Enhancing accuracy and efficiency in stiff ode integration using variable step diagonal bbdf approaches
Recent advancements in mathematical modelling have uncovered a growing number of systems exhibiting stiffness, a phenomenon that challenges the effectiveness of traditional numerical methods. Motivated by the need for more robust numerical techniques to address this issue, this paper presents an enh...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Published: |
Penerbit UTM Press
2024
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/114884/ |
| _version_ | 1848866624294092800 |
|---|---|
| author | Ibrahim, Zarina Bibi Mohd Ijam, Hazizah Aksah, Saufianim Jana Abd Rasid, Norshakila |
| author_facet | Ibrahim, Zarina Bibi Mohd Ijam, Hazizah Aksah, Saufianim Jana Abd Rasid, Norshakila |
| author_sort | Ibrahim, Zarina Bibi |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Recent advancements in mathematical modelling have uncovered a growing number of systems exhibiting stiffness, a phenomenon that challenges the effectiveness of traditional numerical methods. Motivated by the need for more robust numerical techniques to address this issue, this paper presents an enhanced version of the Diagonally Block Backward Differentiation Formula (BBDF) that incorporates intermediate points, known as off-step points, to improve the accuracy and efficiency of solutions for stiff ordinary differential equations (ODEs). The new scheme leverages an adaptive step-size strategy to refine accuracy and efficiency between regular and off-grid integration steps. Theoretical analysis confirms that the proposed scheme is an A-stable and convergent method, as it satisfies the fundamental criteria of consistency, zero-stability, and A-stability. Numerical experiments on single and multivariable systems across varying time scales demonstrate significant improvements in solving stiff ODEs compared to existing techniques. Therefore, the new proposed method is an effective solver for stiff ODEs. |
| first_indexed | 2025-11-15T14:23:33Z |
| format | Article |
| id | upm-114884 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T14:23:33Z |
| publishDate | 2024 |
| publisher | Penerbit UTM Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1148842025-02-06T08:14:12Z http://psasir.upm.edu.my/id/eprint/114884/ Enhancing accuracy and efficiency in stiff ode integration using variable step diagonal bbdf approaches Ibrahim, Zarina Bibi Mohd Ijam, Hazizah Aksah, Saufianim Jana Abd Rasid, Norshakila Recent advancements in mathematical modelling have uncovered a growing number of systems exhibiting stiffness, a phenomenon that challenges the effectiveness of traditional numerical methods. Motivated by the need for more robust numerical techniques to address this issue, this paper presents an enhanced version of the Diagonally Block Backward Differentiation Formula (BBDF) that incorporates intermediate points, known as off-step points, to improve the accuracy and efficiency of solutions for stiff ordinary differential equations (ODEs). The new scheme leverages an adaptive step-size strategy to refine accuracy and efficiency between regular and off-grid integration steps. Theoretical analysis confirms that the proposed scheme is an A-stable and convergent method, as it satisfies the fundamental criteria of consistency, zero-stability, and A-stability. Numerical experiments on single and multivariable systems across varying time scales demonstrate significant improvements in solving stiff ODEs compared to existing techniques. Therefore, the new proposed method is an effective solver for stiff ODEs. Penerbit UTM Press 2024 Article PeerReviewed Ibrahim, Zarina Bibi and Mohd Ijam, Hazizah and Aksah, Saufianim Jana and Abd Rasid, Norshakila (2024) Enhancing accuracy and efficiency in stiff ode integration using variable step diagonal bbdf approaches. Malaysian Journal of Fundamental and Applied Sciences, 20 (5). pp. 1083-1100. ISSN 2289-599X; eISSN: 2289-599X https://mjfas.utm.my/index.php/mjfas/article/view/3530 10.11113/mjfas.v20n5.3530 |
| spellingShingle | Ibrahim, Zarina Bibi Mohd Ijam, Hazizah Aksah, Saufianim Jana Abd Rasid, Norshakila Enhancing accuracy and efficiency in stiff ode integration using variable step diagonal bbdf approaches |
| title | Enhancing accuracy and efficiency in stiff ode integration using variable step diagonal bbdf approaches |
| title_full | Enhancing accuracy and efficiency in stiff ode integration using variable step diagonal bbdf approaches |
| title_fullStr | Enhancing accuracy and efficiency in stiff ode integration using variable step diagonal bbdf approaches |
| title_full_unstemmed | Enhancing accuracy and efficiency in stiff ode integration using variable step diagonal bbdf approaches |
| title_short | Enhancing accuracy and efficiency in stiff ode integration using variable step diagonal bbdf approaches |
| title_sort | enhancing accuracy and efficiency in stiff ode integration using variable step diagonal bbdf approaches |
| url | http://psasir.upm.edu.my/id/eprint/114884/ http://psasir.upm.edu.my/id/eprint/114884/ http://psasir.upm.edu.my/id/eprint/114884/ |