  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 asymptotic method,
in contrast to the well-known method the Method of Matched Asymptotic
Expansions (MMAE), the matching process is not necessary 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
robustness of the methods. Numerical results and the comparisons demonstrate
absolute superiority of SCEM over MMAE for linear problems.
