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http://dx.doi.org/10.5666/KMJ.2021.61.3.591

Higher Order Uniformly Convergent Numerical Scheme for Singularly Perturbed Reaction-Diffusion Problems  

Anilay, Worku Tilahun (Department of Mathematics, Jimma University)
Duressa, Gemechis File (Department of Mathematics, Jimma University)
Woldaregay, Mesfin Mekuria (Department of Applied Mathematics, Adama Science and Technology University)
Publication Information
Kyungpook Mathematical Journal / v.61, no.3, 2021 , pp. 591-612 More about this Journal
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
Finite Element; Fitted Mesh; Parameter Uniform; Singularly Perturbed;
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