A Nonstandard Fitted Operator Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems with a Large Time Delay

Awoke Andargie Tiruneh, Getachew Adamu Derese, Dagnachew Mengstie Tefera and Palle Kiran

International Journal of Mathematics and Mathematical Sciences, 2022, vol. 2022, 1-11

Abstract: 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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:5625049

DOI: 10.1155/2022/5625049

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