On the quasilinear boundary-layer problem and its numerical solution

We obtain improved derivative estimates for the solution of the quasilinear singularly perturbed boundary-value problem. This enables us to modify the transition point between the fine and coarse parts of the Shishkin discretization mesh. The resulting mesh may be denser in the layer than the standard Shishkin mesh. When this is the case, numerical experiments show an improvement in the accuracy of the computed solution.