- - - Department of Mathematics, Faculty of Art and Science, Bitlis Eren University, ۱۳۲۰۰, Bitlis, Turkey.

We consider finite difference method to find best approximation of nonlinear singularly perturbed problem which contains multi-point boundary conditions. We surveyed the asymptotic estimates of the corresponding problem that needs to be solved with maximum principle. We constructed a finite difference scheme by using Bakhvalov mesh. Based on the error estimation, we proved that this method was first-order, uniformly convergent method with in the discrete maximum norm. Finally, we conducted a numerical experiment in order to check the theoretical results

Singular perturbation, finite difference scheme, Bakhvalov mesh, Uniformly convergence, multipoint boundary conditions