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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 ε‐uniformly convergent of O(Δt + N−2ln2N), where Δt and N 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 λ. 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, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnlaaa:v:2021:y:2021:i:1:n:8835595
    DOI: 10.1155/2021/8835595
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    References listed on IDEAS

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    1. Sharifi, Shokofeh & Rashidinia, Jalil, 2016. "Numerical solution of hyperbolic telegraph equation by cubic B-spline collocation method," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 28-38.
    2. Avudai Selvi, P. & Ramanujam, N., 2017. "A parameter uniform difference scheme for singularly perturbed parabolic delay differential equation with Robin type boundary condition," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 101-115.
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