Hybrid one-step block fourth derivative method for the direct solution of third order initial value problems of ordinary differential equations
An efficient one step block method with generalized two-point-hybrid is developed for solving initial value problems of third order ordinary differential equations directly. In driving this algorithm, a power series approximate function is interpolated at {xn, xn+r, xn+s} while its third and fourth...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Academic Publications, Ltd.
2018
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| Online Access: | https://repo.uum.edu.my/id/eprint/27940/1/HJPAM%20119%201%202018%20207%20224.pdf |
| _version_ | 1825805719168876544 |
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| author | Alkasassbeh, Mohammad Omar, Zurni |
| author_facet | Alkasassbeh, Mohammad Omar, Zurni |
| author_sort | Alkasassbeh, Mohammad |
| collection | UUM |
| description | An efficient one step block method with generalized two-point-hybrid is developed for solving initial value problems of third order ordinary differential equations directly. In driving this algorithm, a power series approximate function is interpolated at {xn, xn+r, xn+s} while its third and fourth derivatives are collocated at all points {xn, xn+r, xn+s, xn+1} in the given interval. The proposed method is then tested for initial value problems of third order ordinary differential equations solved previously by other methods. The numerical results
confirm the superiority of the new method to the existing methods regarding accuracy. |
| first_indexed | 2024-07-04T06:36:51Z |
| format | Article |
| id | uum-27940 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T06:36:51Z |
| publishDate | 2018 |
| publisher | Academic Publications, Ltd. |
| record_format | eprints |
| spelling | uum-279402020-12-01T06:04:00Z https://repo.uum.edu.my/id/eprint/27940/ Hybrid one-step block fourth derivative method for the direct solution of third order initial value problems of ordinary differential equations Alkasassbeh, Mohammad Omar, Zurni QA75 Electronic computers. Computer science An efficient one step block method with generalized two-point-hybrid is developed for solving initial value problems of third order ordinary differential equations directly. In driving this algorithm, a power series approximate function is interpolated at {xn, xn+r, xn+s} while its third and fourth derivatives are collocated at all points {xn, xn+r, xn+s, xn+1} in the given interval. The proposed method is then tested for initial value problems of third order ordinary differential equations solved previously by other methods. The numerical results confirm the superiority of the new method to the existing methods regarding accuracy. Academic Publications, Ltd. 2018 Article PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/27940/1/HJPAM%20119%201%202018%20207%20224.pdf Alkasassbeh, Mohammad and Omar, Zurni (2018) Hybrid one-step block fourth derivative method for the direct solution of third order initial value problems of ordinary differential equations. International Journal of Pure and Applied Mathematics, 119 (1). pp. 207-224. ISSN 1311-8080 https://ijpam.eu/contents/2018-119-1/17/ |
| spellingShingle | QA75 Electronic computers. Computer science Alkasassbeh, Mohammad Omar, Zurni Hybrid one-step block fourth derivative method for the direct solution of third order initial value problems of ordinary differential equations |
| title | Hybrid one-step block fourth derivative method for the direct solution of third order initial value problems of ordinary differential equations |
| title_full | Hybrid one-step block fourth derivative method for the direct solution of third order initial value problems of ordinary differential equations |
| title_fullStr | Hybrid one-step block fourth derivative method for the direct solution of third order initial value problems of ordinary differential equations |
| title_full_unstemmed | Hybrid one-step block fourth derivative method for the direct solution of third order initial value problems of ordinary differential equations |
| title_short | Hybrid one-step block fourth derivative method for the direct solution of third order initial value problems of ordinary differential equations |
| title_sort | hybrid one step block fourth derivative method for the direct solution of third order initial value problems of ordinary differential equations |
| topic | QA75 Electronic computers. Computer science |
| url | https://repo.uum.edu.my/id/eprint/27940/1/HJPAM%20119%201%202018%20207%20224.pdf |
| work_keys_str_mv | AT alkasassbehmohammad hybridonestepblockfourthderivativemethodforthedirectsolutionofthirdorderinitialvalueproblemsofordinarydifferentialequations AT omarzurni hybridonestepblockfourthderivativemethodforthedirectsolutionofthirdorderinitialvalueproblemsofordinarydifferentialequations |