In this paper, we present a numerical patching method for solving a class of singularly
perturbed two point boundary value problems with a boundary layer at one end point. In order to
know the behavior of the solution of the singular perturbation problem in the boundary layer
region, it is always suggestive to solve the problem in outer and boundary layer regions
separately. By constructing a modified problem with a boundary layer correction, the boundary
layer is dealt with separately and series method used. The condition at infinity will be applied to
the corresponding Padé approximates of the obtained series solution. Several problems are
solved to demonstrate the applicability and efficiency of the proposed method. It is observed that
the present method approximates the exact solution very well.