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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A second-order accurate linearized difference scheme for the two-dimensional Cahn-Hilliard equation
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by Zhi Zhong Sun PDF
Math. Comp. 64 (1995), 1463-1471 Request permission

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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 1463-1471
  • MSC: Primary 65M06; Secondary 65M12
  • DOI: https://doi.org/10.1090/S0025-5718-1995-1308465-4
  • MathSciNet review: 1308465