Numerical solution of linear dirichlet two-point boundary value problems using block method
This paper presents a direct two-point block one-step method for solving linear Dirichlet boundary value problems (BVPs) directly. The block method is formulated using Lagrange interpolating polynomial. Mathematical problems which involve higher order ordinary differential equations (ODEs) were like...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English English |
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Academic Publications
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30192/1/Numerical%20solution%20of%20linear%20dirichlet%20two.pdf |
| _version_ | 1796971691481497600 |
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| author | Hasni, Mohd Mughti Abdul Majid, Zanariah Senu, Norazak |
| author_facet | Hasni, Mohd Mughti Abdul Majid, Zanariah Senu, Norazak |
| author_sort | Hasni, Mohd Mughti |
| collection | UPM |
| description | This paper presents a direct two-point block one-step method for solving linear Dirichlet boundary value problems (BVPs) directly. The block method is formulated using Lagrange interpolating polynomial. Mathematical problems which involve higher order ordinary differential equations (ODEs) were likely to be reduced into the system of first order equations in order to solve it. However, this method will solve the second order linear Dirichlet BVPs directly without reducing it to the system of first order equations. The direct solution of the linear Dirichlet BVPs will be calculated at the two-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 efficiency and performance of
this method compared to the existing methods. |
| first_indexed | 2024-03-06T08:16:46Z |
| format | Article |
| id | upm.eprints-30192 |
| institution | Universiti Putra Malaysia |
| language | English English |
| last_indexed | 2024-03-06T08:16:46Z |
| publishDate | 2013 |
| publisher | Academic Publications |
| record_format | dspace |
| spelling | upm.eprints-301922015-09-11T02:27:47Z http://psasir.upm.edu.my/id/eprint/30192/ Numerical solution of linear dirichlet two-point boundary value problems using block method Hasni, Mohd Mughti Abdul Majid, Zanariah Senu, Norazak This paper presents a direct two-point block one-step method for solving linear Dirichlet boundary value problems (BVPs) directly. The block method is formulated using Lagrange interpolating polynomial. Mathematical problems which involve higher order ordinary differential equations (ODEs) were likely to be reduced into the system of first order equations in order to solve it. However, this method will solve the second order linear Dirichlet BVPs directly without reducing it to the system of first order equations. The direct solution of the linear Dirichlet BVPs will be calculated at the two-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 efficiency and performance of this method compared to the existing methods. Academic Publications 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30192/1/Numerical%20solution%20of%20linear%20dirichlet%20two.pdf Hasni, Mohd Mughti and Abdul Majid, Zanariah and Senu, Norazak (2013) Numerical solution of linear dirichlet two-point boundary value problems using block method. International Journal of Pure and Applied Mathematics, 85 (3). pp. 495-506. ISSN 1311-8080; ESSN: 1314-3395 http://www.ijpam.eu/contents/2013-85-3/index.html 10.12732/ijpam.v85i3.6 English |
| spellingShingle | Hasni, Mohd Mughti Abdul Majid, Zanariah Senu, Norazak Numerical solution of linear dirichlet two-point boundary value problems using block method |
| title | Numerical solution of linear dirichlet two-point boundary value problems using block method |
| title_full | Numerical solution of linear dirichlet two-point boundary value problems using block method |
| title_fullStr | Numerical solution of linear dirichlet two-point boundary value problems using block method |
| title_full_unstemmed | Numerical solution of linear dirichlet two-point boundary value problems using block method |
| title_short | Numerical solution of linear dirichlet two-point boundary value problems using block method |
| title_sort | numerical solution of linear dirichlet two point boundary value problems using block method |
| url | http://psasir.upm.edu.my/id/eprint/30192/1/Numerical%20solution%20of%20linear%20dirichlet%20two.pdf |
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