Uniformly-Convergent Numerical Methods for a System of Coupled Singularly Perturbed Convection-Diffusion Equations with Mixed Type Boundary Conditions
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Date
2013
Journal Title
Journal ISSN
Volume Title
Publisher
Taylor and Francis Ltd.
Abstract
In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection - diffusion second order ordinary differential equations subject to the mixed type boundary conditions. We prove that the method has almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and also the numerical derivative are established. Numerical results are provided to illustrate the theoretical results. © 2013 Vilnius Gediminas Technical University, 2013.
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Keywords
Boundary conditions, Diffusion in liquids, Error analysis, Finite difference method, Heat convection, Ordinary differential equations, Cubic spline, Finite difference scheme, mid-point scheme, Piecewise uniform mesh, Scaled derivative, Singular perturbation problems, Weakly coupled systems, Numerical methods
Citation
Mathematical Modelling and Analysis, 2013, 18, 5, pp. 577-598