High-order perturbation-difference scheme for a convection–diffusion problem Original Research Article

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 ϵ-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.