Efficient and stable time integration of Cahn–Hilliard equations: explicit, implicit, and explicit iterative schemes

To solve the Cahn–Hilliard equation numerically, a new time integration algorithm is proposed, which is based on a combination of the Eyre splitting and the local iteration modified (LIM) scheme. The latter is employed to tackle the implicit system arising each time integration step. The proposed method is gradient-stable and allows one to use large time steps, whereas, regarding its computational structure, it is an explicit time integration scheme. Numerical tests are presented to demonstrate abilities of the new method and compare it with other time integration methods for Cahn–Hilliard equation.