Parallel block backward differentiation formulas for solving ordinary differential equations.
A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires rep...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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World Academy of Science Engineering and Technology
2008
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| Online Access: | http://psasir.upm.edu.my/id/eprint/16030/ |
| _version_ | 1848842846092656640 |
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| author | Othman, Khairil Iskandar Ibrahim, Zarina Bibi Suleiman, Mohamed |
| author_facet | Othman, Khairil Iskandar Ibrahim, Zarina Bibi Suleiman, Mohamed |
| author_sort | Othman, Khairil Iskandar |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution
of stiff Ordinary Differential Equations (ODEs). Most common
methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I -hβJ . Here, J is the Jacobian matrix of the problem. In this paper,the matrix operations is paralleled in order to reduce the cost of the
iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm. |
| first_indexed | 2025-11-15T08:05:37Z |
| format | Article |
| id | upm-16030 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:05:37Z |
| publishDate | 2008 |
| publisher | World Academy of Science Engineering and Technology |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-160302014-01-10T03:56:44Z http://psasir.upm.edu.my/id/eprint/16030/ Parallel block backward differentiation formulas for solving ordinary differential equations. Othman, Khairil Iskandar Ibrahim, Zarina Bibi Suleiman, Mohamed A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I -hβJ . Here, J is the Jacobian matrix of the problem. In this paper,the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm. World Academy of Science Engineering and Technology 2008 Article PeerReviewed Othman, Khairil Iskandar and Ibrahim, Zarina Bibi and Suleiman, Mohamed (2008) Parallel block backward differentiation formulas for solving ordinary differential equations. World Academy of Science, Engineering and Technology, 16. pp. 54-56. ISSN 2010-376X; ESSN: 2010-3778 English |
| spellingShingle | Othman, Khairil Iskandar Ibrahim, Zarina Bibi Suleiman, Mohamed Parallel block backward differentiation formulas for solving ordinary differential equations. |
| title | Parallel block backward differentiation formulas for solving ordinary differential equations. |
| title_full | Parallel block backward differentiation formulas for solving ordinary differential equations. |
| title_fullStr | Parallel block backward differentiation formulas for solving ordinary differential equations. |
| title_full_unstemmed | Parallel block backward differentiation formulas for solving ordinary differential equations. |
| title_short | Parallel block backward differentiation formulas for solving ordinary differential equations. |
| title_sort | parallel block backward differentiation formulas for solving ordinary differential equations. |
| url | http://psasir.upm.edu.my/id/eprint/16030/ |