Abstract: In this paper we discuss the smoothness of inertial manifolds under time discretization. By the fibre contract principle, see Section 4, we obtain a sufficient condition for C^k(k ≥ 1) inertial manifolds. In view of the numerical computation for dissipative nonlinear evolution equations, it is more important to consider the discretized case than continuous case^[3].

Key words: Nonlinear evolution equation, Inertial Manifold, Time discretization