov, Zahriddin |
| author_facet | K.Eshkuvatov, Zainidin Zulkarnain, Fatimah Samihah Nik Long, Nik Mohd Asri Muminov, Zahriddin |
| author_sort | K.Eshkuvatov, Zainidin |
| collection | UPM |
| description | Simple and efficient convex homotopy perturbation method (HPM) is presented to obtain an approximate solution of hyper-singular integral equations of the first kind. Convergence and error estimate of HPM are obtained. Three numerical examples were provided to verify the effectiveness of the HPM. Comparisons with reproducing kernel method (Chen et al., 2011) for the same number of iteration is also presented. Numerical examples reveal that the convergence of HPM can still be achieved for some problems even if the condition of convergence of HPM is not satisfied. |
| first_indexed | 2024-03-06T10:13:14Z |
| format | Article |
| id | upm.eprints-74519 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T10:13:14Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | upm.eprints-745192019-12-05T03:34:19Z http://psasir.upm.edu.my/id/eprint/74519/ Homotopy perturbation method for the hypersingular integral equations of the first kind K.Eshkuvatov, Zainidin Zulkarnain, Fatimah Samihah Nik Long, Nik Mohd Asri Muminov, Zahriddin Simple and efficient convex homotopy perturbation method (HPM) is presented to obtain an approximate solution of hyper-singular integral equations of the first kind. Convergence and error estimate of HPM are obtained. Three numerical examples were provided to verify the effectiveness of the HPM. Comparisons with reproducing kernel method (Chen et al., 2011) for the same number of iteration is also presented. Numerical examples reveal that the convergence of HPM can still be achieved for some problems even if the condition of convergence of HPM is not satisfied. Elsevier 2018-12 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/74519/1/Homotopy%20perturbation%20method%20for%20the%20hypersingular%20integral%20equations%20of%20the%20first%20kind.pdf K.Eshkuvatov, Zainidin and Zulkarnain, Fatimah Samihah and Nik Long, Nik Mohd Asri and Muminov, Zahriddin (2018) Homotopy perturbation method for the hypersingular integral equations of the first kind. Ain Shams Engineering Journal, 9 (4). 3359 - 3363. ISSN 2090-4479; ESSN: 2090-4495 https://www.sciencedirect.com/science/article/pii/S2090447917301272 10.1016/j.asej.2017.04.010 |
| spellingShingle | K.Eshkuvatov, Zainidin Zulkarnain, Fatimah Samihah Nik Long, Nik Mohd Asri Muminov, Zahriddin Homotopy perturbation method for the hypersingular integral equations of the first kind |
| title | Homotopy perturbation method for the hypersingular integral equations of the first kind |
| title_full | Homotopy perturbation method for the hypersingular integral equations of the first kind |
| title_fullStr | Homotopy perturbation method for the hypersingular integral equations of the first kind |
| title_full_unstemmed | Homotopy perturbation method for the hypersingular integral equations of the first kind |
| title_short | Homotopy perturbation method for the hypersingular integral equations of the first kind |
| title_sort | homotopy perturbation method for the hypersingular integral equations of the first kind |
| url | http://psasir.upm.edu.my/id/eprint/74519/1/Homotopy%20perturbation%20method%20for%20the%20hypersingular%20integral%20equations%20of%20the%20first%20kind.pdf |
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