An Iterative Numerical Algorithm for a Strongly Coupled System of Singularly Perturbed Convection-Diffusion Problems

Authors:
E. O'Riordan;J. Stynes;M. Stynes
Affiliations:
School of Mathematical Sciences, Dublin City University, Ireland;Department of Computing, Cork Institute of Technology, Cork, Ireland;Department of Mathematics, National University of Ireland, Cork, Ireland
Venue:
Numerical Analysis and Its Applications
Year:
2009

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Abstract

An iterative numerical method is constructed for a coupled system of singularly perturbed convection-diffusion-reaction two-point boundary value problems. It combines a standard finite difference operator with a piecewise-uniform Shishkin mesh, and uses a Jacobi-type iteration to compute a solution. Under certain assumptions on the coefficients in the differential equations, a bound on the maximum-norm error in the computed solution is established; this bound is independent of the values of the singular perturbation parameter. Numerical results are presented to illustrate the performance of the numerical method.