Nonstandard finite difference method for time-fractional singularly perturbed convection–diffusion problems with a delay in time
In this work, nonstandard finite difference method is presented for the numerical solution of time-fractional singularly perturbed convection–diffusion problems with a delay in time. The time-fractional derivative is considered in the Caputo sense and discretized using Crank–Nicholson technique. The...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024-02-01
|
| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037424000025 |
| _version_ | 1797260376225611776 |
|---|---|
| author | Worku Tilahun Aniley Gemechis File Duressa |
| author_facet | Worku Tilahun Aniley Gemechis File Duressa |
| author_sort | Worku Tilahun Aniley |
| collection | DOAJ |
| description | In this work, nonstandard finite difference method is presented for the numerical solution of time-fractional singularly perturbed convection–diffusion problems with a delay in time. The time-fractional derivative is considered in the Caputo sense and discretized using Crank–Nicholson technique. Then, a nonstandard finite difference scheme is constructed on a uniform mesh discretization along the spatial direction. The parameter-uniform convergence of the proposed method is proved rigorously and shown to be ɛ-uniform convergent with order of convergence O((Δt)2) along the temporal domain and M−1 along the spatial domain. Finally, the proposed scheme is validated using model examples and the computational results are in agreement with the theoretical expectation. |
| first_indexed | 2024-03-08T14:50:43Z |
| format | Article |
| id | doaj.art-e5020a8480e645dbab4baaf969bb7858 |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-04-24T23:24:20Z |
| publishDate | 2024-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-e5020a8480e645dbab4baaf969bb78582024-03-16T05:09:08ZengElsevierResults in Applied Mathematics2590-03742024-02-0121100432Nonstandard finite difference method for time-fractional singularly perturbed convection–diffusion problems with a delay in timeWorku Tilahun Aniley0Gemechis File Duressa1Department of Mathematics, Jimma University, Jimma, EthiopiaCorresponding author.; Department of Mathematics, Jimma University, Jimma, EthiopiaIn this work, nonstandard finite difference method is presented for the numerical solution of time-fractional singularly perturbed convection–diffusion problems with a delay in time. The time-fractional derivative is considered in the Caputo sense and discretized using Crank–Nicholson technique. Then, a nonstandard finite difference scheme is constructed on a uniform mesh discretization along the spatial direction. The parameter-uniform convergence of the proposed method is proved rigorously and shown to be ɛ-uniform convergent with order of convergence O((Δt)2) along the temporal domain and M−1 along the spatial domain. Finally, the proposed scheme is validated using model examples and the computational results are in agreement with the theoretical expectation.http://www.sciencedirect.com/science/article/pii/S2590037424000025Time-fractionalConvection–diffusionUniformly convergentNonstandardCaputo derivative |
| spellingShingle | Worku Tilahun Aniley Gemechis File Duressa Nonstandard finite difference method for time-fractional singularly perturbed convection–diffusion problems with a delay in time Results in Applied Mathematics Time-fractional Convection–diffusion Uniformly convergent Nonstandard Caputo derivative |
| title | Nonstandard finite difference method for time-fractional singularly perturbed convection–diffusion problems with a delay in time |
| title_full | Nonstandard finite difference method for time-fractional singularly perturbed convection–diffusion problems with a delay in time |
| title_fullStr | Nonstandard finite difference method for time-fractional singularly perturbed convection–diffusion problems with a delay in time |
| title_full_unstemmed | Nonstandard finite difference method for time-fractional singularly perturbed convection–diffusion problems with a delay in time |
| title_short | Nonstandard finite difference method for time-fractional singularly perturbed convection–diffusion problems with a delay in time |
| title_sort | nonstandard finite difference method for time fractional singularly perturbed convection diffusion problems with a delay in time |
| topic | Time-fractional Convection–diffusion Uniformly convergent Nonstandard Caputo derivative |
| url | http://www.sciencedirect.com/science/article/pii/S2590037424000025 |
| work_keys_str_mv | AT workutilahunaniley nonstandardfinitedifferencemethodfortimefractionalsingularlyperturbedconvectiondiffusionproblemswithadelayintime AT gemechisfileduressa nonstandardfinitedifferencemethodfortimefractionalsingularlyperturbedconvectiondiffusionproblemswithadelayintime |