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

Author

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  • Ran, Maohua
  • Zhou, Xiaoyi

Abstract

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 L1 formula. The stability and convergence of the finite difference scheme in the discrete L2-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 α∈(0,1), which is consistent with the phase separation phenomenon.

Suggested Citation

  • Ran, Maohua & Zhou, Xiaoyi, 2021. "An implicit difference scheme for the time-fractional Cahn–Hilliard equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 61-71.
    • Handle: RePEc:eee:matcom:v:180:y:2021:i:c:p:61-71
    DOI: 10.1016/j.matcom.2020.08.021
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    Cited by:

    1. Li, Lili & Zhao, Dan & She, Mianfu & Chen, Xiaoli, 2022. "On high order numerical schemes for fractional differential equations by block-by-block approach," Applied Mathematics and Computation, Elsevier, vol. 425(C).

    More about this item

    Keywords

    Fractional Cahn–Hilliard equation; Implicit difference scheme; Caputo fractional derivative; L1 formula; Stability and convergence;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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