Study on convergence and stability of a conservative difference scheme for the generalized Rosenau-KdV equation

Volume 10, Issue 5, pp 2735--2742 http://dx.doi.org/10.22436/jnsa.010.05.40

Publication Date: May 25, 2017 Submission Date: January 18, 2017

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Authors

Jun Zhou - School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100, China. Maobo Zheng - Chengdu Technological University, Chengdu 610031, China. Xiaomin Dai - Mathematics Teaching and Research Group, Fifth Middle school of Fuling, Chongqing 408000, China.

Abstract

In this paper, a conservative nonlinear implicit finite difference scheme for the generalized Rosenau-KdV equation is studied. Convergence and stability of the proposed scheme are proved by a discrete energy method. The proof with a priori error estimate shows that the convergence rates of numerical solutions are both the second order on time and in space. Meanwhile, numerical experiments are carried out to verify the theoretical analysis and show that the scheme is efficient and reliable.

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Keywords

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

MSC

•  65M06
•  65N30

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