Ordinary Differential Equations

Abstract

The practical implementation of the successive complementary expansion method, SCEM, is presented in this Chapter with applications to functions implicitly defined as solutions of ordinary differential equations. In all the cases, the solution depends on a small parameter leading to a singular perturbation problem. More precisely, the structure of the solution exhibits a boundary layer. The boundary layer is always located in the neighbourhood of a singular point, but this point is not necessarily a part of the boundary of the considered domain. Among the variety of examples found in the literature [17, 42, 48, 72], a selection has been made to enlighten the various aspects of SCEM and its advantages. This is a first step toward the treatment of physical problems governed by partial differential equations.