Controlling the accuracy of unconditionally stable algorithms in Cahn-Hilliard Equation

Given an unconditionally stable algorithm for solving the Cahn-Hilliard equation, we present a general calculation for an analytic time step $\text{d}\tau$ in terms of an algorithmic time step $\text{dt}$. By studying the accumulative multi-step error in Fourier space and controlling the error with arbitrary accuracy, we determine an improved driving scheme $\text{dt}=A{t}^{2\mathrm{/}3}$ and confirm the numerical results observed in a previous study \cite{Cheng1}.