Method of reduction of order for solving singularly perturbed two-point boundary value problems

Abstract

In this paper, a method of reduction of order is proposed for solving singularly perturbed two-point boundary value problems with a boundary layer at one end point. It is distinguished by the following fact: the original singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge–Kutta method is used to solve these initial value problems. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory.