A novel mid-point upwind scheme for fractional-order singularly perturbed convection-diffusion delay differential equation
This study presents a numerical approach for solving temporal fractionalorder singularly perturbed parabolic convection-diffusion differential equations with a delay using a uniformly convergent scheme. We use the asymptotic analysis of the problem to offer a priori bounds on the exact solution and...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Ferdowsi University of Mashhad
2024-12-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_45588_994a451c41f05a5de1f91d5b86fb19f3.pdf |
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| Summary: | This study presents a numerical approach for solving temporal fractionalorder singularly perturbed parabolic convection-diffusion differential equations with a delay using a uniformly convergent scheme. We use the asymptotic analysis of the problem to offer a priori bounds on the exact solution and its derivatives. To discretize the problem, we use the implicit Euler technique on a uniform mesh in time and the midpoint upwind finite difference approach on a piece-wise uniform mesh in space. The proposed technique has a nearly first-order uniform convergence order in both spatial and temporal dimensions. To validate the theoretical analysis of the scheme, two numerical test situations for various values of ε are explored. |
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| ISSN: | 2423-6977 2423-6969 |