On Convergence and Performance of Iterative

We conduct convergence analysis on some classical stationary iterative methods for solving the two dimensional variable coeecient convection-diiusion equation dis-cretized by a fourth-order compact diierence scheme. Several conditions are formulated under which the coeecient matrix is guaranteed to be an M-matrix. We further investigate the eeect of diierent orderings of the grid points on the performance of some stationary iterative methods, multigrid method, and preconditioned GMRES. Three sets of numerical experiments are conducted to study the convergence behaviors of these iterative methods under the innuence of the ow directions, the orderings of the grid points, and the magnitude of the convection coeecients.