Abstract: In this paper, we are devoted to a study of the effect of the treatment of Neumann boundary conditions for one-dimensional advection-diffusion equation by the analysis method, and for tow-dimensional Poisson equation by the numerical test method. The reults show that the scheme is first-order accurate in space (i.e. O(h)can be derived first-order accurate difference solution or second-order solution, and the O(h²) or O(h³) scheme is only derived second-order solution.