Error estimations of Homotopy perturbation method for linear integral and integro-differential equations of the third kind
In this note, convex Homotopy perturbation method (HPM) is presented for the approximate solution of the linear Fredholm-Volterra integral and integro-differential equation. Convergence and rate of convergence of the HPM are proved for both equations. Five numerical examples are provided to verify t...
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| Format: | Article |
| Language: | English |
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2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/54184/ http://psasir.upm.edu.my/id/eprint/54184/1/Error%20estimations%20of%20Homotopy%20perturbation%20method%20for%20linear%20integral%20.pdf |
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| author | Eshkuvatov, Zainidin K. Zulkarnain, F. S. Nik Long, Nik Mohd Asri Muminov, Zahriddin |
| author_facet | Eshkuvatov, Zainidin K. Zulkarnain, F. S. Nik Long, Nik Mohd Asri Muminov, Zahriddin |
| author_sort | Eshkuvatov, Zainidin K. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this note, convex Homotopy perturbation method (HPM) is presented for the approximate solution of the linear Fredholm-Volterra integral and integro-differential equation. Convergence and rate of convergence of the HPM are proved for both equations. Five numerical examples are provided to verify the validity and accuracy of the proposed method. Example reveals that HPM is very accurate and simple to implement for integral and integrodifferential equations. |
| first_indexed | 2025-11-15T10:38:41Z |
| format | Article |
| id | upm-54184 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:38:41Z |
| publishDate | 2016 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-541842018-03-02T07:59:50Z http://psasir.upm.edu.my/id/eprint/54184/ Error estimations of Homotopy perturbation method for linear integral and integro-differential equations of the third kind Eshkuvatov, Zainidin K. Zulkarnain, F. S. Nik Long, Nik Mohd Asri Muminov, Zahriddin In this note, convex Homotopy perturbation method (HPM) is presented for the approximate solution of the linear Fredholm-Volterra integral and integro-differential equation. Convergence and rate of convergence of the HPM are proved for both equations. Five numerical examples are provided to verify the validity and accuracy of the proposed method. Example reveals that HPM is very accurate and simple to implement for integral and integrodifferential equations. 2016-06 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/54184/1/Error%20estimations%20of%20Homotopy%20perturbation%20method%20for%20linear%20integral%20.pdf Eshkuvatov, Zainidin K. and Zulkarnain, F. S. and Nik Long, Nik Mohd Asri and Muminov, Zahriddin (2016) Error estimations of Homotopy perturbation method for linear integral and integro-differential equations of the third kind. Research & Reviews: Journal of Statistics and Mathematical Sciences, 2 (1). pp. 89-97. http://www.rroij.com/open-access/pdfdownload.php?download=open-access/error-estimations-of-homotopy-perturbation-method-for-linear-integral-andintegrodifferential-equations-of-the-third-kind-.pdf&aid=73270 Approximate method; Homotopy perturbation method; Convergence; Error estimate |
| spellingShingle | Approximate method; Homotopy perturbation method; Convergence; Error estimate Eshkuvatov, Zainidin K. Zulkarnain, F. S. Nik Long, Nik Mohd Asri Muminov, Zahriddin Error estimations of Homotopy perturbation method for linear integral and integro-differential equations of the third kind |
| title | Error estimations of Homotopy perturbation method for linear integral and integro-differential equations of the third kind |
| title_full | Error estimations of Homotopy perturbation method for linear integral and integro-differential equations of the third kind |
| title_fullStr | Error estimations of Homotopy perturbation method for linear integral and integro-differential equations of the third kind |
| title_full_unstemmed | Error estimations of Homotopy perturbation method for linear integral and integro-differential equations of the third kind |
| title_short | Error estimations of Homotopy perturbation method for linear integral and integro-differential equations of the third kind |
| title_sort | error estimations of homotopy perturbation method for linear integral and integro-differential equations of the third kind |
| topic | Approximate method; Homotopy perturbation method; Convergence; Error estimate |
| url | http://psasir.upm.edu.my/id/eprint/54184/ http://psasir.upm.edu.my/id/eprint/54184/ http://psasir.upm.edu.my/id/eprint/54184/1/Error%20estimations%20of%20Homotopy%20perturbation%20method%20for%20linear%20integral%20.pdf |