Comparison of a higher order method and the simple upwind and non-monotone methods for singularly perturbed boundary value problems

In this paper, we will present a new scheme for discretization of singularly perturbed boundary value problems based on finite difference methods. This method is a combination of simple upwind scheme and central difference method on a special non-uniform mesh (Shishkin mesh) for the space discretization. Numerical results show that the convergence of method is uniform with respect to singular perturbation parameter and has a higher order of convergence.