Finite difference approximate solutions for the Cahn-Hilliard equation

被引：30
|
作者：
Khiari, N.
Achouri, T.
Ben Mohamed, M. L.
Omrani, K. [1 ]
机构：
[1] Inst Super Sci Appl & Technol Sousse, Sousse 4003, Ibn Khaldoun, Tunisia
[2] Fac Sci Monastir, Monastir 5000, Tunisia
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2007年 / 23卷 / 02期
关键词：
Cahn-Hilliard equation; difference scheme; existence; uniqueness; convergence; linearization;
D O I：
10.1002/num.20189
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we analyze a Crank-Nicolson-type finite difference scheme for the nonlinear evolutionary Cahn-Hilliard equation. We prove existence, uniqueness and convergence of the difference solution. An iterative algorithm for the difference scheme is given and its convergence is proved. A linearized difference scheme is presented, which is also second-order convergent. Finally a new difference method possess a Lyapunov function is presented. (c) 2006 Wiley Periodicals, Inc.
引用
收藏
页码：437 / 455
页数：19
相关论文
共 50 条
  • [1] Solutions of the Cahn-Hilliard equation
    Ugurlu, Yavuz
    Kaya, Dogan
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (12) : 3038 - 3045
  • [2] A stable and conservative finite difference scheme for the Cahn-Hilliard equation
    Daisuke Furihata
    Numerische Mathematik, 2001, 87 : 675 - 699
  • [3] A stable and conservative finite difference scheme for the Cahn-Hilliard equation
    Furihata, D
    NUMERISCHE MATHEMATIK, 2001, 87 (04) : 675 - 699
  • [4] An Explicit Adaptive Finite Difference Method for the Cahn-Hilliard Equation
    Ham, Seokjun
    Li, Yibao
    Jeong, Darae
    Lee, Chaeyoung
    Kwak, Soobin
    Hwang, Youngjin
    Kim, Junseok
    JOURNAL OF NONLINEAR SCIENCE, 2022, 32 (06)
  • [5] Stationary solutions for the Cahn-Hilliard equation
    Wei, JC
    Winter, M
    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1998, 15 (04): : 459 - 492
  • [6] Convergence of solutions to Cahn-Hilliard equation
    Rybka, P
    Hoffmann, KH
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1999, 24 (5-6) : 1055 - 1077
  • [7] A Class of Stable and Conservative Finite Difference Schemes for the Cahn-Hilliard Equation
    Ting-chun WANG
    Li-mei ZHAO
    Bo-ling GUO
    Acta Mathematicae Applicatae Sinica, 2015, 31 (04) : 863 - 878
  • [8] A class of stable and conservative finite difference schemes for the Cahn-Hilliard equation
    Ting-chun Wang
    Li-mei Zhao
    Bo-ling Guo
    Acta Mathematicae Applicatae Sinica, English Series, 2015, 31 : 863 - 878
  • [9] A Class of Stable and Conservative Finite Difference Schemes for the Cahn-Hilliard Equation
    Wang, Ting-chun
    Zhao, Li-mei
    Guo, Bo-ling
    ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2015, 31 (04): : 863 - 878
  • [10] ROTATIONALLY SYMMETRIC SOLUTIONS TO THE CAHN-HILLIARD EQUATION
    Hernandez, Alvaro
    Kowalczyk, Michal
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (02) : 801 - 827
12345