SCEM approach for singularly perturbed linear turning mid-point problems with an interior layer

Singularly perturbed problems are of great significance in applied mathematics, physics and engineering sciences. In this paper, we study an important class of these kind of problems: singularly perturbed two-point turning point problems (TPP's) in ordinary differential equations (ODE's) exhibiting interior layer at the mid-point of their intervals. We consider these type of problems as two different singular perturbation problems which have boundary layer at an end point of their intervals. This study follows the Successive complementary expansion method (SCEM) to solve these two sub-problems. Leaning towards to the (SCEM), there is no need for matching procedure. Morever, the boundary conditions are not satisfied asymptotically, but exactly. Our numerical experiments show that (SCEM) results are in good agreement with exact and previously obtained solutions.