A Legendre-homotopy method for the solutions of higher order boundary value problems
In this paper, the Legendre-homotopy analysis method is proposed using orthogonal Legendre polynomials for the approximate solutions of linear and nonlinear higher order boundary value problems. The deformation equations obtained in this case are easily integrable and the calculations involved in th...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-01-01
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| Series: | Journal of King Saud University: Science |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018364718302386 |
| _version_ | 1828425747642974208 |
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| author | Maasoomah Sadaf Ghazala Akram |
| author_facet | Maasoomah Sadaf Ghazala Akram |
| author_sort | Maasoomah Sadaf |
| collection | DOAJ |
| description | In this paper, the Legendre-homotopy analysis method is proposed using orthogonal Legendre polynomials for the approximate solutions of linear and nonlinear higher order boundary value problems. The deformation equations obtained in this case are easily integrable and the calculations involved in the algorithm are much simpler than the standard homotopy analysis method. The method is numerically illustrated by application on linear and nonlinear higher order boundary value problems. The absolute errors in the approximate solution values are calculated and compared with the results available in literature. The approximate solutions are also compared with the exact solutions through graphical illustrations. The numerical and graphical comparisons reveal that the presented method gives highly accurate results. Keywords: Legendre polynomials, Homotopy analysis method, Higher order boundary value problems |
| first_indexed | 2024-12-10T16:35:47Z |
| format | Article |
| id | doaj.art-692d5f3e75fd425189b8b82b011399b2 |
| institution | Directory Open Access Journal |
| issn | 1018-3647 |
| language | English |
| last_indexed | 2024-12-10T16:35:47Z |
| publishDate | 2020-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of King Saud University: Science |
| spelling | doaj.art-692d5f3e75fd425189b8b82b011399b22022-12-22T01:41:25ZengElsevierJournal of King Saud University: Science1018-36472020-01-01321537543A Legendre-homotopy method for the solutions of higher order boundary value problemsMaasoomah Sadaf0Ghazala Akram1Department of Mathematics, University of the Punjab, Lahore 54590, PakistanCorresponding author.; Department of Mathematics, University of the Punjab, Lahore 54590, PakistanIn this paper, the Legendre-homotopy analysis method is proposed using orthogonal Legendre polynomials for the approximate solutions of linear and nonlinear higher order boundary value problems. The deformation equations obtained in this case are easily integrable and the calculations involved in the algorithm are much simpler than the standard homotopy analysis method. The method is numerically illustrated by application on linear and nonlinear higher order boundary value problems. The absolute errors in the approximate solution values are calculated and compared with the results available in literature. The approximate solutions are also compared with the exact solutions through graphical illustrations. The numerical and graphical comparisons reveal that the presented method gives highly accurate results. Keywords: Legendre polynomials, Homotopy analysis method, Higher order boundary value problemshttp://www.sciencedirect.com/science/article/pii/S1018364718302386 |
| spellingShingle | Maasoomah Sadaf Ghazala Akram A Legendre-homotopy method for the solutions of higher order boundary value problems Journal of King Saud University: Science |
| title | A Legendre-homotopy method for the solutions of higher order boundary value problems |
| title_full | A Legendre-homotopy method for the solutions of higher order boundary value problems |
| title_fullStr | A Legendre-homotopy method for the solutions of higher order boundary value problems |
| title_full_unstemmed | A Legendre-homotopy method for the solutions of higher order boundary value problems |
| title_short | A Legendre-homotopy method for the solutions of higher order boundary value problems |
| title_sort | legendre homotopy method for the solutions of higher order boundary value problems |
| url | http://www.sciencedirect.com/science/article/pii/S1018364718302386 |
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