Energy stable and large time-stepping methods for the Cahn–Hilliard equation

Abstract

We present the numerical methods for the Cahn–Hilliard equation, which describes phase separation phenomenon. The goal of this paper is to construct high-order, energy stable and large time-stepping methods by using Eyre's convex splitting technique. The equation is discretized by using a fourth-order compact difference scheme in space and first-order, second-order or third-order implicit–explicit Runge–Kutta schemes in time. The energy stability for the first-order scheme is proved. Numerical experiments are given to demonstrate the performance of the proposed methods.

Keywords:

• large time-stepping
• implicit–explicit
• Runge–Kutta
• Cahn–Hilliard
• energy stability

2000 AMS Subject Classifications::

• 65N30
• 65N12

Acknowledgements

This work was supported by the National Natural Science Foundation of China(Grant No.11301167), the Natural Science Foundation of Hunan Province,China(Grant No. 14JJ3063, 12JJ6003), ‘Young teachers’ development project’ of Hunan University and the Fundamental Research Funds for the Central Universities. The author would like to thank Prof. Tao Tang of Hong Kong Baptist University for his helpful discussions and suggestions.