Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Higher Order Uniformly Convergent Numerical Scheme for Singularly Perturbed Reaction-Diffusion Problems

  • Received : 2020.04.10
  • Accepted : 2021.02.08
  • Published : 2021.09.30
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Abstract

In this paper, a uniformly convergent numerical scheme is designed for solving singularly perturbed reaction-diffusion problems. The problem is converted to an equivalent weak form and then a Galerkin finite element method is used on a piecewise uniform Shishkin mesh with linear basis functions. The convergence of the developed scheme is proved and it is shown to be almost fourth order uniformly convergent in the maximum norm. To exhibit the applicability of the scheme, model examples are considered and solved for different values of a singular perturbation parameter ε and mesh elements. The proposed scheme approximates the exact solution very well.

Keywords

Acknowledgement

The author would like to thank the referees for their constructive comments and suggestions.

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