Uniform methods for semilinear problems with an attractive boundary turning point


Torsten Linß, Relja Vulanović




Two upwind finite difference schemes are considered for the numerical solution of a class of semilinear convection-diffusion problems with a small perturbation parameter $\varepsilon$ and an attractive boundary turning point. We show that for both schemes the maximum nodal error is bounded by a special weighted $\ell_1$-type norm of the truncation error. These results are used to establish $\varepsilon$-uniform pointwise convergence on Shishkin meshes.