Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method
Spectral homotopy analysis method (SHAM) as a modification of homotopy analysis method (HAM) is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30127/ http://psasir.upm.edu.my/id/eprint/30127/1/Numerical%20solution%20of%20nonlinear%20fredholm%20integro.pdf |
| _version_ | 1848846590073110528 |
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| author | Atabakan, Z. Pashazadeh Nasab, A. Kazemi Kilicman, Adem Eshkuvatov, Zainidin K. |
| author_facet | Atabakan, Z. Pashazadeh Nasab, A. Kazemi Kilicman, Adem Eshkuvatov, Zainidin K. |
| author_sort | Atabakan, Z. Pashazadeh |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Spectral homotopy analysis method (SHAM) as a modification of homotopy analysis method (HAM) is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions. |
| first_indexed | 2025-11-15T09:05:07Z |
| format | Article |
| id | upm-30127 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:05:07Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-301272016-02-12T08:39:20Z http://psasir.upm.edu.my/id/eprint/30127/ Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method Atabakan, Z. Pashazadeh Nasab, A. Kazemi Kilicman, Adem Eshkuvatov, Zainidin K. Spectral homotopy analysis method (SHAM) as a modification of homotopy analysis method (HAM) is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30127/1/Numerical%20solution%20of%20nonlinear%20fredholm%20integro.pdf Atabakan, Z. Pashazadeh and Nasab, A. Kazemi and Kilicman, Adem and Eshkuvatov, Zainidin K. (2013) Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method. Mathematical Problems in Engineering, 2013. art. no. 674364. pp. 1-9. ISSN 1024-123X http://dx.doi.org/10.1155/2013/674364 10.1155/2013/674364 |
| spellingShingle | Atabakan, Z. Pashazadeh Nasab, A. Kazemi Kilicman, Adem Eshkuvatov, Zainidin K. Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method |
| title | Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method |
| title_full | Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method |
| title_fullStr | Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method |
| title_full_unstemmed | Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method |
| title_short | Numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method |
| title_sort | numerical solution of nonlinear fredholm integro-differential equations using spectral homotopy analysis method |
| url | http://psasir.upm.edu.my/id/eprint/30127/ http://psasir.upm.edu.my/id/eprint/30127/ http://psasir.upm.edu.my/id/eprint/30127/ http://psasir.upm.edu.my/id/eprint/30127/1/Numerical%20solution%20of%20nonlinear%20fredholm%20integro.pdf |