A robust uniformly convergent scheme for two parameters singularly perturbed parabolic problems with time delay
A singularly perturbed time delay parabolic problem with two small pa-rameters is considered. The paper develops a finite difference scheme that is exponentially fitted on a uniform mesh in the spatial direction and uses the implicit-Euler method to discretize the time derivative in the temporal dir...
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2023-12-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_43907_c6b2d1382308555f419bf9a91322e100.pdf |
| _version_ | 1827781606163611648 |
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| author | N.T. Negero |
| author_facet | N.T. Negero |
| author_sort | N.T. Negero |
| collection | DOAJ |
| description | A singularly perturbed time delay parabolic problem with two small pa-rameters is considered. The paper develops a finite difference scheme that is exponentially fitted on a uniform mesh in the spatial direction and uses the implicit-Euler method to discretize the time derivative in the temporal direction in order to obtain a better numerical approximation to the solu-tions of this class of problems. We establish the parameter-uniform error estimate and discuss the stability of the suggested approach. In order to demonstrate the improvement in terms of accuracy, numerical results are also shown to validate the theoretical conclusions and are contrasted with the current hybrid scheme. |
| first_indexed | 2024-03-11T15:21:04Z |
| format | Article |
| id | doaj.art-66a8482d53c041d898084a4f590ab79d |
| institution | Directory Open Access Journal |
| issn | 2423-6977 2423-6969 |
| language | English |
| last_indexed | 2024-03-11T15:21:04Z |
| publishDate | 2023-12-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj.art-66a8482d53c041d898084a4f590ab79d2023-10-28T06:44:33ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692023-12-0113Issue 462764510.22067/ijnao.2023.80721.121443907A robust uniformly convergent scheme for two parameters singularly perturbed parabolic problems with time delayN.T. Negero0Department of Mathematics, Wollega University, Nekemte, Ethiopia.A singularly perturbed time delay parabolic problem with two small pa-rameters is considered. The paper develops a finite difference scheme that is exponentially fitted on a uniform mesh in the spatial direction and uses the implicit-Euler method to discretize the time derivative in the temporal direction in order to obtain a better numerical approximation to the solu-tions of this class of problems. We establish the parameter-uniform error estimate and discuss the stability of the suggested approach. In order to demonstrate the improvement in terms of accuracy, numerical results are also shown to validate the theoretical conclusions and are contrasted with the current hybrid scheme.https://ijnao.um.ac.ir/article_43907_c6b2d1382308555f419bf9a91322e100.pdfsingular perturbationtwo parameters parabolic convection-diffusion problemtime delayfitted operator schemethe error estimate |
| spellingShingle | N.T. Negero A robust uniformly convergent scheme for two parameters singularly perturbed parabolic problems with time delay Iranian Journal of Numerical Analysis and Optimization singular perturbation two parameters parabolic convection-diffusion problem time delay fitted operator scheme the error estimate |
| title | A robust uniformly convergent scheme for two parameters singularly perturbed parabolic problems with time delay |
| title_full | A robust uniformly convergent scheme for two parameters singularly perturbed parabolic problems with time delay |
| title_fullStr | A robust uniformly convergent scheme for two parameters singularly perturbed parabolic problems with time delay |
| title_full_unstemmed | A robust uniformly convergent scheme for two parameters singularly perturbed parabolic problems with time delay |
| title_short | A robust uniformly convergent scheme for two parameters singularly perturbed parabolic problems with time delay |
| title_sort | robust uniformly convergent scheme for two parameters singularly perturbed parabolic problems with time delay |
| topic | singular perturbation two parameters parabolic convection-diffusion problem time delay fitted operator scheme the error estimate |
| url | https://ijnao.um.ac.ir/article_43907_c6b2d1382308555f419bf9a91322e100.pdf |
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