Abstract: We proposed a fast and stable numerical method to solve the two-dimensional Cahn-Hilliard equation with constant mobility. The second order finite difference method was used in spatial discretization and Crank-Nicolson method was used in time discretization. We proved theoretically that the discrete energy had the property of dissipation with time evolving. The fixed point iteration method was used to solve the nonlinear algebraic equations in the fully discrete scheme, and the fast discrete cosine transform (FDCT) was used to improve the computational efficiency. The numerical results show that the discrete free energy is non increasing with respect to time, and the method has the advantaes of good stability, small storage and fast computation speed.

Key words: Cahn-Hilliard equation, finite difference method, Crank-Nicolson method, energy dissipation