Extra derivative implicit block methods for integrating general second order initial value problems
This paper focuses on the construction of two-point and three-point implicit block methods for solving general second order Initial Value Problems. The proposed methods are formulated using Hermite Interpolating Polynomial. The block methods approximate the numerical solutions at more than one poin...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia Press
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/80784/ http://psasir.upm.edu.my/id/eprint/80784/1/BLOCK.pdf |
| _version_ | 1848858955798806528 |
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| author | Turki, Mohammed Yousif Ismail, Fudziah Senu, Norazak |
| author_facet | Turki, Mohammed Yousif Ismail, Fudziah Senu, Norazak |
| author_sort | Turki, Mohammed Yousif |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper focuses on the construction of two-point and three-point implicit block methods for solving general second order Initial Value Problems. The proposed methods are formulated using Hermite Interpolating Polynomial. The block methods approximate
the numerical solutions at more than one point at a time directly without reducing the equation into the first order system of ordinary differential equations. In the derivation of the method, the higher derivative of the problem is incorporated into the formula to enhance the efficiency of the proposed methods. The order and zero- stability of the methods are also presented. Numerical results presented show the efficiency of these methods compared to the existing block methods. |
| first_indexed | 2025-11-15T12:21:40Z |
| format | Article |
| id | upm-80784 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:21:40Z |
| publishDate | 2020 |
| publisher | Universiti Putra Malaysia Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-807842021-08-18T01:24:46Z http://psasir.upm.edu.my/id/eprint/80784/ Extra derivative implicit block methods for integrating general second order initial value problems Turki, Mohammed Yousif Ismail, Fudziah Senu, Norazak This paper focuses on the construction of two-point and three-point implicit block methods for solving general second order Initial Value Problems. The proposed methods are formulated using Hermite Interpolating Polynomial. The block methods approximate the numerical solutions at more than one point at a time directly without reducing the equation into the first order system of ordinary differential equations. In the derivation of the method, the higher derivative of the problem is incorporated into the formula to enhance the efficiency of the proposed methods. The order and zero- stability of the methods are also presented. Numerical results presented show the efficiency of these methods compared to the existing block methods. Universiti Putra Malaysia Press 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/80784/1/BLOCK.pdf Turki, Mohammed Yousif and Ismail, Fudziah and Senu, Norazak (2020) Extra derivative implicit block methods for integrating general second order initial value problems. Pertanika Journal of Science and Technology, 28 (3). pp. 951-966. ISSN 0128-7680; ESSN: 2231-8526 http://www.pertanika.upm.edu.my/pjst/browse/regular-issue?article=JST-1902-2020 |
| spellingShingle | Turki, Mohammed Yousif Ismail, Fudziah Senu, Norazak Extra derivative implicit block methods for integrating general second order initial value problems |
| title | Extra derivative implicit block methods for integrating general second order initial value problems |
| title_full | Extra derivative implicit block methods for integrating general second order initial value problems |
| title_fullStr | Extra derivative implicit block methods for integrating general second order initial value problems |
| title_full_unstemmed | Extra derivative implicit block methods for integrating general second order initial value problems |
| title_short | Extra derivative implicit block methods for integrating general second order initial value problems |
| title_sort | extra derivative implicit block methods for integrating general second order initial value problems |
| url | http://psasir.upm.edu.my/id/eprint/80784/ http://psasir.upm.edu.my/id/eprint/80784/ http://psasir.upm.edu.my/id/eprint/80784/1/BLOCK.pdf |