Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Equation with Small Time Delay
In this article, a uniformly convergent numerical scheme is developed to solve a singularly perturbed convection-diffusion equation with a small delay having a boundary layer along the left side. A priori bounds of continuous solution and its derivatives are discussed. To solve the problem, the Cran...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2024/3772081 |
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| author | Sisay Ketema Tesfaye Mesfin Mekuria Woldaregay Tekle Gemechu Dinka Gemechis File Duressa |
| author_facet | Sisay Ketema Tesfaye Mesfin Mekuria Woldaregay Tekle Gemechu Dinka Gemechis File Duressa |
| author_sort | Sisay Ketema Tesfaye |
| collection | DOAJ |
| description | In this article, a uniformly convergent numerical scheme is developed to solve a singularly perturbed convection-diffusion equation with a small delay having a boundary layer along the left side. A priori bounds of continuous solution and its derivatives are discussed. To solve the problem, the Crank–Nicolson scheme in the time direction and the exponentially fitted finite difference scheme in the space direction are used. The stability of the method is analyzed. It is proved that the developed scheme converges uniformly with first order in space and second order in time. To validate the applicability of the theoretical finding of the developed scheme, numerical experiments are carried out by considering two test examples. |
| format | Article |
| id | doaj-art-7b906e27e7da45b4b80f9c2810a1fec3 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7b906e27e7da45b4b80f9c2810a1fec32025-08-20T03:35:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252024-01-01202410.1155/2024/3772081Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Equation with Small Time DelaySisay Ketema Tesfaye0Mesfin Mekuria Woldaregay1Tekle Gemechu Dinka2Gemechis File Duressa3Department of MathematicsDepartment of Applied MathematicsDepartment of Applied MathematicsDepartment of MathematicsIn this article, a uniformly convergent numerical scheme is developed to solve a singularly perturbed convection-diffusion equation with a small delay having a boundary layer along the left side. A priori bounds of continuous solution and its derivatives are discussed. To solve the problem, the Crank–Nicolson scheme in the time direction and the exponentially fitted finite difference scheme in the space direction are used. The stability of the method is analyzed. It is proved that the developed scheme converges uniformly with first order in space and second order in time. To validate the applicability of the theoretical finding of the developed scheme, numerical experiments are carried out by considering two test examples.http://dx.doi.org/10.1155/2024/3772081 |
| spellingShingle | Sisay Ketema Tesfaye Mesfin Mekuria Woldaregay Tekle Gemechu Dinka Gemechis File Duressa Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Equation with Small Time Delay International Journal of Mathematics and Mathematical Sciences |
| title | Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Equation with Small Time Delay |
| title_full | Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Equation with Small Time Delay |
| title_fullStr | Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Equation with Small Time Delay |
| title_full_unstemmed | Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Equation with Small Time Delay |
| title_short | Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Equation with Small Time Delay |
| title_sort | fitted numerical scheme for singularly perturbed convection diffusion equation with small time delay |
| url | http://dx.doi.org/10.1155/2024/3772081 |
| work_keys_str_mv | AT sisayketematesfaye fittednumericalschemeforsingularlyperturbedconvectiondiffusionequationwithsmalltimedelay AT mesfinmekuriawoldaregay fittednumericalschemeforsingularlyperturbedconvectiondiffusionequationwithsmalltimedelay AT teklegemechudinka fittednumericalschemeforsingularlyperturbedconvectiondiffusionequationwithsmalltimedelay AT gemechisfileduressa fittednumericalschemeforsingularlyperturbedconvectiondiffusionequationwithsmalltimedelay |