An Accurate and Stable Multigrid Method 
               for Convection-Diffusion Equations   


          Murli M. Gupta, Jules Kouatchou and Jun Zhang

                          
                 Department of Mathematics 
             The George Washington University
                 Washington, DC 20052, USA
                        
         
                     Abstract: 

We introduce a high-order compact difference scheme with multigrid 
algorithm to solve the convection-diffusion equations with constant 
coefficients. This high-order discretization scheme is shown to be 
more accurate and stable than the usual five-point discretization 
scheme. It solves the convection-diffusion equations directly 
without using any preconditioner or adding any artificial dissipation 
terms. This method is shown to converge faster than some of the 
existing methods and to achieve higher accuracy. Numerical experiments 
are presented to validate the conclusions. 

Please send your comments to: zhang@math.gwu.edu