About the central difference method for singularly perturbed boundary value problems Original Research Article

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(t0) = x0, x(tf) = xf. We assume that a(t) < 0, so the solution x(t) may have a boundary layer in t0. A class of nonuniform meshes is proposed, which ensures accuracy in the layer plus stability and second-order convergence elsewhere.