Variable order block method for solving second order ordinary differential equations
This paper proposed 2-point block backward differentiation formulas (BBDF) of order 3, 4, and 5 for direct solution of second order ordinary differential equations. These methods were derived via backward difference interpolation polynomial with two solutions are prod...
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/82710/ http://psasir.upm.edu.my/id/eprint/82710/1/Variable%20order%20block%20method%20for%20solving%20second%20order%20ordinary%20differential%20equations.pdf |
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| author | Ibrahim, Zarina Bibi Zainuddin, Nooraini Othman, Khairil Iskandar Suleiman, Mohamed Mohd Zawawi, Iskandar Shah |
| author_facet | Ibrahim, Zarina Bibi Zainuddin, Nooraini Othman, Khairil Iskandar Suleiman, Mohamed Mohd Zawawi, Iskandar Shah |
| author_sort | Ibrahim, Zarina Bibi |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper proposed 2-point block backward differentiation formulas (BBDF) of order 3, 4, and 5 for direct solution of second order ordinary differential equations. These methods were derived via backward difference interpolation polynomial with two solutions are produced simultaneously at each step. All the three different orders of 2-point BBDF is implemented in variable order scheme. The scheme utilizes the local truncation error, which is generated by the single order of 2-point BBDF method. Numerical results are presented to illustrate the validity of the proposed scheme. |
| first_indexed | 2025-11-15T12:27:41Z |
| format | Article |
| id | upm-82710 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:27:41Z |
| publishDate | 2019 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-827102020-09-11T05:14:15Z http://psasir.upm.edu.my/id/eprint/82710/ Variable order block method for solving second order ordinary differential equations Ibrahim, Zarina Bibi Zainuddin, Nooraini Othman, Khairil Iskandar Suleiman, Mohamed Mohd Zawawi, Iskandar Shah This paper proposed 2-point block backward differentiation formulas (BBDF) of order 3, 4, and 5 for direct solution of second order ordinary differential equations. These methods were derived via backward difference interpolation polynomial with two solutions are produced simultaneously at each step. All the three different orders of 2-point BBDF is implemented in variable order scheme. The scheme utilizes the local truncation error, which is generated by the single order of 2-point BBDF method. Numerical results are presented to illustrate the validity of the proposed scheme. Penerbit Universiti Kebangsaan Malaysia 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/82710/1/Variable%20order%20block%20method%20for%20solving%20second%20order%20ordinary%20differential%20equations.pdf Ibrahim, Zarina Bibi and Zainuddin, Nooraini and Othman, Khairil Iskandar and Suleiman, Mohamed and Mohd Zawawi, Iskandar Shah (2019) Variable order block method for solving second order ordinary differential equations. Sains Malaysiana, 48 (8). pp. 1761-1769. ISSN 0126-6039 10.17576/jsm-2019-4808-23 |
| spellingShingle | Ibrahim, Zarina Bibi Zainuddin, Nooraini Othman, Khairil Iskandar Suleiman, Mohamed Mohd Zawawi, Iskandar Shah Variable order block method for solving second order ordinary differential equations |
| title | Variable order block method for solving second order ordinary differential equations |
| title_full | Variable order block method for solving second order ordinary differential equations |
| title_fullStr | Variable order block method for solving second order ordinary differential equations |
| title_full_unstemmed | Variable order block method for solving second order ordinary differential equations |
| title_short | Variable order block method for solving second order ordinary differential equations |
| title_sort | variable order block method for solving second order ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/82710/ http://psasir.upm.edu.my/id/eprint/82710/ http://psasir.upm.edu.my/id/eprint/82710/1/Variable%20order%20block%20method%20for%20solving%20second%20order%20ordinary%20differential%20equations.pdf |