A Numerical Patching Method for Solving Singular Perturbation Problems Via Padé Approximates

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.