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.
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O’Riordan, E., Stynes, J., Stynes, M. (2009). An Iterative Numerical Algorithm for a Strongly Coupled System of Singularly Perturbed Convection-Diffusion Problems. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_10
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DOI: https://doi.org/10.1007/978-3-642-00464-3_10
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