Hybrid Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Problem with a Small Time Lag
In this article, a singularly perturbed convection-diffusion problem with a small time lag is examined. Because of the appearance of a small perturbation parameter, a boundary layer is observed in the solution of the problem. A hybrid scheme has been constructed, which is a combination of the cubic...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2023/4382780 |
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| author | Mulunesh Amsalu Ayele Awoke Andargie Tiruneh Getachew Adamu Derese |
| author_facet | Mulunesh Amsalu Ayele Awoke Andargie Tiruneh Getachew Adamu Derese |
| author_sort | Mulunesh Amsalu Ayele |
| collection | DOAJ |
| description | In this article, a singularly perturbed convection-diffusion problem with a small time lag is examined. Because of the appearance of a small perturbation parameter, a boundary layer is observed in the solution of the problem. A hybrid scheme has been constructed, which is a combination of the cubic spline method in the boundary layer region and the midpoint upwind scheme in the outer layer region on a piecewise Shishkin mesh in the spatial direction. For the discretization of the time derivative, the Crank-Nicolson method is used. Error analysis of the proposed method has been performed. We found that the proposed scheme is second-order convergent. Numerical examples are given, and the numerical results are in agreement with the theoretical results. Comparisons are made, and the results of the proposed scheme give more accurate solutions and a higher rate of convergence as compared to some previous findings available in the literature. |
| format | Article |
| id | doaj-art-f5e388166df84e3d9094524467c95f8f |
| institution | Kabale University |
| issn | 1687-0409 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f5e388166df84e3d9094524467c95f8f2025-02-03T06:42:51ZengWileyAbstract and Applied Analysis1687-04092023-01-01202310.1155/2023/4382780Hybrid Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Problem with a Small Time LagMulunesh Amsalu Ayele0Awoke Andargie Tiruneh1Getachew Adamu Derese2Department of MathematicsDepartment of MathematicsDepartment of MathematicsIn this article, a singularly perturbed convection-diffusion problem with a small time lag is examined. Because of the appearance of a small perturbation parameter, a boundary layer is observed in the solution of the problem. A hybrid scheme has been constructed, which is a combination of the cubic spline method in the boundary layer region and the midpoint upwind scheme in the outer layer region on a piecewise Shishkin mesh in the spatial direction. For the discretization of the time derivative, the Crank-Nicolson method is used. Error analysis of the proposed method has been performed. We found that the proposed scheme is second-order convergent. Numerical examples are given, and the numerical results are in agreement with the theoretical results. Comparisons are made, and the results of the proposed scheme give more accurate solutions and a higher rate of convergence as compared to some previous findings available in the literature.http://dx.doi.org/10.1155/2023/4382780 |
| spellingShingle | Mulunesh Amsalu Ayele Awoke Andargie Tiruneh Getachew Adamu Derese Hybrid Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Problem with a Small Time Lag Abstract and Applied Analysis |
| title | Hybrid Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Problem with a Small Time Lag |
| title_full | Hybrid Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Problem with a Small Time Lag |
| title_fullStr | Hybrid Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Problem with a Small Time Lag |
| title_full_unstemmed | Hybrid Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Problem with a Small Time Lag |
| title_short | Hybrid Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Problem with a Small Time Lag |
| title_sort | hybrid fitted numerical scheme for singularly perturbed convection diffusion problem with a small time lag |
| url | http://dx.doi.org/10.1155/2023/4382780 |
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