Numerical treatment of singularly perturbed two point boundary value problems exhibiting boundary layers

A boundary value method for solving a class of nonlinear singularly perturbed two point boundary value problems with a boundary layer at one end is proposed. Using singular perturbation analysis the method consists of solving two problems; namely, a reduced problem and a boundary layer correction problem. We use Pade’ approximation to obtain the solution of the latter problem and to satisfy the condition at infinity. Numerical examples will be given to illustrate the method.

Research highlights
► In this paper we present a boundary value method for solving a class of nonlinear, singularly perturbed two-point boundary value problems with a boundary layer at the left of the underlying interval. This method is based on a different approach which is conceptually closer to the ideas of singular perturbation analysis. By constructing a modified problem with a boundary layer correction, we deal with the boundary layer separately and use series method. The condition at infinity will be applied to the corresponding Pade’ approximates of the obtained series solution. The organization of the paper is as follows. The linear problem is stated in the next section in addition to some theoretical results. In Section 3 we present the nonlinear problem and finally in Section 4 we give examples to illustrate the method.