Energy stable and large time-stepping methods for the Cahn-Hilliard equation

We present the numerical methods for the Cahn-Hilliard equation, which describes phase separation phenomenon. The goal of this paper is to construct high-order, energy stable and large time-stepping methods by using Eyre's convex splitting technique. The equation is discretized by using a fourth-order compact difference scheme in space and first-order, second-order or third-order implicit-explicit Runge-Kutta schemes in time. The energy stability for the first-order scheme is proved. Numerical experiments are given to demonstrate the performance of the proposed methods.