Solution of boundary value problems using two-point direct block method with one-off step point
In this paper, the two-point direct block method with one-off step is considered for solving boundary value problems (BVPs) with Dirichlet boundary conditions. The direct block method with one-off step is of type one-step method where it needs only one-point to start the next block. This method solv...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Pushpa Publishing House
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/63257/ http://psasir.upm.edu.my/id/eprint/63257/1/Solution%20of%20boundary%20value%20problems%20using%20two-point%20direct%20block%20method%20with%20one-off%20.pdf |
| _version_ | 1848854748386557952 |
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| author | Zakaria, Nurul Nadirah Abdul Majid, Zanariah Lee, Lai Soon |
| author_facet | Zakaria, Nurul Nadirah Abdul Majid, Zanariah Lee, Lai Soon |
| author_sort | Zakaria, Nurul Nadirah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, the two-point direct block method with one-off step is considered for solving boundary value problems (BVPs) with Dirichlet boundary conditions. The direct block method with one-off step is of type one-step method where it needs only one-point to start the next block. This method solves the second order BVPs directly without reducing it into the system of first order equations. The solutions are calculated at two-steps simultaneously using constant step size. This method is implemented together with the shooting technique using Newton method to obtain the numerical solution. Numerical results are given to show the performance of this method compared to the existing methods. |
| first_indexed | 2025-11-15T11:14:48Z |
| format | Article |
| id | upm-63257 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:14:48Z |
| publishDate | 2017 |
| publisher | Pushpa Publishing House |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-632572018-09-24T08:50:23Z http://psasir.upm.edu.my/id/eprint/63257/ Solution of boundary value problems using two-point direct block method with one-off step point Zakaria, Nurul Nadirah Abdul Majid, Zanariah Lee, Lai Soon In this paper, the two-point direct block method with one-off step is considered for solving boundary value problems (BVPs) with Dirichlet boundary conditions. The direct block method with one-off step is of type one-step method where it needs only one-point to start the next block. This method solves the second order BVPs directly without reducing it into the system of first order equations. The solutions are calculated at two-steps simultaneously using constant step size. This method is implemented together with the shooting technique using Newton method to obtain the numerical solution. Numerical results are given to show the performance of this method compared to the existing methods. Pushpa Publishing House 2017-01 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/63257/1/Solution%20of%20boundary%20value%20problems%20using%20two-point%20direct%20block%20method%20with%20one-off%20.pdf Zakaria, Nurul Nadirah and Abdul Majid, Zanariah and Lee, Lai Soon (2017) Solution of boundary value problems using two-point direct block method with one-off step point. Far East Journal of Mathematical Sciences, 101 (2). 375 - 394. ISSN 0972-0871 10.17654/MS101020375 |
| spellingShingle | Zakaria, Nurul Nadirah Abdul Majid, Zanariah Lee, Lai Soon Solution of boundary value problems using two-point direct block method with one-off step point |
| title | Solution of boundary value problems using two-point direct block method with one-off step point |
| title_full | Solution of boundary value problems using two-point direct block method with one-off step point |
| title_fullStr | Solution of boundary value problems using two-point direct block method with one-off step point |
| title_full_unstemmed | Solution of boundary value problems using two-point direct block method with one-off step point |
| title_short | Solution of boundary value problems using two-point direct block method with one-off step point |
| title_sort | solution of boundary value problems using two-point direct block method with one-off step point |
| url | http://psasir.upm.edu.my/id/eprint/63257/ http://psasir.upm.edu.my/id/eprint/63257/ http://psasir.upm.edu.my/id/eprint/63257/1/Solution%20of%20boundary%20value%20problems%20using%20two-point%20direct%20block%20method%20with%20one-off%20.pdf |