A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations
Recently, block backward differentiation formulas (BBDFs) are used successfully for solving stiff differential equations. In this article, a class of hybrid block backward differentiation formulas (HBBDFs) methods that possessed A –stability are constructed by reformulating the BBDFs for the numeric...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Multidisciplinary Digital Publishing Institute
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/87576/ http://psasir.upm.edu.my/id/eprint/87576/1/ABSTRACT.pdf |
| _version_ | 1848860462232371200 |
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| author | Ibrahim, Zarina Bibi Mohd Nasarudin, Amiratul Ashikin |
| author_facet | Ibrahim, Zarina Bibi Mohd Nasarudin, Amiratul Ashikin |
| author_sort | Ibrahim, Zarina Bibi |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Recently, block backward differentiation formulas (BBDFs) are used successfully for solving stiff differential equations. In this article, a class of hybrid block backward differentiation formulas (HBBDFs) methods that possessed A –stability are constructed by reformulating the BBDFs for the numerical solution of stiff ordinary differential equations (ODEs). The stability and convergence of the new method are investigated. The methods are found to be zero-stable and consistent, hence the method is convergent. Comparisons between the proposed method with exact solutions and existing methods of similar type show that the new extension of the BBDFs improved the stability with acceptable degree of accuracy. |
| first_indexed | 2025-11-15T12:45:37Z |
| format | Article |
| id | upm-87576 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:45:37Z |
| publishDate | 2020 |
| publisher | Multidisciplinary Digital Publishing Institute |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-875762022-07-06T08:35:19Z http://psasir.upm.edu.my/id/eprint/87576/ A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations Ibrahim, Zarina Bibi Mohd Nasarudin, Amiratul Ashikin Recently, block backward differentiation formulas (BBDFs) are used successfully for solving stiff differential equations. In this article, a class of hybrid block backward differentiation formulas (HBBDFs) methods that possessed A –stability are constructed by reformulating the BBDFs for the numerical solution of stiff ordinary differential equations (ODEs). The stability and convergence of the new method are investigated. The methods are found to be zero-stable and consistent, hence the method is convergent. Comparisons between the proposed method with exact solutions and existing methods of similar type show that the new extension of the BBDFs improved the stability with acceptable degree of accuracy. Multidisciplinary Digital Publishing Institute 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/87576/1/ABSTRACT.pdf Ibrahim, Zarina Bibi and Mohd Nasarudin, Amiratul Ashikin (2020) A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations. Mathematics, 8 (6). pp. 1-19. ISSN 2227-7390 https://www.mdpi.com/2227-7390/8/6/914 10.3390/math8060914 |
| spellingShingle | Ibrahim, Zarina Bibi Mohd Nasarudin, Amiratul Ashikin A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations |
| title | A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations |
| title_full | A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations |
| title_fullStr | A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations |
| title_full_unstemmed | A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations |
| title_short | A class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations |
| title_sort | class of hybrid multistep block methods with a–stability for the numerical solution of stiff ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/87576/ http://psasir.upm.edu.my/id/eprint/87576/ http://psasir.upm.edu.my/id/eprint/87576/ http://psasir.upm.edu.my/id/eprint/87576/1/ABSTRACT.pdf |