Linear B-spline finite element method for the generalized diffusion equation with delay
Abstract Objectives The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson. The be...
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| Format: | Article |
| Language: | English |
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BMC
2022-06-01
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| Series: | BMC Research Notes |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13104-022-06078-0 |
| _version_ | 1817968759579607040 |
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| author | Gemeda Tolessa Lubo Gemechis File Duressa |
| author_facet | Gemeda Tolessa Lubo Gemechis File Duressa |
| author_sort | Gemeda Tolessa Lubo |
| collection | DOAJ |
| description | Abstract Objectives The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson. The benefit of the scheme is that the numerical solution is obtained as a smooth piecewise continuous function which empowers one to find an approximate solution at any desired position in the domain. Result Sufficient and necessary conditions for the numerical method to be asymptotically stable are derived. The convergence of the numerical method is studied. Some numerical experiments are performed to verify the applicability of the numerical method. |
| first_indexed | 2024-04-13T20:12:06Z |
| format | Article |
| id | doaj.art-b08726369c23414b8e76e7031e0e0d66 |
| institution | Directory Open Access Journal |
| issn | 1756-0500 |
| language | English |
| last_indexed | 2024-04-13T20:12:06Z |
| publishDate | 2022-06-01 |
| publisher | BMC |
| record_format | Article |
| series | BMC Research Notes |
| spelling | doaj.art-b08726369c23414b8e76e7031e0e0d662022-12-22T02:31:48ZengBMCBMC Research Notes1756-05002022-06-011511910.1186/s13104-022-06078-0Linear B-spline finite element method for the generalized diffusion equation with delayGemeda Tolessa Lubo0Gemechis File Duressa1Department of Mathematics, Wollega UniversityDepartment of Mathematics, Jimma UniversityAbstract Objectives The main aim of this paper is to develop a linear B-spline finite element method for solving generalized diffusion equations with delay. The linear B-spline basis function is used to discretize the space variable. The time discretization process is based on Crank-Nicolson. The benefit of the scheme is that the numerical solution is obtained as a smooth piecewise continuous function which empowers one to find an approximate solution at any desired position in the domain. Result Sufficient and necessary conditions for the numerical method to be asymptotically stable are derived. The convergence of the numerical method is studied. Some numerical experiments are performed to verify the applicability of the numerical method.https://doi.org/10.1186/s13104-022-06078-0Generalized diffusion equation with delayFinite elementLinear B-spline |
| spellingShingle | Gemeda Tolessa Lubo Gemechis File Duressa Linear B-spline finite element method for the generalized diffusion equation with delay BMC Research Notes Generalized diffusion equation with delay Finite element Linear B-spline |
| title | Linear B-spline finite element method for the generalized diffusion equation with delay |
| title_full | Linear B-spline finite element method for the generalized diffusion equation with delay |
| title_fullStr | Linear B-spline finite element method for the generalized diffusion equation with delay |
| title_full_unstemmed | Linear B-spline finite element method for the generalized diffusion equation with delay |
| title_short | Linear B-spline finite element method for the generalized diffusion equation with delay |
| title_sort | linear b spline finite element method for the generalized diffusion equation with delay |
| topic | Generalized diffusion equation with delay Finite element Linear B-spline |
| url | https://doi.org/10.1186/s13104-022-06078-0 |
| work_keys_str_mv | AT gemedatolessalubo linearbsplinefiniteelementmethodforthegeneralizeddiffusionequationwithdelay AT gemechisfileduressa linearbsplinefiniteelementmethodforthegeneralizeddiffusionequationwithdelay |