a compact stencil (9-point stencil in 2D problems). This is achieved by using the governing differential equation to approximate leading truncation error terms in the central difference scheme. The fourth-order accuracy of the new scheme is demonstrated, as well as its tendency to suppress false oscillations. We study the convergence of point and line stationary iterative methods for solving the linear system arising from the fourth-order compact discretization. We present new techniques to bound the spectral radii of the iteration matrices in terms of the I Reynolds numbers. We also derived analytic formulas for the spectral radii for special values of the cell Reynolds numbers. In addition, we compare the 9-point compact scheme with the traditional 5-point difference discretization schemes and conduct some numerical experiments to supplement our analysis