Modified homotopy perturbation method for integro-differential and hypersingular integral equations
Homotopy perturbation method (HPM) is implemented to solve the mathematical problems. The solution is obtained by taking the summation of infinite series. This thesis present a modification of HPM by equating the second series as zero. Convergence and error estimation of HPM and modified HPM (MHP...
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| Format: | Thesis |
| Language: | English |
| Published: |
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/83565/ http://psasir.upm.edu.my/id/eprint/83565/1/FS%202018%20100%20-%20ir.pdf |
| _version_ | 1848859575903584256 |
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| author | Zulkarnain, Fatimah Samihah |
| author_facet | Zulkarnain, Fatimah Samihah |
| author_sort | Zulkarnain, Fatimah Samihah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Homotopy perturbation method (HPM) is implemented to solve the mathematical
problems. The solution is obtained by taking the summation of infinite series. This
thesis present a modification of HPM by equating the second series as zero. Convergence
and error estimation of HPM and modified HPM (MHPM) are obtained in the
class of C[a;b] for Fredholm-Volterra integral equation (FVIE) problem and Ck(D)
where D is a closed subspace of R2 for higher order FVIDE problem.
Many researchers solved singular integral equation with kernel equal to one. This
study describes the implementation of HPM and MHPM on HSIE of the first kind
with kernel is a constant on a diagonal. Convergence and error estimation are obtained
in the class of Lr [-1;1]. MHPM is also used to solve HSIE of the second
kind.
For all cases, numerical examples are provided to exhibit the efficiency of the methods.
The results obtained are more accurate than the previous works. |
| first_indexed | 2025-11-15T12:31:32Z |
| format | Thesis |
| id | upm-83565 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:31:32Z |
| publishDate | 2018 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-835652022-01-06T03:18:59Z http://psasir.upm.edu.my/id/eprint/83565/ Modified homotopy perturbation method for integro-differential and hypersingular integral equations Zulkarnain, Fatimah Samihah Homotopy perturbation method (HPM) is implemented to solve the mathematical problems. The solution is obtained by taking the summation of infinite series. This thesis present a modification of HPM by equating the second series as zero. Convergence and error estimation of HPM and modified HPM (MHPM) are obtained in the class of C[a;b] for Fredholm-Volterra integral equation (FVIE) problem and Ck(D) where D is a closed subspace of R2 for higher order FVIDE problem. Many researchers solved singular integral equation with kernel equal to one. This study describes the implementation of HPM and MHPM on HSIE of the first kind with kernel is a constant on a diagonal. Convergence and error estimation are obtained in the class of Lr [-1;1]. MHPM is also used to solve HSIE of the second kind. For all cases, numerical examples are provided to exhibit the efficiency of the methods. The results obtained are more accurate than the previous works. 2018-04 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/83565/1/FS%202018%20100%20-%20ir.pdf Zulkarnain, Fatimah Samihah (2018) Modified homotopy perturbation method for integro-differential and hypersingular integral equations. Doctoral thesis, Universiti Putra Malaysia. Mathematics Homotopy equivalences |
| spellingShingle | Mathematics Homotopy equivalences Zulkarnain, Fatimah Samihah Modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| title | Modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| title_full | Modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| title_fullStr | Modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| title_full_unstemmed | Modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| title_short | Modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| title_sort | modified homotopy perturbation method for integro-differential and hypersingular integral equations |
| topic | Mathematics Homotopy equivalences |
| url | http://psasir.upm.edu.my/id/eprint/83565/ http://psasir.upm.edu.my/id/eprint/83565/1/FS%202018%20100%20-%20ir.pdf |