Direct solution of using three point block method of order eight with applications
This study aims to construct an implicit block method with three-point to tackle general second-order ordinary differential equations (ODEs) directly. Hermite Interpolating Polynomial is used as the fundamental function to obtain the proposed method which involved the first and second derivatives of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2021
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| Online Access: | http://psasir.upm.edu.my/id/eprint/96748/ http://psasir.upm.edu.my/id/eprint/96748/1/ABSTRACT.pdf |
| _version_ | 1848862435771940864 |
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| author | Allogmany, Reem Ayed Ismail, Fudziah |
| author_facet | Allogmany, Reem Ayed Ismail, Fudziah |
| author_sort | Allogmany, Reem Ayed |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This study aims to construct an implicit block method with three-point to tackle general second-order ordinary differential equations (ODEs) directly. Hermite Interpolating Polynomial is used as the fundamental function to obtain the proposed method which involved the first and second derivatives of . From the investigation done, it was found that the proposed method is consistent and zero-stable, hence it is convergent. The proposed method’s efficiency was obtained and a comparison was made in terms of accuracy to some existing methods with similar order or higher than it. This new method is able to solve linear and nonlinear initial value problems of the general second-order ODEs and outperformed existing methods with impressive results. Applications of the new method such as in the Fermi-Pasta-Ulam problem and van der Pol oscillator are discussed. |
| first_indexed | 2025-11-15T13:16:59Z |
| format | Article |
| id | upm-96748 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T13:16:59Z |
| publishDate | 2021 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-967482022-12-01T04:34:50Z http://psasir.upm.edu.my/id/eprint/96748/ Direct solution of using three point block method of order eight with applications Allogmany, Reem Ayed Ismail, Fudziah This study aims to construct an implicit block method with three-point to tackle general second-order ordinary differential equations (ODEs) directly. Hermite Interpolating Polynomial is used as the fundamental function to obtain the proposed method which involved the first and second derivatives of . From the investigation done, it was found that the proposed method is consistent and zero-stable, hence it is convergent. The proposed method’s efficiency was obtained and a comparison was made in terms of accuracy to some existing methods with similar order or higher than it. This new method is able to solve linear and nonlinear initial value problems of the general second-order ODEs and outperformed existing methods with impressive results. Applications of the new method such as in the Fermi-Pasta-Ulam problem and van der Pol oscillator are discussed. Elsevier 2021 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/96748/1/ABSTRACT.pdf Allogmany, Reem Ayed and Ismail, Fudziah (2021) Direct solution of using three point block method of order eight with applications. Journal of King Saud University - Science, 33 (2). art. no. 101337. pp. 1-16. ISSN 1018-3647 https://www.sciencedirect.com/science/article/pii/S1018364720304511 10.1016/j.jksus.2020.101337 |
| spellingShingle | Allogmany, Reem Ayed Ismail, Fudziah Direct solution of using three point block method of order eight with applications |
| title | Direct solution of using three point block method of order eight with applications |
| title_full | Direct solution of using three point block method of order eight with applications |
| title_fullStr | Direct solution of using three point block method of order eight with applications |
| title_full_unstemmed | Direct solution of using three point block method of order eight with applications |
| title_short | Direct solution of using three point block method of order eight with applications |
| title_sort | direct solution of using three point block method of order eight with applications |
| url | http://psasir.upm.edu.my/id/eprint/96748/ http://psasir.upm.edu.my/id/eprint/96748/ http://psasir.upm.edu.my/id/eprint/96748/ http://psasir.upm.edu.my/id/eprint/96748/1/ABSTRACT.pdf |