Uniformly convergent non-standard finite difference methods for self-adjoint singular perturbation problems

Abstract

We design non-standard finite difference schemes for self-adjoint singularly perturbed two-point boundary value problems. Essential physical properties (e.g., dissipativity) of the solutions of such problems are captured in the schemes by an appropriate renormalization of the denominator of the discrete derivative. The schemes are analyzed for ε -uniform convergence. Several numerical examples are given to support the predicted theory.