A Numerical Method for a Singularly Perturbed Three-Point Boundary Value Problem

Abstract

The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameter $\epsilon $, of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically.