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
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