A UNIFORM-CONVERGENCE RESULT FOR SEMILINEAR SINGULAR PERTURBATION PROBLEMS VIOLATING THE STANDARD STABILITY CONDITIONQ

Semilinear singularly perturbed boundary value problems are considered in the case when the standard stability condition is not satisfied. B ased on the behavior of the analytic solution which exhibits one or tw o boundary layers of power type, a numerical method is proposed and it s second-order accuracy, uniform in the perturbation parameter, is pro ved. The method uses the classical finite differences on a special non equidistant discretization mesh. Numerical results are presented for a problem arising in application.