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2020 Solving Systems of Singularly Perturbed Convection Diffusion Problems via Initial Value Method
Wondwosen Gebeyaw Melesse, Awoke Andargie Tiruneh, Getachew Adamu Derese
J. Appl. Math. 2020(none): 1-8 (2020). DOI: 10.1155/2020/1062025


In this paper, an initial value method for solving a weakly coupled system of two second-order singularly perturbed Convection–diffusion problems exhibiting a boundary layer at one end is proposed. In this approach, the approximate solution for the given problem is obtained by solving, a coupled system of initial value problem (namely, the reduced system), and two decoupled initial value problems (namely, the layer correction problems), which are easily deduced from the given system of equations. Both the reduced system and the layer correction problems are independent of perturbation parameter, ε . These problems are then solved analytically and/or numerically, and those solutions are combined to give an approximate solution to the problem. Further, error estimates are derived and examples are provided to illustrate the method.


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Wondwosen Gebeyaw Melesse. Awoke Andargie Tiruneh. Getachew Adamu Derese. "Solving Systems of Singularly Perturbed Convection Diffusion Problems via Initial Value Method." J. Appl. Math. 2020 1 - 8, 2020.


Received: 2 July 2019; Accepted: 12 August 2019; Published: 2020
First available in Project Euclid: 14 May 2020

zbMATH: 07195525
MathSciNet: MR4064496
Digital Object Identifier: 10.1155/2020/1062025

Rights: Copyright © 2020 Hindawi


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