Controlling the accuracy of unconditionally stable algorithms in the Cahn-Hilliard equation.

Given an unconditionally stable algorithm for solving the Cahn-Hilliard equation, we present a general calculation for an analytic time step Deltatau in terms of an algorithmic time step Deltat. By studying the accumulative multistep error in Fourier space and controlling the error with arbitrary accuracy, we determine an improved driving scheme Deltat=At(2/3) and confirm the numerical results observed in a previous study [Cheng and Rutenberg, Phys. Rev. E 72, 055701(R) (2005)].