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2020 Uniform Hybrid Difference Scheme for Singularly Perturbed Differential-Difference Turning Point Problems Exhibiting Boundary Layers
Wondwosen Gebeyaw Melesse, Awoke Andargie Tiruneh, Getachew Adamu Derese
Abstr. Appl. Anal. 2020: 1-14 (2020). DOI: 10.1155/2020/7045756

Abstract

In this paper, a class of linear second-order singularly perturbed differential-difference turning point problems with mixed shifts exhibiting two exponential boundary layers is considered. For the numerical treatment of these problems, first we employ a second-order Taylor’s series approximation on the terms containing shift parameters and obtain a modified singularly perturbed problem which approximates the original problem. Then a hybrid finite difference scheme on an appropriate piecewise-uniform Shishkin mesh is constructed to discretize the modified problem. Further, we proved that the method is almost second-order ɛ-uniformly convergent in the maximum norm. Numerical experiments are considered to illustrate the theoretical results. In addition, the effect of the shift parameters on the layer behavior of the solution is also examined.

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Wondwosen Gebeyaw Melesse. Awoke Andargie Tiruneh. Getachew Adamu Derese. "Uniform Hybrid Difference Scheme for Singularly Perturbed Differential-Difference Turning Point Problems Exhibiting Boundary Layers." Abstr. Appl. Anal. 2020 1 - 14, 2020. https://doi.org/10.1155/2020/7045756

Information

Received: 6 November 2019; Accepted: 5 February 2020; Published: 2020
First available in Project Euclid: 27 May 2020

zbMATH: 07245164
MathSciNet: MR4080284
Digital Object Identifier: 10.1155/2020/7045756

Rights: Copyright © 2020 Hindawi

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