Abstract:

 A class of weak nonlinear singularly perturbed boundary value problems with discontinuous source terms is examined. Using the method of boundary functions and smooth sewing orbit, the asymptotic solution of this problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is proved. A numerical result illustrats to the theoretical result.

Key words:  singular perturbation; asymptotic expansion; boundary layer function; invariable manifold