On the Simultaneous Use of Asymptotic and Numerical Methods to Solve Nonlinear Two Point Problems with Boundary and Interior Layers

The purpose of this paper is to provide a broad-brush survey concerning boundary value problems for certain systems of nonlinear singularly perturbed ordinary differential equations. The aim is to emphasize important and difficult open problems needing much more study, in terms of both mathematical and numerical analysis and computational experiments. The presentation will, regrettably, be removed from both direct applications and substantial achievements. Gradually, we will, however, become more specific and ultimately will discuss some currently tractible problems.