A comparison between MMAE and SCEM for solving singularly perturbed linear boundary layer problems

Abstract

In this study, we propose an efficient method so-called Successive
Complementary Expansion Method (SCEM) that is based on generalized
asymptotic expansions, for approximating to the solutions of singularly
perturbed two-point boundary value problems. In this easy-applicable method, in contrast to the well-known method the Method
of Matched Asymptotic Expansions (MMAE) any matching process is not
required to obtain uniformly valid approximations. The key point: A
uniformly valid approximation is adopted first, and complementary functions
are obtained imposing the corresponding boundary conditions. An illustrative
and two numerical experiments are provided to show the implementation and
numerical properties of the present method. Furthermore, MMAE results are
also given in order to compare the numerical robustnesses of the methods.