Formulation of modified variable step block backward differentiation formulae for solving stiff ordinary differential equations
Objectives: A modified variable step block backward differentiation formulae (MVS-BBDF) method is introduced in this paper as another alternative way for solving ordinary differential equations (ODEs). Methods: We demonstrated the detailed formulation of the corrector formulae for MVS-BBDF method wh...
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| Format: | Article |
| Language: | English |
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Indian Society for Education and Environment
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/61914/ http://psasir.upm.edu.my/id/eprint/61914/1/Formulation%20of%20modified%20variable%20step%20block%20backward%20differentiation%20formulae%20for%20solving%20stiff%20ordinary%20differential%20equations%20.pdf |
| _version_ | 1848854516493975552 |
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| author | Asnor, Asma Izzati Mohd Yatim, Siti Ainor Ibrahim, Zarina Bibi |
| author_facet | Asnor, Asma Izzati Mohd Yatim, Siti Ainor Ibrahim, Zarina Bibi |
| author_sort | Asnor, Asma Izzati |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Objectives: A modified variable step block backward differentiation formulae (MVS-BBDF) method is introduced in this paper as another alternative way for solving ordinary differential equations (ODEs). Methods: We demonstrated the detailed formulation of the corrector formulae for MVS-BBDF method which is carried out using Maple software. Then, to validate the performance of the introduced method, we applied it to stiff ODEs problem. Findings: The performance of the method in terms of maximum error and number of total steps taken during the computation are compared with the performance of ode15s and ode23s solver in MATLAB. Consequently, the efficiency of MVS-BBDF shows that it is able to outperform both Matlab’s ODE solver since it produces better accuracy and manages to reduce the number of total step. |
| first_indexed | 2025-11-15T11:11:07Z |
| format | Article |
| id | upm-61914 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:11:07Z |
| publishDate | 2017 |
| publisher | Indian Society for Education and Environment |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-619142019-02-27T04:12:55Z http://psasir.upm.edu.my/id/eprint/61914/ Formulation of modified variable step block backward differentiation formulae for solving stiff ordinary differential equations Asnor, Asma Izzati Mohd Yatim, Siti Ainor Ibrahim, Zarina Bibi Objectives: A modified variable step block backward differentiation formulae (MVS-BBDF) method is introduced in this paper as another alternative way for solving ordinary differential equations (ODEs). Methods: We demonstrated the detailed formulation of the corrector formulae for MVS-BBDF method which is carried out using Maple software. Then, to validate the performance of the introduced method, we applied it to stiff ODEs problem. Findings: The performance of the method in terms of maximum error and number of total steps taken during the computation are compared with the performance of ode15s and ode23s solver in MATLAB. Consequently, the efficiency of MVS-BBDF shows that it is able to outperform both Matlab’s ODE solver since it produces better accuracy and manages to reduce the number of total step. Indian Society for Education and Environment 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/61914/1/Formulation%20of%20modified%20variable%20step%20block%20backward%20differentiation%20formulae%20for%20solving%20stiff%20ordinary%20differential%20equations%20.pdf Asnor, Asma Izzati and Mohd Yatim, Siti Ainor and Ibrahim, Zarina Bibi (2017) Formulation of modified variable step block backward differentiation formulae for solving stiff ordinary differential equations. Indian Journal of Science and Technology, 10 (12). p. 43106. ISSN 0974-6846; ESSN: 0974-5645 http://www.indjst.org/index.php/indjst/article/view/113009 10.17485/ijst/2017/v10i12/113009 |
| spellingShingle | Asnor, Asma Izzati Mohd Yatim, Siti Ainor Ibrahim, Zarina Bibi Formulation of modified variable step block backward differentiation formulae for solving stiff ordinary differential equations |
| title | Formulation of modified variable step block backward differentiation formulae for solving stiff ordinary differential equations |
| title_full | Formulation of modified variable step block backward differentiation formulae for solving stiff ordinary differential equations |
| title_fullStr | Formulation of modified variable step block backward differentiation formulae for solving stiff ordinary differential equations |
| title_full_unstemmed | Formulation of modified variable step block backward differentiation formulae for solving stiff ordinary differential equations |
| title_short | Formulation of modified variable step block backward differentiation formulae for solving stiff ordinary differential equations |
| title_sort | formulation of modified variable step block backward differentiation formulae for solving stiff ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/61914/ http://psasir.upm.edu.my/id/eprint/61914/ http://psasir.upm.edu.my/id/eprint/61914/ http://psasir.upm.edu.my/id/eprint/61914/1/Formulation%20of%20modified%20variable%20step%20block%20backward%20differentiation%20formulae%20for%20solving%20stiff%20ordinary%20differential%20equations%20.pdf |