A Second-order Energy Stable Fourier Spectral Method for the Fractional Cahn-Hilliard Equation

Abstract

In this paper, we presented a second order accurate (in time) energy stable numerical scheme for the Fractional Cahn-Hilliard (CH) equation. Combining the convex splitting method, we applied the implicit backward differentiation formula (BDF2) to derive second order temporal accuracy, and we used the Fourier spectral method for space discrete to obtain the fully discretization scheme. Then we discussed the unique solvability and energy stability. A few numerical experiments were presented to conclude the article.