Stability analysis of singly diagonally implicit block backward differentiation formulas for stiff ordinary differential equations
In this research, a singly diagonally implicit block backward differentiation formulas (SDIBBDF) for solving stiff ordinary differential equations (ODEs) is proposed. The formula reduced a fully implicit method to lower triangular matrix with equal diagonal elements which will results in only one ev...
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| Format: | Article |
| Language: | English |
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MDPI
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/77850/ http://psasir.upm.edu.my/id/eprint/77850/1/77850.pdf |
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| author | Jana Aksah, Saufianim Ibrahim, Zarina Bibi Mohd Zawawi, Iskandar Shah |
| author_facet | Jana Aksah, Saufianim Ibrahim, Zarina Bibi Mohd Zawawi, Iskandar Shah |
| author_sort | Jana Aksah, Saufianim |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this research, a singly diagonally implicit block backward differentiation formulas (SDIBBDF) for solving stiff ordinary differential equations (ODEs) is proposed. The formula reduced a fully implicit method to lower triangular matrix with equal diagonal elements which will results in only one evaluation of the Jacobian and one LU decomposition for each time step. For the SDIBBDF method to have practical significance in solving stiff problems, its stability region must at least cover almost the whole of the negative half plane. Step size restriction of the proposed method have to be considered in order to ensure stability of the method in computing numerical results. Efficiency of the SDIBBDF method in solving stiff ODEs is justified when it managed to outperform the existing methods for both accuracy and computational time. |
| first_indexed | 2025-11-15T12:11:58Z |
| format | Article |
| id | upm-77850 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:11:58Z |
| publishDate | 2019 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-778502020-05-04T16:58:10Z http://psasir.upm.edu.my/id/eprint/77850/ Stability analysis of singly diagonally implicit block backward differentiation formulas for stiff ordinary differential equations Jana Aksah, Saufianim Ibrahim, Zarina Bibi Mohd Zawawi, Iskandar Shah In this research, a singly diagonally implicit block backward differentiation formulas (SDIBBDF) for solving stiff ordinary differential equations (ODEs) is proposed. The formula reduced a fully implicit method to lower triangular matrix with equal diagonal elements which will results in only one evaluation of the Jacobian and one LU decomposition for each time step. For the SDIBBDF method to have practical significance in solving stiff problems, its stability region must at least cover almost the whole of the negative half plane. Step size restriction of the proposed method have to be considered in order to ensure stability of the method in computing numerical results. Efficiency of the SDIBBDF method in solving stiff ODEs is justified when it managed to outperform the existing methods for both accuracy and computational time. MDPI 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/77850/1/77850.pdf Jana Aksah, Saufianim and Ibrahim, Zarina Bibi and Mohd Zawawi, Iskandar Shah (2019) Stability analysis of singly diagonally implicit block backward differentiation formulas for stiff ordinary differential equations. Mathematics, 7 (2). art. no. 211. pp. 1-16. ISSN 2227-7390 https://www.mdpi.com/2227-7390/7/2/211 10.3390/math7020211 |
| spellingShingle | Jana Aksah, Saufianim Ibrahim, Zarina Bibi Mohd Zawawi, Iskandar Shah Stability analysis of singly diagonally implicit block backward differentiation formulas for stiff ordinary differential equations |
| title | Stability analysis of singly diagonally implicit block backward differentiation formulas for stiff ordinary differential equations |
| title_full | Stability analysis of singly diagonally implicit block backward differentiation formulas for stiff ordinary differential equations |
| title_fullStr | Stability analysis of singly diagonally implicit block backward differentiation formulas for stiff ordinary differential equations |
| title_full_unstemmed | Stability analysis of singly diagonally implicit block backward differentiation formulas for stiff ordinary differential equations |
| title_short | Stability analysis of singly diagonally implicit block backward differentiation formulas for stiff ordinary differential equations |
| title_sort | stability analysis of singly diagonally implicit block backward differentiation formulas for stiff ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/77850/ http://psasir.upm.edu.my/id/eprint/77850/ http://psasir.upm.edu.my/id/eprint/77850/ http://psasir.upm.edu.my/id/eprint/77850/1/77850.pdf |