Abstract
In this paper we present a second order numerical scheme for the Cahn-Hilliard equation, with a Fourier pseudo-spectral approximation in space. An additional Douglas-Dupont regularization term is introduced, which ensures the energy stability. The bound of numerical solution in H2h and l? norms are obtained at a theoretical level. Moreover, for the global nature of the pseudo-spectral method, we propose a linear iteration algorithm to solve the non-linear system, due to the implicit treatment for the non-linear term. Some numerical simulations verify the efficiency of iteration algorithm.
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