Solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae
Variable order block backward differentiation formulae (VOHOBBDF) method is employed for treating numerically higher order Ordinary Differential Equations (ODEs). In this respect, the purpose of this research is to treat initial value problem (IVP) of higher order stiff ODEs directly. BBDF method is...
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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/38236/ http://psasir.upm.edu.my/id/eprint/38236/1/38236.pdf |
| _version_ | 1848848823474978816 |
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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 | Variable order block backward differentiation formulae (VOHOBBDF) method is employed for treating numerically higher order Ordinary Differential Equations (ODEs). In this respect, the purpose of this research is to treat initial value problem (IVP) of higher order stiff ODEs directly. BBDF method is symmetrical to BDF method but it has the advantage of producing more than one solutions simultaneously. Order three, four, and five of VOHOBBDF are developed and implemented as a single code by applying adaptive order approach to enhance the computational efficiency. This approach enables the selection of the least computed LTE among the three orders of VOHOBBDF and switch the code to the method that produces the least LTE for the next step. A few numerical experiments on the focused problem were performed to investigate the numerical efficiency of implementing VOHOBBDF methods in a single code. The analysis of the experimental results reveals the numerical efficiency of this approach as it yielded better performances with less computational effort when compared with built-in stiff Matlab codes. The superior performances demonstrated by the application of adaptive orders selection in a single code thus indicate its reliability as a direct solver for higher order stiff ODEs. |
| first_indexed | 2025-11-15T09:40:37Z |
| format | Article |
| id | upm-38236 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:40:37Z |
| publishDate | 2019 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-382362020-05-04T16:04:28Z http://psasir.upm.edu.my/id/eprint/38236/ Solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae Asnor, Asma Izzati Mohd Yatim, Siti Ainor Ibrahim, Zarina Bibi Variable order block backward differentiation formulae (VOHOBBDF) method is employed for treating numerically higher order Ordinary Differential Equations (ODEs). In this respect, the purpose of this research is to treat initial value problem (IVP) of higher order stiff ODEs directly. BBDF method is symmetrical to BDF method but it has the advantage of producing more than one solutions simultaneously. Order three, four, and five of VOHOBBDF are developed and implemented as a single code by applying adaptive order approach to enhance the computational efficiency. This approach enables the selection of the least computed LTE among the three orders of VOHOBBDF and switch the code to the method that produces the least LTE for the next step. A few numerical experiments on the focused problem were performed to investigate the numerical efficiency of implementing VOHOBBDF methods in a single code. The analysis of the experimental results reveals the numerical efficiency of this approach as it yielded better performances with less computational effort when compared with built-in stiff Matlab codes. The superior performances demonstrated by the application of adaptive orders selection in a single code thus indicate its reliability as a direct solver for higher order stiff ODEs. MDPI 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/38236/1/38236.pdf Asnor, Asma Izzati and Mohd Yatim, Siti Ainor and Ibrahim, Zarina Bibi (2019) Solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae. Symmetry, 11 (10). art. no. 1289. pp. 1-10. ISSN 2073-8994 https://www.mdpi.com/2073-8994/11/10/1289 10.3390/sym11101289 |
| spellingShingle | Asnor, Asma Izzati Mohd Yatim, Siti Ainor Ibrahim, Zarina Bibi Solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae |
| title | Solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae |
| title_full | Solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae |
| title_fullStr | Solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae |
| title_full_unstemmed | Solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae |
| title_short | Solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae |
| title_sort | solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae |
| url | http://psasir.upm.edu.my/id/eprint/38236/ http://psasir.upm.edu.my/id/eprint/38236/ http://psasir.upm.edu.my/id/eprint/38236/ http://psasir.upm.edu.my/id/eprint/38236/1/38236.pdf |