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In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation issolved numerically by using the finite difference method in combination with aconvex splitting technique of the energy functional. For the non-stochasticcase, we develop an unconditionally energy stable difference scheme which isproved to be uniquely solvable. For the stochastic case, by adopting the samesplitting of the energy functional, we construct a similar and uniquelysolvable difference scheme with the discretized stochastic term. The resultedschemes are nonlinear and solved by Newton iteration. For the long timesimulation, an adaptive time stepping strategy is developed based on bothfirst- and second-order derivatives of the energy. Numerical experiments arecarried out to verify the energy stability, the efficiency of the adaptive timestepping and the effect of the stochastic term.

An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation