Richardson Extrapolation Method for Singularly Perturbed Coupled System of Convection-Diffusion Boundary-Value Problems
Briti Sundar Deb; and Srinivasan Natesan

doi:10.3970/cmes.2008.038.179
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 38, No. 2, pp. 179-200, 2008
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Keywords Singularly perturbed coupled system of equations, Boundary layer, Piecewise-uniform Shishkin mesh, Richardson extrapolation, Uniform convergence.
Abstract This paper presents an almost second--order uniformly convergent Richardson extrapolation method for convection- dominated coupled system of boundary value problems. First, we solve the system by using the classical finite difference scheme on the layer resolving Shishkin mesh, and then we construct the Richardson approximation solution using the solutions obtained on$N$ and$2N$ mesh intervals. Second-order parameter--uniform error estimate is derived. The proposed method is applied to a test example for verification of the theoretical results for the case$\varepsilon \leq N^{-1}$.
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