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In this paper we consider two difference schemes for numerical solving of aone--dimensional singularly perturbed boundary value problem. We proved an$\varepsilon$--uniform convergence for both difference schemes on a Shiskinmesh. Finally, we present four numerical experiments to confirm the theoreticalresults.

Uniformly Convergent Difference Scheme for a Semilinear Reaction-Diffusion Problem on Shishikin mesh