Science China Mathematics

, Volume 59, Issue 9, pp 1815–1834 | Cite as

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

  • Xiao Li
  • ZhongHua QiaoEmail author
  • Hui Zhang


In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.


Cahn-Hilliard equation stochastic term energy stability convex splitting adaptive time stepping 


65M06 65M12 65Z05 


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© Science China Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijingChina
  2. 2.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHong KongChina
  3. 3.Laboratory of Mathematics and Complex Systems, Ministry of Education and School of Mathematical SciencesBeijing Normal UniversityBeijingChina

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