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Mathematics of Computation

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A second-order accurate linearized difference scheme for the two-dimensional Cahn-Hilliard equation

Author: Zhi Zhong Sun
Journal: Math. Comp. 64 (1995), 1463-1471
MSC: Primary 65M06; Secondary 65M12
MathSciNet review: 1308465
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Abstract: The Cahn-Hilliard equation is a nonlinear evolutionary equation that is of fourth order in space. In this paper a linearized finite difference scheme is derived by the method of reduction of order. It is proved that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete ${L_2}$-norm. The coefficient matrix of the difference system is symmetric and positive definite, so many well-known iterative methods (e.g. Gauss-Seidel, SOR) can be used to solve the system.

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Keywords: Cahn-Hilliard equation, nonlinear evolution equation, finite difference convergence, solvability
Article copyright: © Copyright 1995 American Mathematical Society