Parameter uniform hybrid numerical method for time-dependent singularly perturbed parabolic differential equations with large delay

Autor: Zerihun Ibrahim Hassen, Gemechis File Duressa
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Applied Mathematics in Science and Engineering, Vol 32, Iss 1 (2024)
Druh dokumentu: article
ISSN: 27690911
2769-0911
DOI: 10.1080/27690911.2024.2328254
Popis: In this study, to solve the singularly perturbed delay convection–diffusion–reaction problem, we proposed a hybrid numerical scheme that converges uniformly. Parabolic right boundary layer outcomes from the presence of the small perturbation parameter. To grip this layer behaviour, the problem is solved by Bakhvalov–Shishkin mesh for spatial domain discretization and uniform mesh for temporal domain discretization. A hybrid scheme consisting of a non-polynomial spline scheme for fine mesh and a midpoint upwind scheme for coarse mesh is used to discretize the spatial derivative, while an implicit Euler scheme is used to discretize the time derivative. To make computed solutions more accurate and increase rate of convergence of the scheme, we applied Richardson extrapolation technique. The stability and convergence of the scheme are established. The scheme has a second order of convergence in the discrete supreme norm and is parametric uniformly convergent. The scheme's application is demonstrated through two test problems.
Databáze: Directory of Open Access Journals
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