A high-accuracy conservative difference approximation for Rosenau-KdV equation

Volume 10, Issue 6, pp 3013--3022 http://dx.doi.org/10.22436/jnsa.010.06.15

Publication Date: June 25, 2017 Submission Date: January 16, 2017

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Authors

Jinsong Hu - School of Science, Xihua University, Chengdu 610039, China. Jun Zhou - School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100, China. Ru Zhuo - School of Science, Xihua University, Chengdu 610039, China.

Abstract

In this paper, we study the initial-boundary value problem of Rosenau-KdV equation. A conservative two level nonlinear Crank-Nicolson difference scheme, which has the theoretical accuracy \(O(\tau^2 + h^4)\), is proposed. The scheme simulates two conservative properties of the initial boundary value problem. Existence, uniqueness, and priori estimates of difference solution are obtained. Furthermore, we analyze the convergence and unconditional stability of the scheme by the energy method. Numerical experiments demonstrate the theoretical results.

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Keywords

• Rosenau-KdV equation
• finite difference scheme
• conservative
• convergence
• stability.

MSC

•  65M06
•  65N30

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