Three-step block method for solving nonlinear boundary value problems
We propose a three-step block method of Adam’s type to solve nonlinear second-order two-point boundary value problems of Dirichlet type and Neumann type directly. We also extend this method to solve the system of second-order boundary value problems which have the same or different two boundary cond...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/35851/ http://psasir.upm.edu.my/id/eprint/35851/1/Three-Step%20Block%20Method%20for%20Solving%20Nonlinear%20Boundary.pdf |
| _version_ | 1848848170603249664 |
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| author | Phang, Pei See Abdul Majid, Zanariah Suleiman, Mohamed |
| author_facet | Phang, Pei See Abdul Majid, Zanariah Suleiman, Mohamed |
| author_sort | Phang, Pei See |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We propose a three-step block method of Adam’s type to solve nonlinear second-order two-point boundary value problems of Dirichlet type and Neumann type directly. We also extend this method to solve the system of second-order boundary value problems which have the same or different two boundary conditions. The method will be implemented in predictor corrector mode and obtain the approximate solutions at three points simultaneously using variable step size strategy. The proposed block method will be adapted with multiple shooting techniques via the three-step iterative method. The boundary value problem will be solved without reducing to first-order equations. The numerical results are presented to demonstrate the effectiveness of the proposed method. |
| first_indexed | 2025-11-15T09:30:15Z |
| format | Article |
| id | upm-35851 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:30:15Z |
| publishDate | 2014 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-358512016-02-10T08:48:21Z http://psasir.upm.edu.my/id/eprint/35851/ Three-step block method for solving nonlinear boundary value problems Phang, Pei See Abdul Majid, Zanariah Suleiman, Mohamed We propose a three-step block method of Adam’s type to solve nonlinear second-order two-point boundary value problems of Dirichlet type and Neumann type directly. We also extend this method to solve the system of second-order boundary value problems which have the same or different two boundary conditions. The method will be implemented in predictor corrector mode and obtain the approximate solutions at three points simultaneously using variable step size strategy. The proposed block method will be adapted with multiple shooting techniques via the three-step iterative method. The boundary value problem will be solved without reducing to first-order equations. The numerical results are presented to demonstrate the effectiveness of the proposed method. Hindawi Publishing Corporation 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/35851/1/Three-Step%20Block%20Method%20for%20Solving%20Nonlinear%20Boundary.pdf Phang, Pei See and Abdul Majid, Zanariah and Suleiman, Mohamed (2014) Three-step block method for solving nonlinear boundary value problems. Abstract and Applied Analysis, 2014. art. no. 379829. pp. 1-8. ISSN 1085-3375; ESSN: 1687-0409 http://www.hindawi.com/journals/aaa/2014/379829/abs/ 10.1155/2014/379829 |
| spellingShingle | Phang, Pei See Abdul Majid, Zanariah Suleiman, Mohamed Three-step block method for solving nonlinear boundary value problems |
| title | Three-step block method for solving nonlinear boundary value problems |
| title_full | Three-step block method for solving nonlinear boundary value problems |
| title_fullStr | Three-step block method for solving nonlinear boundary value problems |
| title_full_unstemmed | Three-step block method for solving nonlinear boundary value problems |
| title_short | Three-step block method for solving nonlinear boundary value problems |
| title_sort | three-step block method for solving nonlinear boundary value problems |
| url | http://psasir.upm.edu.my/id/eprint/35851/ http://psasir.upm.edu.my/id/eprint/35851/ http://psasir.upm.edu.my/id/eprint/35851/ http://psasir.upm.edu.my/id/eprint/35851/1/Three-Step%20Block%20Method%20for%20Solving%20Nonlinear%20Boundary.pdf |