Differential transformation method for solving sixth-order boundary value problems of ordinary differential equations
In this study, sixth-order boundary value problems for linear and nonlinear differential equations have been solved by using Differential Transformation Method (DTM). The numerical solutions are given in several examples. For each example, the solution given by DTM is compared with the exact solutio...
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| Format: | Article |
| Language: | English |
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Penerbit UTM Press
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/55527/1/Differential%20transformation%20method%20for%20solving%20sixth-order%20boundary%20value%20problems%20of%20.pdf |
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| author | Che Hussin, Che Haziqah Mandangan, Arif Kilicman, Adem Daud, Muhamad Azlan Juhan, Nurliyana |
| author_facet | Che Hussin, Che Haziqah Mandangan, Arif Kilicman, Adem Daud, Muhamad Azlan Juhan, Nurliyana |
| author_sort | Che Hussin, Che Haziqah |
| collection | UPM |
| description | In this study, sixth-order boundary value problems for linear and nonlinear differential equations have been solved by using Differential Transformation Method (DTM). The numerical solutions are given in several examples. For each example, the solution given by DTM is compared with the exact solution. Absolute relative error (ARE) for each iteration can be computed. Therefore, the maximum absolute relative error (MARE) of the DTM can be obtained. To show that the solution given by the DTM has higher level of accuracy, the absolute relative error of the DTM has been compared with the other methods such as Adomian decomposition method with Green’s function, modified decomposition method (MDM), homotopy perturbation method (HPM), Variational Iteration Method (VIM) and Quintic B-Spline Collocation Method. Comparison graphs are given at the end of this paper. The obtained result shows that the proposed method is able to provide better approximation in term of accuracy. |
| first_indexed | 2024-03-06T09:23:41Z |
| format | Article |
| id | upm.eprints-55527 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:23:41Z |
| publishDate | 2016 |
| publisher | Penerbit UTM Press |
| record_format | dspace |
| spelling | upm.eprints-555272017-09-13T02:58:25Z http://psasir.upm.edu.my/id/eprint/55527/ Differential transformation method for solving sixth-order boundary value problems of ordinary differential equations Che Hussin, Che Haziqah Mandangan, Arif Kilicman, Adem Daud, Muhamad Azlan Juhan, Nurliyana In this study, sixth-order boundary value problems for linear and nonlinear differential equations have been solved by using Differential Transformation Method (DTM). The numerical solutions are given in several examples. For each example, the solution given by DTM is compared with the exact solution. Absolute relative error (ARE) for each iteration can be computed. Therefore, the maximum absolute relative error (MARE) of the DTM can be obtained. To show that the solution given by the DTM has higher level of accuracy, the absolute relative error of the DTM has been compared with the other methods such as Adomian decomposition method with Green’s function, modified decomposition method (MDM), homotopy perturbation method (HPM), Variational Iteration Method (VIM) and Quintic B-Spline Collocation Method. Comparison graphs are given at the end of this paper. The obtained result shows that the proposed method is able to provide better approximation in term of accuracy. Penerbit UTM Press 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/55527/1/Differential%20transformation%20method%20for%20solving%20sixth-order%20boundary%20value%20problems%20of%20.pdf Che Hussin, Che Haziqah and Mandangan, Arif and Kilicman, Adem and Daud, Muhamad Azlan and Juhan, Nurliyana (2016) Differential transformation method for solving sixth-order boundary value problems of ordinary differential equations. Jurnal Teknologi (Sciences and Engineering), 78 (6-4). pp. 13-19. ISSN 0127-9696; ESSN: 2180-3722 http://www.jurnalteknologi.utm.my/index.php/jurnalteknologi/article/view/8969 |
| spellingShingle | Che Hussin, Che Haziqah Mandangan, Arif Kilicman, Adem Daud, Muhamad Azlan Juhan, Nurliyana Differential transformation method for solving sixth-order boundary value problems of ordinary differential equations |
| title | Differential transformation method for solving sixth-order boundary value problems of ordinary differential equations |
| title_full | Differential transformation method for solving sixth-order boundary value problems of ordinary differential equations |
| title_fullStr | Differential transformation method for solving sixth-order boundary value problems of ordinary differential equations |
| title_full_unstemmed | Differential transformation method for solving sixth-order boundary value problems of ordinary differential equations |
| title_short | Differential transformation method for solving sixth-order boundary value problems of ordinary differential equations |
| title_sort | differential transformation method for solving sixth order boundary value problems of ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/55527/1/Differential%20transformation%20method%20for%20solving%20sixth-order%20boundary%20value%20problems%20of%20.pdf |
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