A-stable 2-point block extended backward differentiation formula for solving stiff ordinary differential equations
This paper focuses on derivation of a 2-point block extended backward differentiation formula (BEBDF) for the integration of stiff ordinary differential equations. The formula derived computes two solution values simultaneously in a block and uses an extra future point, thereby having more advantage...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
American Institute of Physics
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57310/ http://psasir.upm.edu.my/id/eprint/57310/1/A-stable%202-point%20block%20extended%20backward%20differentiation%20formula%20for%20solving%20stiff%20ordinary%20differential%20equations.pdf |
| _version_ | 1848853329499652096 |
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| author | Musa, Hamisu Suleiman, Mohamed Ismail, Fudziah |
| author_facet | Musa, Hamisu Suleiman, Mohamed Ismail, Fudziah |
| author_sort | Musa, Hamisu |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper focuses on derivation of a 2-point block extended backward differentiation formula (BEBDF) for the integration of stiff ordinary differential equations. The formula derived computes two solution values simultaneously in a block and uses an extra future point, thereby having more advantage than the conventional block backward differentiation formula (BBDF). The stability region covered the entire negative half plane, proving that the method constructed is A-stable. To validate the method derived, some problems known to be stiff were solved and the results obtained are compared with the existing BBDF in terms of maximum error and computation time. The comparison shows that the error growth for the new method is smaller compared to 2-point BBDF. |
| first_indexed | 2025-11-15T10:52:15Z |
| format | Conference or Workshop Item |
| id | upm-57310 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:52:15Z |
| publishDate | 2011 |
| publisher | American Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-573102017-09-26T04:02:39Z http://psasir.upm.edu.my/id/eprint/57310/ A-stable 2-point block extended backward differentiation formula for solving stiff ordinary differential equations Musa, Hamisu Suleiman, Mohamed Ismail, Fudziah This paper focuses on derivation of a 2-point block extended backward differentiation formula (BEBDF) for the integration of stiff ordinary differential equations. The formula derived computes two solution values simultaneously in a block and uses an extra future point, thereby having more advantage than the conventional block backward differentiation formula (BBDF). The stability region covered the entire negative half plane, proving that the method constructed is A-stable. To validate the method derived, some problems known to be stiff were solved and the results obtained are compared with the existing BBDF in terms of maximum error and computation time. The comparison shows that the error growth for the new method is smaller compared to 2-point BBDF. American Institute of Physics 2011 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57310/1/A-stable%202-point%20block%20extended%20backward%20differentiation%20formula%20for%20solving%20stiff%20ordinary%20differential%20equations.pdf Musa, Hamisu and Suleiman, Mohamed and Ismail, Fudziah (2011) A-stable 2-point block extended backward differentiation formula for solving stiff ordinary differential equations. In: 5th International Conference on Research and Education in Mathematics (ICREM5), 22-24 Oct. 2011, Bandung, Indonesia. (pp. 254-258). 10.1063/1.4724149 |
| spellingShingle | Musa, Hamisu Suleiman, Mohamed Ismail, Fudziah A-stable 2-point block extended backward differentiation formula for solving stiff ordinary differential equations |
| title | A-stable 2-point block extended backward differentiation formula for solving stiff ordinary differential equations |
| title_full | A-stable 2-point block extended backward differentiation formula for solving stiff ordinary differential equations |
| title_fullStr | A-stable 2-point block extended backward differentiation formula for solving stiff ordinary differential equations |
| title_full_unstemmed | A-stable 2-point block extended backward differentiation formula for solving stiff ordinary differential equations |
| title_short | A-stable 2-point block extended backward differentiation formula for solving stiff ordinary differential equations |
| title_sort | a-stable 2-point block extended backward differentiation formula for solving stiff ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/57310/ http://psasir.upm.edu.my/id/eprint/57310/ http://psasir.upm.edu.my/id/eprint/57310/1/A-stable%202-point%20block%20extended%20backward%20differentiation%20formula%20for%20solving%20stiff%20ordinary%20differential%20equations.pdf |