Direct two point block one-step method for solving general second order ordinary differential equations.
A direct two-point block one-step method for solving general second-order ordinary differential equations (ODEs) directly is presented in this paper. The one-step block method will solve the second-order ODEs without reducing to first-order equations. The direct solutions of the general second-order...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2012
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| Online Access: | http://psasir.upm.edu.my/id/eprint/25027/ http://psasir.upm.edu.my/id/eprint/25027/1/Direct%20two%20point%20block%20one.pdf |
| _version_ | 1848845197364953088 |
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| author | Abdul Majid, Zanariah Mokhtar, Nur Zahidah Suleiman, Mohamed |
| author_facet | Abdul Majid, Zanariah Mokhtar, Nur Zahidah Suleiman, Mohamed |
| author_sort | Abdul Majid, Zanariah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A direct two-point block one-step method for solving general second-order ordinary differential equations (ODEs) directly is presented in this paper. The one-step block method will solve the second-order ODEs without reducing to first-order equations. The direct solutions of the general second-order ODEs will be calculated at two points simultaneously using variable step size. The method is formulated using the linear multistep method, but the new method possesses the desirable feature of the one-step method. The implementation is based on the predictor and corrector formulas in the P E (C E) m mode. The stability and precision of this method will also be analyzed and deliberated. Numerical results are given to show the efficiency of the proposed method and will be compared with the existing method. |
| first_indexed | 2025-11-15T08:42:59Z |
| format | Article |
| id | upm-25027 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:42:59Z |
| publishDate | 2012 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-250272016-06-30T05:18:21Z http://psasir.upm.edu.my/id/eprint/25027/ Direct two point block one-step method for solving general second order ordinary differential equations. Abdul Majid, Zanariah Mokhtar, Nur Zahidah Suleiman, Mohamed A direct two-point block one-step method for solving general second-order ordinary differential equations (ODEs) directly is presented in this paper. The one-step block method will solve the second-order ODEs without reducing to first-order equations. The direct solutions of the general second-order ODEs will be calculated at two points simultaneously using variable step size. The method is formulated using the linear multistep method, but the new method possesses the desirable feature of the one-step method. The implementation is based on the predictor and corrector formulas in the P E (C E) m mode. The stability and precision of this method will also be analyzed and deliberated. Numerical results are given to show the efficiency of the proposed method and will be compared with the existing method. Hindawi Publishing Corporation 2012 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/25027/1/Direct%20two%20point%20block%20one.pdf Abdul Majid, Zanariah and Mokhtar, Nur Zahidah and Suleiman, Mohamed (2012) Direct two point block one-step method for solving general second order ordinary differential equations. Mathematical Problems in Engineering, 2012 (184253). pp. 1-16. ISSN 1024-123X 10.1155/2012/184253 |
| spellingShingle | Abdul Majid, Zanariah Mokhtar, Nur Zahidah Suleiman, Mohamed Direct two point block one-step method for solving general second order ordinary differential equations. |
| title | Direct two point block one-step method for solving general second order ordinary differential equations. |
| title_full | Direct two point block one-step method for solving general second order ordinary differential equations. |
| title_fullStr | Direct two point block one-step method for solving general second order ordinary differential equations. |
| title_full_unstemmed | Direct two point block one-step method for solving general second order ordinary differential equations. |
| title_short | Direct two point block one-step method for solving general second order ordinary differential equations. |
| title_sort | direct two point block one-step method for solving general second order ordinary differential equations. |
| url | http://psasir.upm.edu.my/id/eprint/25027/ http://psasir.upm.edu.my/id/eprint/25027/ http://psasir.upm.edu.my/id/eprint/25027/1/Direct%20two%20point%20block%20one.pdf |