One step block method for solving third order ordinary differential equations directly
The purpose of this research is to discuss a direct two-point one step block method for solving general third-order initial value problems (IVPs) of ordinary differential equations (ODEs) using constant step size. The proposed method will compute the approximation solutions directly without reducing...
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| Format: | Article |
| Language: | English |
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Malaysian Mathematical Sciences Society and Universiti Putra Malaysia
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/75134/ http://psasir.upm.edu.my/id/eprint/75134/1/One%20step%20block%20method%20for%20solving%20third%20order%20ordinary%20differential%20equations%20directly%20.pdf |
| _version_ | 1848857613090947072 |
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| author | Hasan, E. Abdul Majid, Zanariah |
| author_facet | Hasan, E. Abdul Majid, Zanariah |
| author_sort | Hasan, E. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The purpose of this research is to discuss a direct two-point one step block method for solving general third-order initial value problems (IVPs) of ordinary differential equations (ODEs) using constant step size. The proposed method will compute the approximation solutions directly without reducing to systems of first order ODEs at two-points in a block simultaneously. Lagrange polynomial has been used to derive the block method. The order, zero stability and consistency of the resulting method also will be discussed. In the numerical results, the method shown to be more accurate and less total function calls compare to the existing method when solving the general third order ODEs. |
| first_indexed | 2025-11-15T12:00:20Z |
| format | Article |
| id | upm-75134 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:00:20Z |
| publishDate | 2018 |
| publisher | Malaysian Mathematical Sciences Society and Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-751342019-11-27T08:32:36Z http://psasir.upm.edu.my/id/eprint/75134/ One step block method for solving third order ordinary differential equations directly Hasan, E. Abdul Majid, Zanariah The purpose of this research is to discuss a direct two-point one step block method for solving general third-order initial value problems (IVPs) of ordinary differential equations (ODEs) using constant step size. The proposed method will compute the approximation solutions directly without reducing to systems of first order ODEs at two-points in a block simultaneously. Lagrange polynomial has been used to derive the block method. The order, zero stability and consistency of the resulting method also will be discussed. In the numerical results, the method shown to be more accurate and less total function calls compare to the existing method when solving the general third order ODEs. Malaysian Mathematical Sciences Society and Universiti Putra Malaysia 2018 Article NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/75134/1/One%20step%20block%20method%20for%20solving%20third%20order%20ordinary%20differential%20equations%20directly%20.pdf Hasan, E. and Abdul Majid, Zanariah (2018) One step block method for solving third order ordinary differential equations directly. Discovering Mathematics, 40 (2). 72 - 81. ISSN 2231-7023 http://einspem.upm.edu.my/ojs/index.php/dismath/article/view/12 |
| spellingShingle | Hasan, E. Abdul Majid, Zanariah One step block method for solving third order ordinary differential equations directly |
| title | One step block method for solving third order ordinary differential equations directly |
| title_full | One step block method for solving third order ordinary differential equations directly |
| title_fullStr | One step block method for solving third order ordinary differential equations directly |
| title_full_unstemmed | One step block method for solving third order ordinary differential equations directly |
| title_short | One step block method for solving third order ordinary differential equations directly |
| title_sort | one step block method for solving third order ordinary differential equations directly |
| url | http://psasir.upm.edu.my/id/eprint/75134/ http://psasir.upm.edu.my/id/eprint/75134/ http://psasir.upm.edu.my/id/eprint/75134/1/One%20step%20block%20method%20for%20solving%20third%20order%20ordinary%20differential%20equations%20directly%20.pdf |