Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay
In this paper, singularly perturbed differential equations having both small and large delay are considered. The considered problem contains large delay parameter on the reaction term and small delay parameter on the convection term. The solution of the problem exhibits interior layer due to the del...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2023-11-01
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| Series: | Acta Universitatis Sapientiae: Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/ausm-2023-0004 |
| _version_ | 1797561928250294272 |
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| author | Debela Habtamu Garoma Duressa Gemechis File |
| author_facet | Debela Habtamu Garoma Duressa Gemechis File |
| author_sort | Debela Habtamu Garoma |
| collection | DOAJ |
| description | In this paper, singularly perturbed differential equations having both small and large delay are considered. The considered problem contains large delay parameter on the reaction term and small delay parameter on the convection term. The solution of the problem exhibits interior layer due to the delay parameter and strong right boundary layer due to the small perturbation parameter ε. The resulting singularly perturbed problem is solved using exponential fitted operator method. The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, one model problem is considered for numerical experimentation. |
| first_indexed | 2024-03-10T18:21:37Z |
| format | Article |
| id | doaj.art-1787248f1e6e45eba4dc33f414f08ecf |
| institution | Directory Open Access Journal |
| issn | 2066-7752 |
| language | English |
| last_indexed | 2024-03-10T18:21:37Z |
| publishDate | 2023-11-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Acta Universitatis Sapientiae: Mathematica |
| spelling | doaj.art-1787248f1e6e45eba4dc33f414f08ecf2023-11-20T07:17:10ZengSciendoActa Universitatis Sapientiae: Mathematica2066-77522023-11-01151546910.2478/ausm-2023-0004Parametric uniform numerical method for singularly perturbed differential equations having both small and large delayDebela Habtamu Garoma0Duressa Gemechis File11Jimma University, College of Natural Sciences, Jimma, Ethiopia2Jimma University, College of Natural Sciences, Jimma, EthiopiaIn this paper, singularly perturbed differential equations having both small and large delay are considered. The considered problem contains large delay parameter on the reaction term and small delay parameter on the convection term. The solution of the problem exhibits interior layer due to the delay parameter and strong right boundary layer due to the small perturbation parameter ε. The resulting singularly perturbed problem is solved using exponential fitted operator method. The stability and parameter uniform convergence of the proposed method are proved. To validate the applicability of the scheme, one model problem is considered for numerical experimentation.https://doi.org/10.2478/ausm-2023-0004arithmetical functionmöbius function11a25 |
| spellingShingle | Debela Habtamu Garoma Duressa Gemechis File Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay Acta Universitatis Sapientiae: Mathematica arithmetical function möbius function 11a25 |
| title | Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay |
| title_full | Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay |
| title_fullStr | Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay |
| title_full_unstemmed | Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay |
| title_short | Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay |
| title_sort | parametric uniform numerical method for singularly perturbed differential equations having both small and large delay |
| topic | arithmetical function möbius function 11a25 |
| url | https://doi.org/10.2478/ausm-2023-0004 |
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