Direct fifth order block backward differentiation formulas for solving second order ordinary differential equations
In this paper, a new fifth order Direct Block Backward Differentiation Formula (5-DBBDF) for solving second order stiff ordinary differential equations (ODEs) is presented. Five backwards steps are used to generate the coefficients of the 5-DBBDF. This method approximates the solutions at two points...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Faculty of Science, Chiang Mai University
2016
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/55533/ http://psasir.upm.edu.my/id/eprint/55533/1/Direct%20fifth%20order%20block%20backward%20differentiation%20formulas%20for%20solving%20second%20order%20.pdf |
| _version_ | 1848852828625305600 |
|---|---|
| author | Zainuddin, Nooraini Ibrahim, Zarina Bibi Othman, Khairil Iskandar Suleiman, Mohamed |
| author_facet | Zainuddin, Nooraini Ibrahim, Zarina Bibi Othman, Khairil Iskandar Suleiman, Mohamed |
| author_sort | Zainuddin, Nooraini |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, a new fifth order Direct Block Backward Differentiation Formula (5-DBBDF) for solving second order stiff ordinary differential equations (ODEs) is presented. Five backwards steps are used to generate the coefficients of the 5-DBBDF. This method approximates the solutions at two points concurrently by using fixed step size and solved the second order ODEs directly without reducing the ODEs to a system of first order. Numerical results on some standard problems found in the literature are presented to validate the accuracy of the proposed method. |
| first_indexed | 2025-11-15T10:44:17Z |
| format | Article |
| id | upm-55533 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:44:17Z |
| publishDate | 2016 |
| publisher | Faculty of Science, Chiang Mai University |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-555332017-09-13T02:14:12Z http://psasir.upm.edu.my/id/eprint/55533/ Direct fifth order block backward differentiation formulas for solving second order ordinary differential equations Zainuddin, Nooraini Ibrahim, Zarina Bibi Othman, Khairil Iskandar Suleiman, Mohamed In this paper, a new fifth order Direct Block Backward Differentiation Formula (5-DBBDF) for solving second order stiff ordinary differential equations (ODEs) is presented. Five backwards steps are used to generate the coefficients of the 5-DBBDF. This method approximates the solutions at two points concurrently by using fixed step size and solved the second order ODEs directly without reducing the ODEs to a system of first order. Numerical results on some standard problems found in the literature are presented to validate the accuracy of the proposed method. Faculty of Science, Chiang Mai University 2016-10 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/55533/1/Direct%20fifth%20order%20block%20backward%20differentiation%20formulas%20for%20solving%20second%20order%20.pdf Zainuddin, Nooraini and Ibrahim, Zarina Bibi and Othman, Khairil Iskandar and Suleiman, Mohamed (2016) Direct fifth order block backward differentiation formulas for solving second order ordinary differential equations. Chiang Mai Journal of Science, 43 (5). pp. 1171-1181. ISSN 0125-2526; ESSN: 2465-3845 http://epg.science.cmu.ac.th/ejournal/ |
| spellingShingle | Zainuddin, Nooraini Ibrahim, Zarina Bibi Othman, Khairil Iskandar Suleiman, Mohamed Direct fifth order block backward differentiation formulas for solving second order ordinary differential equations |
| title | Direct fifth order block backward differentiation formulas for solving second order ordinary differential equations |
| title_full | Direct fifth order block backward differentiation formulas for solving second order ordinary differential equations |
| title_fullStr | Direct fifth order block backward differentiation formulas for solving second order ordinary differential equations |
| title_full_unstemmed | Direct fifth order block backward differentiation formulas for solving second order ordinary differential equations |
| title_short | Direct fifth order block backward differentiation formulas for solving second order ordinary differential equations |
| title_sort | direct fifth order block backward differentiation formulas for solving second order ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/55533/ http://psasir.upm.edu.my/id/eprint/55533/ http://psasir.upm.edu.my/id/eprint/55533/1/Direct%20fifth%20order%20block%20backward%20differentiation%20formulas%20for%20solving%20second%20order%20.pdf |