A Nonstandard Fitted Operator Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems with a Large Time Delay
In this paper, we design and investigate a higher order ε-uniformly convergent method to solve singularly perturbed parabolic reaction-diffusion problems with a large time delay. We use the Crank–Nicolson method for the time derivative, while the spatial derivative is discretized using a nonstandard...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/5625049 |
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| author | Awoke Andargie Tiruneh Getachew Adamu Derese Dagnachew Mengstie Tefera |
| author_facet | Awoke Andargie Tiruneh Getachew Adamu Derese Dagnachew Mengstie Tefera |
| author_sort | Awoke Andargie Tiruneh |
| collection | DOAJ |
| description | In this paper, we design and investigate a higher order ε-uniformly convergent method to solve singularly perturbed parabolic reaction-diffusion problems with a large time delay. We use the Crank–Nicolson method for the time derivative, while the spatial derivative is discretized using a nonstandard finite difference approach on a uniform mesh. Furthermore, to improve the order of convergence, we used the Richardson extrapolation technique. The designed scheme converges independent of the perturbation parameter (ε-uniformly convergent) and also achieves fourth-order convergent in both time and spatial variables. Two model examples are considered to demonstrate the applicability of the suggested method. The proposed method produces better accuracy and a higher rate of convergence than some methods that appear in the literature. |
| format | Article |
| id | doaj-art-bd245e9f75d0435d8899f87feaa1cb16 |
| institution | DOAJ |
| issn | 1687-0425 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-bd245e9f75d0435d8899f87feaa1cb162025-08-20T03:05:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/5625049A Nonstandard Fitted Operator Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems with a Large Time DelayAwoke Andargie Tiruneh0Getachew Adamu Derese1Dagnachew Mengstie Tefera2Department of MathematicsDepartment of MathematicsDepartment of MathematicsIn this paper, we design and investigate a higher order ε-uniformly convergent method to solve singularly perturbed parabolic reaction-diffusion problems with a large time delay. We use the Crank–Nicolson method for the time derivative, while the spatial derivative is discretized using a nonstandard finite difference approach on a uniform mesh. Furthermore, to improve the order of convergence, we used the Richardson extrapolation technique. The designed scheme converges independent of the perturbation parameter (ε-uniformly convergent) and also achieves fourth-order convergent in both time and spatial variables. Two model examples are considered to demonstrate the applicability of the suggested method. The proposed method produces better accuracy and a higher rate of convergence than some methods that appear in the literature.http://dx.doi.org/10.1155/2022/5625049 |
| spellingShingle | Awoke Andargie Tiruneh Getachew Adamu Derese Dagnachew Mengstie Tefera A Nonstandard Fitted Operator Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems with a Large Time Delay International Journal of Mathematics and Mathematical Sciences |
| title | A Nonstandard Fitted Operator Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems with a Large Time Delay |
| title_full | A Nonstandard Fitted Operator Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems with a Large Time Delay |
| title_fullStr | A Nonstandard Fitted Operator Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems with a Large Time Delay |
| title_full_unstemmed | A Nonstandard Fitted Operator Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems with a Large Time Delay |
| title_short | A Nonstandard Fitted Operator Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems with a Large Time Delay |
| title_sort | nonstandard fitted operator method for singularly perturbed parabolic reaction diffusion problems with a large time delay |
| url | http://dx.doi.org/10.1155/2022/5625049 |
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