A Uniformly Convergent Collocation Method for Singularly Perturbed Delay Parabolic Reaction-Diffusion Problem

Fasika Wondimu Gelu and Gemechis File Duressa

Abstract and Applied Analysis, 2021, vol. 2021, 1-11

Abstract:

In this article, a numerical solution is proposed for singularly perturbed delay parabolic reaction-diffusion problem with mixed-type boundary conditions. The problem is discretized by the implicit Euler method on uniform mesh in time and extended cubic B-spline collocation method on a Shishkin mesh in space. The parameter-uniform convergence of the method is given, and it is shown to be - uniformly convergent of , where and denote the step size in time and number of mesh intervals in space, respectively. The proposed method gives accurate results by choosing suitable value of the free parameter . Some numerical results are carried out to support the theory.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:8835595

DOI: 10.1155/2021/8835595

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