Finite difference discretization of the Rosenau-RLW equation |
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Authors: | Xintian Pan Kelong Zheng Luming Zhang |
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Institution: | 1. School of Mathematics and Information Science , Weifang University , Weifang , 261061 , China panxintian@yahoo.com.cn;3. School of Science , Southwest University of Science and Technology , Mianyang , 621010 , China;4. Department of Mathematics , Nanjing University of Aeronautics and Astronautics , Nanjing , 210016 , China |
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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. |
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Keywords: | Rosenau-RLW equation C–N conservative scheme existence convergence stability |
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