High-order perturbation-difference scheme for a convection-diffusion problem

Finite difference methods with uniform meshes are considered for a one-dimensional singularly perturbed convection-diffusion problem. In order to obtain high-order of convergence, the difference methods are combined with a perturbation technique. The methods have E-uniform convergence and do not give non-physical oscillations in the numerical solutions. Existence and corresponding error estimates of the solution for the difference schemes have been shown. Numerical experiments are provided to back up the analysis. (C) 2000 Elsevier Science S.A. All rights reserved. MSG: 65L10; 65L12; 65L20.