On the solutions of three-point boundary value problems using variational-fixed point iteration method
Given a three-point fourth-order boundary value problems y(iv) + p(x)y’’’ + r(x)y’ + s(x)y = f(x), a ≤ x ≤ b such that y(a) = y(b) = y’’(b) = y’’(α) = 0, a ≤ α ≤ b; where p, q, r, s, f ϵ C [a, b] , we combine the application of variational iteration method and fixed point iteration process to constr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/51922/1/51922.pdf |
| _version_ | 1796975640266670080 |
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| author | Kilicman, Adem Wadai, Mutah |
| author_facet | Kilicman, Adem Wadai, Mutah |
| author_sort | Kilicman, Adem |
| collection | UPM |
| description | Given a three-point fourth-order boundary value problems y(iv) + p(x)y’’’ + r(x)y’ + s(x)y = f(x), a ≤ x ≤ b such that y(a) = y(b) = y’’(b) = y’’(α) = 0, a ≤ α ≤ b; where p, q, r, s, f ϵ C [a, b] , we combine the application of variational iteration method and fixed point iteration process to construct an iterative scheme called variational-fixed point iteration method that approximates the solution of three-point boundary value problems. The success of the variational or weighted residual method of approximation from a practical point of view depends on the suitable selection of the basis function. The method is self correcting one and leads to fast convergence. Problems were experimented to show the effectiveness and accuracy of the proposed method. |
| first_indexed | 2024-03-06T09:14:23Z |
| format | Article |
| id | upm.eprints-51922 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:14:23Z |
| publishDate | 2016 |
| publisher | Springer |
| record_format | dspace |
| spelling | upm.eprints-519222017-05-03T04:28:46Z http://psasir.upm.edu.my/id/eprint/51922/ On the solutions of three-point boundary value problems using variational-fixed point iteration method Kilicman, Adem Wadai, Mutah Given a three-point fourth-order boundary value problems y(iv) + p(x)y’’’ + r(x)y’ + s(x)y = f(x), a ≤ x ≤ b such that y(a) = y(b) = y’’(b) = y’’(α) = 0, a ≤ α ≤ b; where p, q, r, s, f ϵ C [a, b] , we combine the application of variational iteration method and fixed point iteration process to construct an iterative scheme called variational-fixed point iteration method that approximates the solution of three-point boundary value problems. The success of the variational or weighted residual method of approximation from a practical point of view depends on the suitable selection of the basis function. The method is self correcting one and leads to fast convergence. Problems were experimented to show the effectiveness and accuracy of the proposed method. Springer 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/51922/1/51922.pdf Kilicman, Adem and Wadai, Mutah (2016) On the solutions of three-point boundary value problems using variational-fixed point iteration method. Mathematical Sciences, 10 (1). pp. 33-40. ISSN 2008-1359; ESSN: 2251-7456 http://rd.springer.com/article/10.1007/s40096-016-0175-z 10.1007/s40096-016-0175-z |
| spellingShingle | Kilicman, Adem Wadai, Mutah On the solutions of three-point boundary value problems using variational-fixed point iteration method |
| title | On the solutions of three-point boundary value problems using variational-fixed point iteration method |
| title_full | On the solutions of three-point boundary value problems using variational-fixed point iteration method |
| title_fullStr | On the solutions of three-point boundary value problems using variational-fixed point iteration method |
| title_full_unstemmed | On the solutions of three-point boundary value problems using variational-fixed point iteration method |
| title_short | On the solutions of three-point boundary value problems using variational-fixed point iteration method |
| title_sort | on the solutions of three point boundary value problems using variational fixed point iteration method |
| url | http://psasir.upm.edu.my/id/eprint/51922/1/51922.pdf |
| work_keys_str_mv | AT kilicmanadem onthesolutionsofthreepointboundaryvalueproblemsusingvariationalfixedpointiterationmethod AT wadaimutah onthesolutionsofthreepointboundaryvalueproblemsusingvariationalfixedpointiterationmethod |