Solving second order linear dirichlet and Neumann boundary value problems by block method
In this paper, the direct three-point block one-step methods are considered for solving linear boundary value problems (BVPs) with two different types of boundary conditions which is the Dirichlet and Neumann boundary conditions. This method will solve the second order linear BVPs directly witho...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English English |
| Published: |
International Association of Engineers
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30195/ http://psasir.upm.edu.my/id/eprint/30195/1/Solving%20second%20order%20linear%20dirichlet%20and%20Neumann%20boundary%20value%20problems%20by%20block%20method.pdf |
| _version_ | 1848846608582574080 |
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| author | Abdul Majid, Zanariah Hasni, Mohd Mughti Senu, Norazak |
| author_facet | Abdul Majid, Zanariah Hasni, Mohd Mughti Senu, Norazak |
| author_sort | Abdul Majid, Zanariah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, the direct three-point block one-step
methods are considered for solving linear boundary value
problems (BVPs) with two different types of boundary conditions which is the Dirichlet and Neumann boundary conditions. This method will solve the second order linear BVPs directly without reducing it to the system of first order equations. The direct solution of these two types of BVPs will be calculated at three points simultaneously using constant step size. This method will be used together with the linear shooting technique to construct
the numerical solution. The implementation is based on the
predictor and corrector formulas in the PE(CE)r mode.
Numerical results are given to show the performance of this
method compared to the existing methods. |
| first_indexed | 2025-11-15T09:05:25Z |
| format | Article |
| id | upm-30195 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T09:05:25Z |
| publishDate | 2013 |
| publisher | International Association of Engineers |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-301952015-09-18T07:33:32Z http://psasir.upm.edu.my/id/eprint/30195/ Solving second order linear dirichlet and Neumann boundary value problems by block method Abdul Majid, Zanariah Hasni, Mohd Mughti Senu, Norazak In this paper, the direct three-point block one-step methods are considered for solving linear boundary value problems (BVPs) with two different types of boundary conditions which is the Dirichlet and Neumann boundary conditions. This method will solve the second order linear BVPs directly without reducing it to the system of first order equations. The direct solution of these two types of BVPs will be calculated at three points simultaneously using constant step size. This method will be used together with the linear shooting technique to construct the numerical solution. The implementation is based on the predictor and corrector formulas in the PE(CE)r mode. Numerical results are given to show the performance of this method compared to the existing methods. International Association of Engineers 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30195/1/Solving%20second%20order%20linear%20dirichlet%20and%20Neumann%20boundary%20value%20problems%20by%20block%20method.pdf Abdul Majid, Zanariah and Hasni, Mohd Mughti and Senu, Norazak (2013) Solving second order linear dirichlet and Neumann boundary value problems by block method. IAENG International Journal of Applied Mathematics, 43 (2). pp. 71-76. ISSN 1992-9978; ESSN:1992-9986 http://www.iaeng.org/IJAM/issues_v43/issue_2/ English |
| spellingShingle | Abdul Majid, Zanariah Hasni, Mohd Mughti Senu, Norazak Solving second order linear dirichlet and Neumann boundary value problems by block method |
| title | Solving second order linear dirichlet and Neumann boundary value problems by block method |
| title_full | Solving second order linear dirichlet and Neumann boundary value problems by block method |
| title_fullStr | Solving second order linear dirichlet and Neumann boundary value problems by block method |
| title_full_unstemmed | Solving second order linear dirichlet and Neumann boundary value problems by block method |
| title_short | Solving second order linear dirichlet and Neumann boundary value problems by block method |
| title_sort | solving second order linear dirichlet and neumann boundary value problems by block method |
| url | http://psasir.upm.edu.my/id/eprint/30195/ http://psasir.upm.edu.my/id/eprint/30195/ http://psasir.upm.edu.my/id/eprint/30195/1/Solving%20second%20order%20linear%20dirichlet%20and%20Neumann%20boundary%20value%20problems%20by%20block%20method.pdf |