Two-point block method for Van der Pol equation
The second order ordinary differential equations (ODEs) of Van der Pol equation is treated by using the two-point block backward differentiation formula. Two types of Van der Pol equation which are stiff and nonstiff are considered. The main motivation of this study is to solve the Van der Pol equat...
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| Format: | Article |
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Academy of Sciences Malaysia
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/86412/ |
| _version_ | 1848860224831619072 |
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| author | Zainuddin, Nooraini Ibrahim, Zarina Bibi |
| author_facet | Zainuddin, Nooraini Ibrahim, Zarina Bibi |
| author_sort | Zainuddin, Nooraini |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The second order ordinary differential equations (ODEs) of Van der Pol equation is treated by using the two-point block backward differentiation formula. Two types of Van der Pol equation which are stiff and nonstiff are considered. The main motivation of this study is to solve the Van der Pol equation directly instead of reducing it to a system of first order equation. The two-point block method is implemented in constant step size and will produce two approximated solutions for each step. Some numerical results are presented, and the comparisons are made with the existing solvers for both stiff and nonstiff ODE to validate the numerical performance of the two-point block method. |
| first_indexed | 2025-11-15T12:41:50Z |
| format | Article |
| id | upm-86412 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T12:41:50Z |
| publishDate | 2020 |
| publisher | Academy of Sciences Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-864122022-10-19T01:43:41Z http://psasir.upm.edu.my/id/eprint/86412/ Two-point block method for Van der Pol equation Zainuddin, Nooraini Ibrahim, Zarina Bibi The second order ordinary differential equations (ODEs) of Van der Pol equation is treated by using the two-point block backward differentiation formula. Two types of Van der Pol equation which are stiff and nonstiff are considered. The main motivation of this study is to solve the Van der Pol equation directly instead of reducing it to a system of first order equation. The two-point block method is implemented in constant step size and will produce two approximated solutions for each step. Some numerical results are presented, and the comparisons are made with the existing solvers for both stiff and nonstiff ODE to validate the numerical performance of the two-point block method. Academy of Sciences Malaysia 2020 Article PeerReviewed Zainuddin, Nooraini and Ibrahim, Zarina Bibi (2020) Two-point block method for Van der Pol equation. ASM Science Journal, 13. pp. 1-5. ISSN 1823-6782 https://www.akademisains.gov.my/asmsj/article/two-point-block-method-for-van-der-pol-equation/ 10.32802/asmscj.2020.sm26(4.26) |
| spellingShingle | Zainuddin, Nooraini Ibrahim, Zarina Bibi Two-point block method for Van der Pol equation |
| title | Two-point block method for Van der Pol equation |
| title_full | Two-point block method for Van der Pol equation |
| title_fullStr | Two-point block method for Van der Pol equation |
| title_full_unstemmed | Two-point block method for Van der Pol equation |
| title_short | Two-point block method for Van der Pol equation |
| title_sort | two-point block method for van der pol equation |
| url | http://psasir.upm.edu.my/id/eprint/86412/ http://psasir.upm.edu.my/id/eprint/86412/ http://psasir.upm.edu.my/id/eprint/86412/ |