ABOUT THE CENTRAL DIFFERENCE METHOD FOR SINGULARLY PERTURBED BOUNDARY-VALUE-PROBLEMS

In this paper we give a detailed analysis of the central difference sc heme applied to the linear second-order equation epsilon x '' = a(t)x' + b(t)x + f(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 b oundary layer in t(0). A class of nonuniform meshes is proposed, which ensures accuracy in the layer plus stability and second-order converg ence elsewhere.