An implicit difference scheme for the time-fractional Cahn-Hilliard equations

In this paper, an efficient finite difference scheme is developed for solving the time-fractional Cahn-Hilliard equations which is the well-known representative of phase-field models. The time Caputo derivative is approximated by the popular L-1 formula. The stability and convergence of the finite difference scheme in the discrete L-2-norm are proved by the discrete energy method. To compare and observe the phenomenon of solution, a generalized difference scheme based on the graded mesh in time is also given. The dynamics of the solution and accuracy of the schemes are verified numerically. Numerical experiments show that the solution of the time-fractional Cahn-Hilliard equation always tends to be in an equilibrium state with the increase of time for different values of order alpha is an element of (0,1), which is consistent with the phase separation phenomenon. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This paper develops an efficient finite difference scheme for solving the time-fractional Cahn-Hilliard equations, and numerical experiments verify its stability, convergence, dynamics of the solution, and accuracy of the schemes. The solution of the time-fractional Cahn-Hilliard equation tends to an equilibrium state with the increase of time, consistent with the phase separation phenomenon.