About the central difference method for singularly perturbed boundary value problems

Abstract

In this paper we give a detailed analysis of the central difference scheme applied to the linear second-order equation ɛx″ = a( t) x′ + b( t) x + ƒ( t), with two-point boundary conditions x( t 0) = x 0 , x( t f) = x f. We assume that a( t) < 0, so the solution x( t) may have a boundary layer in t 0. A class of nonuniform meshes is proposed, which ensures accuracy in the layer plus stability and second-order convergence elsewhere.