This paper presents a kind of new Crank-Nicolson difference scheme for one and two dimensional convection-diffusion equations. It also gives the alternating direction method for two-dimensional problems. Because the coefficient matrix formed by the scheme is always diagonally dominant, the scheme can be solved by general iteration method. In this paper, we prove that the new CN scheme for one dimensional problems is convergent with respect to discrete L^2 norm with orderO(△t^2+△th+h^2). We also prove that the new CN scheme for two dimensional problems is stable by discrete Fourier method. Finally, numerical examples show that the method in this paper is very effective for solving convection-diffusion equations.
