On large time-stepping methods for the Cahn–Hilliard equation

In this work, we will analyze a class of large time-stepping methods for the Cahn–Hilliard equation. The equation is discretized by Fourier spectral method in space and semi-implicit schemes in time. For first-order semi-implicit scheme, the stability and convergence properties are investigated based on an energy approach. Here stability means that the decay of energy is preserved. The numerical experiments are used to demonstrate the effectiveness of the large time-stepping approaches.