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

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  • Fasika Wondimu Gelu
  • Gemechis File Duressa

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.

Suggested Citation

  • Fasika Wondimu Gelu & Gemechis File Duressa, 2021. "A Uniformly Convergent Collocation Method for Singularly Perturbed Delay Parabolic Reaction-Diffusion Problem," Abstract and Applied Analysis, Hindawi, vol. 2021, pages 1-11, March.
    • Handle: RePEc:hin:jnlaaa:8835595
    DOI: 10.1155/2021/8835595
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    Cited by:

    1. Abey Sherif Kelil & Appanah Rao Appadu, 2022. "On the Numerical Solution of 1D and 2D KdV Equations Using Variational Homotopy Perturbation and Finite Difference Methods," Mathematics, MDPI, vol. 10(23), pages 1-36, November.

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