Finite difference discretization of the Rosenau-RLW equation

Abstract

In this paper, numerical solutions of the Rosenau-RLW equation are considered using Crank–Nicolson type finite difference method. Existence of the numerical solutions is derived by Brouwer fixed point theorem. A priori bound and the error estimates as well as conservation of discrete mass and discrete energy for the finite difference solutions are discussed. Unconditional stability, second-order convergence and uniqueness of the scheme are proved using discrete energy method. Some numerical experiments have been conducted in order to verify the theoretical results.

Keywords:

• Rosenau-RLW equation
• C–N conservative scheme
• existence
• convergence
• stability

AMS Subject Classifications:

• 65M06
• 65N30

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Erratum

Acknowledgements

This work is supported by the Natural Science Foundation of China (No. 11201343) and Natural Science Foundation of Shandong Province (ZR2012AM017) and the Youth Research Foundation of WFU (No. 2011Z17). The authors would like to thank the editor and the reviewers for their valuable comments.