Fifth order two-point block backward differentiation formulas for solving ordinary differential equations.
The new method derived is called the fifth order two-point Block Backward Differentiation Formulas (BBDF(5)) method for solving first order stiff Ordinary Differential Equations (ODEs). This method possesses the requirement for stiffly stable and suitable to solve stiff problems. We also discussed...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English English |
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Hikari Ltd
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/25030/ http://psasir.upm.edu.my/id/eprint/25030/1/Fifth%20order%20two.pdf |
| _version_ | 1848845198165016576 |
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| author | Ibrahim, Zarina Bibi Suleiman, Mohamed Othman, Khairil Iskandar Nasir, N. A. A. M. |
| author_facet | Ibrahim, Zarina Bibi Suleiman, Mohamed Othman, Khairil Iskandar Nasir, N. A. A. M. |
| author_sort | Ibrahim, Zarina Bibi |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The new method derived is called the fifth order two-point Block Backward Differentiation Formulas (BBDF(5)) method for solving first order stiff Ordinary Differential Equations (ODEs). This method possesses the requirement for stiffly stable and suitable to solve stiff problems.
We also discussed further the implementation of the method using Newton Iteration. The numerical results are presented to verify the efficiency of this method as compared to the Classical Backward Differentiation Formula (BDF) method and ode15s in Matlab. The BBDF(5) method outperformed the BDF method and ode15s in terms of maximum error and execution time. |
| first_indexed | 2025-11-15T08:43:00Z |
| format | Article |
| id | upm-25030 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T08:43:00Z |
| publishDate | 2011 |
| publisher | Hikari Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-250302015-09-23T02:00:07Z http://psasir.upm.edu.my/id/eprint/25030/ Fifth order two-point block backward differentiation formulas for solving ordinary differential equations. Ibrahim, Zarina Bibi Suleiman, Mohamed Othman, Khairil Iskandar Nasir, N. A. A. M. The new method derived is called the fifth order two-point Block Backward Differentiation Formulas (BBDF(5)) method for solving first order stiff Ordinary Differential Equations (ODEs). This method possesses the requirement for stiffly stable and suitable to solve stiff problems. We also discussed further the implementation of the method using Newton Iteration. The numerical results are presented to verify the efficiency of this method as compared to the Classical Backward Differentiation Formula (BDF) method and ode15s in Matlab. The BBDF(5) method outperformed the BDF method and ode15s in terms of maximum error and execution time. Hikari Ltd 2011 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/25030/1/Fifth%20order%20two.pdf Ibrahim, Zarina Bibi and Suleiman, Mohamed and Othman, Khairil Iskandar and Nasir, N. A. A. M. (2011) Fifth order two-point block backward differentiation formulas for solving ordinary differential equations. Applied Mathematical Sciences, 5 (71). pp. 3505-3518. ISSN 1312-885X http://www.m-hikari.com/ English |
| spellingShingle | Ibrahim, Zarina Bibi Suleiman, Mohamed Othman, Khairil Iskandar Nasir, N. A. A. M. Fifth order two-point block backward differentiation formulas for solving ordinary differential equations. |
| title | Fifth order two-point block backward differentiation formulas for solving ordinary differential equations. |
| title_full | Fifth order two-point block backward differentiation formulas for solving ordinary differential equations. |
| title_fullStr | Fifth order two-point block backward differentiation formulas for solving ordinary differential equations. |
| title_full_unstemmed | Fifth order two-point block backward differentiation formulas for solving ordinary differential equations. |
| title_short | Fifth order two-point block backward differentiation formulas for solving ordinary differential equations. |
| title_sort | fifth order two-point block backward differentiation formulas for solving ordinary differential equations. |
| url | http://psasir.upm.edu.my/id/eprint/25030/ http://psasir.upm.edu.my/id/eprint/25030/ http://psasir.upm.edu.my/id/eprint/25030/1/Fifth%20order%20two.pdf |