Diagonally implicit block backward differentiation formula with optimal stability properties for stiff ordinary differential equations
This paper aims to select the best value of the parameter ρ from a general set of linear multistep formulae which have the potential for efficient implementation. The ρ -Diagonally Implicit Block Backward Differentiation Formula ( ρ -DIBBDF) was proposed to approximate the solution for stiff Ordinar...
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| Format: | Article |
| Language: | English |
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Multidisciplinary Digital Publishing Institute
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/82778/ http://psasir.upm.edu.my/id/eprint/82778/1/Diagonally_Implicit_Block_Backward_Differentiation.pdf |
| _version_ | 1848859351612129280 |
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| author | Mohd Ijam, Hazizah Ibrahim, Zarina Bibi |
| author_facet | Mohd Ijam, Hazizah Ibrahim, Zarina Bibi |
| author_sort | Mohd Ijam, Hazizah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper aims to select the best value of the parameter ρ from a general set of linear multistep formulae which have the potential for efficient implementation. The ρ -Diagonally Implicit Block Backward Differentiation Formula ( ρ -DIBBDF) was proposed to approximate the solution for stiff Ordinary Differential Equations (ODEs) to achieve the research objective. The selection of ρ for optimal stability properties in terms of zero stability, absolute stability, error constant and convergence are discussed. In the diagonally implicit formula that uses a lower triangular matrix with identical diagonal entries, allowing a maximum of one lower-upper (LU) decomposition per integration stage to be performed will result in substantial computing benefits to the user. The numerical results and plots of accuracy indicate that the ρ -DIBBDF method performs better than the existing fully and diagonally Block Backward Differentiation Formula (BBDF) methods. |
| first_indexed | 2025-11-15T12:27:58Z |
| format | Article |
| id | upm-82778 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:27:58Z |
| publishDate | 2019 |
| publisher | Multidisciplinary Digital Publishing Institute |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-827782021-12-03T02:15:51Z http://psasir.upm.edu.my/id/eprint/82778/ Diagonally implicit block backward differentiation formula with optimal stability properties for stiff ordinary differential equations Mohd Ijam, Hazizah Ibrahim, Zarina Bibi This paper aims to select the best value of the parameter ρ from a general set of linear multistep formulae which have the potential for efficient implementation. The ρ -Diagonally Implicit Block Backward Differentiation Formula ( ρ -DIBBDF) was proposed to approximate the solution for stiff Ordinary Differential Equations (ODEs) to achieve the research objective. The selection of ρ for optimal stability properties in terms of zero stability, absolute stability, error constant and convergence are discussed. In the diagonally implicit formula that uses a lower triangular matrix with identical diagonal entries, allowing a maximum of one lower-upper (LU) decomposition per integration stage to be performed will result in substantial computing benefits to the user. The numerical results and plots of accuracy indicate that the ρ -DIBBDF method performs better than the existing fully and diagonally Block Backward Differentiation Formula (BBDF) methods. Multidisciplinary Digital Publishing Institute 2019-11-01 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/82778/1/Diagonally_Implicit_Block_Backward_Differentiation.pdf Mohd Ijam, Hazizah and Ibrahim, Zarina Bibi (2019) Diagonally implicit block backward differentiation formula with optimal stability properties for stiff ordinary differential equations. Symmetry, 11 (11). art. no. 1342. pp. 1-18. ISSN 2073-8994 https://www.mdpi.com/2073-8994/11/11/1342 10.1155/2012/767328 |
| spellingShingle | Mohd Ijam, Hazizah Ibrahim, Zarina Bibi Diagonally implicit block backward differentiation formula with optimal stability properties for stiff ordinary differential equations |
| title | Diagonally implicit block backward differentiation formula with optimal stability properties for stiff ordinary differential equations |
| title_full | Diagonally implicit block backward differentiation formula with optimal stability properties for stiff ordinary differential equations |
| title_fullStr | Diagonally implicit block backward differentiation formula with optimal stability properties for stiff ordinary differential equations |
| title_full_unstemmed | Diagonally implicit block backward differentiation formula with optimal stability properties for stiff ordinary differential equations |
| title_short | Diagonally implicit block backward differentiation formula with optimal stability properties for stiff ordinary differential equations |
| title_sort | diagonally implicit block backward differentiation formula with optimal stability properties for stiff ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/82778/ http://psasir.upm.edu.my/id/eprint/82778/ http://psasir.upm.edu.my/id/eprint/82778/ http://psasir.upm.edu.my/id/eprint/82778/1/Diagonally_Implicit_Block_Backward_Differentiation.pdf |