This article is concerned with the development of fast iterative methods for the numerical analysis of linear partial differential equation. In this work convection–diffusion equation with a small parameter multiplying with diffusion term is considered. A fourth-order compact difference scheme with uniform mesh points is employed to discretize a 2‒dimmensional convection-diffusion equation.

         Finally, we compared multigrid method with fourth order compact difference scheme with the standard second order central difference scheme.  Numerical results show the efficiency of this method.

Keywords:     Multigrid Method, Convection-Diffusion equation, Fourth order compact scheme