Numerical solution of singular perturbation problems via deviating arguments

Abstract

We present a new approach to numerically solving linear, singularly perturbed two point boundary value problems in ordinary differential equations with a boundary layer on the left end of the interval. The original problem is divided into outer and inner region problems. A terminal boundary condition in the implicit form is derived. Then, the outer region problem is solved as a two point boundary value problem (TPBVP), and an explicit terminal boundary condition is obtained. In turn, a new inner region problem is obtained and solved as a TPBVP using the explicit terminal boundary condition. The proposed method is iterative on the terminal point of the inner region. Some numerical examples have been solved to demonstrate the applicability of the method.