Journal
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
Volume 23, Issue 2, Pages 437-455Publisher
JOHN WILEY & SONS INC
DOI: 10.1002/num.20189
Keywords
Cahn-Hilliard equation; difference scheme; existence; uniqueness; convergence; linearization
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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.
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