Abstract
In this article, we obtain the numerical solution of singularly perturbed system of parabolic convection–diffusion problems exhibiting boundary layer. The proposed numerical scheme consists of the backward-Euler method for the time derivative and an upwind finite difference scheme for the spatial derivatives. We analyze the scheme on a piecewise-uniform Shishkin mesh for the spatial discretization to establish uniform convergence with respect to the perturbation parameters. For the proposed scheme, the stability analysis is presented and parameter-uniform error estimate is derived. In order to validate the theoretical results, we have carried out some numerical experiments.
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