On Convergence and Performance of Iterative
                  Methods with Fourth-Order Compact Schemes

                                  Jun Zhang

                          Department of Mathematics
                       The George Washington University
                             Washington, DC, USA
                                     and
               Department of Computer Science and Engineering 
                           University of Minnesota
                          Minneapolis, MN 55455, USA

                                   Abstract

We study the convergence and performance of iterative methods with the
fourth-order compact discretization schemes for the one and two dimensional
convection-diffusion equations.  For the one dimensional problem, we
investigate the symmetrizability of the coefficient matrix and derive
analytical formula for the spectral radius of the point Jacobi iteration
matrix.  For the two dimensional problem, we conduct Fourier analysis to
determine the error reduction factors of several basic iterative methods and
comment on their potential use as the smoothers for the multi-level methods.
Finally, we perform numerical experiments to verify our Fourier analysis
results.

Key words:  Convection-diffusion equation, iterative methods, fourth-order
compact discretization schemes.