Solving the singularly perturbation problems of delay differential equations numerically
Singular perturbation problems with delay argument have arisen in practical problems such as in modeling neuronal stochastic behavior, rotation movement of sunflower, respiratory physiology processes, and optimal control theory. This study is important because solving a real problem analytically is...
| Main Authors: | , , |
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| Format: | Article |
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Badih/Ghusayni
2021
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| Online Access: | http://psasir.upm.edu.my/id/eprint/95109/ |
| _version_ | 1848862073107251200 |
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| author | Jaaffar, Nur Tasnem Abdul Majid, Zanariah Senu, Norazak |
| author_facet | Jaaffar, Nur Tasnem Abdul Majid, Zanariah Senu, Norazak |
| author_sort | Jaaffar, Nur Tasnem |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Singular perturbation problems with delay argument have arisen in practical problems such as in modeling neuronal stochastic behavior, rotation movement of sunflower, respiratory physiology processes, and optimal control theory. This study is important because solving a real problem analytically is tedious, so we propose a numerical method to approximate these problems. In this article, the multistep block method is developed to solve problems concerning second order delay differential equations that involved singular perturbation problems. The process consists of using block technique where three points approximate solutions are computed at the same time. Each of the three points is directly integrated once and twice and approximated by using Lagrange interpolation. Predictor and corrector techniques are applied to obtain the accuracy of the method with the corrector |
| first_indexed | 2025-11-15T13:11:13Z |
| format | Article |
| id | upm-95109 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:11:13Z |
| publishDate | 2021 |
| publisher | Badih/Ghusayni |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-951092023-04-12T04:09:26Z http://psasir.upm.edu.my/id/eprint/95109/ Solving the singularly perturbation problems of delay differential equations numerically Jaaffar, Nur Tasnem Abdul Majid, Zanariah Senu, Norazak Singular perturbation problems with delay argument have arisen in practical problems such as in modeling neuronal stochastic behavior, rotation movement of sunflower, respiratory physiology processes, and optimal control theory. This study is important because solving a real problem analytically is tedious, so we propose a numerical method to approximate these problems. In this article, the multistep block method is developed to solve problems concerning second order delay differential equations that involved singular perturbation problems. The process consists of using block technique where three points approximate solutions are computed at the same time. Each of the three points is directly integrated once and twice and approximated by using Lagrange interpolation. Predictor and corrector techniques are applied to obtain the accuracy of the method with the corrector Badih/Ghusayni 2021 Article PeerReviewed Jaaffar, Nur Tasnem and Abdul Majid, Zanariah and Senu, Norazak (2021) Solving the singularly perturbation problems of delay differential equations numerically. International Journal of Mathematics and Computer Science, 16 (3). 1003 - 1016. ISSN 1814-0424; ESSN: 1814-0432 http://ijmcs.future-in-tech.net/Volume16.3.htm |
| spellingShingle | Jaaffar, Nur Tasnem Abdul Majid, Zanariah Senu, Norazak Solving the singularly perturbation problems of delay differential equations numerically |
| title | Solving the singularly perturbation problems of delay differential equations numerically |
| title_full | Solving the singularly perturbation problems of delay differential equations numerically |
| title_fullStr | Solving the singularly perturbation problems of delay differential equations numerically |
| title_full_unstemmed | Solving the singularly perturbation problems of delay differential equations numerically |
| title_short | Solving the singularly perturbation problems of delay differential equations numerically |
| title_sort | solving the singularly perturbation problems of delay differential equations numerically |
| url | http://psasir.upm.edu.my/id/eprint/95109/ http://psasir.upm.edu.my/id/eprint/95109/ |