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A three‐level linearized finite difference scheme for the camassa–holm equation
Author(s) -
Cao HaiYan,
Sun ZhiZhong,
Gao GuangHua
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21819
Subject(s) - mathematics , camassa–holm equation , partial differential equation , finite difference method , nonlinear system , finite difference scheme , finite difference , mathematical analysis , norm (philosophy) , scheme (mathematics) , finite difference coefficient , space (punctuation) , first order partial differential equation , finite element method , mixed finite element method , integrable system , linguistics , philosophy , physics , quantum mechanics , political science , law , thermodynamics
The Camassa–Holm (CH) system is a strong nonlinear third‐order evolution equation. So far, the numerical methods for solving this problem are only a few. This article deals with the finite difference solution to the CH equation. A three‐level linearized finite difference scheme is derived. The scheme is proved to be conservative, uniquely solvable, and conditionally second‐order convergent in both time and space in the discrete L ∞ norm. Several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 451–471, 2014
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