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Abstract
A class of singular perturbation problems is considered. In order to solve them a numerical-asymptotic method is constructed in which asymptotic solution techniques are combined with standard numerical methods. The proposed method is distinguished by the following facts: First, we construct the division point which divides the initial interval into two subintervals, so that the layer belongs only to one of them. The division point is constructed in such a way that it provides the best possible accuracy of such a combined method. The inner solution problem is solved as a two point boundary value problem, where the terminal boundary conditions are supplied by the solution of reduced problem. As the outer solution the solution of reduced problem is taken. A numerical example is included.