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Analysis of an Il’in Scheme for a System of Singularly Perturbed Convection-Diffusion Equations
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Abstract
In this paper, a numerical solution for a system of singularly perturbed convection-diffusion equations is studied. The system is discretized by the Il’in scheme on a uniform mesh. It is proved that the numerical scheme has first order accuracy, which is uniform with respect to the perturbation parameters. We show that the condition number of the discrete linear system obtained from applying the Il’in scheme for a system of singularly perturbed convection-diffusion equations is O(N) and the relevant coefficient matrix is well conditioned in comparison with the matrices obtained from applying upwind finite difference schemes on this problem. Numerical results confirm the theory of the method.
KeywordsConvection-DiffusionIl’in SchemeUniform ConvergenceSingular PerturbationCondition Number
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